MFBM Subgroup Contributed Talks

Fatemeh Sadat Fatemi Nasrollahi

Pennsylvania State University

"Attractor identification method based on generalized positive feedback loops and their functional relationships"

Boolean modeling has been shown to successfully capture the attractors (emergent behaviors) in complex systems. Here we propose an efficient attractor finding method that relies on the identification of stable motifs [1] in Boolean models of plant-pollinator community assembly [2]. Stable motifs are the smallest positive cycles in the network that can sustain a specific state regardless of the state of the nodes outside the stable motif. We find that stable motifs can have three types of functional relationships with each other: Mutual exclusivity: Two stable motifs stabilizing the same node(s) but in different states; Conditionality: Stabilization of a stable motif only when a set of conditions are met via the stabilization of a different stable motif; Logical determination: Automatic stabilization of a stable motif as a result of stabilization of another stable motif. Based on these relationships, we developed an algorithm to identify all self-consistent mutually exclusive groups of stable motifs, and showed that stabilization of any of these groups leads to a distinct attractor. We applied this algorithm to 4000 networks of 40-100 species, compared its performance with three other attractor identification methods, and showed that it can speed and simplify the attractor identification task considerably.

Megan Coomer

Melbourne University

"Shaping the Epigenetic Landscape: Complexities and Consequences"

The metaphor of Waddington's epigenetic landscape has become an iconic representation of cellular differentiation. Single-cell transcriptomic data allows us to probe this landscape and gain insights into the regulatory dynamics underlying developmental processes. Reconstructing such landscapes from data has typically been based on strong assumptions about the dynamics of cells through gene expression state. Often, concepts from equilibrium thermodynamics have been used. Since biological processes are inherently noisy it is important to consider the presence of stochastic fluctuations in this context. We use a simple model to highlight complexities and limitations that arise when reconstructing the potential landscape in the presence of stochasticity. Specifically, we contrast ways in which additive and multiplicative noise shape the landscape on top of the deterministic dynamics. We show that the subtle interplay between the deterministic and stochastic components of the system's dynamics can have very unsubtle consequences: depending on the dynamics and noise, even qualitative features of the system dynamics — number and nature of stationary points — can change. Casual or ad hoc modelling of noise in the underlying regulatory networks can mask these effects. We end with a discussion of how this can be accounted for when considering single cell transcriptomic data.

Kumar Saurabh

National Taiwan University

"MATHEMATICAL MODELING OF ION CHANNEL FLOW WITHIN CONTINUUM FRAMEWORK"

Within the continuum framework, ion transport can be described using Poisson-Nernst-Planck (PNP) equations. Although accurate for dilute flows, PNP equations are not appropriate for modeling flows with high ion concentration or flows where non-ionic interactions are important. For ion channel flow, several extensions to continuum theory has been proposed. Effect of finite size of ion can be modeled by including either Lennard-Jones potential [1, 2, 3] in the energetic formulation or Bikerman model [4, 5]. For effect of ion solvation, Born energy model can be included in the system [3, 4]. Additionally, to account for spatial variation of dielectric behavior of the aqueous medium on can resort to nonlocal electrostatics [5]. Numerically, the system is modeled using lattice Boltzmann method (LBM) in conjunction with immersed boundary method (IBM) to address the boundary conditions. Further, to reduce computational cost, the code has been parallelized on multiple GPUs using CUDA platform. These mathematical models have been successfully implemented for ion flow through SARS-CoV-1 and SARS-CoV-2 E protein ion channel, TRPV channel etc. In this study, we intend to explore the role and effect of these mathematical models on ion transport through a potassium channel.

Nayana Wanasingha

Department of Mathematical Sciences, University of Cincinnati

"Molecular mechanisms regulating frequecy demultiplication of circadian rhythms in Neurospora Crassa"

Subharmonic entrainment or frequency demultiplication is a characteristic of circadian systems, which is the ability to entrain to cycles that are submultiples of external cycles. In this study, we used mathematical modeling and experiments to investigate potential mechanisms regulating frequency demultiplication under different temperature cycles in a model filamentous fugus, Neurospora crassa. Our results indicate that frequency demultiplication is a manifestation of the entrainment of circadian clock to external cycles and depends on the endogenous period and the strength and type of external cycles. Theoretical analysis reveals two necessary conditions to reproduce experimentally observed frequency demultiplication and frequency driven phenotypes: 1) temperature-modulated frq transcription and translation, and 2) a low level of cooperativity of transcriptional regulation of frq. In summary, we used mathematical modeling and experiments to uncover the architecture of circadian systems regulating frequency demultiplication, which broadens our fundamental understanding of entrainment of circadian rhythms.