Click to view posters for each subgroup
Adelle Coster
(MFBM)
University of New South Wales, Sydney Australia
"The Distance Between: Stochastic Models of Cellular Protein Transport"
Translocation of proteins is essential for cell metabolism. Whilst mean-field models of the molecular movements within cells have identified dominant processes at the macroscopic scale, stochastic models may provide further insight into mechanisms at the molecular scale. The aim of this study was to develop a distance metric between stochastic data sets which evolve over time. This would enable the quantitative comparison of the outputs of a candidate stochastic model and the different experimental measurements of the system. A candidate stochastic model is developed for the translocation in mammalian cells of the insulin-dependent glucose transporter protein, GLUT4. The model is a closed queueing network. Various outputs of the system are compared to different experimental data sets, and synthetic data produced. Using empirical probability distributions to compare the time courses of stochastic measurements with the stochastic outputs of the model, we test different quantitative comparisons between the model output and the synthetic data, with the ultimate aim of driving parameter inference and model selection.
Alexey A. Tokarev
(MFBM)
People’s Friendship University of Russia (RUDN University)
"Velocity-Amplitude relationship in the Gray-Scott autowave model in isolated conditions"
Various chemical and biological systems involve autocatalytic steps and positive feedbacks which in spatial conditions can give them properties of active media, in particular autowave properties. The main autowave characteristics are velocity and amplitude. This report considers the autowave velocity-amplitude relation in the general mathematical model of active reactant formation from precursor with cubic kinetics followed by a linear inhibition/death step – the Gray-Scott model – in isolated conditions. The way to derive the explicit velocity-amplitude relation is proposed. This approach may be useful for investigation of more complex active media systems in biochemistry, combustion, and disease control. The work has been supported by the «RUDN University Program 5-100» and by the Ministry of Science and Higher Education of the Russian Federation, agreement no. 075-03-2020-223/3 (FSSF-2020-0018).
Atchuta Srinivas Duddu
(MFBM)
Indian Institute of Science
"Multistability in cellular differentiation enabled by a mutually antagonistic triad"
Identifying the design principles of complex regulatory networks driving cellular decision-making remains essential to decode embryonic development as well as enhance cellular reprogramming. A well-studied network motif involved in cellular decision-making is a toggle switch – a set of two opposing transcription factors A and B, each of which is a master regulator of a specific cell-fate and can inhibit the activity of the other. A toggle switch can lead to two possible states – (high A, low B) and (low A, high B), and drives the ‘either-or’ choice between these two cell-fates for a common progenitor cell. However, the principles of coupled toggle switches remains unclear. Here, we investigate the dynamics of three master regulators A, B and C inhibiting each other, thus forming three coupled toggle switches to form a toggle triad. Our simulations show that this toggle triad can drive cells into three phenotypes – (high A, low B, low C) , (low A, high B, low C), and (low A, low B, high C). This network can also allow for hybrid or ‘double positive’ phenotypes – (high A, high B, low C), (low A, high B, high C) and (high A, low B, high C), especially upon including self-activation loops on A, B and C. Finally, we apply our results to understand the cellular decision-making in terms of differentiation of naïve CD4+ T cells into Th1, Th2 and Th17 states, where hybrid Th1/Th2 and hybrid Th1/Th17 cells have been reported in addition to the Th1, Th2 and Th17 ones. Our results offer novel insights into the design principles of a multistable network topology and provides a framework for synthetic biology to design tristable systems.
Baylor Fain
(MFBM)
Texas Christian Univsersity
"Modeling the impact of inoculum dose and transmission mode on viral infection with an agent-based model"
In a virus study, the inoculum dose is the initial amount of virus used. It is correlated to the initial amount of cells that become infected at the start of the study and thereby also correlated with the amount of virus that will be produced by infected cells at the beginning of that study. Those virus spread through a body in two known ways: cell free transmission and cell to cell transmission. While previous research has investigated viruses based on free cell transmission, few models have incorporated cell to cell transmission leading to unclear results and bias to certain variables. This research accounts for both modes of transmission, using an agent-based framework, and varies the initial amount of virus, to understand how inoculum dose affects the two transmission modes. Utilizing parallel processing, the model represents virus infection and spread in a two-dimensional layer of cells in order to generate total virus over time graphs for corresponding initial amount of virus. This project demonstrates how a combination of agent-based models and parallel processing can allow researchers to perform the rapid and large simulations necessary for viral dynamics research efficiently and affordably.
