Mathematical Biology Seminar - Spring 2021 | Department of Mathematical Sciences

For questions about the seminar schedule, please contact James Maclaurin

February 2 Jonathan Cannon, MIT Postdoctoral Associate, Sinha Lab Rhythmic Entrainment as Dynamic Inference When presented with complex rhythmic auditory stimuli, humans are able to track underlying temporal structure (e.g., a ``beat''), both covertly and with their movements. This capacity goes far beyond that of a simple entrained oscillator, drawing on contextual and enculturated timing expectations and adjusting rapidly to perturbations in event timing, phase, and tempo. I propose that the problem of rhythm tracking is most naturally characterized as a problem of continuously estimating an underlying phase and tempo based on precise event times and their correspondence to timing expectations. I formalize this problem as a case of inferring a distribution on a hidden state from point process data in continuous time: either Phase Inference from Point Process Event Timing (PIPPET) or Phase And Tempo Inference (PATIPPET). This approach to rhythm tracking generalizes to non-isochronous and multi-voice rhythms. We demonstrate that these inference problems can be approximately solved using a variational Bayesian method that generalizes the Kalman-Bucy filter to point-process data. These solutions reproduce multiple characteristics of overt and covert human rhythm tracking, including period-dependent phase corrections, illusory contraction of unexpectedly empty intervals, and failure to track excessively syncopated rhythms, and could be plausibly approximated in the brain. PIPPET can serve as the basis for models of performance on a wide range of timing and entrainment tasks and opens the door to even richer predictive processing and active inference models of rhythmic timing.
February 16 Cliff Kerr, Institute for Disease Modeling Rhythmic Entrainment as Dynamic Inference When presented with complex rhythmic auditory stimuli, humans are able to track underlying temporal structure (e.g., a ``beat''), both covertly and with their movements. This capacity goes far beyond that of a simple entrained oscillator, drawing on contextual and enculturated timing expectations and adjusting rapidly to perturbations in event timing, phase, and tempo. I propose that the problem of rhythm tracking is most naturally characterized as a problem of continuously estimating an underlying phase and tempo based on precise event times and their correspondence to timing expectations. I formalize this problem as a case of inferring a distribution on a hidden state from point process data in continuous time: either Phase Inference from Point Process Event Timing (PIPPET) or Phase And Tempo Inference (PATIPPET). This approach to rhythm tracking generalizes to non-isochronous and multi-voice rhythms. We demonstrate that these inference problems can be approximately solved using a variational Bayesian method that generalizes the Kalman-Bucy filter to point-process data. These solutions reproduce multiple characteristics of overt and covert human rhythm tracking, including period-dependent phase corrections, illusory contraction of unexpectedly empty intervals, and failure to track excessively syncopated rhythms, and could be plausibly approximated in the brain. PIPPET can serve as the basis for models of performance on a wide range of timing and entrainment tasks and opens the door to even richer predictive processing and active inference models of rhythmic timing.
March 2 Andrea Barreiro, Southern Methodist University Dissecting the Mechanisms of Retronasal Olfaction Flavor perception is a fundamental governing factor of feeding behaviors and associated diseases such as obesity. Smells that enter the nose retronasally, i.e. from the back of the nasal cavity, play an essential role in flavor perception. Previous studies have demonstrated that orthonasal olfaction (nasally inhaled smells) and retronasal olfaction involve distinctly different brain activation, even for identical odors. However, the neural mechanisms that might underlie this difference are as yet unknown. In this talk I will report on our efforts to document and explain these differences. First, we investigated selectivity by recording from olfactory bulb (OB) and piriform cortex (PC) of anesthetized rats. We found that cells in the rat olfactory bulb show cell-specific and dynamic selectivity to orthonasal vs. retronasal stimuli. Second, our modeling study shows that when the olfactory bulb receives different input from orthonasal vs. retronasal sources, the retronasal input is selectively amplified by the olfactory bulb circuit. Finally, why does the bulb receive different input based on the direction of the air flow in the first place? We hypothesize that this difference originates, in part, because of fluid mechanical forces at the periphery: olfactory receptor neurons respond to mechanical, as well as chemical stimuli. If time permits I will show very preliminary results demonstrating that forces differ for orthonasal vs. retronasal air flow; i.e. inspiration vs. exhalation.
March 9 Hanspeter Herzel, Institute for Theoretical Biology, Charité and Humboldt University Berlin This seminar will be held at 10:30AM The Circadian Clock as a System of Coupled Oscillators Many organisms exhibit intrinsic self-sustained oscillators to adapt to rhythmic environmental conditions. This circadian clock is generated by gene-regulatory networks in a cell autonomous manner. Mathematical modeling contributes to an understanding of rhythm generation and synchronization. The clock is generated by delayed negative feedback loops. We present a 5-gene model fitted to measured gene expression profiles. It turns out that even for such a relatively small model many parameter configurations can reproduce the available data. Analyzing ensembles of these optimized models we can extract tissue-specific motifs including a “repressilator”. The intrinsic clock is entrained to external zeitgebers such as light, temperature, and meals. Interestingly, the phases of entrainment (“chronotypes”) are quite variable. Using oscillator theory and two-dimensional bifurcation diagrams (“Arnold tongues and onions”) we discuss the differences of “morning larks” and “night owls”.
