Mathematical Neuroscience Subgroup (NEUR)

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Sub-group minisymposia

Mathematical neuroscience

Organized by: Sunil Modhara (University of Nottingham, United Kingdom), Stephen Coombes (University of Nottingham, United Kingdom), Ruediger Thul (University of Nottingham, United Kingdom), Daniele Avitabile (Vrije Universiteit Amsterdam, Netherlands)

  • Sunil Modhara (University of Nottingham, United Kingdom)
    "Neural fields with rebound currents: novel routes to patterning"
  • The understanding of how spatio-temporal patterns of neural activity may arise in the cortex of the brain has advanced with the development and analysis of neural field models. To replicate this success for sub-cortical tissues, such as the thalamus, requires an extension to include relevant ionic currents that can further shape firing response. Here we advocate for one such approach that can accommodate slow currents. By way of illustration we focus on incorporating a T-type calcium current into the standard neural field framework. Direct numerical simulations are used to show that the resulting tissue model has many of the properties seen in more biophysically detailed model studies, and most importantly the generation of oscillations, waves, and patterns that arise from rebound firing. To explore the emergence of such solutions we focus on one- and two-dimensional spatial models and show that exact solutions describing homogeneous oscillations can be constructed in the limit that the firing rate nonlinearity is a Heaviside function. A linear stability analysis, using techniques from non-smooth dynamical systems, is used to determine the points at which bifurcations from synchrony can occur. Furthermore, we construct periodic travelling waves and investigate their stability with the use of an appropriate Evans function. The stable branches of the dispersion curve for periodic travelling waves are found to be in excellent agreement with simulations initiated from an unstable branch of the synchronous solution.
  • Louisiane Lemaire (Inria Sophia Antipolis Méditerranée Research Centre, France)
    "Mathematical model of the mutations of a sodium channel (NaV1.1) capturing both migraine and epilepsy scenarios"
  • NaV1.1 is a Na+ voltage-gated channel expressed in GABAergic neurons, crucial for their excitability. Gain-of-function mutations of this channel cause familial hemiplegic migraine type 3 (FHM3), while loss-of-function mutations lead to epilepsy. The pathological mechanisms are unclear. Cortical spreading depression (CSD) is a wave of intense firing followed by depolarization block, propagating in the cortex. In the case of FHM3, it is thought that CSD sensitizes meningeal nociceptors, inducing headache. However, the link between FHM3 mutations and the initiation of CSD remains to be understood. We develop a two-neuron (GABAergic and pyramidal) conductance-based model with dynamic ion concentrations, since the considered pathologies disrupt ionic gradients. Keeping the other parameter values unchanged, we implement FMH3 mutations using persistent Na+ current and epilepsy ones with reduced transient Na+ current. Our results suggest the importance of other mechanisms of action of NaV1.1 mutations than changes in the firing frequency of GABAergic neurons. In our model, FHM3 mutations modify ion fluxes at each action potential. The resulting accumulation of extracellular potassium facilitates CSD initiation and reduces its latency, in agreement with recent experimental findings. Epilepsy mutations make the GABAergic neuron more susceptible to depolarization block. The removal of their inhibitory restraint causes a simultaneous increase of the pyramidal cell's firing frequency.
  • Manu Kalia (University of Twente, Netherlands)
    "Modeling ischemic vulnerability at the tripartite synapse"
  • The work that I will present is about single-cell neuron-astrocyte interactions at the synapse. The model considered describes ion dynamics at such an interaction during ischemia (which means low oxygen due to reduced blood flow, say, during the onset of stroke). I will present some results about bistability in the model and the tipping from one state to another, and some predictions about possible pharmacological blockers to recover cells from ischemic injury.
  • John Rinzel (New York University, USA)
    "A neuronal model for learning to keep a rhythmic beat"
  • When listening to music, we typically lock onto and move to a beat (1-6 Hz). Behavioral studies on such synchronization (Repp 2005) abound, yet the neural mechanisms remain poorly understood. Some models hypothesize an array of self-sustaining entrainable neural oscillators that resonate when forced with rhythmic stimuli (Large et al. 2010). In contrast, our formulation focuses on event time estimation and plasticity: a neuronal beat generator that adapts its intrinsic frequency and phase to match the extermal rhythm. The model quickly learns new rhythms, within a few cycles as found in human behavior. When the stimulus is removed the beat generator continues to produce the learned rhythm in accordance with a synchronization continuation task.

How neuronal network circuit attributes influence neural activity, coding, and learning

Organized by: Cheng Ly (Virginia Commonwealth University, United States), Pamela Pyzza (Kenyon College, United States)

  • Paulina Volosov (Hillsdale College, United States)
    "How to Use Minimal Information to Reconstruct Neuronal Networks"
  • We investigate the relationship between functional and architectural connectivity in the cerebral cortex by means of network reconstruction via time-delayed spike-train correlation. We begin by reconstructing the entire network, and then we sample the matrix randomly and use the tool of matrix completion to fill-in the rest of the network. To be more experimentally valid, we next examine a small “slice” or submatrix of the network and determine how much information we can deduce about the whole network from this small piece. An examination of the spectral properties of connectivity matrices forms a major part of this analysis.
  • Michelle Craft (Virginia Commonwealth University, United States)
    "Analyzing the differences in olfactory bulb spiking with ortho- and retronasal stimulation"
  • Olfaction is a key sense for many cognitive and behavioral tasks, and is particularly unique because odors can naturally enter the nasal cavity from the front or rear, i.e., ortho- and retro-nasal, respectively. Yet little is known about the differences in coordinated spiking in the olfactory bulb (a key odor processing center) with ortho versus retro stimulation, let alone how these different modes of olfaction may alter coding of odors. We simultaneously record many cells in rat olfactory bulb to assess the differences in spiking statistics, and develop a biophysical olfactory bulb network model to study the reason for these differences. Using theoretical and computational methods, we find that the olfactory bulb transfers input statistics differently for retro stimulation relative to ortho stimulation. Furthermore, our models show that the temporal profile of inputs is crucial for capturing our data and is thus a distinguishing feature between ortho and retro stimulation, even at the olfactory bulb. Understanding the spiking dynamics of the olfactory bulb with both ortho and retro stimulation is a key step for ultimately understanding how the brain codes odors with different modes of olfaction.
  • Andrea Barreiro (Southern Methodist University, United States)
    "Cell assembly detection in low firing-rate spike train data"
  • Cell assemblies, defined as groups of neurons forming temporal spike coordination, are thought to be fundamental units supporting major cognitive functions. Detecting cell assemblies is challenging since they can occur at a range of time scales and with a range of precisions, from synchronous spikes to co-variations in firing rate. A recently published cell assembly detection (CAD) algorithm (Russo and Durstewitz, 2017) addresses this ambiguity in time scale and precision; however, it is limited to spike trains with a relatively high number of total spikes, a condition which is frequently not met by the low temporal resolution data produced by calcium imaging. We first show how the CAD method can be modified to apply to sparse spike train data. This allows us to detect assemblies in calcium imaging data of neuronal activity in the CA1 region of the hippocampus, a brain region critical for encoding and generalizing contextual memories, during contextual fear conditioning training and tests. We found that assemblies in hippocampus play a role in encoding and retrieving contextual memories. In particular, there exists a group of assemblies whose exploratory activities predict the animal’s ability to distinguish different contexts. Moreover, the mechanisms for processing contextual information are different between two genetically distinct strains of mice that are included in the experiments.
  • Wilten Nicola (University of Calgary, Canada)
    "One-shot learning of spike-sequences in the hippocampus using theta-oscillations"
  • The hippocampus is capable of rapidly learning incoming information, even if that information is only observed once. Further, this information can be replayed in a compressed format during Sharp Wave Ripples (SPW-R). We leveraged state-of-the-art techniques in training recurrent spiking networks to demonstrate how primarily interneuron networks can: 1) generate internal theta sequences to bind externally elicited spikes in the presence of septal inhibition, 2) compress learned spike sequences in the form of a SPW-R when septal inhibition is removed, 3) generate and refine gamma-assemblies during SPW-R mediated compression, and 4) regulate the inter-ripple-interval timing between SPW-R’s in ripple clusters. From the fast time scale of neurons to the slow time scale of behaviors, interneuron networks and theta oscillations serve as the scaffolding for one-shot learningby replaying, refining, and regulating spike sequences.

Ionic Flow through Membrane Channels

Organized by: Peter Bates (Michigan State University), Weishi Liu (Mathematics, U. Kansas, USA), Mingji Zhang (Mathematics, New Mexico Tech., USA)
Note: this minisymposia has multiple sessions. The second session is MS09-NEUR.

  • Bob Eisenberg (Molecular Biophysics & Physiology, Rush University, USA)
    "Maxwell’s Core Equations Exact, Universal, and Scary"
  • When the Maxwell equations are written without a dielectric constant, they are universal and exact, for biological and technological applications, from inside atoms to between stars. Dielectric and polarization phenomena need then to be described by stress strain relations for charge, that show how charge redistributes when the electric field is changed, in each system of interest. Conservation of total current (including the ethereal displacement current ε_0  ∂E∕∂t) is then as exact as the Maxwell equations themselves and independent of any property of matter. It is a consequence of the Lorentz invariance of the elementary charge, a property of all locally inertial systems, described by the theory of relativity. Exact Conservation of Total Current allows a redefinition of Kirchhoff’s current law that is itself exact. In unbranched systems like circuit components or ion channels, conservation of total current becomes equality. Spatial dependence of total current disappears in that case. Hopping phenomena disappear. Spatial Brownian motion disappears. The infinite variation of a Brownian model of thermal noise becomes the zero spatial variation of total current. Maxwell’s Core Equations become a perfect (spatial) low pass filter. An Exact and Universal theory of Electrodynamics is a scary challenge to scientists like me, trained to be skeptical of all sweeping claims to perfection.
  • Jianing Chen (Mathematics, New Mexico Tech., USA)
    "Effects on zero-current ionic flows from ion sizes via PNP system with boundary layers"
  • We study the qualitative properties of zero-current ionic flows via Poisson-Nernst-Planck systems for two oppositely charged particles with boundary layers. Local Bikerman’s hard-sphere model is included in the system to account for finite ion size effects. Of particular interest is to examine the effects on the zero-current ionic flows from finite ion sizes, diffusion coefficients, ion valences and boundary layers due to the violation of electroneutrality boundary conditions. The nonlinear interplays among those system parameters are characterized in detail, which provides better understandings of the internal dynamics of ionic flows through membrane channels.
  • Francisco Bezanilla (Biochemistry and Molecular Biology and Institute for Biophysical Dynamics, University of Chicago and CINV, University of Valparaiso, Chile., USA)
    "Voltage sensors and ion channel opening"
  • The generation of the nerve impulse (action potential) depends on voltage-dependent sodium channels that must open before voltage-dependent potassium channels. We will briefly explain the voltage sensors that give voltage dependence of the ion channels. The voltage sensors have intrinsic charges in the channel protein which move in the cell membrane electric field and generate gating currents. Experiments with voltage clamp and site-directed fluorescence describe molecular details of the voltage sensor operation indicating the paths followed by the charged arginine residues within the protein core. A detailed study of the residues in the core show that the nature of the side chains determine that Na channels are faster than K channels. The canonical coupling of the voltage sensor to the conduction pore is via the linker between transmembrane segments S3 and S4. We will describe that the proximity of the S4 segment of the voltage sensor and the S5 segment of the pore region makes another noncanonical coupling pathway. The molecular basis of this pathway will be described.
  • Pei Liu (Mathematics, U. Minnesota, USA)
    "Ion-dependent DNA Configuration in Bacteriophage Capsids"
  • Bacteriophages densely pack their long dsDNA genome inside a protein capsid. The conformation of the viral genome inside the capsid is consistent with a hexagonal liquid crystalline structure, and experimental results have confirmed that it depends on environmental ionic conditions. In this work, we propose a biophysical model to describe the dependence of DNA configurations inside bacteriophage capsids on ions types and concentrations. The total free energy of the system combines the liquid crystal free energy, the electrostatic energy and the Lennard--Jones energy. The equilibrium points of this energy solve a highly nonlinear, second order partial differential equation (PDE) that defines the distributions of DNA and the ions inside the capsid. We develop a computational approach to simulate predictions of our model. The numerical results show good agreement with existing experiments and molecular dynamics simulations.

