MBI Videos
2016 Undergraduate Capstone Conference
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Dylana WilhelmDemonstrating one of the most incredible examples of collective behavior among social insects, the self-assembling structures formed by army ants of the species Eciton hamatum provide a clear benefit to the entire colony. In order to navigate the rough and complex terrain of the tropical forests of Central and South America, these nomadic ants use their bodies to create temporary bridges for their nest mates to travel over. These living bridges are uniquely complex in their ability to adapt their size according to traffic and assemble across a wide variety of environments. While these bridges provide a short cut in the foraging trail, the dynamics of their formation suggest the existence of a cost-benefit trade-off, in which the benefit of increased efficiency must be balanced by the cost of removing workers from the foraging pool to form the structure. To examine this trade-off, we extend the work of an existing publication to construct mathematical models of self-assembly which represent different configurations of the local environment. These models will be used to generate predictions about the bridge location that maximizes the foraging rate of the colony.
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Daniel AbramsExtravagant and costly ornaments (e.g., deer antlers or peacock feathers) are found throughout the animal kingdom. Charles Darwin was the first to suggest that female courtship preferences drive ornament development through sexual selection. In this talk I will describe a minimal mathematical model for the evolution of animal ornaments, and will show that even a greatly simplified model makes nontrivial predictions for the types of ornaments we expect to find in nature.
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Ben ColemanHelicobacter pylori is a Gram negative bacterial pathogen that infects the stomachs of half of all people. While most H. pylori infections result in asymptomatic gastritis, about 10% result in gastric and duodenal ulcers and 1-2% result in non-cardia stomach cancer. H. pylori is the only bacterium that is classified by the World Health Organization as a carcinogen.
H. pylori’s helical shape is important for stomach colonization; in a mouse model of infection, straight-rod mutants of H. pylori are ten times less efficient at colonization than their wild-type helical counterparts. Several proteins have been found that are essential for maintaining helical cell shape. Many of these proteins are enzymes that directly modify cell wall structure. The non-enzymatic cell shape determining proteins may help localize these enzymes. One of these is CcmA, a putative cytoskeletal protein, which I hypothesize to localize preferentially to areas with particular cell surface curvatures to help pattern helical shape in wild-type cells. To study this, I use an advanced 3D cell modelling algorithm to measure the precise shape of the cells and the localization of CcmA. CcmA shows enrichment along the major helical axis, which corresponds to Gaussian curvatures between 0 and 10 ?m-2. In addition to studying CcmA localization in wild-type cells, I have studied it in ?csd2 and ?csd6 mutants, which have a curved- and straight-rod shape respectively. In the mutant cells, I found the surprising result that CcmA is more enriched at regions with negative Gaussian curvature. This implies that Csd2/6 functionality are essential to CcmA’s proper localization. In addition to showing the mislocalization of CcmA, I helped improve the throughput of this cell shape modeling method and data analytics package. The localization of these cell shape proteins furthers our understanding of the basic science of cell shape determination and may be useful in the development of novel therapeutics that target cell shape to fight against this insidious pathogen.
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Hsien-Te KaoSystems of individual oscillators that are coupled via regularly emitted pulses are ubiquitous in biology. Examples include fireflies that synchronize their blinking light pattern and neurons that communicate via action potentials. We aim to understand the emergence of synchronous behavior in these systems mathematically using cellular automata. We generalize the fireflies cellular automaton developed by Lyu to study the impact of coupling range on inhibitory pulse-coupled oscillators in one-dimension. From numerical simulation, we discover four ordered phase-regimes: phase-fixating, clustering, over-coupled, and chaotic. We adapt mathematical techniques developed by Fisch for the cyclic cellular automaton to prove that synchronization does not occur when the coupling range is small. This complements a recent result by Lyu and Sivakoff, who show that local synchronization (clustering) occurs at intermediate coupling range.
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Myson BurchPeripheral arterial disease (PAD) is a major health problem in which arteries within the systemic vasculature become partially or fully blocked, often due to atherosclerosis, leading to a significant reduction in blood flow to tissue. Patients often require surgical bypass grafts to restore flow to their tissue; in extreme cases, amputation is required. The absence of data regarding the relative importance of adaptations in collateral arteries, arterioles, and capillaries to compensation after arterial occlusion is a major roadblock for the development of successful and noninvasive therapies for PAD patients. The objective of this project is to integrate experimental and theoretical techniques to assess the significance of changes in vascular segments at rest and during exercise subsequent to a major arterial occlusion on an acute and chronic time frame. Model-predicted values of vascular resistance are compared with experimental studies to validate the model. The model is extended to predict changes in vessel diameter according to mechanistic responses to pressure, shear stress, and metabolism following an occlusion. Theoretical results suggest that therapies that increase collateral diameter in combination with distal microcirculation adaptations provide the maximum benefit to patients with PAD. Ultimately this project offers a first step in optimizing experimental design and diagnostic criteria to focus on the most relevant vascular segments in studies of vascular compensation in health and disease.
