Organized by: Wing-Cheong Lo, Weitao Chen, Wenrui Hao, Leili Shahriyari
Note: this minisymposia has multiple sessions. The other session is MS06-CDEV-1.

• Arthur D. Lander University of California Irvine, Irvine, CA (Center for Complex Biological Systems, and Department of Developmental and Cell Biology)
  "Control and Stability in Proliferative Dynamics"
The control of cell proliferation—the central process in creating, maintaining, and regenerating tissues of defined sizes and shapes—is a tricky business, because proliferation is fundamentally autocatalytic, and therefore prone to instability. Yet multicellular organisms achieve great feats of speed, precision, and stability in the production and maintenance of tissues. Moreover, they do so in the face of considerable stochasticity in the outcomes of cell divisions. Experimental studies have identified generic strategies—all based on some form of collective integral feedback—that can be shown, mathematically, to achieve many of these control objectives. However, the reliance of such strategies on cell-cell interaction creates fragilities, arising from limits on the distances over which intercellular signals spread; limits on the time scales over which perturbations can be managed; and situational ultrasensitivity to stochastic fluctuations. I will discuss the tradeoffs these fragilities impose, and how they influence what control organisms can achieve safely. I will raise the possibility that such fragilities create opportunities for rare, stochastic progression to states of uncontrolled growth, i.e., cancer, and suggest that such transitions provide a better model for cancer initiation than current models based on genetic determinism.
• Dongbin Xiu Ohio State University (Department of Mathematics)
  "Data driven modeling of partially observed biological systems"
We present a framework of flow map learning (FML) for predictive modeling of unknown dynamical systems from measurement data, with applications to biological systems. The method is designed to discover the flow map operator behind the data and utilize deep neural network (DNN) as the main numerical technique for the discovery. Once an accurate DNN model for the flow map is constructed, it serves as a predictive model for the unknown system and enables us to conduct long-term system prediction and analysis. The FML framework is highly versatile, as it allows one to construct accurate models when only a limited subset of the system parameters and state variables are observed.
• Tau-Mu Yi University of California, Santa Barbara (Molecular, Cellular, and Developmental Biology)
  "Systems Biology of Cell Polarity in Yeast"
Gradient sensing and response is a basic cellular behavior. Cells sense a chemical gradient and then respond by moving or projecting up the gradient. During this process of breaking symmetry, protein components localize to the front (or back) of the cell resulting in cell polarity. In this work, we characterized an information measure for cell polarity that applies to non-motile cells responding to a chemical gradient. The central idea is that polarization represents information about the direction of the gradient. Building upon previous work in the literature, we applied a theory of optimal gradient sensing and response in the presence of external noise based on the information capacity of a Gaussian channel. We compared the theory to experimental data on yeast mating projection growth in a pheromone gradient and demonstrated that slow ligand binding to receptor is the limiting factor in yeast gradient sensing. Finally, we showed that temporal averaging can help overcome the slow binding rate to achieve greater accuracy but resulting in a slow mating response.
• Avner Friedman Ohio State University (Department of Mathematics)
  "How breast cancer metastasize into the bone"
Bone marrow is a “fertile soil” for growth and proliferation of cancer cells. But in order to metastasize into the bone, breast cancer cells first need to degrade and weaken the hard layer at the bone surface. To facilitate this process they secret, sometime in advance, organelles (called exosomes) that contain DNA, mRNA , microRNA and proteins. It is now known that some of the microRNAs destroy the balance between bone formation and bone resorption, which results in bone lesions, and allow cancer cells to penetrate into the bone interior. In this talk I shall describe this process by a mathematical model, and introduce drugs that can increase bone density to the normal level and thus may protect the bone from invasion by cancer cells. This work is jointly with Nourridine Siewe.
• Chiu-Yen Kao Claremont McKenna College (Mathematical Sciences)
  "Our math and biology journey: A tribute to Ching-Shan Chou"
In this talk, I will bring you to a time machine ride to get to know Professor Ching-Shan Chou’s background, interests that we shared, and work that we had done together. In particular, highlight book projects, common interests, research works on propagation of cutaneous thermal injury, vibration of rods and plates, and fast sweeping methods for steady state problems for hyperbolic conservation laws.

Organized by: Wanda Strychalski, Alexander Hoover
Note: this minisymposia has multiple sessions. The other session is MS06-CDEV-2.