Hibernation and circadian rhythms: the differences and the possible interactions

Organized by: Shingo Gibo (RIKEN, Japan) and Gen Kurosawa (RIKEN, Japan)

  • Elena Gracheva (Yale School of Medicine, United States of America)
    "Neurophysiological adaptations to the unique lifestyle in mammalian hibernators"
  • Mammalian hibernation is fascinating. During a short period of time, hibernating animals undergo dramatic adaptive changes, including a reduction in heart and respiration rate and a decrease in core body temperature from 37°C (98.6°F) to 4°C (39°F), yet they do not experience cold-induced pain, and their organs continue to function despite being cold and deprived of oxygen for 8 month out of the year! Moreover, since these animals do not eat or drink during hibernation, they must rely solely on the management and utilization of their internal resources for long-term survival. How hibernators achieve such a remarkable physiological adaptation, remains unknown. We use hibernating 13-lined Ground squirrels (an obligatory hibernator) and Syrian hamsters (a non-obligatory hibernator), to tackle fundamental biological questions from perspectives unachievable using the standard animal models alone. Specifically, we are interested in studying molecular evolution of mammalian hibernation and cellular adaptations that these animals evolve in order to survive prolonged periods of hypothermia, water deprivation and starvation. We are also trying to pinpoint the molecular and physiological basis of hibernation induction. Comparative analysis of three rodent species—such as ground squirrels, hamsters and mice (non-hibernator)—at the behavioral, cellular and molecular levels, will help us to delineate the multitude of adaptations that hibernators evolved in order to survive harsh environment and as a result came to inhabit a wide geographical range.
  • Tanya Leise (Amherst College, United States of America)
    "Analysis of the Circadian Rhythms of Brown Bears During Winter Dormancy"
  • Applications of wavelet transforms and other methods will be demonstrated in the context of activity and body temperature records of brown bears under different entrained and free-running conditions, including during winter dormancy. Wavelet-based methods can be useful in quantifying properties of circadian rhythms, including period, phase, amplitude, quality of rhythms, and coherence between simultaneously recorded rhythms. I will also highlight the quite distinct types of information provided by discrete versus continuous wavelet transforms methods. In particular, the analysis indicates that the circadian system is functional in torpid bears even when housed in constant darkness and it continues to be responsive to phase-shifting effects of light.
  • Hsin-tzu Wang (The University of Tokyo, Japan)
    "Cold Ca2+ signaling for temperature compensation of circadian rhythms"
  • Reaction rates of almost all biochemical processes change with temperature. On the other hand, oscillation speed of the circadian clock remains nearly unchanged in a physiological range of temperatures, and this feature common to the circadian clocks is termed temperature compensation. In chemical biological screening, we found that inhibitor of Na+/Ca2+ exchanger (NCX) or Ca2+/calmodulin dependent protein kinase II (CaMKII) remarkably increased Q10 value of the period length of gene expression rhythms in mammalian fibroblasts. In response to temperature decrease, NCX elevates intracellular Ca2+ and activates CaMKII. Activated CaMKII accelerates transcriptional oscillations of clock genes, so that the period of circadian clock remains stable. Moreover, Ca2+ signal is also important for high-amplitude oscillation of the circadian rhythms, and CaMKII alleviates amplitude reduction by temperature decrease to prevent loss of cellular rhythmicity at low temperature. In mouse spontaneous behavioral rhythms, disruption of CaMKII activity caused significant decrease of the rhythmicity. Therefore, we propose that cold NCX-Ca2+-CaMKII signaling is a crucial regulator of the amplitude and the period length of the temperature-compensated circadian rhythms.
  • Shingo Gibo (RIKEN iTHEMS, Japan)
    "Waveform analysis reveals the mechanisms for circadian rhythms and hibernation"
  • Organisms have evolved many oscillatory systems such as circadian rhythms and hibernation. The waveforms of the biological oscillations are of various shapes. This may indicate that the various waveforms contain the important information for understanding the biological systems. In this talk, by analyzing waveform pattern, we theoretically consider (i) circadian clocks and (ii) hibernation. First, we study the robustness of circadian period to temperature. The circadian clocks consist of complex biochemical networks. Although most biochemical reactions accelerate with increasing temperature, the period of circadian clocks is stable to temperature changes. This phenomenon is called as “temperature compensation,” and the mechanism has been unclear. To understand the condition of temperature compensation, we analyzed a mathematical model for circadian clocks. Then, we found that the waveforms of gene-activity rhythms should become more non-sinusoidal when reactions become faster and simultaneously, the circadian period becomes longer or remains unchanged. From this result, we predict that the waveforms should be more distorted at higher temperature in order to achieve temperature compensated period. Next, we analyzed the temporal pattern of hibernation. Under cold and short photoperiodic conditions, Syrian hamsters enter hibernation spontaneously. During hibernation, their body temperature shows fluctuation between euthermia and hypothermia with a certain period of several days. It is called 'torpor-arousal cycle'. In this study, we analyzed the time-series of body temperature during hibernation by using generalized harmonic analysis. Then, we found that the period of torpor-arousal cycle gradually changes at hundred-days scale.

Recent advances in mathematical neuroscience: cortically inspired models for vision and synaptic plasticity

Organized by: Luca Calatroni (Laboratoire I3S, CNRS, UCA & Inria Sophia Antipolis Méditerranée, France), Mathieu Desroches (MathNeuro Project-Team, Inria Sophia Antipolis Méditerranée & Université Côté d’Azur, France), Valentina Franceschi (Dipartimento di Matematica, Università degli Studidi Padova, Italy), Dario Prandi (Université Paris-Saclay, CNRS, CentraleSupélec, L2S, France)
Note: this minisymposia has multiple sessions. The second session is MS17-NEUR.

  • Laurent Perrinet (INT, CNRS - Aix-Marseille Université, France)
    "Pooling in a predictive model of V1 explains functional and structural diversity across species"
  • Neurons in the primary visual cortex are selective to orientation with various degrees of selectivity to the spatial phase, from high selectivity in simple cells to low selectivity in complex cells. Various computational models have suggested a possible link between the presence of phase invariant cells and the existence of cortical orientation maps in higher mammals’ V1. These models, however, do not explain the emergence of complex cells in animals that do not show orientation maps. In this study, we build a model of V1 based on a convolutional network called Sparse Deep Predictive Coding (SDPC) and show that a single computational mechanism, pooling, allows the SDPC model to account for the emergence of complex cells as well as cortical orientation maps in V1, as observed in distinct species of mammals. By using different pooling functions, our model developed complex cells in networks that exhibit orientation maps (e.g., like in carnivores and primates) or not (e.g., rodents and lagomorphs). The SDPC can therefore be viewed as a unifying framework that explains the diversity of structural and functional phenomena observed in V1. In particular, we show that orientation maps emerge naturally as the most cost-efficient structure to generate complex cells under the predictive coding principle.
  • Rufin Van Rullen (CerCo, CNRS and ANITI, Universite de Toulouse, France)
    "Deep predictive coding for more robust and human-like vision"
  • I will report on a series of experiments with deep convolutional neural networks augmented with feedback connections. The dynamics of the network are governed by predictive coding objectives, similar to those that have been proposed to explain neural activity in the brain. Compared to the standard feed-forward networks, these predictive coding networks can be more robust to noise and against certain adversarial attacks. They also respond to visual illusions (in particular, illusory contours from Kanisza shapes) in a way that is more similar to biological perception.
  • Yuri Elias Rodrigues (INRIA/IPMC/Université Côte d'Azur, France)
    "Modelling the experimental heterogeneity of synaptic plasticity"
  • Discovering the rules of synaptic plasticity is an important step for understanding brain learning. Existing plasticity models are either 1) top-down and interpretable, but not flexible enough to account for experimental data, or 2) bottom-up and biologically realistic, but too intricate to interpret and hard to fit data. We fill the gap between these approaches by uncovering a new plasticity rule based on a geometrical readout mechanism that flexibly maps synaptic enzyme dynamics to plasticity outcomes. We apply this readout to a multi-timescale model of hippocampal synaptic plasticity induction that includes electrical dynamics, calcium, CaMKII and Calcineurin, and accurate representation of intrinsic noise sources. Using a single set of model parameters, we demonstrate the robustness of this plasticity rule by reproducing nine published ex vivo experiments covering various spike-timing and frequency-dependent plasticity induction protocols, animal ages, and experimental conditions. Our model should facilitate experimental design since each variable identify a biological counterpart bridging experiment and simulation.
  • Halgurd Taher (Inria Sophia Antipolis-Méditerranée Research Centre, France)
    "Bursting in a next generation neural mass model with synaptic dynamics: a slow-fast approach"
  • We report a detailed analysis on the emergence of bursting in a recently developed neural mass model, that takes short-term synaptic plasticity into account. Neural mass models are capable of mimicking the collective dynamics of large scale neuronal populations in terms of a few macroscopic variables like mean membrane potential and firing rate. The one being used here particularly important, as it represents an exact meanfield limit of synaptically coupled quadratic integrate & fire neurons, a canonical model for type I excitability. In absence of synaptic dynamics, a periodic external current with a slow frequency ϵ can lead to burst-like dynamics. The firing patterns can be understood using techniques of singular perturbation theory, specifically slow-fast dissection. In the model with synaptic dynamics the separation of timescales leads to a variety of slow-fast phenomena and their role for bursting is rendered inordinately more intricate. Canards are one of the main slow-fast elements on the route to bursting. They describe trajectories evolving nearby otherwise repelling invariant sets of the system and are found in the transition region from subthreshold dynamics to bursting. For values of the timescale separation nearby the singular limit ϵ → 0, we report peculiar jump-on canards, which block a continuous transition to bursting. In the biologically more plausible regime this transition becomes continuous and bursts emerge via consecutive spike-adding. The onset of bursting is of complex nature and involves mixed-type like torus canards, that form the very first spikes of the burst and revolve nearby repelling limit cycles. We provide numerical evidence for the same mechanisms to be responsible for the emergence of bursting in the quadratic & fire network with plastic synapses. The main conclusions apply for the network, thanks to the exactness of the meanfield limit.

Effects of stochasticity and heterogeneity on networks' synchronization properties

Organized by: Zahra Aminzare (University of Iowa, United States), Vaibhav Srivastava (Michigan State University, United States)
Note: this minisymposia has multiple sessions. The second session is MS07-NEUR.

