MBI Videos
2014 Undergraduate Capstone Conference
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Jennifer HouserNeural thalamocortical circuits relay external sensations from to the thalamus to the cortex where sensory information is then processed. Feedforward inhibition involving a subtype of fast-spiking interneurons, which are marked by the calcium-binding protein parvalbumin, reduce the chance that a postsynaptic neuron will fire an action potential. Consequences on the circuit due to the absence of parvalbumin expression in fast-spiking neurons in schizophrenia patients are caused by fast-spiking latency. In this presentation, we present a conventional neuron model. We will show how to develop a mathematical model to incorporate a latency effect as well as show numerical simulations.
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Benjamin LiskaCalcium is a mineral essential to many systems of life. As such, the body regulates levels of calcium in the blood plasma very tightly through a process known as calcium homeostasis. The controlling mechanisms in this process include parathyroid hormone, calcitonin, vitamin D, and the mineral phosphate. Much research has been done on the biology of this system but it is not understood completely. Recently, work has been done to mathematically model this system, however, these models are very complex. In this talk, we will provide a simplified mathematical model of calcium homeostasis that still captures biologically relevant mechanisms. Using the modeling software COPASI (Hoops 2006), we will show numerical simulations and comparisons to experimental data. An analysis of the stability of our nonlinear model provides insights into our dynamical system. We will conclude by showing ways we can predict how various diseases can disturb calcium homeostasis and provide suggestions for further investigation that could lead to effective treatments.
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Madeline Edwards, Akira HoriguchiTranscription factors (TFs) often bind to specific DNA sequences to promote or block gene expression. The interactions between TFs and target DNA sequences may be regulated by DNA methylation. It has been well recognized that DNA methylation plays an important role in neural differentiation, which is determined by a cascade of TFs. However, the epigenetic regulated TF programs critical to brain development remain largely unexplored.
To fill in such a knowledge gap, we first analyzed mammalian brain methylomes to identify genomic loci differentially methylated during development. We compiled a set of experimentally validated TF binding sites from TRANSFAC 7.0, JASPAR 2014, and UniPROBE databases, and applied HOMER to identify TFs of which binding sites enriched in genomic regions hypomethylated in neurons and glial cells, respectively. Using MEME Suite and ClusterZ, we then determined pairs of TFs with binding sites frequently overlapped. With the Cytoscape program, we created a network of possible TF interactions, which can either be complex formation or regulatory. This predicted network provides novel insight to the epigenetic regulation controlling brain development.
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William Duncan, China MauckStereocilia are highly regulated structures vital for hearing and balance in mammals. However, it is not known how their lengths are maintained. Models have been made to study possible mechanisms for actin filament maintenance in cellular protrusions, but they rely on actin treadmilling, which recent work suggests does not occur in stereocilia. We modify an existing model of motor and cargo distributions in cellular protrusions to account for the absence of treadmilling. We consider cargo which is incorporated at the tip of stereocilia as would be typical of actin cross-linking proteins. The qualitative properties of the distributions do not change by removing retrograde flow from the model, but there is less cargo along the majority of the stereocilium with retrograde flow. With degradation of the motors and cargo, the proteins are concentrated at the tip of the stereocilium as is seen in experimental data.
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Rebecca Law, Brady MeltonCriminal penalties for driving while intoxicated (DWI) in North Carolina are based on hard thresholds; for example, having a blood alcohol content (BAC) at or above 0.08 is considered legally impaired. However, BAC measurements are typically taken using breathalyzers, which are subject to measurement error. Additionally, breathalyzer readings in North Carolina are truncated, i.e. a person blowing a 0.079 would have a breathalyzer reading of 0.07. The purpose of our research is to explore this error and to construct recommendations for both law enforcement and courtroom decisions. Using data collected from breathalyzer tickets in Orange County, we have estimated the measurement error using a truncated random effects model and have calculated a prediction interval to determine any individual’s true BAC given the individual’s breathalyzer results. We also ran a parallelized simulation study to determine the effects of the distribution parameters on our model, and plan on exploring factors such as temperature, humidity, and machine calibration. We have created two lookup tables to determine an individuals true BAC, one based on prediction intervals, and the other on the probability that an individual’s true BAC is above 0.08. Using these lookup tables, the courts can determine the strength of evidence in DWI cases.
