Effects of stochasticity and heterogeneity on networks' synchronization properties

Tuesday, June 15 at 09:30am (PDT)
Tuesday, June 15 at 05:30pm (BST)
Wednesday, June 16 01:30am (KST)

SMB2021 SMB2021 Follow Monday (Tuesday) during the "MS07" time block.
Note: this minisymposia has multiple sessions. The second session is MS06-NEUR (click here).

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Zahra Aminzare (University of Iowa, United States), Vaibhav Srivastava (Michigan State University, United States)


Coupled dynamical systems provide an essential theoretical framework for modeling various natural or physical networks and analyzing their collective behavior, such as synchronization. These simple models often miss environmental fluctuations as well as internal and external disturbances which are ubiquitous in such networks. Therefore, a stochastic and heterogeneous dynamics approach provides a significant compromise to keep modeling complexity tractable and still capture important phenomena. The mini-symposium brings together mathematicians and experimentalists working on synchronization problems in neuronal networks, bio-molecular networks, and social networks.

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.

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Virtual conference of the Society for Mathematical Biology, 2021.