  • James Roberts (QIMR Berghofer Medical Research Institute, Australia)
    "Noise-enhanced synchronization of dynamics on the human connectome"
  • Synchronization is a collective mechanism by which oscillatory networks achieve their functions. However, it is not well understood how potentially disruptive external inputs like stochastic perturbations affect synchronization. This is particularly so for real-world systems with relatively complex network topologies and dynamical properties, such as the human brain. Here, we aim to address this problem using a large-scale model of the human brain network (i.e., the human connectome). Using the Kuramoto model, we show that when nodes in the network are coupled at some critical strength, a counterintuitive phenomenon emerges where the addition of noise increases the synchronization of global and local dynamics, with structural hub nodes benefiting the most. We link this stochastic synchronization effect to the intrinsic hierarchy of neural timescales of the brain and the heterogeneous complex topology of the connectome. We find that the human connectome supports the formation of frustrated clusters, which, in the presence of moderate levels of noise, reconfigure via phase shifts and frequency shifts to increase the overall synchronization. Overall, the work provides theoretical insights into the emergence and mechanisms of stochastic synchronization, highlighting its putative contribution in achieving network integration underpinning brain function.
  • Giovanni Russo (University of Salerno, Italy)
    "On noise-induced phenomena in complex networks"
  • This talk is focused on the study of noise-induced emerging behaviors in complex networks. We will explore how the interplay between the dynamics at the nodes, the network topology and noise diffusion processes play a key role in determining stability of certain manifolds in the network state-space. After introducing the mathematical framework, we present a perhaps counter-intuitive result for network synchronization. Indeed we show how certain noise diffusion processes (also termed as relative-state- dependent noise) force stability of the synchronization/consensus manifold that, without noise, would be unstable. Applications of the results to biochemical systems are also discussed.
  • Matin Jafarian (Delft University of Technology, Netherlands)
    "Stochastic stability of discrete-time phase-coupled oscillators"
  • In this talk, we study the conditions of stochastic stability for a class of discrete-time phase-coupled oscillators. We introduce the notion of stochastic phase-cohesiveness using the concept of Harris recurrency of Markov chains. We study the stochastic phase-cohesiveness of oscillators in a network with an underlying connected topology subject to both multiplicative and additive stochastic uncertainties. We derive sufficient conditions for achieving the phase-cohesiveness considering stochastic uncertainties realized according to probability distributions with both positive and negative mean values. We further discuss the phase-cohesiveness of oscillators in a random network as a special case of the aforementioned problem.
  • Supravat Dey (University of Delaware, United States)
    "Role of intercellular coupling and delay on the synchronization of biomolecular clocks"
  • Living cells encode diverse biological clocks for circadian timekeeping and formation of rhythmic structures during embryonic development. These biomolecular clocks are subject to unavoidable fluctuations due to the inherent stochasticity of biochemical reactions. How do these clocks synchronize across cells through intercellular coupling mechanisms? To address this question, we leverage the classical motif for genetic clocks, the Goodwin oscillator, where a gene product inhibits its own synthesis via time-delayed negative feedback. More specifically, we study an interconnected system of two identical Goodwin oscillators (each operating in a single cell), where state information is conveyed between cells via a signaling pathway whose dynamics is modeled as a first-order system. Our results show intercellular coupling strength and intercellular time delay play a vital role in the synchronization of the coupled oscillators.

Effects of stochasticity and heterogeneity on networks' synchronization properties

Organized by: Zahra Aminzare (University of Iowa, United States), Vaibhav Srivastava (Michigan State University, United States)
Note: this minisymposia has multiple sessions. The second session is MS06-NEUR.

  • Zack Kilpatrick (University of Colorado Boulder, United States)
    "Heterogeneity Improves Speed and Accuracy in Social Networks"
  • How does temporally structured private and social information shape collective decisions? To address this question we consider a network of rational agents who independently accumulate private evidence that triggers a decision upon reaching a threshold. When seen by the whole network, the first agent’s choice initiates a wave of new decisions; later decisions have less impact. In heterogeneous networks, first decisions are made quickly by impulsive individuals who need little evidence to make a choice but, even when wrong, can reveal the correct options to nearly everyone else. We conclude that groups comprised of diverse individuals can make more efficient decisions than homogenous ones. In addition, we extend this analysis to the groups of agents receiving correlated observations, showing the first agent to decide is less accurate in this case.
  • Hermann Riecke (Northwestern University, United States)
    "Paradoxical Phase Response and Enhanced Synchronizability of Gamma-Rhythms by Desynchronization"
  • Neurons are often observed to form large ensembles that fire coherently and rhythmically, constituting a macroscopic collective oscillation. The synchronization of such γ -rhythms arising in different brain areas is thought to be relevant for the communication between these brain areas and has been implicated in various cognitive functions. What determines whether these collective oscillations can synchronize with each other or with periodic external inputs? We show that, surprisingly, both uncorrelated noise and heterogeneity in the neuronal properties can enhance the synchronizability of γ -rhythms. They do that by reducing the within-network synchrony. This allows external inputs to conspire with the within-network inhibition to change the number of neurons that participate in the rhythm, which changes the frequency of the rhythm substantially and enhances its synchronizability. A characteristic feature of this mechanism is a paradoxical phase response of the collective oscillation: external input can advance the rhythm although they directly delay each individual neuron and vice versa. We demonstrate this for various types of neuron models in networks supporting ING- and PING-rhythms. We use direct numerical simulations of spiking networks as well as the adjoint method for the phase-response curve within the exact mean-field theory of Lorentzian networks of quadratic-integrate-fire neurons.
  • James MacLaurin (New Jersey Institute of Technology, United States)
    "Stochastic Oscillations Emerging from the Stochastic Pulling Forces of Microtubules"
  • Following early work of Grill and Kruse, it is well known that the mitotic spindle pole can oscillate during cell division. The oscillation arises due to the growth of cytoskeletal microtubules - these radiate outwards and attach to two poles. This oscillatory behavior can arise during asymmetric cells divisions that result in daughter cells of unequal sizes. The spindle is essential to organize chromosome segregation during mitosis but also to define the constriction place at which the original cell is divided. The original model due to Grill and Kruse assumes that the microtubules and motors can be well-approximated as a continuum, and thereby modeled using PDEs and ODEs. In this work we develop a finite-size microscopic model, with microtubules detaching and reattaching in a stochastic manner. Furthermore, in our model the binding of individual microtubules is affected by the density of microtubules that are already attached. We perform stochastic simulations, and use analytic methods to project the cumulative effects of the stochasticity onto the limit cycle. We also demonstrate that the continuum model arises in the large size limit of this finite size system.
  • Jonathan Touboul (Brandeis University, United States)
    "Noise-induced synchronization and anti-resonance in interacting excitable systems; Applications to Deep Brain Stimulation in Parkinson’s Disease"
  • In large networks of excitable elements driven by noise, a surprising regime of orderly, perfectly synchronized periodic solutions arises for intermediate levels of noise, as the network transitions from clamping around the stable equilibrium at low noise, to asynchrony at high noise. I will present a theory for the emergence of these synchronized oscillations due to noise. This noise-induced synchronization, distinct from classical stochastic resonance, is fundamentally collective in nature. Indeed, I show that, for noise and coupling within specific ranges, an asymmetry in the transition rates between a resting and an excited regime progressively builds up, leading to an increase in the fraction of excited neurons eventually triggering a chain reaction associated with a macroscopic synchronized excursion and a collective return to rest where this process starts afresh, thus yielding the observed periodic synchronized oscillations. We further uncover a novel antiresonance phenomenon in this regime: noise-induced synchronized oscillations disappear when the system is driven by periodic stimulation with frequency within a specific range (high relative to the spontaneous activity). In that antiresonance regime, the system is optimal for measures of information transmission. This observation provides a new hypothesis accounting for the efficiency of high-frequency stimulation therapies, known as deep brain stimulation, in Parkinson’s disease, a neurodegenerative disease characterized by an increased synchronization of brain motor circuits. We further discuss the universality of these phenomena in the class of stochastic networks of excitable elements with specific coupling and illustrate this universality by analyzing various classical models of neuronal networks. Altogether, these results uncover some universal mechanisms supporting a regularizing impact of noise in excitable systems, reveal a novel antiresonance phenomenon in these systems, and propose a new hypothesis for the efficiency of high-frequency stimulation in Parkinson’s disease.

Modeling cardiac electrophysiology and pharmacology in health and disease

Organized by: Seth Weinberg (The Ohio State University, United States) & Eleonora Grandi (UC Davis, United States)

  • Eric Sobie (Icahn School of Medicine at Mount Sinai, United States)
    "Creating cell-specific models to infer changes to pig myocyte physiology after myocardial infarction"
  • Following myocardial infarction (MI), the region surrounding the infarct scar, known as the border zone (BZ), undergoes heterogeneous remodeling. These changes impact the cardiomyocytes’ electrophysiological behavior resulting in variable changes between myocytes depending on whether cells are near or remote from the BZ. In this study we sought to understand these heterogeneous electrophysiological changes by constraining model parameters, in a cell-by-cell manner, to fit data obtained in individual cells. In experiments, action potentials and intracellular calcium were recorded in cells with and without MI, in the border zone and remote from the MI. A genetic algorithm was run to estimate the ionic conductances in each cell studied (> 40), and repeated runs were performed to estimate the extent to which each conductance was identifiable. Results indicate which conductances exhibit more or less variability than others, and how conductances are altered by MI, in both regions. Overall, the study suggests a methodology for understanding complex disease states in which several variables have been altered.
  • Haibo Ni (University of California Davis, United States)
    "Quantifying cAMP- and Ca(2+)-dependent proarrhythmic mechanisms using populations of atrial myocyte and tissue models"
  • The β-adrenergic receptor (βAR)/cAMP/PKA and multifunctional Ca(2+)-calmodulin-dependent protein kinase II (CaMKII) signaling pathways are key regulators of cardiac excitation-contraction coupling (ECC) by modulating multiple common downstream targets. Hyperactivation of both signaling pathways contributes to the initiation and maintenance of atrial fibrillation (AF), the world’s most common arrhythmia. Here, we developed a novel computational model of human atrial myocytes to couple electrophysiology and Ca(2+) handling with detailed descriptions of βAR/cAMP/PKA and CaMKII pathways. Populations of atrial myocytes revealed a synergy between the PKA and CaMKII effects on the atrial ECC proteins by promoting a vicious cycle of Ca(2+) and membrane potential instabilities. Logistic regression analyses uncovered the relative roles of the ECC proteins and the signaling components in generating cellular arrhythmogenic events. Further, we constructed 2D heterogeneous atrial tissue models and demonstrated that βAR stimulation and CaMKII hyperactivation promote arrhythmogenicity by invoking spontaneous Ca(2+)-overload-mediated action potentials, whereas CaMKII inhibition substantially reduced the vulnerability. Our simulations highlight a novel role of CaMKII-dependent cell-to-cell uncoupling in exacerbating the arrhythmia. Collectively, our simulations reveal synergy in PKA and CaMKII effects on cellular- and tissue-level arrhythmogenic outcomes, and depict a novel paradigm for Ca(2+)-CaMKII-dependent involvement in both enhanced triggered activity and conduction disturbances in AF. These findings suggest that interrupting the vicious cycle of Ca(2+)-CaMKII-Ca(2+) (e.g., via CaMKII inhibition) may be a valuable pharmacotherapy approach to counteract both triggers and functional substrate in AF.
  • Nicolae Moise (The Ohio State University, United States)
    "Intercalated Disk Nanoscale Structure Regulates Cardiac Conduction"
  • The intercalated disk (ID) is a specialized subcellular region that provides electrical and mechanical connections between myocytes in the heart. The ID has a clearly defined passive role in cardiac tissue, transmitting mechanical forces and electrical currents between cells. Recent studies have shown that Na+ channels, the primary current responsible for cardiac excitation, are preferentially localized at the ID, particularly within nanodomains around mechanical and gap junctions, and that perturbations of ID structure alter cardiac conduction. This suggests that the ID may play an important, active role in regulating conduction. However, the structure of the ID and intercellular cleft are not well characterized, and to date, no models have incorporated the influence of ID structure on conduction in cardiac tissue. In this study, we developed an approach to generate realistic finite element model (FEM) meshes replicating ID nanoscale structure, based on experimental measurements from transmission electron microscopy (TEM) images. We then integrated measurements of the intercellular cleft electrical conductivity, derived from the FEM meshes, into a novel cardiac tissue model formulation. FEM-based calculations predict that the distribution of cleft conductances is sensitive to regional changes in ID structure, specifically the intermembrane separation and gap junction distribution. Tissue-scale simulations demonstrated that ID structural heterogeneity leads to significant spatial variation in electrical polarization within the intercellular cleft. Importantly, we find that this heterogeneous cleft polarization regulates conduction by desynchronizing the activation of post-junctional Na+ currents. Additionally, these heterogeneities lead to a weaker dependence of conduction velocity on gap junctional coupling, compared with prior modeling formulations that neglect or simplify ID structure. Further, we find that disruption of local ID nanodomains can lead to either conduction slowing or enhancing, depending on gap junctional coupling strength. Overall, our study demonstrates that ID nanoscale structure can play a significant role in regulating cardiac conduction.
  • Jonathan Silva (Washington University in St. Louis, United States)
    "Using molecular detail and genetic background to predict patient response to anti-arrhythmic therapy"
  • Small molecule anti-arrhythmic therapies are generally considered to be moderately effective in suppressing arrhythmia, and patient outcomes are highly variable. This situation persists even when the genetic background that predisposes patients with congenital arrhythmias is known. We investigated the variability in patient response to the class I anti-arrhythmic molecule, mexiletine, in patients who were diagnosed with Long QT Syndrome Type 3. These patients harbor disease-linked variants in the gene that encodes the cardiac Na+ channel. Our results showed that variant effects on the voltage sensing domain of repeat III (VSD-III) of the Na+ channel could be used to predict whether patients were well-treated with mexiletine therapy with a partial least squares regression approach. A follow-on kinetic model that described the molecular details of the channel and block by mexiletine suggests a novel therapeutic approach by targeting VSD-III. Ongoing work is focused on developing new methods to create optimized kinetic channel models and testing whether the correlation between variant effects on VSD-III and mexiletine therapeutic outcomes holds for the general population.

