Mathematical Biology Seminar - Spring 2025
Seminars are typically held on Wednesdays from 1:00 - 2:00 PM as hybrid talks unless otherwise noted. The in-person presentation will take place in CULM 505 with a Zoom option for virtual attendees.
For questions about the seminar schedule, please contact James MacLaurin.
February 12
Dirk Bucher, NJIT
Consistency vs. flexibility: Convergent co-modulation decreases inter-individual variability and increases intra-individual similarity of neural circuit activity
Neural circuits are always under the influence of multiple neuromodulators that tune synaptic interactions and neuronal excitability. Therefore, neuromodulation is thought to be at the core of the nervous system’s ability to produce different versions of activity to adapt to different behavioral needs. As such, different neuromodulators are often associated with different behavioral contexts and co-modulation with multiple signaling molecules is thought to vastly expand the repertoire of possible circuit states. However, different modulators can have overlapping cellular and subcellular targets, and thus convergence and occlusion may limit that repertoire.
Our experimental data from recordings of rhythmic motor activity in the crustacean stomatogastric nervous system shows that convergent co-modulation with different neuropeptides results in consistent circuit activation that, with increasing numbers of modulators, becomes less dependent on the specific identity of the modulators involved. In addition, we show that convergent co-modulation reduces variability across individuals, i.e., co-modulation increases consistency of circuit activation at the population level. Both results do not contradict the notion of neuromodulation as key to neural flexibility but rather suggest a push-pull mechanism between converging and diverging cellular effects that promotes both flexibility and stability.
I will present some of our experimental results and discuss theoretical and mathematical considerations of possible underlying mechanisms.
February 19
Nir Gavish, Technion Israel Institute of Technology
Challenging Conventional Epidemiological Theories: Coexistence and Oscillations in Multi-Strain Epidemic
During the COVID-19 pandemic, variants constantly emerged and interacted with existing ones. Our data-driven research showed that a variant with a basic reproduction number as high as 10 can defy conventional theory. Motivated by this, the talk will present two works on the dynamics of epidemic systems with two strains that provide partial cross-immunity to each other.
In the first part, we challenge the validity of the exclusion principle at a limit in which one strain has a vast competitive advantage over the other strains. We show that when one strain is significantly more transmissible than the other, an epidemic system with partial cross-immunity can reach a stable endemic equilibrium in which both strains coexist with comparable prevalence. Thus, the competitive exclusion principle does not always apply.
The second part explores conditions under which a two-strain epidemic model with partial cross-immunity can lead to self-sustained oscillations. Contrary to previous findings, our results indicate that oscillations can occur even with weak cross-immunity and weak asymmetry. Using asymptotic methods, we reveal that the steady state of coexistence becomes unstable near specific curves in the parameter space, leading to oscillatory solutions for any basic reproduction number greater than one. Numerical simulations support our theoretical findings, highlighting an unexpected oscillatory region.
February 26
Toshiyuki Ogawa, Meiji University
Pattern dynamics appearing on compact metric graph
The study of reaction-diffusion equations on metric graphs has been drawing attention recently. Here, we focus on pattern dynamics on compact metric graphs. We consider systems of reaction-diffusion equations on compact metric graphs with natural boundary conditions, namely, Neumann‒Kirchhoff conditions. Suppose additionally the system has Turing or Wave instability. Then, we may see pattern onsets depending on the lengths of the edges. By using the normal form analysis and symmetry arguments we study the local bifurcation structures around the bifurcation points.
This talk is based on the ongoing joint work between Shunsuke Kobayashi(Miyazaki University) and Takashi Sakamoto(Meiji University).
March 12
Denis Patterson, Durham University
Title/Abstract Forthcoming
March 26
Joshua Meisel, The City University of New York (CUNY)
Title/Abstract Forthcoming
April 16
Ashok Litwin-Kumar, Columbia University
Connectivity structure and dynamics of nonlinear recurrent neural networks
I will discuss recent progress we have made on understanding the chaotic dynamics of random recurrent neural networks. I will start by describing a cavity method approach we developed that allowed us to calculate the linear embedding dimension of chaotic attractor of neural activity in the classic random network model of Sompolinsky, Crisanti, and Sommers (1988). This revealed surprising features of how activity in random networks is coordinated across populations of neurons. I will then discuss generalizations of this approach to networks with additional structure, such as networks with "effective low-rank" connectivity. Finally, I will discuss how we are trying to use this theory to understand how neural activity changes across behavioral states.
April 21
Sungsik Kong, ICERM/Brown University
Title/Abstract Forthcoming
April 30
Jana Gevertz, The College of New Jersey
Title/Abstract Forthcoming
Last Updated: February 10, 2025