• Hongfei Chen Tulane University (Department of Mathematics)
  "Effects of Choanoflagellate Colony Shape on Hydrodynamic Performance"
Choanoflagellates are believed to be the closest animal relatives and are considered important in the study of animal tissue evolution. In their preferred environment, these microorganisms form a relaxed colony with flagella pointing-inward. However, when conditions become unfavorable, they contract and invert the colony, causing the flagella to point outward. Our proposed coarse model produces the same averaged far field flow as a single cell, and we use it to analyze the feeding and swimming behaviors of the two different colonies.
• Nigar Karimli Indiana University-Purdue University Indianapolis (Mathematics)
  "A three-dimensional mathematical model of a viscoelastic osteocyte immersed in flow"
Osteocytes make up 90-95% of all bone cells in an adult skeleton and are responsible for regulating bone remodeling through mechanotransduction (how the cells sense and convert mechanical signals into biochemical signals). In order to better understand the localization of forces on and around an osteocyte, which is essential for understanding mechanotransduction, we have developed a 3D mathematical model of an osteocyte and its interaction with surrounding flow. Our model includes the cell modeled as an interconnected network of viscoelastic elements. We have incorporated forces to model non-negligible bending rigidity, total and local area conservation of the membrane, and total volume conservation. We calculate these solid forces from the corresponding energy functions using the principle of virtual work. Additionally, we use the lattice-Boltzmann method (D3Q19) to model the flow in and around the osteocyte, and the immersed boundary method to handle fluid-structure interactions. After verifying proper model implementation, we have been able to produce simulations of an idealized ellipsoidal osteocyte immersed in flow and advecting along a channel. The model produces estimates for the typical motion and forces experienced by the osteocyte. In preparation for comparing our model with collaborators’ experiments involving stationary cells subjected to shear flow in a channel, we have also investigated and will share typical cellular dynamics that result when the cell is additionally anchored to an underlying surface.
• Sharon R. Lubkin North Carolina State University (Mathematics)
  "Geometry, pattern, and mechanics of notochords"
Chordocytes, in early zebrafish and other teleost notochords, have been shown to pack in a small number of stereotyped patterns. Mutations or treatments which disrupt the typical patterning are associated with developmental defects, including scoliosis. The dominant WT “staircase” pattern is the only regular pattern displaying transverse eccentricity. Morphometry and pattern analysis have established a length ratio governing which patterns will be observed. Physical models of cell packing in the notochord have established relationships between this geometric ratio, a mechanical tension ratio, the transverse aspect ratio, pattern, pressure, and taper. Since a major function of the early notochord is to act as both a column and a beam, we aim to understand the overall resistance to compression and bending in terms of these mesoscale cell/tissue properties. To frame the relationships between these properties, we have developed a model of the notochord as an elastic closed-cell foam, packed in either the “staircase” or “bamboo” pattern. A pressure study reveals a surprising lack of shape change as internal notochord pressure is varied, and determines the tension ratio between different surfaces in the notochord in terms of the relative stiffnesses and internal pressure. A bending study reveals that deformations of the model notochords are well described by classical beam theory, and determines the flexural rigidity of the model notochords in terms of relative stiffnesses and pressure. We find that the staircase pattern is more than twice as stiff as the bamboo pattern. Moreover, the staircase pattern is more than twice as stiff in lateral bending as in dorsoventral bending. This biomechanical difference may provide a specific developmental advantage to regulating the cell packing pattern in early-stage notochords.
• Kendall Gibson Tulane University (Mathematics)
  "Modeling the elastohydrodynamics of swimming choanoflagellates"
Choanoflagellates are aquatic single-cell microswimmers that prey on bacteria, and they are of interest in the study of the origins of multicellularity due to their ability to form large colonies. Structurally, they consist of a cell body, a flagellum, and a collar of microvilli. Our model treats the flagellum and the microvilli as elastic Kirchhoff rods whose shapes may be altered due to fluid-structure interactions. In addition to understanding the effect of compliance of these structures on the swimming of a single organism, we aim to study the hydrodynamic interaction of two choanoflagellates and how the collars might affect synchronization of the flagella.

Organized by: Christopher Heggerud, Tyler Meadows
Note: this minisymposia has multiple sessions. The other session is MS06-ECOP-1.