Ionic Flow through Membrane Channels

Organized by: Peter Bates (Michigan State University), Weishi Liu (Mathematics, U. Kansas, USA), Mingji Zhang (Mathematics, New Mexico Tech., USA)
Note: this minisymposia has multiple sessions. The second session is MS03-NEUR.

  • Tom DeCoursey (Department of Physiology & Biophysics Rush University Medical Center, USA)
    "Proton Selective Conduction Through hHV1, the Human Voltage-gated Proton Channel"
  • Voltage-gated proton channels are unique ion channels, because the molecule is a free-standing voltage-sensing domain with an intrinsic proton conduction pathway. An exquisite proton selectivity mechanism excludes all other ions. How proton channels achieve this selectivity will be discussed. An essential element is an aspartic acid residue located within a narrow region at the center of the membrane. The aspartate is likely hydrogen-bonded to one of the three arginine residues. An approaching hydronium ion breaks the hydrogen bonds to allow proton conduction. When the channel is closed, a hydrophobic region prevents proton leakage through the pore.
  • Mingji Zhang (Mathematics, New Mexico Tech., USA)
    "Competition between Cations via Classical Poisson–Nernst–Planck Models with Small Permanent Charges"
  • We study a one-dimensional Poisson–Nernst–Planck system for ionic flow through a membrane channel. Nonzero but small permanent charge, the major structural quantity of an ion channel, is included in the model. Two cations with the same valences and one anion are included in the model, which provides more rich and complicated correlations or interactions between ions. The cross-section area of the channel is included in the system, providing important information on the geometry of the three-dimensional channel, which is critical for our analysis. Geometric singular perturbation analysis is employed to establish the existence and local uniqueness of solutions to the system for small permanent charges. Treating the permanent charge as a small parameter, through regular perturbation analysis, we are able to derive approximations of the individual fluxes explicitly, and this allows us to study the competition between two cations, which is related to the selectivity phenomena of ion channels. Numerical simulations are performed to provide a more intuitive illustration of our analytical results, and they are consistent.
  • Hamid Mofidi (Mathematics, U. Iowa, USA)
    "Effects of ion size on current and fluxes via hard-sphere PNP models"
  • This reports on studies of a one-dimensional version of a Poisson-Nernst-Planck-type system with a local hard-sphere potential model for ionic flow through a membrane channel with fixed boundary ion concentrations (charges) and electric potentials. The research is directed to set up a simple structure defined by permanent charges with two mobile ion species. A local hard-sphere potential that depends pointwise on ion concentrations is incorporated in the model to evaluate ion-size influences on the ionic flow. The model problem is treated as a boundary value problem of a singularly perturbed differential system, and the analysis is based on the geometric singular perturbation theory. We examine ion size effects on the flow rate of matter through a cross-section by treating the ion sizes as small parameters.
  • Weishi Liu (Mathematics, U. Kansas, USA)
    "Permanent charge effects on ionic flow"
  • Permanent charge is the most important structure of an ion channel.   In this talk, we will report our studies toward an understanding of permanent charges on ionic flow via a quasi-one-dimensional Poisson-Nernst-Planck (PNP) model.    The permanent charges are limited to a special case of piecewise constant with one non-zero portion. For ionic mixtures with one cation species and one anion species, a fairly rich behavior of permanent charge effects is revealed from rigorous analyses based on a geometric framework for PNP and from numerical simulations guided by the analytical results.   For ionic mixtures with two cation species and one anion species, richer behavior is expected and our preliminary analytical results identify a number of these, including some not-so-intuitive ones.

The Control of the Cardiovascular System in Health and Disease

Organized by: Mette Olufsen (North Carolina State University, USA), Brian Carlson (University of Michigan, USA), Justen Geddes (North Carolina State University, USA)
Note: this minisymposia has multiple sessions. The second session is MS12-NEUR.

  • Leszek Pstras (Nalecz Institute of Biocybernetics and Biomedical Engineering, Polish Academy of Sciences, Warsaw, Poland)
    "Blood Volume Regulation During Hemodialysis"
  • Hemodialysis is the most common renal replacement therapy allowing for the removal of excess body water and waste products of metabolism in patients with chronic or acute kidney failure. Unfortunately, this life-sustaining treatment often puts a lot of strain on the cardiovascular system. During a typical dialysis session, a few liters of fluid are gradually removed from the blood flowing through the dialyzer, which usually leads to a progressive decrease in blood volume. The proper function of the cardiovascular system relies then on the microvascular absorption of fluid from tissues (the vascular refilling mechanism) and the activity of blood pressure regulatory mechanisms. In many dialysis patients, however, these mechanisms work insufficiently, leading to a drop in blood pressure and accompanying symptoms. Intradialytic hypotension is a multi-factorial and still not fully understood phenomenon and remains the major issue in dialysis units for both patients and staff. In this talk, a lumped-parameter mathematical model of the cardiovascular response to hemodialysis will be presented to discuss the cardiovascular regulatory mechanisms focusing on the mechanical aspects of blood volume regulation at the level of microcirculation.
  • Nikolai L. Bjørdalsbakke (Norwegian University of Science and Technology, Trondheim, Norway)
    "Is Non-Invasive Finger Pressure Informative About Cardiovascular Adaptation to Physical Activity Interventions?"
  • Non-invasive finger pressure is a simple and flexible method to continuously record blood pressure waves in various clinical settings; however, the waveform is substantially different from the central aortic blood pressure waveform, and further the systolic and diastolic values may differ from hypertension research's gold standard of 24 hour ambulatory brachial-cuff measured systolic and diastolic blood pressure. We present preliminary analysis of non-invasive finger pressure before and after physical activity intervention in pre-hypertensive and hypertensive adults. Additionally, we present the results of interpreting these blood pressure data through both mechanistic and data driven models as a means to quantify cardiovascular adaptations.
  • Justen Geddes (North Carolina State University, Raleigh, NC, USA)
    "Cardiovascular Regulation in POTS Patients"
  • Postural Orthostatic Tachycardia Syndrome (POTS) is characterized by an excessive increase in heart rate upon an upright postural change along with the presence of orthostatic symptoms possibly caused by an overactive baroreflex control system. The main contributor to heart-rate control is the baroreflex control system, a negative feedback system operating at a resonance frequency of ~0.1 Hz. Another sign that the control system is overactive is that POTS patients exhibit larger low-frequency (~0.1 Hz) heart rate and blood pressure oscillations than controls. In this talk we use signal processing to demonstrate the presence of 0.1 Hz oscillations and we build a cardiovascular systems model predicting baroreflex control of heart rate and blood pressure for controls and POTS patients. The cardiovascular model uses an RC electrical circuit analogy while the baroreflex control is modeled using first-order equations controlling heart rate, vascular resistance, and cardiac contractility ensuring saturation at high and low pressure. Our model is able to predict amplified low-frequency oscillations observed in POTS patient heart rate and blood pressure data both at rest and during head-up tilt, and we show how control changes for the various hypothesized causes of POTS known as endophenotypes.
  • Feng Gu (University of Michigan, Ann Arbor, MI and Xiangya Hospital, Central South University, Changsha, Hunan, China, USA)
    "Probing the Potential Role of Intermittent Functioning of Baroreflexes in the Etiology of Hypertension Using an Integrated Computational and Experimental Approach"
  • The potential role of the baroreflexes in long‐term arterial blood pressure (BP) regulation and in the etiology of primary hypertension have been long debated. To elucidate the potential mechanisms underlying the pathophysiology of primary hypertension, we analyzed dynamic baroreflex responses to spontaneous fluctuations in arterial pressure in the conscious spontaneously hypertensive rat (SHR), the most widely used genetic rat model of primary hypertension, as well as in the Wistar-Kyoto (WKY), the Dahl salt-sensitive, the Dahl salt-resistant, and the Sprague-Dawley rat. Observations revealed the existence of long intermittent periods (lasting up to several minutes) of continuous engagement and disengagement of baroreflex-mediated control of heart rate. Analysis of these intermittent periods reveals a predictive relationship between increased mean arterial pressure and progressive baroreflex disengagement that is present in the SHR and WKY strains but absent in others. To further investigate the mechanism underlying the intermittent baroreflexes engagement/disengagement, video was recorded during measurements of spontaneous dynamic baroreflex function in animals. Preliminary results indicate a positive correlation between baroreflex disengagement periods and activity levels. Measurements on human subjects reveal that, rather than the relationship between BP and progressive baroreflex disengagement observed in the rat models, baroreflex disengagement is more closely associated with arterial blood pH, suggesting a competitive interaction between baroreflex- and chemoreflex-mediated regulation of autonomic function. Based on these observations we hypothesize that chemoreflex-mediated sympathetic outflow can override baroreflex-derived parasympathetic outflow causing an apparent intermittent functioning of the baroreflex and potentially leading to hyper-sympathetic activity. We further hypothesize that in the SHR rat this intermittent chemoreflex-mediated override of the baroreflex contributes chronically elevated BP.

The Control of the Cardiovascular System in Health and Disease

Organized by: Mette Olufsen (North Carolina State University, USA), Brian Carlson (University of Michigan, USA), Justen Geddes (North Carolina State University, USA)
Note: this minisymposia has multiple sessions. The second session is MS11-NEUR.