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Omar KhanPurinergic P2X receptors are a family of seven (labeled P2X1-7R) ATP-gated non-selective cation channels, ubiquitously expressed in the body. Abnormalities in them could lead to tissue inflammation and chronic pain. All members of this family are trimeric channels with three agonist binding sites that are activated and opened when occupied by ATP. The kinetics of activation (rising phase of current), desensitization (decay of current in the presence of ATP) and deactivation (decay of current after removal of ATP) are receptor-specific. The P2X4 subunit is the most widely distributed in the brain. Homomeric P2X4Rs desensitize with moderate rates, and desensitization is coupled to extensive internalization and recycling of receptors to the membrane. P2X4R is allosterically modulated by ivermectin (IVM), which increases both the ATP potency and the peak amplitude of the current (i.e., induces receptor sensitization), reduces the desensitization rate, greatly prolongs deactivation of current after ATP removal, and alters the recycling process. Many aspects of P2X4R gating have not yet been clarified and there is no comprehensive mathematical model describing its kinetics. No rationale has been provided for how IVM rescues receptors from desensitization, why it slows receptor deactivation, or why it affects receptor recycling. Using electro-physiological (current-recording) data from Stojilkovic Lab (NIH), we will be developing Markov state models and conducting systematic model comparisons and parameter optimization methods by utilizing Markov Chain Monte Carlo techniques based on Bayesian Theory, to determine the most likely model and parameter set(s) that can capture the kinetics of these receptors. The goal is to produce a model that can successfully explain the underlying mechanism of desensitization, recycling, and IVM-dependent sensitization in P2X4Rs. The parameter set(s) will be retrieved from probability distributions generated from these iterative methods.
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Gregory McCarthyI am working with Jacqueline M. Dresch (Mathematics, Amherst College) and Robert A. Drewell (Biology, Amherst and Mount Holyoke Colleges) on parameter sensitivity analysis of a dynamic model of eukaryotic gene regulation in the Drosophila embryo. I am primarily concerned with understanding the relative importance of various components of the system, such as transcription and translation, as well as the biological and mathematical interpretations of. I performed sensitivity analysis on a model with initial inputs corresponding to both maternal genes and housekeeping genes in Drosophila melanogaster at various points across the anterior-posterior axis of the embryo as well as at various time points during early development. I compared my individual parameter sensitivities to values found experimentally in the study conducted by Li et. al. (PeerJ, 2014) and considered how these sensitivities change spatially and temporally during development. I found that the calculated parameter sensitivities on a simplified version of the reaction-diffusion model developed in Dresch et. al. (SIAM J. Appl. Math, 2013) are in agreement with those generated by the biological experiments of Li et al. As such, this appears to be a valid model to use for dynamic gene regulation. Additionally, the sensitivities for all genes considered exhibit competitive dynamic behavior across the development window. This suggests the importance of considering a dynamic model of gene regulation.
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Hannah BiegelAbstract not submitted.
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Rebecca DoergeThis is an exciting and influential time for the field of Statistics in science. Technological advances in genetic, genomic, and the other 'omic sciences are providing large amounts of complex data that are presenting a number of challenges for the biological community. Many of these challenges are deeply rooted statistical issues that involve experimental design. Although there are many different computational tools for processing these data, there are a limited number of statistical methods for analyzing them, and even fewer that acknowledge the unique nature of these data. After a discussion about experimental design for next-generation sequencing experiments, a simple approach based on a two-stage Poisson model for modeling RNA sequencing data will be presented for the purpose of testing biologically important changes in gene expression. If time allows, a new approach that addresses sequence tag abundance, and the need to adjust for it in next-generation sequencing data, will be presented. The advantages of these approaches are demonstrated through simulations and real data applications.
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Jane CoonsCophylogenetics is the study of the evolutionary relationships between taxonomical units that are believed to be evolving concomitantly. We examine the combinatorial properties of the cophylogenetic distance metric, k-interval cospeciation, which was introduced by Huggins, Owen and Yoshida in their 2012 paper, "First steps toward the geometry of cophylogeny." We determined that k-interval cospeciation is a unique discrete distance metric which can quantify a degree of global congruence between two phylogenetic trees while allowing for local incongruence. We counted the size of the neighborhood of trees which satisfy the largest possible k-interval cospeciation with a given tree. Due to the way this neighborhood of trees grows as a proportion of all possible trees, we believe that k-interval cospeciation may prove useful for analyzing data obtained through simulations.