• Kara Taylor University of Florida (Department of Biology)
  "Simulating microbial metacommunities within the constraints of expected mean-variance relationships"
Taylor's Power Law (TPL) is one of the few established laws in ecology, applicable to both single-species populations and communities. The relationship between species abundance means and variances calculated across mixed-species aggregates is an indicator of joint species distribution. Additionally, TPL is useful for diagnosing instances of observed unusual population distribution. One such instance is sample saturation, in which the finite capacity of a sample unit is reached, variance declines, and the mean-variance relationship takes on an inverse parabolic shape. High-diversity systems like microbiomes are excellent for exploring the properties of community TPLs; however, their complexity obfuscates analysis of generating processes. Agent-based models are a useful tool in studying complex systems. In these bottom-up models, system-level properties emerge from numerous interactions in a set environment. By altering the processes defining interactions between individuals, one can change the state of an emergent property in a quantifiable way. In this simulation study, we use an agent-based model to test ecological processes that generate abundance mean-variance relationships observed in nature. The processes under investigation are dispersal, diversification, and ecological drift, parameterized as inter-host transmission, microbial speciation rate, and microbial growth under host growth conditions, respectively. The model utilizes a finite area (simulating a host gut, for example) for microbial occupancy, and as such, we expect to observe sample saturation. We find that, of the three processes parameterized, microbial dispersal between hosts alone acts to stabilize TPL towards expectation. In the absence of dispersal, sample saturation affects the TPL of rare species but not dominant species. This effect generates aberrant mean-variance relationships across the community that we tentatively interpret as Allee effects in the closed environment. In this system, dispersal may be stabilizing because it allows poor competitors to be rescued by neighboring populations, thereby alleviating positive density dependence.
• James Powell Utah State University (Mathematics and Statistics)
  "Homogenization across scales reveals relative strengths of environmental and direct transmission of Chronic Wasting Disease in deer"
Chronic Wasting Disease is an untreatable, fatal prion disease of deer and related species, spread both directly and by indirect contact with environmental reservoirs of the pathogen. Over the last twenty years the disease has spread across North America, and prevalence is approaching 40% in some highly impacted areas. The prion, a misfolded version of a naturally occurring protein, is very stable and remains infectious for years, even when exposed to ambient cold, heat and UV. However, experiments indicate that indirect transmission depends on exceeding a critical exposure. Thus the infectious landscape is sensitive to deer aggregation (and subsequent pathogen deposition) in desirable habitats, which vary on the scale of tens of meters, while home ranges are of kilometer size and some individuals relocate home ranges over tens of kilometers. We introduce a reaction-diffusion PDE model, including terms for pathogen deposition and critical environmental hazard to exposure. The model includes spatially explicit aggregation and the potential for developing prion hot-spots via an ecological diffusion model for deer movement. The technique of homogenization reveals emergent disease behavior on large scales, and the impact of critical exposure integrated across aggregating habitats appears as an Allee effect for disease prevalence. This raises the possibility that waves of disease are `pushed’ by the accumulation of prions in pathogen reservoirs, as opposed to being `pulled’ by the movement of infected individuals into regions where R0 > 1. In fact, parameter estimates show that the critical population susceptible density is almost always too high to give R0>1 via direct transmission. We tease out the relative contribution of indirect and direct transmission pathways for CWD spread in southwestern Wisconsin, USA, the epicenter of an outbreak which has been spreading among White Tail Deer for over twenty years.
• Chris Heggerud UC Davis (Environmental Science and Policy)
  "A model free method of predicting transient dynamics."
Transient dynamics are referred to as those dynamics that happen on ecologically relevant timescales, in which classical modelling techniques often fail to capture. Due to the ever changing environments and ecosystems, increased interest has been placed on the study of transient dynamics. However, many of the advances made towards understanding transients are fundamentally mathematical and beg to be connected to ecology and ecological data. In this talk I will show how uniting the underlying theory of dynamical attractors and empirical dynamical modelling we can understand when an ecological system is in a transient state based solely on ecological time series data. We further show that several metrics can be used to predict when a transient event is coming to an end. This work connects the mathematical literature on transient dynamics to the real-world application of understanding transients and short term changes in ecological systems.
• Punit Gandhi Virginia Commonwealth University (Department of Mathematics and Applied Mathematics)
  "Conceptual modeling of dryland vegetation patterns across timescales"
Strikingly regular, large-scale patterns of vegetation growth were first documented by aerial photography in the Horn of Africa circa 1950 and are now known to exist in drylands across the globe.  The patterns often appear on very gently sloped terrain as bands of dense vegetation alternating with bare soil, and models suggest that they may be a strategy for maximizing usage of the limited water available.  A particular challenge for modeling these patterns is appropriately resolving fast processes such as surface water flow during rainstorms while still being able to capture slow dynamics such as the uphill migration of the vegetation bands, which has been observed to occur on the scale of a band width per century.  We propose a pulsed-precipitation model that treats rainstorms as an instantaneous kick to the soil water as it interacts with vegetation on the timescale of plant growth. The model allows for predictions about the influence of storm characteristics on the large-scale patterns. Analysis and simulations suggest that the distance water travels on the surface before infiltrating into the soil during a typical storm plays a key role in determining the spacing between the bands.

Organized by: Omar Saucedo, Bren Case, Lauren Childs
Note: this minisymposia has multiple sessions. The other session is MS06-MEPI-1.