  • Brian E. Carlson (University of Michigan, Ann Arbor, MI, USA)
    "Using Modeling to Understand Pathophysiology in the Cardiovascular Control System"
  • The state of the cardiovascular system can be assessed from time-series signals including heart rate and blood pressure. Characteristics of these signals are used to determine pathophysiology. Experienced clinicians can visually inspect signals and with high level of certainty determine key observed dynamics however analysis with computational models can uncover the underlying mechanisms driving these dynamics. This talk will address how mathematical modeling can be utilized to predict patient specific dynamics for patients with altered cardiovascular control system, including patients with heart failure and pulmonary hypertension. Focus will be on studying dynamics observed in response to an orthostatic challenge including the Valsalva maneuver and active standing. It is believed that through the analysis of these cardiovascular challenges a deeper level phenotyping of changes within the cardiovascular control system can be revealed. To understand how the system is impacted we use models to analyze patient specific changes observed during active standing, a Valsalva maneuver (breath holding), and deep breathing.
  • John S. Clemmer (Department of Physiology and Biophysics, University of Mississippi Medical Center, Jackson, MS, USA)
    "Physiological Modeling of Hypertensive Kidney Disease in African Americans"
  • Chronic kidney disease (CKD) is characterized by the progressive functional loss of nephrons and hypertension (HTN). Successful antihypertensive regimens attenuate the progression of CKD. While studies suggest that calcium channel blocker (CCB) therapy mitigates the decline in renal function in humans with essential HTN, there are few long-term clinical studies that determine the impact of CCBs in patients with hypertensive CKD. Dihydropyridine (DHP) or L-type CCBs preferentially vasodilate the afferent arteriole and have been shown to accelerate CKD in African Americans with low renal function, but the mechanisms are unknown. We used an established integrative mathematical model of human physiology, HumMod, to create a virtual population of African Americans using clinical data (ALLHAT trial). We tested the hypothesis that DHP CCB therapy exacerbates pressure-induced glomerular injury in hypertensive CKD. After two years of simulating angiotensin converting enzyme (ACE) inhibition or CCB, there were statistically similar blood pressure and glomerular filtration rate (GFR) before and after treatment as compared to African American patients. ACE inhibition decreased blood pressure in the virtual population and was not associated with significant changes in glomerular pressure or injury. However, despite having significant falls in blood pressure, chronic CCB therapy was associated with increases in glomerular pressure and significantly increased glomerular damage. High glomerular injury or pressure and single nephron GFR predicted glomerulosclerosis in these models. The results from these simulations suggest that DHP (L-type) CCBs may potentiate glomerular HTN in at risk African Americans (low renal function) and that efferent arteriolar vasodilation with blockers of the renin-angiotensin system may ameliorate CKD progression. While these simulations and results are clinically relevant, the predictions presented in these simulations are to be considered hypotheses until confirmed with experimental and clinical investigation.
  • Peng Li (Brigham and Women’s Hospital, Harvard Medical School, Boston, MA, USA)
    "Resting Heart Rate Complexity and All-Cause and Cardiorespiratory Mortality in a Middle-to-Older Aged, Population Cohort"
  • Spontaneous heart rate fluctuations contain rich information related to health and illness in terms of physiological complexity, an accepted indicator of plasticity and adaptability. However, it is challenging to make inferences on complexity from shorter, more practical epochs of data. Distribution entropy (DistEn) is a recently introduced complexity measure that is designed specifically for shorter duration heartbeat recordings. We hypothesized that reduced DistEn predicts increased mortality in a large population cohort. The prognostic value of DistEn was examined in 7,631 middle-older aged UK Biobank participants who had 2-minute resting electrocardiograms (ECG) conducted (mean age 59.5 years; 60.4% female). During a median follow-up period of 7.8 years, 451 (5.9%) participants died. In Cox proportional hazards models with adjustment for demographics, lifestyle factors, physical activity, cardiovascular risks, and comorbidities, for each 1 standard deviation decrease in DistEn, the risk increased by 36%, 56% and 73%, for all-cause, cardiovascular and respiratory disease related mortality, respectively. These effect sizes were equivalent to the risk of death from being over 5 years older, having been a former smoker or suffering from diabetes mellitus. Lower DistEn was most predictive of death in those under 55 years with a prior myocardial infarction, representing an additional 56% risk for mortality compared to older subjects without. These observations remained after controlling for traditional mortality predictors, resting heart rate and HRV. Resting heart rate complexity from short, resting ECGs was independently associated with mortality in middle to older aged adults. These risks appear most pronounced in middle-aged subjects with prior MI, and may uniquely contribute to mortality risk screening.
  • Ashwin Belle (Fifth Eye Inc., Ann Arbor, MI, USA)
    "Hemodynamic Monitoring: Seeing the Unseen"
  • This talk will discuss the various challenges in cardiac monitoring particularly from a hemodynamic perspective and also discuss some of the current methods and research efforts to predict future cardiovascular events from real-time data. This discussion will be from a commercial prospective of how to plumb the interface between mathematics and diagnostics for better treatment and outcome. A project using real time clinical data to predict future cardiovascular events was developed from a concept at the University of Michigan where sophisticated machine learning was applied to an information-dense ECG signal to predict patient deterioration in the context of hypovolemia. Bringing this research concept to the commercial arena involved developing a data collection framework along with software tools and computational infrastructure. This was the birth of of the company Fifth Eye which brings this technology to the clinic.

Mathematical modeling approaches to understanding pain processing and chronic pain therapies

Organized by: Jennifer Crodelle (Middlebury College, USA), Kevin Hannay (University of Michigan, USA), Victoria Booth (University of Michigan, USA)

  • Jennifer Crodelle (Middlebury College, USA)
    "Firing-rate models for analyzing spinal circuit motifs underlying chronic pain"
  • Neuronal circuitries underlying the processing of pain signaling in the dorsal horn of the spinal cord are complex and not yet completely understood. In addition, changes induced in those circuitries due to nerve injury in chronic pain patients have been attributed to multiple pathologies at the cellular and synaptic levels. Using a firing-rate model formalism for activity of projection and interneuron neuronal populations, we construct models of multiple identified microcircuits that process mechanical sensory and nociceptive input to analyze how their parallel filtering of incoming signals affects projection neuron responses. We use the model to investigate how different proposed chronic pain pathologies disrupt and distort microcircuit processing to result in allodynia and hyperalgesia.
  • Warren Grill (Department of Biomedical Engineering, Duke University, USA)
    "Network Models to Analyze and Design Spinal Cord Stimulation for Chronic Pain"
  • Spinal cord stimulation (SCS) is an established treatment for chronic pain, but neither the neural mechanisms underlying SCS nor the relationship between the applied parameters of SCS and its clinical efficacy have been fully characterized. We developed and validated biophysical models of dorsal column axons as well as the dorsal horn neural circuit that processes peripheral sensory inputs, including nociceptive information. We simulated the effects of SCS across a range of frequencies and amplitudes on the activity of model dorsal column axons and model wide dynamic range projection neurons. SCS applied at amplitudes as low as 60% of the predicted sensory threshold activated model dorsal column axons, and the pattern of resulting activity was irregular and strongly dependent on the stimulation amplitude. These model-based predictions were validated with in vivo recordings from single dorsal column axons in anesthetized rats. The increased activity in dorsal column axons generated by SCS drove activity in model inhibitory interneurons and subsequently reduced model wide dynamic range neuron firing rates. Changes in model wide dynamic range neuron firing rate varied non-monotonically with stimulation amplitude and rate, and maximum inhibition occurred at 75-85% of sensory threshold and at rates between 50-90 Hz. Further in vivo recordings showed that net inhibition of putatively excitatory neurons was maximal at 80% of the predicted sensory threshold. The new understanding resulting from the implementation and validation of biophysically-based computations models provides a platform to guide the design of novel methods of stimulation
  • Steven A Prescott (Neurosciences and Mental Health, The Hospital for Sick Children; Department of Physiology and Institute of Biomedical Engineering, University of Toronto , Canada)
    "Altered processing of tactile input due to chloride dysregulation in the spinal dorsal horn "
  • Synaptic inhibition in the dorsal horn of the spinal cord plays a key role in processing somatosensory input. Weakened inhibition can cause light touch to be mistakenly perceived as painful – a phenomenon known as mechanical allodynia, which is common after nerve injury. Nerve injury induces many changes in the spinal dorsal horn, including weakened inhibition. This disinhibition is due primarily to chloride dysregulation caused by downregulation of the potassium-chloride co-transporter KCC2. KCC2 normally keeps intracellular chloride at a low concentration, thus maintaining the chloride driving force that GABAA and glycine receptors rely on to mediate inhibition. Weakened inhibition causes receptive fields to expand, which in turn affects spatial summation. Weakened inhibition also ungates polysynaptic pathways, allowing low-threshold inputs to activate projection neurons that are normally activated exclusively by high-threshold inputs. In this talk, I will discuss experimental data and our efforts to incorporate those data into a circuit-level model of the spinal dorsal horn. 
  • Scott Lempka (Department of Biomedical Engineering, University of Michigan; Department of Anesthesiology, University of Michigan; Biointerfaces Institute, University of Michigan, USA)
    "Computational modeling of neural recruitment during spinal cord stimulation for pain"
  • Spinal cord stimulation (SCS) is a popular neurostimulation therapy for severe chronic pain. To improve stimulation efficacy, multiple modes are now used in the clinic. Clinical observations have produced speculation that these modes target different neural elements and/or work via distinct mechanisms of action. However, in humans, these hypotheses cannot be conclusively answered via experimental methods. Therefore, we utilized computational modeling to assess the response of primary afferents, interneurons, and projection neurons to multiple forms of SCS. We used this modeling approach to understand how various technical and physiological factors, such as neuron geometry and waveform patterns (e.g., burst and kilohertz-frequency SCS), affect the cellular response to SCS. In our simulations, local cell thresholds were always higher than afferent thresholds, arguing against direct recruitment of these interneurons and projection neurons. Furthermore, all of the clinical SCS waveforms had the same relative neural recruitment order, albeit with different absolute thresholds. This result suggests that these SCS modalities do not exert differential effects through distinct recruitment profiles. These results motivate future work to contextualize clinical observations across conventional and emerging SCS paradigms.

Multi-scale Physiological Systems

Organized by: Saeed Farjami (University of Surrey, United Kingdom), Anmar Khadra (McGill University, Canada)
Note: this minisymposia has multiple sessions. The second session is MS15-NEUR.

  • Saeed Farjami (University of Surrey, United Kingdom)
    "Non-sequential Spike Adding in Cerebellar Stellate Cells"
  • Cerebellar Stellate Cells are spontaneously spiking. Recently, our colleagues have recorded bursting activities in these cells by applying pharmacological agents known for blocking certain ion currents. Such activities are usually modelled in the form of systems with different time scales. When the slow variables are treated as parameters, the fast subsystem can provide good insights into the dynamics of the full model. Using slow-fast analysis, we explain the underlying mechanisms responsible for generating types of bursting emerging in the model. Also, a bifurcation analysis of the full model reveals the effect of different doses of the pharmacological agents on the system dynamics. Moreover, our investigations show that the number of spikes in an active phase of bursting changes when parameters of the system fluctuate. However, in contrast to former studies, adding new spikes does not happen sequentially. In this talk, we will discuss such phenomena and try to shed light on their underlying dynamics.
  • Michael Forrester (University of Nottingham, United Kingdom)
    "Using a multiscale next-generation neural-mass model to fit neuroimaging data"
  • Owing to their formulation as exact mean-field representations of neural oscillators, next-generation neural mass models are natural candidates to explore neurological phenomena related to local, and non-local, synchronisation in the brain, such as beta-rebound/beta-burst effects and large-scale functional connectivity. Here, we demonstrate applications of one such model over varying spatial scales and highlight its usefulness in exploring the importance of features of the underlying neuron model, such as gap-junction coupling and synaptic reversal potentials, in emergent large-scale population dynamics.
  • Victoria Booth (University of Michigan, USA)
    "Dynamics and bifurcations of sleep-wake behavior"
  • While transitions between sleep and wake states happen quickly, the timing of these transitions are modulated by the slower processes of the 24 h circadian rhythm and the homeostatic sleep drive, the irresistible urge for sleep after being awake. We are developing and analyzing mathematical models of neuronal sleep-wake regulatory networks to understand how the interaction of fast and slow processes dictate the timing and durations of sleep and wake episodes. In this talk, I will discuss recent analyses of solutions of these models based on construction of circle maps that have allowed identification of the bifurcations underlying the transitions of sleep-wake behavior over human development and across species.
  • Sue Ann Campbell (University of Waterloo, Canada)
    "Time delays may enhance or impede synchronization in brain networks"
  • We study the effect of time-delays in a neural field model for a brain network. The model considered is a network of Wilson-Cowan nodes with inhibitory weights dynamically modified to represent homeostatic regulation. Without time delay, the system has been shown to exhibit rich dynamics including oscillations, mixed-mode oscillations, and chaos. Synchronization of the nodes depends on the connectivity structure of the network. Using the Master Stability formalism, we show that time delays in the connections between the nodes 1) may stabilize brain dynamics by temporarily preventing the onset to oscillatory and pathologically synchronized dynamics, and 2) may enhance or diminish synchronization depending on the underlying eigenvalue spectrum of the connectivity matrix.