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Ksenia SokolovaAllometry is the study of how one trait is related to another. Historically, allometry was concerned with how characteristics of an organism change with size. Today, there are three distinct types of allometries studied: ontogenetic allometry - scaling of traits over the developmental time in one individual, static allometry - scaling of traits in different individuals at the same developmental time and evolutionary allometry - scaling of traits measured in different species. Since variation in size at any fixed moment in time is a consequence of growth and ontogenetic allometry, it is of biological interest to investigate the relationship between these three factors. By expressing the growth of two traits through a Gompertz function, it is possible to derive a complex formula for ontogenetic allometry that agrees with the data. Study of individual growth curves shows that there is a relationship between final size, displacement of the function along the x-axis and the growth rate within one trait. There is also a relationship between the final sizes for two different traits, which represents static allometry for fully developed organisms.
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Ralf Bundschuh -
Allen Alvarez-Loya, Andres Rodriguez -
Joseph Ballardo, Andre Hernandez-EspietSince humans spend large amounts of time sleeping, it is natural and important for us to study and understand the mechanisms involved. Specifically, the mechanisms underlying sleep-wake transitions are not well understood. It has been reported that the wake bouts for humans follow a power law distribution, while sleep bouts follow an exponential distribution. In this project, we aim to gain a better understanding of the power laws produced by a stochastic competitive graph model, which could be relevant for the study of the human wake bouts. We are studying how the power law scaling exponent varies with the structure of the random graph and with the excitatory and inhibitory degrees of the nodes. Additionally, we consider different methods for calculating bouts, based on how the transition interval into (or out of) wake is treated.
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Erin AngeliniAdipogenesis is the process by which precursor cells develop into mature adipocytes, or fat-storing cells. From a 2012 study by Park et al., we expanded a deterministic model of the transcriptional network of adipogenesis to include a module for adiponectin (AdipoQ) production, an insulin-sensitizing hormone secreted by adipocytes. We analyzed two possible implementations for the adiponectin module to determine if variability within the system parameters alone is sufficient to explain the adipocyte heterogeneity observed in a study by Loo et al. For each model, we first characterized overall susceptibility to noise by calculating the relative local sensitivity of AdipoQ and fat to various parameters. We then simulated the experiment done by Loo et al. with 30% added noise to determine if our system could replicate their data. Our results show that only the model where fat increases the degradation of adiponectin fits the trends observed in the Loo study, indicating that it is more likely than the model where fat decreases the synthesis of adiponectin.
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Jessica Butts, Mitchell MeyerA collection of ancient enzymes was studied using Bayesian Phylogenetics methodology to estimate the distribution of amino acids at the root of the tree of life under the assumption that the most conserved regions should best reflect the prebiotic availability of amino acids. Different measures of conservation were compared with the putative order of appearance of the amino acids on earth, and a generally positive association was found. This supports other independent lines of research on this topic indicating that more conserved sites contain older amino acids, such as glycine and alanine.
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Amanda HamptonThe focus of the project is to track the disappearance in the developing brain of a specific type of neural transmission through electrical synapses called gap junctions. These gap junctions are pathways between neurons made of proteins that allow electrical communication. Experimentalists have found evidence for the presence, and subsequent disappearance of these gap junctions during the first few postnatal weeks, ranging from 100% to 50% for inhibitory interneurons. Studies have also been done to determine the role of gap junction pruning in determining adult synaptic transmission.
This project will focus on modeling the effect of gap junction pruning on the network behavior in the developing cortex. Understanding how neurons interact in the cortex of a developing brain is important because the cortex is responsible for learning and cognitive thinking.
We use Hodgkin-Huxley differential equations to model the membrane potential of a neuron. The gap junctions are modeled by an additional term in the Hodgkin-Huxley equations that describes the exchange of voltage between electrically connected neurons. We form a realistic network by including 25% inhibitory and 75% excitatory neurons, as well as including synaptic transmission. Using data regarding neuronal firing rates and gap junction presence collected through the analysis of prior experiments, we form a network that has decreasing gap junction connectivity as the brain develops. We use this model to gain further insight on how decreasing gap junction connectivity affects network behavior.
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Genevera AllenInferring networks from big biomedical data is important for understanding complex biological systems and visually exploring big data. In this talk, we highlight new inference methods for graphical models inspired by neuroimaging data and integrative genomics. First, functional brain networks are important for understanding brain organization and dysfunction in neurological diseases. In population studies, scientists seek to estimate and then test for differences in brain networks related to disease or other clinical features. We present a new framework for testing populations of graphical models and apply these methods to several functional MRI studies. Second, new genomic technologies allow scientists to profile nearly every molecular aspect of a sample; but, this data is big and of mixed types (e.g. continuous, binary, counts, etc.). We introduce new integrative graphical models that give the first general multivariate distribution for mixed data and apply these to build integrative cancer genomic networks.