• Madeline A. E. Peters Michigan State University (Microbiology and Molecular Genetics)
  "Challenges in forming inferences from limited data: a case study of malaria parasite maturation"
Inferring biological processes from population dynamics is a common challenge in ecology, particularly when faced with incomplete data. This challenge extends to inferring parasite traits from within-host infection dynamics. We focus on rodent malaria infections (Plasmodium berghei), a system for which previous work inferred an immune-mediated extension in the length of the parasite development cycle within red blood cells. By developing a system of delay-differential equations to describe within-host infection dynamics and simulating data, we demonstrate the potential to obtain biased estimates of parasite (and host) traits when key biological processes are not considered. Despite generating infection dynamics using a fixed parasite developmental cycle length, we find that known sources of measurement bias in parasite stage and abundance data can affect estimates of parasite developmental duration, with stage misclassification driving inferences about extended cycle length. We discuss alternative protocols and statistical methods that can mitigate such misestimation.
• Bren Case University of Vermont (Computer Science)
  "Restricted Marginal Divergence: an efficient Bayesian measure of practical identifiability for nonlinear systems in biology and epidemiology"
Practical identifiability (PI) analysis seeks to quantify the reliability in estimates a researcher can expect when fitting a mathematical model to data. Such analyses generally reflect an intrinsic property of a particular model and proposed experimental design, rather than uncertainty in any single realization of data. Traditionally, PI has been studied using the variance-covariance matrix of an estimator for the true parameter values. However, such second-order approximations underestimate uncertainty in limited data settings, where the distribution of plausible values may be incorrectly centered or highly skewed. Here we introduce a novel method, the Restricted Marginal Divergence, which reflects the average amount of posterior shrinkage that would occur in a Bayesian analysis, without requiring computationally expensive methods such as MCMC. We show the method has attractive properties in both limited and big data regimes, and discuss its relationship to other PI methods. An in-depth application of the method follows, illustrating the amount of time that is required to learn different model-based summary statistics in an emerging epidemic, such as the basic reproductive number or fraction of individuals who will become infected.
• All Participants
  "Open Forum"
The last 30 minutes of this session will include an open forum for discussion with speakers and participants.

Organized by: Joshua Caleb Macdonald, Hayriye Gulbudak
Note: this minisymposia has multiple sessions. The other session is MS06-MEPI-2.

• Summer Atkins Louisiana State University (Department of Mathematics and Statistics)
  "An immuno-epidemiological model of foot-and-mouth disease in African buffalo"
We present a novel immuno-epidemiological model of Foot-and-Mouth Disease (FMD) in African buffalo host population. Upon infection, the hosts can undergo two phases, namely the acute and the carrier stages. In our model, we divide the infectious population based upon these two stages so that we can dynamically capture the immunological characteristics of both phases of the disease and to better understand the carrier’s role in transmission. We first define the within-host immune kinetics dependent basic disease reproduction R0 and show that it is a threshold condition for the local stability of the disease-free equilibrium and existence of endemic equilibrium. By using a sensitivity analysis (SA) approach developed for multi-scale models, we assess the impact of the acute infection and carrier phase immunological parameters on R0. Interestingly, our numerical results show that the within-carrier infected host immune kinetics parameters and the susceptible individual recruitment rates play significant roles in disease persistence, which are consistent with experimental and field studies.
• Leah LeJeune Virginia Tech (Department of Mathematics)
  "Cross-immunity and transmission influences in a multistrain host-pathogen cholera model"
We investigate possible long-term outcomes of the spread of cholera in a human population by considering the effects of pathogen growth in the environment and strain diversity on human transmission and recovery dynamics. The bacteria Vibrio cholerae relies heavily upon an aquatic reservoir as a transmission route. There are two main cholera strains, called serotypes, which induce distinct host immune response, with a degree of cross-immunity upon recovery. To better understand disease dynamics to combat future outbreaks, this work combines and extends two previously studied ordinary differential equation epidemiological models to consider interactions between the host population and two strains of the pathogen in an aquatic reservoir. Of particular interest are undamped, anti-phase periodic solutions which display a type of coexistence observed in past outbreaks where strains routinely switch dominance. Equilibria analysis and simulations show cross-immunity and transmission pathways are key influencers of oscillatory dynamics and should be considered when constructing efficient control measures against outbreaks.
• Alun L. Lloyd North Carolina State University (Biomathematics Graduate Program and Department of Mathematics)
  "Spatial Spread of Dengue Virus: Appropriate Spatial Scales for Transmission"
Dengue virus is the most significant viral mosquito-borne infection in terms of its human impact. Mathematical modeling has contributed to our understanding of its transmission and control strategies aimed at halting its spread. We consider the spread of dengue at the level of a city. Because the Aedes aegypti mosquito that transmits dengue has relatively low dispersal over its lifetime, human movement plays a major role in its spread and the household is a key spatial scale on which transmission occurs. Simple multi-patch deterministic models---metapopulation models, which consider the population to be described as a network of well-mixed patches---have been used to model city-level spatial spread and can provide expressions for key epidemiological quantities such as the basic reproduction number, $R_0$. We compare dynamics predicted by such models with results from individual-based network models and illustrate several discrepancies. We argue that the small size of households and local depletion of susceptibles are key features of the dynamics that are not captured in the standard $R_0$ analysis of the ODE model. In order to gain analytic understanding, we propose the use of household-level models, which can be analyzed using branching process theory. Our work, which echoes results previously found for directly-transmitted infections, highlights the importance of correctly accounting for the relevant spatial scales on which transmission occurs.
• Erin Gorsich University of Warwick (Zeeman Institute for Systems Biology and Infectious Disease Epidemiology)
  "Modelling endemic Rift Valley fever virus"
Rift Valley fever (RVF) is a mosquito-borne virus that causes haemorrhagic fever in livestock and wildlife, as well as spill-over infections in humans. Large-scale epidemics occur sporadically in Africa following heavy rainfall. In some regions, infection also cycles endemically at low levels in livestock, yet the mechanisms influencing transmission and the scale at which they occur remains relatively unknown. Here, we integrate a mathematical model with longitudinal infection, entomological and climate data from multiple villages in Kwazulu-Natal, South Africa. Our modelling approach accounts for nonlinearities in the risk of exposure, susceptible depletion, and variable sampling effort to evaluate potential drivers of infection. Hypotheses representing high heterogeneity in RVF incidence across the study villages were supported, and variation was mechanistically explained by climatic and entomological data. This highlights the value of methods that harness statistical model selection in a mechanistic framework.