March 30 Morgan Craig, Universite de Montreal Understanding Immune Communication Networks using Empirical Dynamics Both local and long-distance signalling are necessary for immune cell communication, which is critical for maintaining efficient and effective immune regulation. The sheer number of cell/cytokine interactions in the immune system complicates our ability to broadly understand the regulation of immune responses, and the pathophysiology of acute and chronic immune disorders. A central challenge is translating clinical, observational understanding into mechanisms. In this talk, I will discuss our approach to unraveling immune communication networks. For this, we applied a collection of novel quantitative techniques and models to a rare blood disorder called cyclic thrombocytopenia, which manifests clinically as oscillating platelet and thrombopoietin concentrations with periods of thrombocytopenia. Our results help to rectify the transmission of signals in the immune system both cell-to-cell and distally. I will discuss how this is helpful both preclinically and clinically for designing improved therapies and novel diagnostic tools, and establishing effective therapeutic schedules to help treat disease.
April 6 Chun Liu, Illinois Institute of Technology Energetic Ariational Approaches (EnVarA) for Active Materials and Reactive Fluids Active materials and reactive fluids consists of those materials that consume or convert energy to generate motion and deformations. They are involved in many biological activities and in most time, the principle characteristics of living organisms. In this talk, we will present a derivation and generalization of the mass action kinetics of chemical reactions using an energetic variational approach. The method enables us to capture the coupling and competition of various mechanisms, including mechanical effects such as diffusion, viscoelasticity in polymerical fluids and muscle contraction, as well as the thermal effects. We will also discuss several applications under this approach, in particular, the modeling of wormlike micellar solutions. This is a joint work with Bob Eisenberg, Pei Liu, Yiwei Wang and Tengfei Zhang.
April 7 Calvin Zhang-Molina, University of Arizona This seminar will be held at 1:30PM Modeling Synaptic Dynamics with Randomness and Plasticity Synaptic transmission is the mechanism of information transfer from one neuron to another. The dynamics of synaptic transmission determines the efficacy of information transfer from one neuron to another, and also with the outside world via sensory and motor systems. We aim to develop a theoretical framework that bridges dynamical systems, stochastic processes, optimal filtering, and control principles to understand neuronal information processing across the synaptic, neural circuit, and systems levels. In this talk, I will present a simple model of stochastic vesicle release that includes facilitation based on experimental data. I will then apply this model to study the interaction of facilitation and depression in synaptic transmission. (Joint work with Charles S. Peskin, New York University.)
April 13 Qixuan Wang, Department of Mathematics, University of California, Riverside Modeling of Growth: What Do We Learn from Hair Follicles? Hair follicles are stem cell-rich skin mini-organs that can undergo oscillation-like cycles of regeneration throughout their lifetimes. In recent years, hair follicle has emerged as a leading model system for studying general mechanisms of stem cell control, tissue patterning during morphogenesis, regeneration and aging. Recent experimental results have elucidated how certain signaling pathways regulate cell divisions, differentiation and programmatic death in different parts of the follicle. However, an integrated regulatory mechanism of hair follicle growth dynamics is still unclear at present. In particular, two crucial questions stay unresolved: 1) how does the hair follicle know if it has reached the maximum length, and 2) how does the hair follicle know when to terminate anagen and enter catagen? To answer these questions, we recently developed a new multiscale model on hair follicle growth. We proposed the Heterogeneous Response Hypothesis on the follicle growth control mechanism: heterogeneity in the responses of cells of the same type is crucial in regulating the follicle growth dynamics, both spatially and temporally. In this talk, I will present our recent modeling and experimental results, and discuss how the new hypothesis would contribute to the general study of growth control. (This work is in joint with Christian Fernando, Maksim Plikus and Qing Nie.)
April 27 Giovanna Guidoboni, University of Missouri Multiscale/Multiphysics Modeling of Ocular Physiology: The Eye as a Window on the Body The eye is the only place in the human body where vascular and hemodynamic features can be observed and measured easily and non-invasively down to the capillary level. Numerous clinical studies have shown correlations between alterations in ocular blood flow and ocular diseases (e.g. glaucoma, age-related macular degeneration, diabetic retinopathy), neurodegenerative diseases (e.g. Alzheimer’s disease, Parkinson’s disease) and other systemic diseases (e.g. hypertension, diabetes). Thus, deciphering the mechanisms governing ocular blood flow could be the key to the use of eye examinations as a non-invasive approach to the diagnosis and continuous monitoring for many patients. However, many factors influence ocular hemodynamics, including arterial blood pressure, intraocular pressure, cerebrospinal fluid pressure and blood flow regulation, and it is extremely challenging to single out their individual contributions during clinical and animal studies. In the recent years, we have been developing mathematical models and computational methods to aid the interpretation of clinical data and provide new insights in ocular physiology in health and disease. In this talk, we will review how these mathematical models have helped elucidate the mechanisms governing the interaction between ocular biomechanics, hemodynamics, solute transport and delivery in health and disease. We will also present a web-based interface that allows the user to run and utilize these models independently, without the need of advanced software expertise.