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Benjamin J Jessie
(MFBM)
Texas Christian University
"Respiratory Syncytia Virus"
Respiratory syncytial virus (RSV) is a common, contagious infection of the lungs and the respiratory tract. RSV is characterized by syncytia, which are multinuclear cells created by cells that have fused together. Because of experimental limitations, it is difficult to measure characteristics such as viral production rate and lifespan of the syncytia cells. We use mathematical models to study how different assumptions about the viral production and lifespan of syncytia change the resulting infection to determine whether indirect measurements can be used in place of experimental results.
Bertin Hoffman
(MFBM)
University of Applied Sciences Stralsund
"The initial engraftment of tumor cells is critical for the future growth pattern"
Xenograft mouse models are used to study mechanisms of tumor growth and metastasis formation as well as investigating the efficacy of different therapeutic interventions. After injection the engrafted cells form a local tumor nodule whose size can be measured repeatedly during an experiment. The so obtained experimental growth data can be described mathematically by suitable growth functions, the choice of which is not always obvious. By applying nonlinear curve fitting, growth parameters can be determined that provide information on the tumor growth.
We used self-generated synthetic data including random measurement errors to research the accuracy of parameter estimation based on caliper-measured experimental tumor data. Fit metrics were investigated to identify the most appropriate growth function for a given synthetic dataset. For curve fitting with fixed initial tumor volume, we varied the fixed initial tumor volume during curve fitting to investigate the effect on the resulting estimated parameters. To determine the number of tumor cells that survive initially after injection into mice, we performed ex vivo bioluminescence imaging of the tumor nodules on day 1, 2, 4 and 8 after injection. By this experimental approach we determined the effect of incorrect assumed initial tumor volume in experiments.
An incorrect assumed value of the initial tumor volume during the parameter estimation process leads to large deviations in the resulting growth parameters. Therefore, the actual number of cancer cells engrafting directly after subcutaneous injection is critical for future tumor growth and distinctly influences the parameters for tumor growth by curve fitting.
Hoffmann, B., Lange, T., Labitzky, V., Riecken, K., Wree, A., Schumacher, U., Wedemann, G. The initial engraftment of tumor cells is critical for the future growth pattern: a mathematical study based on simulations and animal experiments. BMC Cancer 20, 524 (2020). https://doi.org/10.1186/s12885-020-07015-9
Carley Cook
(MFBM)
Oklahoma State University
"Mathematical modeling of the relationship between T cell produced Wnt10b and the bone remodeling cycle"
Bone health is determined by many factors including the remodeling cycle. At any time, many sections of bone are going through a remodeling cycle. Depending on different signaling factors, the cycle will end with the same amount of bone as at the beginning of the remodeling cycle (healthy) or increased or decreased amounts of bone (these changes contribute to chronic bone diseases). Recently immune cells have been identified as major signaling factors for this process. However, it is unclear how and to what extent they affect bone homeostasis. One way to better understand this phenomenon is to consider different foods or medicines that activate immune cells. LGG, for example, is a probiotic that increases butyrate production in the gut. Butyrate has been shown to indirectly increase bone density through a series of interconnected processes throughout the body that involve immune cells. One key process is the stimulation by regulatory T cells of production of Wnt10b within the bone compartment. This process has been shown to increase bone density. To quantify the bone density change caused by butyrate production a multi-compartment mathematical model was developed in two parts. The first part of the model predicts how much Wnt10b is increased in the bone marrow through the immune response (the processes occurring outside of the bone compartment and not included in this talk), and the second part predicts the change in bone homeostasis caused by the increase of Wnt10b (inside the bone compartment). Here, we focus on the bone compartment. Wnt10b has been shown to alter osteoblastgenesis, osteoblast apoptosis rate, and osteoblast bone formation rate, which collectively lead to the increase of bone density. To model this change, we adapted a previously published and well-cited model of bone remodeling. This ODE model includes the cell types typically involved in remodeling such as osteoclasts, osteoblasts, and osteocytes. The model also includes an ODE that tracks the amount of bone present at the remodeling site. We have adjusted the three terms related to an increase of Wnt10b by adding three new parameters. The parameters are estimated using data collected on mice. However, because our model is based on human physiology only normalized information will be used. The data was taken from graphs in a consistent manner by utilizing Plot Digitizer. The values of the parameters are found using MATLAB lsqcurvefit and differential equation solver ode45. This model was then validated using a separate set of mice data. The completed model connects immune system T cells to the bone remodeling cycle. This model improves the understanding of immune cell disturbances to bone homeostasis and can help identify targets for medical intervention of bone loss.