Organized by: Cheng Ly, Janet Best, Pamela Pyzza, Yangyang Wang
Note: this minisymposia has multiple sessions. The other session is MS06-NEUR-1.

• Ngoc Anh Phan University of Iowa (Department of Mathematics)
  "Robustness of mixed mode oscillations and mixed mode bursting oscillations in three-timescale neuronal systems."
We are concerned with two types of complex oscillatory dynamics that frequently occur in multiple-timescale dynamical systems, namely mixed mode oscillations (MMOs) and mixed mode bursting oscillations (MMBOs). These phenomena involve the alternation of small-amplitude oscillations (SAOs) and large-amplitude oscillations or bursting oscillations. SAOs during the silent phase can arise from canard dynamics associated with folded singularities or a slow passage through a delayed Andronov-Hopf bifurcation (DHB) of the fast subsystem. In this work, we investigate the dynamic mechanisms underlying MMOs and MMBOs in two three-timescale neuronal systems. We identify the conditions under which the two separate mechanisms in the two-timescale setting, canard and DHB, can interact in the three-timescale context to produce more robust MMOs or MMBOs. This work can shed light on the fundamental principles governing these complex oscillatory behaviors in multiple-timescale systems.
• Sushmita John University of Pittsburgh (Mathematics)
  "Slow negative feedback enhances robustness of square-wave bursting"
Square-wave bursting is an activity pattern common to a variety of neuronal and endocrine cell models that has been linked to central pattern generation for respiration and other physiological functions. Many of the reduced mathematical models that exhibit square-wave bursting yield transitions to an alternative pseudo-plateau bursting pattern with small parameter changes. This susceptibility to activity change could represent a problematic feature in settings where the release events triggered by spike production are necessary for function. In this work, we analyze how model bursting and other activity patterns vary with changes in a timescale associated with the conductance of a fast inward current. Specifically, using numerical simulations and dynamical systems methods, such as fast-slow decomposition and bifurcation and phase-plane analysis, we demonstrate and explain how the presence of a slow negative feedback associated with a gradual reduction of a fast inward current in these models helps to maintain the presence of spikes within the active phases of bursts. Therefore, although such a negative feedback is not necessary for burst production, we find that its presence generates a robustness that may be important for function.
• Victoria Booth University of Michigan (Mathematics)
  "Neural rhythms generated by spatially heterogeneous neuromodulation"
Oscillatory neural firing activity or neural rhythms, have been shown to play critical roles in perception, attention, learning, and memory, especially rhythms in the theta (5-10 Hz) and gamma (30-100Hz) frequency bands. Available data suggest that forebrain acetylcholine (ACh) signaling promotes gamma and theta rhythms, although the mechanism has not been identified. Recent evidence suggests that cholinergic signaling is both temporally and spatially constrained, in contrast to the traditional notion of slow, spatially homogeneous, and diffuse neuromodulation. Using biophysically-based excitatory-inhibitory (E-I) neural network models, we find that spatially constrained cholinergic stimulation can generate theta-modulated gamma rhythms. We simulate the effects of ACh on neural excitability by varying the conductance of a muscarinic receptor-regulated K+ current. In E-I networks with local excitatory connectivity and global inhibitory connectivity, we demonstrate that stable gamma- modulated firing arises within regions with high ACh signaling, while theta or mixed theta- gamma activity occurs at the peripheries of these regions. High gamma activity also alternates between different high ACh regions, at theta frequency. Our results are the first to indicate a causal role for spatially heterogenous ACh signaling in the emergence of theta-gamma rhythmicity.
• Fernando Antoneli Universidade Federal de Sao Paulo (Centro de Bioinformatica Medica)
  "Network Dynamics: Theory and Examples"
A coupled cell system is a network of interacting dynamical systems. Dynamical network models assume that the output from each node is important and that signals from two or more nodes can be compared so that a notion of pattern of synchrony makes sense. One may ask: How does network architecture (who is talking to whom) affect the kinds of synchronous solutions that are expected in network equations. This talk will discuss necessary and sufficient conditions for synchrony in terms of network architecture, spatio-temporal symmetries of periodic solutions, as well as some curious synchrony-breaking bifurcations.

