Invited Paper Session Abstracts - Trends in Mathematical and Computational Biology

Modeling Growth & Reproduction in Bromeliads: A Tour of Modeling Methods

8:00 a.m. - 8:20 a.m.
Erin Bodine, Rhodes College

The plant family Bromeliaceae contains over 3000 species of rosette-structured flowering plants (commonly known as bromeliads), and includes the pineapple and Spanish moss. The long lifespan of many Bromeliaceae species (up to 100 years in some species) can make it difficult to in situ study the growth and reproduction of individual rosettes over their lifetime. However, this provides fertile ground for developing mathematical and computational models that can simulate and predict growth, reproduction, and population dynamics across many decades. These models have the additional benefit of allowing for simulations which consider the impact of changing environmental conditions, like climate change or the introduction of invasive species. In this talk, we will tour the variety of mathematical models being used to simulate bromeliad growth & reproduction, from simple single equation continuous functions and discrete difference equations to more intricate models of systems of differential equations and agents-based models. Each model provides a different lens from which to view and understand bromeliad growth and reproduction.

Gut Instincts: A Data Driven Approach to Mouse Colon Modeling

8:30 a.m. - 8:50 a.m.
Andrea Welsh, University of Pittsburgh

Colon motility, the spontaneous self-generated movement and motion of the colon muscle and its cells, is produced by activity in different types of cells such as myenteric neurons of the enteric nervous system (ENS), neurons of the autonomic nervous system (ANS) and interstitial cells of Cajal (ICC). Two colon motor patterns observed experimentally are proximal motor complexes (pMCs) often associated with the propulsion of fecal contents, and ripple contractions which are involved in mixing and absorption. It has been observed that the pMCs can occur without fecal matter present, but it is poorly understood how these spontaneous CMs occur. How ICC and neurons of the ENS and ANS interact to initiate and influence colon motility is still not completely understood. This makes it difficult to develop new therapies to restore function in pathological conditions. This talk will discuss the development of a data-driven model of the ICCs and neurons that also captures the spontaneous global dynamics like pMCs that are observed in the colon and give insight to how pMCs occur.

An Evolutionary Game Theory Model of Altruism via Arrhenotoky

9:00 a.m. - 9:20 a.m.
Olivia J. Chu, Dartmouth College
Zachary Nathan, Dartmouth College

Arrhenotoky is a unique biological mechanism in which unfertilized eggs give rise to haploid male offspring, while fertilized eggs give rise to diploid female offspring. In this work, we build a mathematical model for the arrhenotoky replicator dynamics of a beehive by adopting an evolutionary game theory framework. Using this model, we investigate the evolution of altruistic behavior in a beehive, looking particularly at hive success over a variety of parameters, controlling for altruism in workers and the queen. We find that the most reproductively successful hives have completely altruistic workers that donate all of their resources to the queen, as well as a somewhat altruistic queen that donates a small proportion of her resources to drone bees. Through these results, our model explains in part the evolutionary adoption of altruistic behavior by insects with arrhenotoky reproductive dynamics.

Algebraic Methods for Detecting Convex Combinatorial Neural Codes

9:30 a.m. - 9:50 a.m.
Nora Youngs, Colby College

A major problem in neuroscience is to understand how the brain uses neural activity to understand the external world. Combinatorial information in the firing patterns of neurons often reflects important features of the stimuli that generated these patterns. How can we efficiently extract such information from the neural code? This talk will introduce some of the algebraic methods currently in use for understanding the combinatorial structure of neural codes, and also discuss how this structure can be used to infer features of the underlying space.

Exploring the Roles of Interneuron Subtypes in Network Dynamics

10:00 a.m. - 10:20 a.m.
Madeline M. Edwards, University of Pittsburgh

Neural modulation in aroused states can provide insights into the specific roles of synaptic connections and unique populations that compose the network. Modulation of input is necessary for processing and interacting with our surrounding environment. Three interneuron inhibitory subtypes populations, Parvalbumin (PV), Somatostatin (SOM), and Vasoactive Intestinal Peptide (VIP) have been identified as key players of the modulation of input. Optogenetic stimulation of inhibitory subtypes demonstrates different responses across different subtype populations such as modulation power of dominating frequency or the appearance of gamma oscillations. To investigate each population's contributing role in modulation of synchrony, we begin by imposing static current to individual cell populations representing an aroused state observed experimentally. Initial probing of individual populations with imposed static input result in three distinct network states: (i) subcircuit activity, (ii) weak synchrony activity, and (iii) strong synchrony activity. The three network states are consistently generated for each population receiving static input. Transitions from state (i) to (ii) to (iii) are consistently generated by applying activating input to E or SOM, or by applying inactivating input to PV or VIP. Our model is a spatially organized spiking neuron model with a single excitatory population, three distinct inhibitory populations, and feedforward input. The connectivity of the network is randomly generated and distance dependent. Each population is modeled as an exponential integrate and fire neuron with parameters specific to each population type influenced by biologically observed characteristics. We will describe the specific functions of each population in the network across arousal states. We will be able to elucidate changes in dynamics due to changes in the connectivity for each population. This work provides a foundational understanding for the modulation of network activity with respect to four unique populations where the results can provide further inside into future experiments.