Cristeta Jamilla
(MFBM)
University of the Philippines Diliman
"Inverse Problems for Neutral Delay Differential Equations using Nature-Inspired Optimization Algorithms"
Neutral delay differential equations (NDDEs) are useful in modelling real life phenomenon which includes time lag. In this paper, we use nature-inspired algorithms to solve inverse problems involving NDDEs. Specifically, we show how the nature-inspired optimization algorithms can be effective in estimating parameters of NDDEs. We compare the following recent algorithms: (1) particle swarm optimization, (2) genetic algorithm with multi-parent crossover, (3) whale optimization algorithm, (4) crow search algorithm, and (5) cuckoo algorithm.
Debasmita Mukherjee
(MFBM)
Department of Statistics, Sunandan Divatia School of Science, SVKM’s NMIMS Deemed to be University, Mumbai, 400056, India
"Atherosclerosis: A Mathematical Overview"
Atherosclerosis is a chronic inflammatory disease occurs due to plaque accumulation in the intima, the innermost layer of artery. Atherosclerosis is one of the prime causes behind several cardiovascular diseases over the worldwide. Here the entire biochemical process of atherosclerotic plaque formation is presented in terms of an autonomous system of ten nonlinear ordinary differential equations. Concentrations of low density lipoproteins (LDLs), high density lipoproteins (HDLs), free radicals, oxidized LDLs, chemoattractant, monocytes, macrophages, T-cells, smooth muscle cells (SMCs) and the necrotic core (or plaque cells) are assumed as the dependent variables in this nonlinear system. The present model has been found to be globally stable. Quasi steady state approximation theory is used to reduce the ten dimensional nonlinear system into a three dimensional nonlinear system. Numerical analysis of this reduced system has revealed the impact of some significant model parameters, which can be taken forward to develop some clinical strategies in controlling this disease dynamics.
Donggu Lee
(MFBM)
Konkuk University
"Role of OCT1 in regulation of miR-451-LKB1-AMPK-OCT1-mTOR core signaling network and cell invasion in glioblastoma."
Glioblastoma multiforme (GBM) is the most aggressive form of brain cancer with the short median survival time. GBM is characterized by the hallmarks of aggressive proliferation and critical cellular infiltration. miR-451 and their downstream molecules (LKB1, AMPK, OCT1, mTOR) are known to play a pivotal role in regulation of the balance of proliferation and aggressive invasion in response to metabolic stress in a tumor microenvironment (TME). Recent studies show that OCT1 and LKB1 play a significant role in regulation of the mutual inhibition between cell proliferation and migration. In this work, we develop a mathematical model of signaling pathway dynamics in GBM evolution with particular focus on the relative balance of proliferative capacity and invasion potential. In the present work we represent the miR-451/LKB1/AMPK/OCT1/mTOR pathway by a simple model and show how the effects of fluctuating glucose on tumor cells need to be reprogrammed by taking into account the recent history of glucose variations and an AMPK/miR-451 reciprocal feedback loop. The simulations show how variations in glucose significantly affect the level of signaling molecules and, in turn, lead to critical cell migration.