Organized by: Richard Bertram

• Wilfredo Blanco Figuerola State University of Rio Grande do Norte (Department of Computer Science)
  "Population Bursting in Modular Neural Networks"
Population bursts are observed in developing neural systems and in some fully developed neural systems. These can be achieved in networks in which synaptic connections are fully excitable, with no inhibitory connections. We have previously shown mechanisms and properties of such population bursts in purely excitatory neural systems, but only in unstructured networks, as would be expected in developing neural systems. In this presentation, we explore emergent dynamics in modular networks, focusing on how both intra- and inter-cluster connectivity impacts the behavior of the full population of cells.
• Mehran Fazli Henry M. Jackson Foundation for the Advancement of Military > Medicine, Inc., Bethesda, MD, USA (Austere Environments Consortium for Enhanced Sepsis Outcomes (ACESO))
  "Gene bundling: a new approach to clustering and reversed engineering of gene expression network"
Sepsis, responsible for one in five deaths globally, results from the body's response to inflammation caused by infection and can lead to life-threatening tissue damage. Detecting gene expression patterns that signify infection severity or type may improve patient diagnosis and care. The Austere environments Consortium for Enhanced Sepsis Outcomes (ACESO) conducts an international observational study to boost sepsis patient survival rates. In this research, we develop a new parameter-free algorithm for gene correlation-based clustering, founded on graph-theoretic concepts and spectral clustering. Blood samples collected upon hospital admission from 505 participants at ACESO sites in the United States, Ghana, and Cambodia are used for this algorithm. The subsequent transcriptomic data is employed to create and evaluate this innovative clustering approach. A single dataset can yield various clustering configurations, each highlighting distinct aspects of the data. Our primary aim is to build the necessary mechanisms to capture these aspects and achieve optimal gene clusters composed of genes that co-cluster in the most prevalent clustering schemes using spectral theory. This method, referred to as gene bundling, is both straightforward and versatile, permitting the analysis of diverse clustering scales to determine the optimal gene clustering. Using our sepsis dataset, we found that gene bundles have a strong connection to known biological pathways. Furthermore, by utilizing 28-day mortality data and a scoring system, we identified gene bundles that distinguish survivors and non-survivors within the entire population. Employing a multi-layered bundling scheme allows us to reverse-engineer the bundle-bundle interaction network. This algorithm holds promise for deepening our understanding of biological pathway interaction networks in sepsis patients, ultimately contributing to progress in sepsis diagnosis, prognosis, and therapy.
• Bhargav Karamched Florida State University (Mathematics)
  "How do Heterogeneity and Correlated Information Affect Decision-Making in Social Networks?"
Normative models are often used to describe how humans and animals make decisions. These models treat deliberation as the accumulation of uncertain evidence that terminates with a commitment to a choice. Such models exhibit two major limitations: (1) they model decision-making by individuals in isolation; (2) they assume observations are conditionally independent. Humans and animals often make decisions based on their own observations in conjunction with information provided by their peers. How should classical drift-diffusion models of decision-making be generalized to situations where decisions are made by networks of individuals? How does heterogeneity in network makeup affect collective decisions? We find that heterogeneous networks collectively make faster and more accurate decisions than homogeneous networks of identical observers. Moreover, individuals rarely observe independent data in making a decision. How does correlated information affect decision-making in networks? Surprisingly, we find that early decisions are less accurate than later decisions even in networks of identical agents who have the same criteria to make a decision! Our models are for idealized situations but can provide insight into strategies for optimizing individual and collective decision-making.
• Brad Peercy University of Maryland, Baltimore County (UMBC) (Mathematics and Statistics)
  "Loss of Synchrony to Silencing in Networks of Excitable Cells: Impact of Cell and Coupling Heterogeneity in Small Network Examples"
Experiments on pancreatic islets have raised a question about the potential unitary impact of certain cells in islet synchrony. Previous modeling to corroborate these findings under the suggested conditions proved unfruitful, but wide parameter searches did identify cases where silencing or ablating individual beta cells could completely or nearly completely silence islet behavior. We term such islets as 'switch' islets and such critical cells as 'switch' cells. We describe our efforts to create minimal examples representative of 'switch' behavior. This includes three cell beta cell networks and a small 2D grid network of simpler two-variable excitable cells. We find examples of 'switch' behavior in each case.