February 2

Jonathan Cannon, MIT Postdoctoral Associate, Sinha Lab

Rhythmic Entrainment as Dynamic Inference

When presented with complex rhythmic auditory stimuli, humans are able to track underlying temporal structure (e.g., a ``beat''), both covertly and with their movements. This capacity goes far beyond that of a simple entrained oscillator, drawing on contextual and enculturated timing expectations and adjusting rapidly to perturbations in event timing, phase, and tempo. I propose that the problem of rhythm tracking is most naturally characterized as a problem of continuously estimating an underlying phase and tempo based on precise event times and their correspondence to timing expectations. I formalize this problem as a case of inferring a distribution on a hidden state from point process data in continuous time: either Phase Inference from Point Process Event Timing (PIPPET) or Phase And Tempo Inference (PATIPPET). This approach to rhythm tracking generalizes to non-isochronous and multi-voice rhythms. We demonstrate that these inference problems can be approximately solved using a variational Bayesian method that generalizes the Kalman-Bucy filter to point-process data. These solutions reproduce multiple characteristics of overt and covert human rhythm tracking, including period-dependent phase corrections, illusory contraction of unexpectedly empty intervals, and failure to track excessively syncopated rhythms, and could be plausibly approximated in the brain. PIPPET can serve as the basis for models of performance on a wide range of timing and entrainment tasks and opens the door to even richer predictive processing and active inference models of rhythmic timing.