Editha Jose
(MFBM)
University of the Philippines Los Banos
"Complex Balanced Equilibria of Weakly Reversible Poly-PL Kinetic Systems and Evolutionary Games"
This talk is concerned with chemical reaction networks endowed with poly-PL kinetics, that is, the positive linear combination of power law kinetic systems. We discovered that complex balanced equilibria exist for weakly reversible poly-PL kinetics with zero kinetic reactant deficiency. The result is then applied to evolutionary games with replicator dynamics such that the polynomial payoff functions lead to polynomial kinetic systems, a subset of poly-PL kinetic systems. In particular,
sufficient conditions to admit a zero kinetic reactant deficiency were derived for games with nonlinear payoff functions and poly-PL kinetics, allowing the application
of the main result.
Emily Zhang
(MFBM)
NC State
"Personalized Time Series Forecasting of Blood Glucose Levels"
The development of data-driven capabilities for feedback control in the treatment of Type 1 Diabetes (T1D) requires the accurate prediction of future blood glucose (BG) levels. Specifically, the ability to predict BG levels in 30 and 60 minute time horizons could enable the time-dependent adjustment of treatment in response to the ensuing status of the patient, i.e., if hyper/hypo-glycemia occurs. By providing real-time data from continuous BG monitors, wearable sensor measurements, and self-reporting through mobile applications, the BG Level Prediction Challenge has enabled the capability to test whether models calibrated to individual-level data could ultimately be used for making individualized treatment decisions in T1D.
We trained and analyzed several direct prediction strategies, including different neural network architectures, reservoir computing, and linear regression. We found that the use of multiple linear regression models was the most accurate prediction strategy, and that reservoir computing has both the prediction power and the ability to recover the dynamics from missing intervals.
Erica M. Rutter
(MFBM)
University of California, Merced
"Predicting Bladder Pressure and Contractions with Dense Time-Series Data"
Bladder dysfunction due to spinal cord injury can result in incontinence and the inability to effectively void the bladder. Electrical stimulation of nerves in the bladder during a contraction can inhibit bladder contractions (eliminating incontinence) or excite bladder contractions to ensure the bladder is completely voided. However, determining when a bladder contraction will occur remains an active area of research. Our goal is to infer bladder pressure from external urethral sphincter electromyography (EUS EMG) readings from experimental data using rats. Due to the extremely dense time-series data, traditional mathematical modeling techniques are not applicable. Instead, we employ statistical methods (such as LASSO) and machine learning methods (recurrent neural networks) to make predictions of bladder pressure from external nerve data. Furthermore, to address inter-individual heterogeneity between rats, we applied a multi-task learning algorithm in which each individual rat’s prediction was a separate task – producing more generalizable results. These bladder pressures were then used to predict the onset of bladder contractions with high sensitivity and specificity.
Erik Amezquita
(MFBM)
Michigan State University
"Quantifying barley morphology using Euler characteristic curves"
Shape is data and data is shape. Biologists are accustomed to thinking about how the shape of biomolecules, cells, tissues, and organisms arise from the effects of genetics, development, and the environment. Less often do we consider that data itself has shape and structure, or that it is possible to measure the shape of data and analyze it.
Topological Data Analysis is a novel mathematical discipline that uses principles from algebraic topology to comprehensively measure shape in datasets. Using a function that relates the similarity of data points to each other, we can monitor the evolution of topological features—connected components, loops, and voids. This evolution, a topological signature, concisely summarizes large, complex datasets. Here, we focus on quantifying the morphology of barley spikes and seeds using topological descriptors based on the Euler characteristic and relate the output back to genetic information. The vision of TDA, that data is shape and shape is data, will be relevant as biology transitions into a data-driven era where meaningful interpretation of large datasets is a limiting factor.