Organized by: Yangjin Kim, Magdalena Stolarska
Note: this minisymposia has multiple sessions. The other session is MS06-ONCO-1.

• Magdalena Stolarska Univeristy of St. Thomas (Mathematics)
  "On the significance of membrane unfolding and cortical stress generation in cell movement"
Cell motility play a critical role in cancer metastasis. Active deformation of the lipid bilayer and underlying actin cortex are important aspects of cell motility but have generally been overlooked in mathematical models. Membrane dynamics, including unfolding and exocytosis from intracellular reservoirs to the lipid bilayer, is necessary for large changes in cell shape, which occur during cell spreading and motility (Figard & Sokac, BioArchitecture, 2014) and for the release of membrane tension that occurs during these shape changes (Pontes et al., J Cell Bio, 2017). Actomyosin contraction of the underlying cortical layer also locally controls variations in cell shape and modes of motility (Salbreux et al., Cell, 2012). The aim of this work is to understand how active deformation of the membrane allows for large deformations of the cell and to understand how local active deformation of the actin cortex leads to amoeboid cell movement. To do this, two related mathematical models are presented. In both models the cell is treated as a viscous fluid that is surrounded by a viscoelastic membrane-cortex pair. Active deformation of the membrane or cell cortex is incorporated into the model via an additive decomposition of the rate of deformation tensor, the active part of which can depend on mechanical or biochemical components of the model, such as membrane tension or local myosin concentration. Using finite element simulations of the model we show that active membrane deformations, such as unfolding, and myosin-based contractility of the cortical layer are required for controlling various modes of cell motility.
• Jay Stotsky University of Minnesota (School of Mathematics)
  "Cell Cortex Mechanics and Cell Swimming"
The cell-cortex is a dense layer of cytoskeletal proteins lying underneath the cell-membrane of many types of cells. Because of its proximity to the cell-membrane, it exerts forces on the membrane precipitating movement and shape-change in cells. In turn, coordinated movement and shape-change are pivotal in cancer metastasis and in biological development. Thus, understanding the mechanical behavior of the cortex is an important area of study that can yield insights into a broad array of challenging questions in biology and medicine. However, the cortex also exhibits complicated behaviors that cannot be fully explained by present models. It is an active material, meaning that it converts chemical (or other forms of) energy into mechanical stress, and it is continually remodeled as the proteins that make up the cytoskeleton turn over and are recycled. In this talk, I will discuss recent work towards developing more realistic models, and computational tools to study the cell cortex. This area of research is exciting because of the many applications to biology and medicine and because it lies at the intersection of a diverse array of topics including differential geometry, thermodynamics, numerical analysis, and biomechanics.
• Donggu Lee Konkuk University (Mathematics / Seoul, Republic of Korea)
  "Optimal strategies of oncolytic virus-bortezomib therapy"
Proteasome inhibition and oncolytic virotherapy are two emerging targeted cancer therapies. Bortezomib, a proteasome inhibitor, disrupts the degradation of proteins in the cell leading to accumulation of unfolded proteins inducing apoptosis. Oncolytic virotherapy uses genetically modified oncolytic viruses (OV) to infect cancer cells, induce cell lysis, and activate an antitumor response. In this work, optimal control theory is utilized to minimize the cancer cell population by identifying strategic injection protocols of bortezomib and OV. Two different therapeutic protocols are explored: (i) Periodic bortezomib and single administrations of OV therapy; (ii) Alternating sequential combination therapy. These strategies support timely bortezomib and OV injection. Relative doses and administrative costs of the two anti-cancer agents for each approach are qualitatively presented. This study provides potential combination therapeutic strategies in cancer treatment.
• Yangjin Kim Konkuk University (Department of Mathematics)
  "Activated NOTCH induced monocyte recruitment suppresses anti-tumor immunity with virotherapy"
The impact of NOTCH signaling on immune therapy is understudied. We found that activation of NOTCH signaling promotes an MDSC enriched immune suppressive environment in brain tumors that limits the benefit from oncolytic immunotherapy. We developed a mathematical model, based on a system of partial differential equations, for the role of NOTCH signaling and macrophages in regulation of tumor growth dynamics and in control of anti-tumor efficacy in onvolytic virus therapy. Experimental data from RNA sequencing and CHIP-PCR indicated that infected tumor cells induced ADAMTS1 expression via RBP-j mediated canonical NOTCH signaling, which then enhanced macrophage recruitment in tumors. We found that Jag1 (NOTCH ligand) expressing macrophages created a feed forward loop in TME that amplified NOTCH signaling in tumor cells distant from sites of viral infection. Then, we investigated how macrophages are recruited to oHSV treated tumors and how these immune cells induce CCL2 production via TLR activation. The critical phenotypic switch towards an M2 phenotype that were immunosuppressive and induced tumor growth, played a significant role in regulation of the immune-tumor dynamics. We tested several hypotheses on the pharmacologic blockade of NOTCH signaling and possible rescue of a CD8 dependent anti-tumor memory response that enhanced therapeutic efficacy of oHSV therapy.