Multi-scale Physiological Systems

Organized by: Saeed Farjami (University of Surrey, United Kingdom), Anmar Khadra (McGill University, Canada)
Note: this minisymposia has multiple sessions. The second session is MS14-NEUR.

  • Anmar Khadra (McGill University, Canada)
    "Characterizing the spatiotemporal patterns produced by an excitable fish keratocyte model"
  • The spatiotemporal dynamics of self-organizing lamellipodium in crawling keratocytes have been previously studied using a partial differential equation model to understand the three main patterns of activity observed in such cells, including stalling, waving and smooth motility. The model consisted of three key variables: the density of barbed actin filaments, nascent adhesions (NAs) and VASP, an anti-capping protein that gets sequestered by NAs during maturation. Using parameter sweeping, the distinct regimes of behaviour associated with the three activity patterns were identified. By converting the PDE model into an ODE model, we successfully examined the excitability properties of this system and determined all of its patterns of activity. Our results revealed that there are two additional regimes not previously identified: bistability and type IV excitability. We found that these regimes are also present in the PDE model. Applying slow-fast analysis on the ODE model as well as machine-learning based image analysis showed that the ODE model exhibits a canard explosion through a folded-saddle and that rough motility seen in keratocytes is likely due to noise-dependent motility governed by dynamics at the interface of bistability and type IV excitability. The two parameter bifurcation suggested that the increase in the proportion of rough motion is due to a shift in activity towards the bistable and type IV excitable regimes induced by a decrease in NA maturation rate. In this talk, I will provide a summary of these findings.
  • Theodore Vo (Monash University, Australia)
    "Big Ducks in the Heart"
  • Early afterdepolarizations (EADs) are voltage oscillations observed during the repolarization phase of the cardiac action potential, and are a potentially lethal source of cardiac arrhyth- mia. Experiments have shown that the production of EADs can depend on the complex interplay between cellular ion channel properties, the extrinsic chemical environment, and the rate of sinoa- trial pacing. However, the mechanisms by which alterations in these qualities induce EADs are not well understood. In this work, we analyse a canonical model of the electrical activity in a cardiac cell using geometric singular perturbation techniques. We demonstrate that the EADs are canard-induced mixed-mode oscillations, and explain the essential role that canards play in producing the rich set of model EAD behaviours, some of which have also been observed in experiments. This dynamical viewpoint gives predictive power that is beyond that of the bio- physical explanation alone while also uncovering a common mechanism for phenomena observed in experiments on both atrial and ventricular cardiac cells.
  • Sushmita John (University of Pittsburgh, USA)
    "Transitions in neuronal bursting types"
  • Bursting patterns that fall into an intermediate category between square-wave (fold-homoclinic burst) and pseudo-plateau bursting (fold-subcritical Hopf. burst) have been observed in the voltage recordings of many bursting neurons. Existing research shows that certain mathematical models for these neurons exhibit a transition between square-wave and pseudo-plateau bursting patterns with small parameter changes. However, this transition may be dysfunctional for neurons that necessarily need to spike during the burst. In this work, we study in detail the transition from square-wave to pseudo-plateau bursting patterns seen in neuronal models. We explore properties and parameters of different models to identify the features of currents that affect this transition. The analysis is done using numerical simulations and dynamical systems methods such as fast/slow analysis, bifurcation theory and phase-plane analysis. This approach also helps us to fully characterize intermediate bursting patterns and compare them to the activity seen in bursting neuron types such as respiratory neurons. This is joint work with Dr. Jonathan Rubin.
  • André Longtin (University of Ottawa, Canada)
    "Multi-delay control, communication and complexity"
  • Physiological control is inherently slow with delays that can easily exceed the overall response time of a system’ components to time-varying inputs. It is also the case that control may encompass many subunits that act in concert, and that this involves multiple delays that can span milliseconds to seconds. It is generally assumed that the combination of nonlinearity and delays can lead to oscillatory and even more complex behaviour such as chaos or hyperchaos. But there is a point when multiple delays are present where one starts to think in terms of distributions of delays, and of their simplifying action on network dynamics via the integro-differential formulation of the dynamics. This talk will discuss this transition, and show how complexity collapses when there is a low density of delays. We will also discuss these results in the context of understanding the response properties of such multi-delay systems.

Recent advances in mathematical neuroscience: cortically inspired models for vision and synaptic plasticity

Organized by: Luca Calatroni (Laboratoire I3S, CNRS, UCA & Inria Sophia Antipolis Méditerranée, France), Mathieu Desroches (MathNeuro Project-Team, Inria Sophia Antipolis Méditerranée & Université Côté d’Azur, France), Valentina Franceschi (Dipartimento di Matematica, Università degli Studidi Padova, Italy), Dario Prandi (Université Paris-Saclay, CNRS, CentraleSupélec, L2S, France)
Note: this minisymposia has multiple sessions. The second session is MS05-NEUR.

  • Marcelo Bertalmío (Spanish National Research Council (CSIC), Spain)
    "Evidence for the intrinsically nonlinear nature of receptive fields in vision"
  • The responses of visual neurons, as well as visual perception phenomena in general, are highly nonlinear functions of the visual input, while most vision models are grounded on the notion of a linear receptive field (RF). The linear RF has a number of inherent problems: it changes with the input, it presupposes a set of basis functions for the visual system, and it conflicts with recent studies on dendritic computations. Here we propose to model the RF in a nonlinear manner, introducing the intrinsically nonlinear receptive field (INRF). Apart from being more physiologically plausible and embodying the efficient representation principle, the INRF has a key property of wide-ranging implications: for several vision science phenomena where a linear RF must vary with the input in order to predict responses, the INRF can remain constant under different stimuli. We also prove that Artificial Neural Networks with INRF modules instead of linear filters have a remarkably improved performance and better emulate basic human perception.
  • Emre Baspinar (CNRS/NeuroPSI, France)
    "A biologically-inspired model for Poggendorff type illusions"
  • In this talk, we will see a new biologically-inspired sub-Riemannian model employing Wilson-Cowan type mean field equations described in the model geometry proposed in [1], and in a similar fashion as in [2]. The model is applied to reproducing orientation-dependent Poggendorff- type illusions. The novelty of the model is that it embeds sub-Riemannian diffusion into the neuronal interaction term appearing in the mean field equations. This tunes the neuronal interactions in agreement with the functional architecture of the visual cortex. [1] G. Citti and A. Sarti, “A cortical based model of perceptual completion in the roto-translation space,” Journal of Mathematical Imaging and Vision, vol. 24, no. 3, pp. 307–326, 2006. [2] M. Bertalmío, L. Calatroni, V. Franceschi, B. Franceschiello, and D. Prandi, “Cortical-inspired Wilson–Cowan type equations for orientation-dependent contrast perception modelling,” Journal of Mathematical Imaging and Vi- sion, pp. 1–19, 2020.
  • Rasa Gulbinaite (Netherlands Institute for Neuroscience, The Netherlands)
    "Resonance frequencies in the visual cortex and illusory perception"
  • Sensory cortices stimulated by rhythmic sounds, lights, or touch will respond in a rhythmic manner at frequencies identical or harmonically related to the stimulus. These responses are maximal when a certain cortical circuit is driven at or close to the frequencies it generates naturally. The resonance frequencies are also tightly linked to the system's response to a single impulse (impulse response function). Using examples from human EEG studies and widefield glutamate imaging in mice, I will demonstrate that resonance phenomena are preserved across species and across spatial scales of neural activity; and illustrate how stimulation at resonance frequencies can create illusory percepts.
  • Ludovic Sacchelli (LAGEPP, Université Claude Bernard Lyon 1 (UCBL), France)
    "Cortical-inspired sound processing: hearing with the visual cortex"
  • We propose a mathematical model of sound reconstruction based on a functional architecture of the auditory cortex (A1). The model is inspired by the geometrical modeling of vision, where variational information in the perceived image plays a major role. Sound processing in A1 occurs in the time frequency domain, where sound signals can be understood as images where times plays a fundamental role. In order to respect these symmetries, the inclusion of variational information in sounds translates to a lift from the time frequency domain to the Heisenberg group. In that space, sound signals undergo reconstruction via adapted Wilson-Cowan integro-differential equations that we illustrate with preliminary numerical experiments.

Mathematical Models for Decision-Making

Organized by: Nicholas Barendregt (University of Colorado Boulder, United States), Jonathan Rubin (University of Pittsburgh, United States)

  • Nicholas Barendregt (University of Colorado Boulder, United States)
    "Normative and dynamic decision urgency in unpredictable environments"
  • Decision-making in uncertain environments often requires adaptive forms of evidence accumulation, but less is known about the decision rules needed to achieve optimal performance. While recent studies of decision models in stochastic and dynamic environments have resulted in several phenomenological models, such as the monotonically collapsing decision threshold of the “urgency-gating model” (UGM), we lack a general, normative description of decision rules and their relation to human decision-making. In this talk, we will develop a normative, Bayes-optimal framework for decision tasks in uncertain and dynamic environments. Using the classic “tokens task” paradigm, we apply Bayesian model fitting and model comparison methods to the normative model, the UGM, and several other heuristic models. Our work demonstrates that the humans using the normative strategy exhibit non-monotonic urgency and identifies regions of parameter space where different types of urgency are optimal. Extending these methods to tasks where the reward for a correct response varies in time, we again find that normative decision rules exhibit rich non-monotonic behavior, providing testable hypotheses for experimentalists to probe in future psychophysics tasks.
  • Timothy Verstynen (Carnegie Mellon University, United States)
    "Rethinking the computational architecture of cortico-basal ganglia-thalamic pathways"
  • Humans and other mammals exhibit a high degree of control when selecting actions in noisy contexts, quickly adapting to unexpected outcomes in order to better exploit opportunities arising in the future. This flexible decision-making is mediated, in part, by cortico-basal-ganglia-thalamic (CBGT) circuits that both control action selection and use feedback signals to modify future decisions. In this talk we will highlight how new insights into the circuit-level architecture of CBGT pathways are informing our understanding of the algorithms of decision-making and learning. Specifically we will show how components of the CBGT circuit map to modifiable parameters that balance the speed-accuracy tradeoff during adaptive decision making.
  • Alex Roxin (Centre de Recerca Matemàtica, Spain)
    "Bump attractor dynamics underlying stimulus integration in perceptual estimation tasks"
  • Perceptual decision and continuous stimulus estimation tasks involve making judgments based on accumulated sensory evidence. Network models of evidence integration usually rely on competition between neural populations each encoding a discrete categorical choice. By design, these models do not maintain information of the integrated stimulus (e.g. the average stimulus direction in degrees) that is necessary for a continuous perceptual judgement. Here, we show that the continuous ring attractor network can integrate a stimulus feature such as orientation and track the stimulus average in the phase of its activity bump. We reduced the network dynamics of the ring model to a two-dimensional equation for the amplitude and the phase of the bump. Interestingly, these reduced equations are nearly identical to an optimal integration process for computing the running average of the stimulus orientation. They differ only in the intrinsic dynamics of the amplitude, which affects the temporal weighting of the sensory evidence. Whether the network shows early (primacy), uniform or late (recency) weighting depends on the relative strength of sensory stimuli compared to the amplitude of the bump and on the initial state of the network. The specific relation between the internal network dynamics and the sensory inputs can be modulated by changing a single parameter of the model, the global excitatory drive. We show that this can account for the heterogeneity of temporal weighting profiles observed in humans integrating a stream of oriented stimulus frames. Our findings point to continuous attractor dynamics as a plausible mechanism underlying stimulus integration in perceptual estimation tasks.
  • Wiktor Mlynarski (Institute of Science and Technology Austria, Austria)
    "Attention as efficient and adaptive inference in dynamic environments"
  • Top-down attention is thought to reflect allocation of limited processing resources to task-relevant computations and representations. According to this hypothesis, attentional processing could be characterized by two fundamental theoretical frameworks: probabilistic inference and efficient coding. Probabilistic inference specifies optimal strategies for learning about relevant properties of the environment from local and ambiguous sensory signals. Efficient coding provides a normative approach to study encoding of natural stimuli in resource-constrained sensory systems. By emphasizing different aspects of information processing they provide complementary approaches to study sensory computations. Here we attempt to bring them together by developing general principles that underlie the tradeoff between energetic cost of sensory coding and accuracy of perceptual inferences. We then apply these general principles to optimize a model of population coding in the visual cortex. The model dynamically adapts a representation of natural images to support maximally accurate perceptual inference at minimal activity cost. The resulting optimality predictions reproduce measured properties of attentional modulation in the visual system and generate novel hypotheses about the functional role of top-down feedback, response variability, and noise correlations. Our results suggest that a range of seemingly disparate attentional phenomena can be derived from a general theory combining probabilistic inference with efficient coding in a dynamic environment.