Fillipe H Georgiou
(MFBM)
University of Newcastle
"Modelling Locust Foraging And Its Effect On Swarm Formation"
Having plagued mankind for millennia, locust swarms continue to be a major threat to agriculture, effecting every continent except Antarctica and impacting the lives of 1 in 10 people. Locusts are short horned grasshoppers that exhibit two behaviour types depending on their local population density. These are; solitarious, where they will actively avoid other locusts, and gregarious, where they will actively seek them out. It is in this gregarious state that locusts can form massive and destructive swarms or plagues. These large scale group dynamics arise through simple individual and environment interactions.
At longer time-scales, environmental conditions such as rain events synchronize locust lifecycles and can lead to repeated outbreaks. At shorter time-scales, changes in the distribution of food can have an effect on locust gregariazation. By modifying a multi-population aggregation equation to include locust-environment dynamics we are able to investigate the effect of different food distributions on locust swarming.
Our results suggest that there is an optimal food width for locust swarm formation, and that as food becomes more densely packed gregarious locusts are able to outcompete their solitarious peers.
Florian Franke
(MFBM)
HTW Dresden
"Is Cell segregation just like oil and water: A phase field approach"
Understanding the segregation of cells is crucial to answer questions about tissue formation in embryos or tumour progression. According to Steinberg's differential adhesion hypothesis [1] the separation of cells can be compared to the separation of two liquids, e.g. water and oil. Specifically, it was proposed, that similarly to the demixing of fluids, differences in the strengths of the adhesive forces in homo- and heterotypic cell contact lead to all sorting. This hypothesis has been tested on the basis of cell-based models which simulate motile cells with differential adhesive interaction on the basis of probability cellular automaton models [2]. On the other hand, the segregation of fluids like water and Oil can be well described by phase-field models as the Cahn-Hilliard-equation. Here we ask, weather the two approaches can be related to each other and how under such a relation depends on the details of the cell-based model.
We develop and test various order parameters which allow assuming the degree of segregation during time in both, cell-based probability cellular automaton models for cell sorting and phase-field models for the demixing of fluids. We identify typical benchmark scenarios where the agreement between both model classes shall be maximized and calibrate the phase-field model such that it best fit to in-silico data produced by specific cell-based models of sorting. We evaluate the good-ness of fit in these scenarios and relate out findings to the original differential adhesion hypothesis.
Furkan Kurtoglu
(MFBM)
Indiana University
"Temporospatial Modeling of CRC-CAF relation using molecular and tissue level"
Molecular communication between cells is a complex system when we think that the system consists of intelligent agents and microenvironment. In our project, we aimed to computationally model molecular communication between Colorectal Cancer Cells (CRCs) and Cancer-Associated Fibroblasts (CAFs) using a multi-scale agent-based modeling approach. To create this model, each cell is assumed as an agent that can change their behavior according to the microenvironment. We are using 3-D physics-based intelligent system simulator software that is called PhysiCell. While each cell is an off-lattice centered agent, the microenvironment is designed as a structured Cartesian grid. Microenvironment stores a number of external metabolites that cells can uptake from it or secrete to it with specific transfer reactions. Each cell has custom cell data that corresponds to some phenotypic attributes such as cell cycle, death, pressure. This data-structure also can be used for intracellular metabolite concentrations. Intracellular chemical reactions are modeled as ODEs that are represented as Systems Biology Markup Language (SBML). The ODE model includes a pseudo-metabolite that is called 'Energy'. This chemical is a bridge between intracellular-level and tissue-level with determining cellular cycle rate and death rate. The cross-platform 'Lib-roadrunner' is used to solve SBML models in one molecular time step. Integrating SBML to multi-scale models required to solve some design problems, such as, integration of uptake rates or defining transportable species. In addition, SBML parameters is stored as PhysiCell variable therefore each cell can have unique kinetic parameters which yields heterogeneity in the tumor. As the main goal, integrating molecular simulations with each agent might help us to understand cellular behaviors in complex systems.