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Olga Dorabiala -
Madison Sanden -
Harrison Weissman -
Matthew MossCellular processes in neural tissues generate movement of electrical charges. Multiple techniques for measuring this electrical activity allow for characterization of cellular processes at different scales of the brain tissue. In particular, electrodes inserted deep into the brain record electric fields referred to as the local field potential (LFP? Buzsáki, et al., 2012). It is believed that LFP characterize inputs to the network of neurons surrounding the electrode. However, the contributions of other sources to LFP are actively discussed. In cortical networks, LFPs are strongly correlated with another measure of the electrical activity spike recordings from individual neurons. Thus, the neurons contribute to LFP, and it is possible to figure out their individual contributions through the use of a linear filtering mechanism (Rasch, et al., 2009). First, we successfully repeated this analysis in the rat Prefrontal Cortex (PFC). However, this has proven not to be possible in other areas, such as the midbrain. In particular, neurons in the Ventral Tegmental Area (VTA) are not as well spatially aligned as cortical neurons and fire mostly asynchronously, which leads us to believe that their electric fields may cancel instead of summing in the LFP readings. Because of this, the local LFP signal may be dominated by volume conducted signals from other brain regions. A combination of current source density (CSD) analysis and Independent Component Analysis (ICA) has been used in previous work by ?eski et al. (2009) to solve this problem. We used this approach on the VTA single unit and LFP signals This method allowed us to find the specific sources of LFP signals in the VTA and the contribution of particular neurons to the cumulative LFP.
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Matthew MorenoAnt foraging behavior is a collective decision making process in which, through individual interactions between ants and pheromone deposition, a colony of ants selects and exploits a path to follow between their nest and a food source. Research into the collective decision making strategies of ants, in addition to characterizing the biological mechanisms and emergent properties of the foraging process, has the potential to be leveraged into applications such as swarm robotics and commercial logistics management. Although ant foraging behavior has been extensively studied on flat terrains, ant foraging over uneven terrains is not well studied. This research presents an individual-based set of differential equations to model ant foraging behavior over uneven terrain in an enclosed arena. This model is employed to investigate the characteristics of foraging paths that ants tend towards when foraging over simple inclines of varying magnitudes. Numerical solutions of the model predict that, over most inclines, ants tend to favor the direct path between nest and food.
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Amanda CameronMuscular dystrophy (MD) disease dynamics are characterized by structural and functional perturbations that perpetuate disease progression. Developing mathematical models to understand and treat MD involves the integration of previously established immunological and mechanical representations of these factors that bolster disease progression. In this article, we review these models as well as examine key molecular and cellular perspectives to better understand MD's pathogenesis and subsequent progression. Molecular factors that contribute to MD include mitochondrial and genetic components; both drive cellular metabolism, communication and signaling. Furthermore, these molecular factors leave cells vulnerable to mechanical stress which can activate an immunological cascade that can weaken cells and surrounding tissues. This review article provides an essential, brief, biological background for mechanisms modeled. Given the application of developed immunological and molecular models to a wider variety of neurodegenerative diseases linked by related mitochondrial and genetic deficits, understanding and modeling MD is highly applicable.
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Matthew MorenoAnt foraging behavior is a collective decision making process in which, through individual interactions between ants and pheromone deposition, a colony of ants selects and exploits a path to follow between their nest and a food source. Research into the collective decision making strategies of ants, in addition to characterizing the biological mechanisms and emergent properties of the foraging process, has the potential to be leveraged into applications such as swarm robotics and commercial logistics management. Although ant foraging behavior has been extensively studied on flat terrains, ant foraging over uneven terrains is not well studied. This research presents an individual-based set of differential equations to model ant foraging behavior over uneven terrain in an enclosed arena. This model is employed to investigate the characteristics of foraging paths that ants tend towards when foraging over simple inclines of varying magnitudes. Numerical solutions of the model predict that, over most inclines, ants tend to favor the direct path between nest and food.
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Daniel GriffinAstrocytes are the most common glial cells in the brain and are crucial in maintaining key functions of the brain. It has been shown experimentally that astrocytes communicate via calcium signals, and they regulate extracellular sodium and potassium concentrations. Mathematical models have been established to investigate either these calcium dynamics or these sodium-potassium dynamics of astrocytes, but no model has been published that investigates the interaction between these two systems. Here, we take the first steps toward such a model by allowing for the communication between calcium and sodium via the sodium-calcium exchanger. With this full model, we investigate the potential impact of sodium-calcium exchanger over-expression, and also describe one mechanism by which astrocyte calcium signaling may impact neuronal activity.