Organized by: Melissa Stadt
Note: this minisymposia has multiple sessions. The other session is MS06-OTHE-1.

• Melissa M. Stadt University of Waterloo (Applied Mathematics)
  "Maternal calcium homeostasis: A mathematical analysis of the differential impacts of pregnancy and lactation"
Calcium plays an essential role in many physiological functions such as skeletal mineralization, muscle contractions, blood clotting, and cell signaling. While extracellular calcium makes up less than 1% of total body calcium, it is tightly regulated since too high or too low calcium levels can have dangerous effects on the body. During pregnancy and lactation, there is excess demand on the maternal body due to the needs of the fetus or milk, therefore major adaptations must occur. Despite having a similar additional calcium demand, maternal adaptations in pregnancy and lactation differ. During pregnancy, intestinal absorption of calcium is massively increased in the mother’s body to meet the needs of the developing fetus. However, during lactation, calcium is resorbed from the bones to meet the needs of milk production. The goal of this project is to develop the first pregnancy- and lactation-specific mathematical models of calcium regulation. Model analysis reveals how both differential adaptations support the calcium demands of the fetus or milk while maintaining normal calcium ranges in the maternal body. 
• Karin Leiderman University of North Carolina at Chapel Hill (Mathematics, Computational Medicine)
  "Mathematical modeling to understand the effects of estrogen on platelet activation"
Activated platelets are essential for hemostasis and blood clotting. The activation process is a coordinated sequence of events that begins at the platelet membrane where ligands bind receptors and initiate internal signaling pathways. Estrogen has been observed to both reduce and enhance platelet responsiveness in the literature, with varying estrogen concentrations having potentially different effects. It is not yet known if these observed changes are due to estrogen receptor signaling only, or if there are other mechanisms also at play. One idea is that estrogen could induce changes in membrane properties that alter the signaling pathways leading to platelet activation. It is known that signal transduction is partially regulated by membrane properties like fluidity and lipid rafts, and that steroid hormones directly affect these types of membrane properties. We developed a mathematical model that considers both possibilities. First, it considers the downstream signaling effects that estrogen binding to estrogen receptors have on platelet activation. Second, we also assume that high levels of estrogen alter the fluidity of platelet membranes, which affects the binding dynamics of the collagen receptor, glycoprotein VI, and ultimately platelet activation. Our model qualitatively captures flow cytometry data showing similar dose response curves for platelet activation due to collagen related peptides and similar biphasic responses whereby platelet activation increases with low levels of estrogen but then decreases sharply with high estrogen levels.
• Tony Humphries McGill University (Mathematics and Statistics)
  "Sex Specific Mathematical Modelling of Erythropoiesis"
The human body produces more than 10^{11} blood cells per day, in a very dynamic process which can be affected by many factors including infection, hypoxia, blood loss and donation, and exogeneous drug administration. Blood cell production takes place in the bone marrow and is difficult to observe directly, while circulating concentrations of mature blood cells are easily measured. This makes hematopoiesis an interesting target for mathematical modelling which was already recognised in the 1970s, and there has been a wealth of mathematical modelling in the last 50 years. However, this modelling almost exclusively ignores sex-specific differences. In this talk we will describe the development of a sex-specific model of erythropoiesis. As well as the need to obtain parameter values for both sexes, the sex specific modelling provides the opportunity to explore some aspects of erythropoiesis which are less well understood, including the affects of male and female sex hormones. We apply our mathematical model to several situations including modelling blood donations for both sexes, while also incorporating the menstrual cycle in the female model. This collaboration started as a project at the 2023 Modelling Sex Differences in Physiology Workshop at the Banff International Research Station.