Gess Iraji
(MFBM)
Brandeis University
"Modeling Clogging of Red Blood Cells in Microfluidic Devices with Simple Geometry"
We develop a basic model to investigate clogging of red blood cells in diagnostic microfluidic devices that sort cells based on their deformability. We analyze the effects of specific clogging rate functions on the progression of clogging in a device with simple geometry. We confirm our results using stochastic simulations and numerical methods for solving ordinary differential equations.
Jared Barber
(MFBM)
Indiana University-Purdue University Indianapolis
"Mathematical and mechanical models of cell motion"
Metastasis plays a significant role in many of breast cancer deaths. The traditional route for metastasis involves several steps including successful penetration of a vessel (intravasation), passage through the circulatory system to the site of metastasis (translocation), and exiting of that vessel (extravasation). Decreasing the frequency of any of these events can help mitigate the effects of breast cancer on the approximately 3.5 million Americans affected by the disease. Experiments also suggest that mechanotransduction, a process by which mechanical forces initiate cellular processes, may play an important role in such events. Because of these observations, we have begun developing a mechanical model of breast cancer cell dynamics that is force-based and, therefore, readily informs us about force levels cells may experience during events like intravasation, translocation, and extravasation. We will share results where the model is used to simulate breast cell passage through a tapered microfluidic channel. These results show that a two-dimensional network of damped springs (viscoelastic elements) submersed in surrounding Stokes flow can be used to reproduce qualitative agreement with experiments. They further show that such a model can be used with sensitivity analysis to consider how different cell properties affect cellular dynamics. While such results are focused on translocation and physical forces (without biochemistry), additional extensions of the model are currently in progress. We will share these extensions including development of a three-dimensional version of the model as well as use of an alternative approach, the immersed boundary method, to model such cells. Both of these efforts suggest this particular modeling approach is relatively versatile and useful for considering cell migration, osteocyte dynamics, and mechanically transduced biochemical products.
Joseph S Abrams
(MFBM)
University of Saskatchewan
"A CELL-BASED MODEL OF INTERCELLULAR MECHANICS DURING CPA EQUILIBRATION IN PREANTRAL OVARIAN FOLLICLES"
The rational design of cryopreservation protocols is an effective method for improving the outcome of sample survival. Cryopreservation of preantral ovarian follicles is an experimental therapy for fertility preservation and is of particular value in prepubescent cancer patients. Post-cryopreservation survival of this tissue is unsatisfactorily low for clinical use. Current tissue models of cryopreservation are largely focused on mass transport and the cytotoxicity of cryopreservatives, however, the potential mechanical damage to intracellular connections in response to mass transport is not considered. Intracellular connections between the granulosa cells and the oocyte in ovarian follicles, known as transzonal projections (TZPs), previously, have been shown to sever during cryopreservation. We hypothesized that the damage to TZP’s is due to variation in mass transport responses between heterogeneous cell types. Here we present a cell-based model, informed by experimentation, to capture mass transport, toxicity, and intracellular connections during the equilibration phase of cryopreservation. Using this model we explore several methods for improving cryopreservation protocols with a focus on improving TZP survival and thus post-thaw functionality.
Source of Funding: This work was supported by funding from the Canadian National Science and Engineering Research Council (RGPIN-2017-06346), the US National Institute of Child Health and Human Development (5R01HD083930-02) and the National Institute of Health (P51OD011092). Funding from the National Institute of Health supports the Oregon National Primate Research Center (ONPRC.