Biological Rhythms and Motor Control

Organized by: Yangyang Wang (University of Iowa, USA), Peter Thomas (Case Western Reserve University, USA)
Note: this minisymposia has multiple sessions. The second session is MS20-NEUR.

  • Yangyang Wang (University of Iowa, USA)
    "Shape and timing: using variational analysis to dissect motor robustness"
  • To survive and reproduce, an animal must adjust to changes in its internal state and the external environment. We refer to the ability of a motor system to maintain performance despite perturbations as “robustness”. Although it is well known that sensory feedback supports robust adaptive motor behaviors, specific mechanisms of robustness are not well understood either experimentally or theoretically. In this work, we explore how sensory feedback could alter a neuromechanical trajectory to enhance robustness for motor control. As a concrete example, we focus on a piecewise smooth neuromechanical model of triphasic motor patterns in the feeding apparatus of the marine mollusk, Aplysia californica. We investigate the mechanisms by which sensory feedback generates robust adaptive behavior, quantify the robustness of the Aplysia model to the applied perturbation (increased mechanical load), and compare them to experimental observations.
  • Zhuojun Yu (Case Western Reserve University, USA)
    "A homeostasis criterion for Limit cycle systems based on infinitesimal shape response curves"
  • Homeostasis occurs in a control system when a quantity remains approximately constant as a parameter, representing an external perturbation, varies over some range. Golubitsky and Stewart (J.~Math.~Biol., 2017) developed a notion of infinitesimal homeostasis for equilibrium systems using singularity theory. Rhythmic physiological systems (breathing, locomotion, feeding) maintain homeostasis through control of large-amplitude limit cycles rather than equilibrium points. Here we take an initial step to study (infinitesimal) homeostasis for limit-cycle systems in terms of the emph{average} of a quantity taken around the limit cycle. We apply the infinitesimal shape response curve (iSRC) introduced by Wang et al.~(SIAM J.~Appl.~Dyn.~Sys, to appear) to study infinitesimal homeostasis for limit-cycle systems in terms of the emph{mean} value of a quantity of interest, averaged around the limit cycle. Using the iSRC, which captures the linearized emph{shape} displacement of an oscillator upon a static perturbation, we provide a formula for the derivative of the averaged quantity with respect to the control parameter. Our expression allows one to identify homeostasis points for limit cycle systems in the averaging sense. We demonstrate in the Hodgkin-Huxley model and in a metabolic regulatory network model that the iSRC-based method provides an accurate representation of the sensitivity of averaged quantities.
  • Silvia Daun (University of Cologne, Germany)
    "Stimulus transformation into motor action: Dynamic graph analysis on neural oscillations reveals aging effects on brain network communication"
  • Cognitive performance slows down with increasing age. This includes cognitive processes that are essential for the performance of a motor act, such as the slowing down in response to an external stimulus. The objective of this study was to identify aging-associated functional changes in the brain networks that are involved in the transformation of external stimuli into motor action. To investigate this topic, we employed dynamic graphs based on phase-locking of Electroencephalography signals recorded from healthy younger and older subjects while performing a simple visually-cued finger-tapping task. The network analysis yielded specific age-related network structures varying in time in the low frequencies (2-7 Hz), which are closely connected to stimulus processing, movement initiation and execution in both age groups. The networks in older subjects, however, contained several additional, particularly interhemispheric, connections and showed an overall increased coupling density. Cluster analyses revealed reduced variability of the subnetworks in older subjects, particularly during movement preparation. In younger subjects, occipital, parietal, sensorimotor and central regions were-temporally arranged in this order-heavily involved in hub nodes. Whereas in older subjects, a hub in frontal regions preceded the noticeably delayed occurrence of sensorimotor hubs, indicating different neural information processing in older subjects. All observed changes in brain network organization, which are based on neural synchronization in the low frequencies, provide a possible neural mechanism underlying previous fMRI data, which report an overactivation, especially in the prefrontal and pre-motor areas, associated with a loss of hemispheric lateralization in older subjects.
  • Ansgar Bueschges (University of Cologne, Germany)
    "Task-specificity in the control of insect walking"
  • When terrestrial animals locomote through their environment they need to control the rhythmic stepping movements of each leg as well as the coordination between all stepping legs, being it two, four, six or eight legs to continuously assure stability as well as to optimally serve the actual behavioral task. The presentation will report recent advances in unravelling the neural organization and operation of the walking system in six legged insects by focusing on walking direction and speed in the fruit fly. Individual descending interneurons from the brain were identified, which are in charge of controlling walking direction. Fruit flies generate a continuum of interleg coordination patterns spanning from wave gait to tetrapod to tripod coordination with increasing walking speed from less than one bodylength/s to more than 15 bodylengths/s assuring optimal stability. Removal of single legs indicates that the leg muscle control system of the fruit fly is organized in a modular fashion with segmental rhythm generating networks.

Biological Rhythms and Motor Control

Organized by: Yangyang Wang (University of Iowa, USA), Peter Thomas (Case Western Reserve University, USA)
Note: this minisymposia has multiple sessions. The second session is MS19-NEUR.

  • Jon Rubin (University of Pittsburgh, USA)
    "Combining rhythm generation and pattern formation in a core respiratory neural circuit"
  • Although respiration seems simple on the surface (breathe in, breathe out, repeat!), looks can be deceiving. In this talk, I will (briefly) comment on two of the topics under active debate in the theory of the neural generation of respiratory rhythms. First, I will consider the issue of how rhythmic activity in the inspiratory core (in the famous pre-Botzinger complex of the mammalian brain stem) can succeed or fail to recruit widespread neural activation and motor output. This work, with Ryan Phillips, is done in the setting of Hodgkin-Huxley type neural models with synaptic coupling that also takes into account dynamics of certain relevant ion concentrations. Second, I will consider what happens when this rhythmic activity is embedded in the full neural circuit for respiration. This part of the talk will be based on work with Jeff Smith done in the simpler setting of coupled relaxation oscillators.
  • Casey Diekman (New Jersey Institute of Technology, USA)
    "Oxygen handling and parameter space interrogation in a minimalist closed-loop model of the respiratory oscillator"
  • Silent Hypoxemia, or happy hypoxemia is a puzzling phenomenon in which patients who have contracted COVID-19 exhibit very low oxygen saturations (SaO2 < 80%) yet experience no discomfort in breathing, or dyspnea. The mechanism by which this blunted response to hypoxia occurs is unknown. Our group has previously shown that a computational model (Diekman et al, 2017, J. Neurophys.) of the respiratory neural network can be used to test hypotheses focused on changes in chemosensory inputs to the central pattern generator (CPG). We hypothesize that altered chemosensory function at the level of the carotid bodies and/or the nucleus tractus solitarii are responsible for this blunted response to hypoxia. In this talk, we will use our model to explore this hypothesis by altering the properties of the gain function representing oxygen sensing inputs to the CPG. (Joint work with Christopher G. Wilson, Loma Linda University, and Peter J. Thomas, Case Western Reserve University.)
  • Todd Young (Ohio University, USA)
    "An Altered Van der Pol Oscillator and Stomatogastric Ganglion"
  • In the Stomatogastric Ganglion or Pyloric Network of Lobsters the LP neuron bursts 1:1 with a pacemaker group (PD) in the intact network. However, isolated LP neurons cycle much more slowly than the pacemaker group. How is the LP neuron able to adjust its firing rate to match the fast pacemaker? We propose that an alteration of a slow conductance is sufficient to explain this phenomenon and we illustrate the principal in an altered van der Pol system.
  • Yaroslav Molkov (Georgia State University, USA)
    "Control of steering in quadrupedal locomotion"
  • Traditionally, the studies of locomotor control in mammalian quadrupeds focus on spinal neural circuit organization that underlies varying patterns of limb movements (gaits) depending on the locomotor speed and other conditions. This intricate circuit includes neural rhythm generators that provide alternating flexion and extension phases for each limb, network interconnections between the generators providing proper interlimb coordination, descending control signals as well as proprioceptive feedback from the limbs. In the related experiments, the animal movements are usually restricted to walking or running along a straight path on a treadmill or over ground. Besides, to isolate particular functional components, the animals are often suspended or partly fixed. These restrictions make the balance control mechanisms irrelevant. However, during such complex maneuvers as turning, the timing of limb lifting and landing as well as limb positioning have to be tightly coordinated with the position of the center of mass to prevent the animal from falling. In addition, during turning movements quadrupedal mammals actively involve head/shoulder turning and body bending which further adds to the complexity of the control system. In this talk, we will use the experimental data on freely moving mice to develop a simple mathematical model of quadrupedal locomotion that includes a balance control system interacting with the locomotor pattern generating circuits. We show that the balance control is involved not only in complex maneuvers but also operates during straight-line locomotion. We argue that body bending is a mechanism involved in the appropriate limb positioning which is an integral part of the balance control system and as such is necessary for efficient turning. (Joint work with Ilya Rybak, Drexel University.)