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Spencer WhitemanOpen-angle glaucoma (OAG) is characterized by progressive retinal ganglion cell death and vision loss. Although elevated intraocular pressure is the primary risk factor for OAG, several studies have shown that impaired perfusion and oxygen delivery to retinal ganglion cells may also contribute to OAG pathophysiology. In this study, a realistic vascular network model of the mouse retina is developed based on previously published confocal microscopy images and modeling data. A mathematical model based on Green’s functions is applied to this network to predict tissue oxygenation in a healthy retina. The model will be extended to predict the conditions that lead to observed tissue oxygenation changes in glaucoma patients. Preliminary model predictions suggest that theoretical models in combination with oximetry measures are needed to guide the differentiation and identification of the most relevant risk factors for OAG.
Mentor: Julia Arciero, Department of Mathematical Sciences, Purdue School of Science, IUPUI
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Benjamin Hamm, Jamal Moss, Paulina SpencerAbstract not submitted.
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Casey ShiringReal-life data is necessary for the application and validation of mathematical models. However, if data are missing from a dataset, the validity and usefulness of said dataset is diminished. One way to remedy this problem is by using multiple imputation - an advanced statistical method to predict the value of missing data points. As an application, we use a dataset containing clinical and other data for 109 patients through the course of a study on Intermittent Androgen Suppression therapy for prostate cancer. A model of prostate cancer treatment by Everett et al. is then fitted to the data. We examine the effects of multiple imputation on the parameter fitting and on prediction of off-treatment time span of the Everett et al. model by comparing the quality of fitting and the model’s performance in those predictions using the imputed data and using the unimputed data. Finally, we explore differences in model parameters between castration-sensitive and castration-resistant prostate cancer patients. We conclude that multiple imputation for time-series datasets improves the predictive ability of the Everett et al. model, although it does so somewhat inconsistently. Furthermore, in observing differences in parameterization between castration-sensitive and castration-resistant patients, we conclude that the androgen-independent castration-resistant cell death rate differs in a statistically significant manner between these patient types.
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Emery BrownGeneral anesthesia is a drug-induced, reversible condition comprised of five behavioral states: unconsciousness, amnesia (loss of memory), analgesia (loss of pain sensation), akinesia (immobility), and hemodynamic stability with control of the stress response. The mechanisms by which anesthetic drugs induce the state of general anesthesia are considered one of the biggest mysteries of modern medicine. We study three problems to decipher this mystery. First, we present findings from our human studies of general anesthesia using combined fMRI/EEG recordings, high-density EEG recordings and intracranial recordings which have allowed us to give a detailed characterization of the neurophysiology of loss and recovery of consciousness due to propofol. Second, we present a neuro-metabolic model of burst suppression, the profound state of brain inactivation seen in deep states of general anesthesia. We show that our characterization of burst suppression can be used to design a closed-loop anesthesia delivery system for control of a medically-induced coma. Finally, we demonstrate that the state of general anesthesia can be rapidly reversed by activating specific brain circuits. Our results show that it is now possible to have a detailed neurophysiological understanding of the brain under general anesthesia, and that this understanding, can be used to control anesthetic states. Hence, general anesthesia is not a mystery.
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Dominick DiMercurio, Pranjal SinghCell migration is a critical and recurrent phenomenon in animal biology; migration is a key feature in wound healing, immune function, and embryo development. In particular, egg chamber developmental stages in Drosophila melanogaster, a model organism for human genetics, provide a suitable opportunity to investigate migratory regulation. An important process in oogenesis is when the epithelial border cells on the anterior end of the egg chamber move toward the oocyte. A key molecular pathway in this process involves the uptake of the ligand Unpaired by follicle cells, which causes the signaling molecule Signal Transducer and Activator of Transcription (STAT) to activate transcription of downstream targets that promote migration. In genetic analyses of D. melanogaster ovaries that had reduced STAT expression via RNA interference (RNAi), we reproduced phenotypes of partially delayed or completely inhibited migratory behaviors compared to sibling controls. To investigate this phenomenon mathematically, we used a previously derived system of differential equations that modeled the signaling pathway, reduced the system with simplifying assumptions, and introduced a parameter to account for the effect of RNAi on mRNA that encoded STAT. Through computational methods, we simulated time courses of select proteins and created a bifurcation diagram of their steady states. Moving forward, research into this process could examine the biological bases for temporal variation in RNAi-based effects on protein expression as predicted in our mathematical models. This research will help biologists obtain a better understanding of mechanisms for cell migration, which may itself lead to insights on migratory pathways for the metastasis of cancer and the occurrence of other developmental defects.