February 16

Cliff Kerr, Institute for Disease Modeling

Rhythmic Entrainment as Dynamic Inference

March 2

Andrea Barreiro, Southern Methodist University

Dissecting the Mechanisms of Retronasal Olfaction

Flavor perception is a fundamental governing factor of feeding behaviors and associated diseases such as obesity. Smells that enter the nose retronasally, i.e. from the back of the nasal cavity, play an essential role in flavor perception. Previous studies have demonstrated that orthonasal olfaction (nasally inhaled smells) and retronasal olfaction involve distinctly different brain activation, even for identical odors. However, the neural mechanisms that might underlie this difference are as yet unknown. In this talk I will report on our efforts to document and explain these differences.

First, we investigated selectivity by recording from olfactory bulb (OB) and piriform cortex (PC) of anesthetized rats. We found that cells in the rat olfactory bulb show cell-specific and dynamic selectivity to orthonasal vs. retronasal stimuli. Second, our modeling study shows that when the olfactory bulb receives different input from orthonasal vs. retronasal sources, the retronasal input is selectively amplified by the olfactory bulb circuit.

Finally, why does the bulb receive different input based on the direction of the air flow in the first place? We hypothesize that this difference originates, in part, because of fluid mechanical forces at the periphery: olfactory receptor neurons respond to mechanical, as well as chemical stimuli. If time permits I will show very preliminary results demonstrating that forces differ for orthonasal vs. retronasal air flow; i.e. inspiration vs. exhalation.

March 9

Hanspeter Herzel, Institute for Theoretical Biology, Charité and Humboldt University Berlin

*This seminar will be held at 10:30AM*

The Circadian Clock as a System of Coupled Oscillators

Many organisms exhibit intrinsic self-sustained oscillators to adapt to rhythmic environmental conditions. This circadian clock is generated by gene-regulatory networks in a cell autonomous manner. Mathematical modeling contributes to an understanding of rhythm generation and synchronization.

The clock is generated by delayed negative feedback loops. We present a 5-gene model fitted to measured gene expression profiles. It turns out that even for such a relatively small model many parameter configurations can reproduce the available data. Analyzing ensembles of these optimized models we can extract tissue-specific motifs including a “repressilator”.

The intrinsic clock is entrained to external zeitgebers such as light, temperature, and meals. Interestingly, the phases of entrainment (“chronotypes”) are quite variable. Using oscillator theory and two-dimensional bifurcation diagrams (“Arnold tongues and onions”) we discuss the differences of “morning larks” and “night owls”.

March 30

Morgan Craig, Universite de Montreal

Understanding Immune Communication Networks using Empirical Dynamics

Both local and long-distance signalling are necessary for immune cell communication, which is critical for maintaining efficient and effective immune regulation. The sheer number of cell/cytokine interactions in the immune system complicates our ability to broadly understand the regulation of immune responses, and the pathophysiology of acute and chronic immune disorders. A central challenge is translating clinical, observational understanding into mechanisms. In this talk, I will discuss our approach to unraveling immune communication networks. For this, we applied a collection of novel quantitative techniques and models to a rare blood disorder called cyclic thrombocytopenia, which manifests clinically as oscillating platelet and thrombopoietin concentrations with periods of thrombocytopenia. Our results help to rectify the transmission of signals in the immune system both cell-to-cell and distally. I will discuss how this is helpful both preclinically and clinically for designing improved therapies and novel diagnostic tools, and establishing effective therapeutic schedules to help treat disease.