Sub-group contributed talks

NEUR Subgroup Contributed Talks

  • Sishu Shankar Muni School of Fundamental Sciences, Massey University, New Zealand
    "Dynamics of the discretised Izhikevich neuron model"
  • When analyzing neuron models, ODE(Ordinary Differential Equation)-based models are used to study the characteristics of neurons and in turn understand the various complexities of neurons and their relations with abnormalities and hazards. But the biggest challenge of ODE-based models are its computational complexities and hence researchers started focusing on less complex models resulting in discrete models of neurons. A neuron exhibits bursting and spiking behavior depending on the resetting process which happens in every iteration step. In ODE models this iteration step decides the accuracy of the neuron models while in discrete models the iteration step is one and hence the accuracy is not affected. In this talk, I am going to introduce the discrete Izhikevich model which is modified version of the well-known ODE based Izhikevich neuron model. I analyze the complete dynamical properties and bifurcation patterns of the discretised model. It is found that a careful application of electric field on embryonic neuronal cells have led to their growth in cultures. Therefore, it is of interest to consider the effect of external electromagnetic field on the dynamical behavior of the neurons. I will show how the dynamics changes when external electromagnetic field is applied.
  • Marina Chugunova University of Waterloo, Canada
    "Calcium dynamics in the gonadotropin-releasing hormone neurons"
  • Located in hypothalamus, the gonadotropin-releasing hormone (GNRH) neurons trigger the reproductive axis by the synchronized release of gonadotropin-releasing hormone. The action potential propagating along the neuron's membrane activates the voltage-gated calcium channels, and the influx of the extracellular calcium activates the internal calcium stores. The resulting increase of the calcium ion concentration is crucial for the hormone exocytosis. The existing models of this phenomenon successfully explain the calcium transients along the dendrite of the GnRH neuron. However, the latest experimental results show a dramatic increase in the amplitude of the calcium concentration transients with the propagation along the dendrite. We conjecture that this amplitude increase is, in fact, the main reason for the synchronized release of the GnRH hormone and offer a new model for the calcium dynamics. The computational results based on the suggested model correlate with the experimental data.
  • John Parker University of New Hampshire
    "Existence of Cupolets in Chaotic Hindmarsh-Rose Neural Model"
  • This talk focuses on the Hindmarsh-Rose neuron model in a chaotic regime, and we consider a mechanism by which the system enters into a periodic state when driven by a signal from a chain of neurons. Previous work in nonlinear dynamics has shown that chaotic systems may be driven into periodic states (called cupolets) when driven by instantaneous impulses, using information theoretic and graph theoretic methods. In related work studying a coupled two cell FitzHugh-Nagumo neural model, it was possible for the combined system to enter into chaotic behavior, and through interaction and neural learning, mutually stabilized periodic states could be achieved. However, cupolet states were not possible because of the low dimensionality of the individual neurons. Here, we show that the Hindmarsh-Rose model, in a chaotic regime, may exhibit stabilized cupolets when impulses are applied on two Poincare surfaces. We report on several interesting properties of the cupolets. We then show how certain interactions between cupolets lead to chaotic stabilization in neural systems, with examples including a bidirectional neural system, a chain of neurons, and a feedback network. We conclude with a discussion of the implications and future directions of this research.
  • Christina Pospisil USA
    "Mathematical Models for Living Forms in Medical Physics Submodel 2: Information-Coding and Information-Processing through Nerves"
  • This talk continues the presentation Mathematical Models for Living Forms in Medical Physics Submodel 1: The information processing from teeth to Nerves from the Biophysics Annual Meeting 2020 Conference and American Physical Society Conferences. In the Submodel 1 the information processing from teeth to the nerves is modeled. The information is passed via p-waves through the tooth layers enamel and dentin. Odontoblasts located in the liquid in the tubules of the tooth dentin layer perform finally the transformation into electrical information (an electrical signal) that passes along nerves. The Submodel 2 of the project is dedicated to the information coding of the information from an entity hitting/touching a tooth and to the information processing of the coded unit through the nerves. Emphasized are the information representation as an electrical code and the coded information flow in the living system.

NEUR Subgroup Contributed Talks

  • Dr Paul A Roberts University of Sussex
    "What the Zebrafish's Eye Tells the Zebrafish's Brain"
  • While basic retinal architecture is conserved across vertebrates, each species' retina is unique, having evolved to detect and interpret the visual scenes particular to its environment. It is therefore important to build towards a broad understanding of the types of computations performed within the eyes of different species. Here, adult zebrafish are of particular interest. While considerable work has gone into studying the structure and function of the larval visual system, we know comparatively little about visual function in adults which differ vastly in size, swimming speed and visual-ecological niche. Anatomically, the mere 4,000 retinal ganglion cells (RGCs) of the larval eye increase to around 150,000 in the adult, all crammed into an eye that remains substantially smaller than that of the mouse with its 50,000 RGCs. What do all these “extra” RGCs encode, and how uniformly are any computations performed across different parts of the eye?In this work we take a truly interdisciplinary approach, combining cutting edge experimental techniques with the latest theoretical methods. In this way, we aim to build towards a first overview of the major visual computations performed by the adult zebrafish eye.
  • Ana Georgina Flesia Universidad Nacional de Córdoba
    "boosting confidence in detecting time-dependent ultradian rhythms using wavelet analysis"
  • Recently, biologists have shown fractal and oscillatory characteristics in animal behaviortime series. Aspects so different can be explained by a model with added components thatinclude deterministic cycles (ultradian and circadian rhythms), polynomial tendencies, and anunderlying nonlinear process with stationary increments. Such components can be extractedfrom the data using wavelet analysis by selecting the transformation appropriately. In this talk, we will discuss a five-step method that describes the data without making any parametric assumptions about trends in the frequency or amplitude of the components signals and is resilient to noise.1. Visual inspection by Continuous wavelet transform based on real Gaussian motherwavelet in the Cartesian time scale plane2. Visual inspection by Continuous wavelet transform based on complex Morlet motherwavelet in the Polar time scale plane.3. Modal frequency detection by Synchrosqueezed wavelet transform, a linear timescale analysis followed by a synchrosqueezing technique.4. Modal frequency corroboration by Empirical wavelet transform, a wavelet analysis in theFourier domain followed by frequency segmentation to extract the modal components.5- Quantification of coherence and phase difference between different series.
  • Euimin Jeong KAIST
    "Different oscillatory mechanisms between LN and DN in drosophila clock"
  • In Drosophila, circadian rhythms are regulated by about 150 pacemaker neurons. In each pacemaker neuron, circadian gene expression is driven by a transcriptional-translational feedback loop (TTFL). Interestingly, with dCLK-Δ mutation, which has impaired binding with PER, the amplitude of PER rhythms is greatly reduced in small ventral lateral neurons (sLNvs), but not in dorsal neuron 1s (DN1s). We investigated this unexpected difference between LNvs and DN1s by developing a mathematical model describing the TTFL. Our model predicted the differences in the molecular stoichiometry and regulatory mechanism of clock proteins between sLNvs and DN1s, which were validated by the experiments. We will discuss the biological significance of those differences between LNvs and DN1s for circadian clock system to work.

Sub-group poster presentations

NEUR Posters

NEUR-1 (Session: PS02)
Leonid Rubchinsky Indiana University Purdue University Indianapolis and Indiana University School of Medicine
"Modeling intermittent synchronization of gamma-band neural oscillations"

Synchronization in neural system plays important role in many brain functions such as perception and memory. Abnormal synchronization can be observed in neurological disorders such as Parkinson's disease, schizophrenia, autism, and addiction. Neural synchronization is frequently intermittent even in a short time scale. That is, neural systems exhibit intervals of synchronization followed by intervals of desynchronization. Thus, neural circuits dynamics may show different distributions of duration of desynchronization even if the synchronization strength is similar. In general, some partially synchronized systems can exhibit a few but long desynchronized intervals while other systems can yield many but short desynchronized intervals. Experimental data thus far has shown that neural synchronization follows the latter trend in either healthy or diseased brains. In this study, we use a conductance-based PING network to study neural synchronization specifically in the low gamma band. This study explores the cellular and synaptic effects on the temporal patterning of the partially synchronized model gamma rhythms and considers potential functional implications of different temporal patterns.

NEUR-3 (Session: PS03)
Hammed Olawale Fatoyinbo Massey University, New Zealand
"Stability of Travelling Waves in Electrically Coupled Smooth Muscle Cells"

Travelling waves play a vital role in understanding electrical activities in a population of excitable cells, for example, the propagation of signals in neurons. We aim to study the spatiotemporal patterns arising from a reaction-diffusion model of smooth muscle cells. Modulating model parameters, different forms of patterns including propagating pulses and fronts are observed. I will discuss the existence and stability analysis of the travelling waves. The shooting method is considered to approximate the wave speeds of the travelling waves, it turns out that the results are very similar to the wave speeds of the pulse and front solutions estimated from direct simulations of the model. Additionally, the spectral stability of the travelling wave solutions is investigated.

NEUR-4 (Session: PS03)
Zakaria Shams Siam North South University
"Estimation of Motor Nerve Conduction Velocity Distribution: A Frequency Domain Approach"

Estimation of motor nerve conduction velocity distribution (NCVD) from the compound muscle action potential (CMAP) is a challenging problem for a long period, which would be a useful tool for evaluating the peripheral neuropathies by assessing the electrophysiological characteristics of the peripheral nerves. In the present study, we have analyzed the CMAP of ulnar nerves from the human subjects in the frequency domain. In this regard, we have expressed the collected CMAP as a circular convolution of the motor unit action potential (MUAP) and their associated delay sequence. The frequency domain analysis of the collected two CMAP's having different stimulating-recording distances helped us separate the delay sequence without even using any prior MUAP model. Finally, we have exploited the derived delay sequence to estimate the motor NCVD of ulnar nerve. Furthermore, we have estimated the derived MUAP using the frequency domain analysis. Our derived results conformed well to the previous NCVD studies and the histology results as well. The applied technique would be a helpful tool as it is non-invasive and offers a direct way to estimate the motor NCVD from the CMAP's.

NEUR-5 (Session: PS03)
Rubyat Tansnuva Hasan North South University
"Estimation of Motor Nerve Conduction Velocity Distribution: A Continuous Approach"

Estimation of motor nerve conduction velocity distribution (NCVD) from the compound muscle action potential (CMAP) is a challenging and long-studied problem in nerve conduction study. In the present study, we have explored a new approach to determine the motor NCVD from the corresponding CMAP in a non-invasive manner using a continuous approach. In our study, we have taken the diphasic sinusoidal function and also the Hermite polynomial function to simulate the motor unit action potential (MUAP). We have experimented the efficacy of different polynomial functions of different degrees and also the gaussian and double gaussian distributions etc. to model the motor NCVD. Then, using the forward approach of nerve conduction, we have synthetically created the CMAP function. The continuous function of motor NCVD in our modeling helps us exploit the gradient optimization technique to solve the inverse problem of nerve conduction, i.e., estimation of motor NCVD from CMAP minimizing the least-square error. Our estimated results conformed well to the synthetically created CMAP dataset. The proposed technique is non-invasive and offers a way to estimate the motor NCVD from the corresponding CMAP's in a continuous approach which would be a useful tool for detecting the peripheral neuropathies.

NEUR-6 (Session: PS03)
Zeinab Tajik Mansoury University of Tehran
"Dynamical Analysis of Hippocampal Circuitry under Opioid Addiction Suggests the Mechanism of the Relapse"

Drug Addiction affects the limbic system by forming a memory in the hippocampus. Recently, we studied the effect of opioid addiction using a mean-field tripartite model for two pairs of pre and post-synaptic neurons and an astrocyte in the hippocampus. The results indicated an increase in the synchrony of neurons during opioid addiction, which represents memory formation. We added a network modeled by a correlation coefficient that shows the amount of convergence of the network. The neurons' output frequencies have feedback on input frequencies through this network. A first-order ODE models the network feedback on the inputs. The bifurcation diagram of average output frequency versus cues frequency during the withdrawal state indicates bistability. The dynamical analysis indicates that the high-frequency equilibrium points representing opioid addiction can cause relapse at withdrawal state.

NEUR-7 (Session: PS03)
Seokjoo Chae Korea Advanced Institute of Science and Technology
"The data-based inference method reveals the network structure of the SCN"

The suprachiasmatic nucleus (SCN) is the central circadian pacemaker in mammals. Even though the SCN is composed of thousands of heterogeneous self-oscillating cells, the SCN can synchronize its component oscillators through the SCN neuronal network. To understand the SCN network structure, previous methods used the time series data to infer the network structure. However, because the SCN is synchronized, previous methods falsely inferred the network as if all the SCN cells were coupled with each other. To circumvent this, we develop a novel data-based method, which can successfully infer the SCN network from the time series data. In particular, our method accurately infers the SCN network with single-cell resolution bioluminescence data from 2,000 synchronized mice SCN cells. Furthermore, our method can infer the directionality of the coupling between SCN cells.