This work was funded in part through an Undergraduate Biology Mathematics (UBM) Research Award from the National Science Foundation under Grant No. DBI 1031420, PIs Drs. Leips and Neerchal.
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Bohyun KimWe created a mathematical model to describe core (body) temperature responses to exercise at different ambient temperatures based on an experiment data. In the experiment, rats were forced to run on a treadmill at different speeds. Their core temperature time-series were recorded during 15 min runs with speeds 0, 6, 12, and 18 m/min at 0 incline in cool (24°C, T1) and hot (32°C, T2) environment. At T1 there was a temperature drop during first 5 min, while at T2 temperature did not change during that period. After 5 min, temperature started rising linearly at both T1 and T2 until the treadmill was stopped. The slope of this linear increase remained constant for all four speeds at T1, whereas at T2 it progressively steepened with the speed increase. To explain these findings, we have designed a model which consisted of two body components exchanging heat: the core and muscles. The core dissipated heat proportionally to difference between the core and ambient temperatures. This model was formally described by a system of two differential equations. All parameters of the system were subject to fit the average temperature response curves obtained from the experiment. Hypothermia during the first 5 min at T1 was interpreted as a result of decreased thermogenesis in the core to compensate for the heat generated by locomotion on the treadmill. This drop was not observed at T2 because heat production in the core was too small, and no further decrease was possible. The linear increase of core body temperature after 5 min was a result of heat generation in muscles. We hypothesize that exercise activates thermoregulatory inhibition of thermogenesis and/or increases heat dissipation, which prevents excessive heat accumulation during exercise in cool environment. However, at high ambient temperature this thermoregulatory compensation is impossible because the core metabolism cannot be reduced any further, while heat dissipation is already at its maximum. Therefore, heat generation by exercise added to heat accumulation and presented itself as an increased rate of the temperature growth. We conclude that compensatory mechanisms in the thermoregulatory system may underlie some controversial results concerned with the role of locomotion in the body temperature dynamics.
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Danya MuraliSchizophrenia, a psychiatric disorder, is a condition of core cognitive defects partly due to reductions in gamma oscillations. Gamma oscillations (20-80Hz) are neural correlates of certain cognitive effects. They are created by the Pyramidal Interneuron Network Gamma containing inhibitory, excitatory and chandelier cells. Post-mortem schizophrenic brains have shown a reduction in synaptic connectivity of inhibitory and excitatory cells, and an increase in chandelier connectivity. We hypothesize that an increase in chandelier cell connectivity can compensate for the reduction in other synapses. Using the integrate-and-fire equations, we derive a firing rate model and later extend to a spiking model to test this hypothesis. We find that within a certain range of reversal potential and strength, chandelier cells have the ability to compensate for the reduction of both inhibition and excitation; and return the system to firing gamma oscillations.
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Neda Jamshidi-AzadAbstract not submitted.
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Emily MeyerAbstract not submitted.
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Jamie Cyr, Tanya KaragiannisAbstract not submitted.
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Lauren LembckePeripheral arterial disease (PAD), in which arterial blockages prevent normal blood flow from perfusing the area distal of the blockage, can lead to claudication and limb ischemia. Collateral vessels provide an alternate pathway for the blood flow to reach that area. The collateral pathways compensate for the blockage by increasing diameter, number, and length of vessels. It remains unclear if the most significant compensation occurs by new small arteriole growth or an increase in the size of small arteries. A mathematical model of resistors is used to investigate the factors of collateral compensation which have the greatest influence on restoring blood flow.
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Yating WangAbstract not submitted.