April 6

Chun Liu, Illinois Institute of Technology

Energetic Ariational Approaches (EnVarA) for Active Materials and Reactive Fluids

Active materials and reactive fluids consists of those materials that consume or convert energy to generate motion and deformations. They are involved in many biological activities and in most time, the principle characteristics of living organisms. In this talk, we will present a derivation and generalization of the mass action kinetics of chemical reactions using an energetic variational approach. The method enables us to capture the coupling and competition of various mechanisms, including mechanical effects such as diffusion, viscoelasticity in polymerical fluids and muscle contraction, as well as the thermal effects. We will also discuss several applications under this approach, in particular, the modeling of wormlike micellar solutions. This is a joint work with Bob Eisenberg, Pei Liu, Yiwei Wang and Tengfei Zhang.

April 7

Calvin Zhang-Molina, University of Arizona

*This seminar will be held at 1:30PM*

Modeling Synaptic Dynamics with Randomness and Plasticity

Synaptic transmission is the mechanism of information transfer from one neuron to another. The dynamics of synaptic transmission determines the efficacy of information transfer from one neuron to another, and also with the outside world via sensory and motor systems. We aim to develop a theoretical framework that bridges dynamical systems, stochastic processes, optimal filtering, and control principles to understand neuronal information processing across the synaptic, neural circuit, and systems levels. In this talk, I will present a simple model of stochastic vesicle release that includes facilitation based on experimental data. I will then apply this model to study the interaction of facilitation and depression in synaptic transmission. (Joint work with Charles S. Peskin, New York University.)

April 13

Qixuan Wang, Department of Mathematics, University of California, Riverside

Modeling of Growth: What Do We Learn from Hair Follicles?

Hair follicles are stem cell-rich skin mini-organs that can undergo oscillation-like cycles of regeneration throughout their lifetimes. In recent years, hair follicle has emerged as a leading model system for studying general mechanisms of stem cell control, tissue patterning during morphogenesis, regeneration and aging. Recent experimental results have elucidated how certain signaling pathways regulate cell divisions, differentiation and programmatic death in different parts of the follicle. However, an integrated regulatory mechanism of hair follicle growth dynamics is still unclear at present. In particular, two crucial questions stay unresolved: 1) how does the hair follicle know if it has reached the maximum length, and 2) how does the hair follicle know when to terminate anagen and enter catagen? To answer these questions, we recently developed a new multiscale model on hair follicle growth. We proposed the Heterogeneous Response Hypothesis on the follicle growth control mechanism: heterogeneity in the responses of cells of the same type is crucial in regulating the follicle growth dynamics, both spatially and temporally. In this talk, I will present our recent modeling and experimental results, and discuss how the new hypothesis would contribute to the general study of growth control. (This work is in joint with Christian Fernando, Maksim Plikus and Qing Nie.)

April 27

Giovanna Guidoboni, University of Missouri

Multiscale/Multiphysics Modeling of Ocular Physiology: The Eye as a Window on the Body

The eye is the only place in the human body where vascular and hemodynamic features can be observed and measured easily and non-invasively down to the capillary level. Numerous clinical studies have shown correlations between alterations in ocular blood flow and ocular diseases (e.g. glaucoma, age-related macular degeneration, diabetic retinopathy), neurodegenerative diseases (e.g. Alzheimer’s disease, Parkinson’s disease) and other systemic diseases (e.g. hypertension, diabetes). Thus, deciphering the mechanisms governing ocular blood flow could be the key to the use of eye examinations as a non-invasive approach to the diagnosis and continuous monitoring for many patients.

However, many factors influence ocular hemodynamics, including arterial blood pressure, intraocular pressure, cerebrospinal fluid pressure and blood flow regulation, and it is extremely challenging to single out their individual contributions during clinical and animal studies. In the recent years, we have been developing mathematical models and computational methods to aid the interpretation of clinical data and provide new insights in ocular physiology in health and disease. In this talk, we will review how these mathematical models have helped elucidate the mechanisms governing the interaction between ocular biomechanics, hemodynamics, solute transport and delivery in health and disease. We will also present a web-based interface that allows the user to run and utilize these models independently, without the need of advanced software expertise.

Updated: April 7, 2021