Conflict of Interest: None to disclose
Jungmin Han
(MFBM)
National Institutes of Health
"Missing Data Imputation and Gene Network Inference in Single Cell Analysis"
With advances in single-cell techniques, collecting a large quantity of data has become more accessible and efficient. In contrast, the increased complexity of data has made it more challenging to draw biologically relevant conclusions. As a result, there is an increase in demand for computational methods capable of dealing with such complexity and of providing some predictive deductions from the data. In this study, we present the use of neural networks in imputing missing data and a novel method for the inference of a gene network using least absolute deviation regression. Fowlkes et al. (Cell, 2008) published a set of gene expressions measured from 6078 Drosophila blastoderm during six different time cohorts that spanned the 50 minutes prior to the onset of gastrulation. Out of 95 genes and four proteins, only 27 of them had complete temporal information from all the cells, while the rest were measured only in a subset of cells. The missing data constituted about 37% of the whole data set. To impute the missing data, we trained and tested neural networks with one hidden layer on the complete 27 genes as predictors and the genes that were measured only in subsets of cells as targets. With the trained neural network, we imputed the missing gene expressions. To test the imputation method’s performance, we arbitrarily selected three genes from the complete 27 genes and randomly removed time points from their gene profiles. Then, the missing values were imputed using the same method. The medians of the imputed values were compared to those of the observed values and showed negligible differences. We then used a variation of least absolute deviation regression to infer a mechanistic model of the gene network that governs the discrete gene dynamics. The accuracy of the model was compared to those of mechanistic models inferred with a standard least squared regression and with non-mechanistic neural networks with multiple hidden layers. The models were used to predict the gene profiles given the initial values, and the errors were computed. Since the regression methods have different cost functions, we compared the distributions of errors in two metrics, in $L_{1}$ norm and $L_{2}^{2}$ norm. The model inferred with the least absolute deviation regression showed higher predictive power than the models using other methods. The data set was titrated to a smaller sample size to evaluate performance. In the limit of small sample size, the model inferred with our choice of regression performed better than the one inferred with least squared regression, but not as well as the trained neural networks.
Marc Pereyra
(MFBM)
FIAS
"3D Particle image velocimetry (PIV) analysis of cellular migration during embryonic development"
Light-sheet fluorescence microscopy (LSFM) has been used to generate three dimensional datasets of the embryonic development of some organisms. This allows to study the three dimensional morphological changes and to identify embryonic structures throughout development. Visual evaluation of these datasets offers qualitative descriptions of embryonic events, but quantitative and rigorous analysis pipelines are required. This talks is about quantitatively characterizing cellular migration from such 3D datasets of the embryonic development of Tribolium Castaneum [1]. In order to analyse the volumes we implemented a 3D particle image velocimetry (PIV) analysis. This analysis is borrowed form the field of fluid mechanics, where small fluorescent or reflective particles are suspended in a fluid with turbulent flow, and the change in position of the moving particles is used as an indirect measure of direction and velocity of the flow. Overall, the availability of quantitative measurement from these datasets enables the elaboration and testing of mathematical models about embryonic events of interest.
Pappu Kumar
(MFBM)
Hotilal Ramnath College, Amnour(Jai Prakash University, Chapra)
"Theoretical investigation of non-equilibrium bio-heat transfer during thermal therapy"
This study theoretically investigates the non-equilibrium heat transfer within living biological tissues during different thermal therapy applications. Numerical solution of the present problem has been done by Chebyshev wavelet Galerkin method. The use of Chebyshev wavelet is found to be accurate, simple and fast. Larger differences in the temperature prediction at the treatment position have been observed using different equilibrium and non-equilibrium based bioheat models. It is observed that the porosity and the convective heat transfer are the factors that contribute most to the non-equilibrium heat transfer within living biological tissues. The whole analysis is presented in dimensionless form.
Pau Capera Aragones
(MFBM)
Universität Bayreuth
"A mechanistic partial integro-differential equations model for bumblebee foraging behaviour"
Bumblebees provide valuable pollination services to crops around the world. Empirical evidence has suggested that the addition of wildflower adjacent to cultivated crops could increase its pollination services. However, a quantification of the location, quantity and type of the wildflowers needed to optimize the pollination services is unknown and a call for modellers has been made.Here we develop a partial integro-differential equation model to predict the spatial distribution of foraging bumblebees in dynamic heterogeneous landscapes. The foraging population is divided into two subpopulations engaged in intensive search mode (modelled by diffusion) and extensive search mode (modelled by advection) respectively. Our model considers the effects of resource-dependent transition rates between movement modes, resource depletion, central-place foraging behaviour and the effects of memory in the spatial distribution of foraging bees.
We use our model to quantify the benefits that planting wildflowers adjacent to a crop can have on its pollination services and show that small plantations in specific locations can lead to an increase of crop's pollination services.
Pedro Vilanova
(MFBM)
NJIT
"Synchronization in Stochastic Oscillators Subject to Common Extrinsic Noise"
In this work we study the level of synchronization in stochastic biochemical reaction networks that support stable mean-field limit cycles and are subject to common external switching noise. Synchronization in stochastic limit cycle oscillators due to common noise is usually demonstrated by applying Ito's Lemma to the logarithm of the phase difference. However, this argument cannot be straightforwardly extended to our case because of its discrete state space. Assuming the intrinsic and extrinsic noise operate at different time-scales, we prove that the average level of synchronization is of order of the rate of the intrinsic noise (inversely proportional to the system volume) times the square of the switching rate of the external noise. Moreover, we show in numerical experiments the approximate asymptotic value of the synchronization level by applying this result to classical oscillators found in the literature. Joint work with James MacLaurin.
Phillip Rossbach
(MFBM)
Unknown
"Determination of the critical adhesion parameter for the sorting behavior of a cell system with several cell types using statistical learning methods"
The process of cell sorting plays an essential role in development and maintenance of tissues. To understand the basic mechanisms of this process, mathematical modeling can assist cell biological research by providing means to analyze the consequences of different hypotheses on the underlying mechanisms. Three basic theoretical descriptions of cell segregation already exist: the Differential Surface Contraction Hypothesis of Harris (1976), the Differential Interface Tension Hypothesis of Brodland and Chen (2000) and the Differential Adhesion Hypothesis (DAH) of Steinberg. In DAH it is assumed that cell sorting is determined by quantitative differences in cell type speciffc intercellular adhesion strengths. An implementation of the DAH is the cell based Differential Migration Model (DMM) by Voss-Bohme and Deutsch. This DMM is based on modulated migration properties of cells with respect to their intercellular adhesion strengths and allows to study analytically the factors that determine pattern formation during cell sorting. In particular, a critical adhesion parameter for systems with two cell types can be derived analytically which predicts the sorting pattern of the two cell types as a function of the intercellular adhesion strengths. Here, we investigate numerically the existence of a critical parameter which determines the sorting behavior for more complex systems with more than two cell types. We rely on in-silico time-series data that is produced by a probabilistic cellular automaton which emulates the DMM and classify the segregation behavior using statistical learning methods such as Support Vector Machines and Logistic Regression Models. The well-understood case of two cell-types is used as benchmark-problem to evaluate our tools. The order parameter and statistical learning tools developed in this context provide a methodic approach applicable to the analysis of spatio-temporal in-vitro data, as well.
Pooja Dnyane
(MFBM)
CSIR-National Chemical Laboratory
"Boolean Model for Melanogenesis"
Melanogenesis is a highly regulated process through which the pigment melanin is produced in the skin cells. Irregularities in the molecular events that govern the process of skin pigmentation can cause disorders like vitiligo. In order to understand the biology of disease progression, it is important to have an in depth understanding of intracellular events. Mathematical models provide an integrated view of intracellular signaling. There are very few models to date that incorporate intracellular processes relevant to melanogenesis and only one to our knowledge that simulates the dynamics of response to varying levels of input. Here, we report the formulation of the largest Boolean model (265 nodes) for melanogenesis to date. The model was built on the basis of a detailed interaction network graph published by Raghunath et al. Through additional manual curation of the reported interactions, we converted the graph into a set of Boolean rules, following the procedure of the first Boolean model (61 nodes) for melanogenesis published by Lee et al. Simulations show that the predicted response to varying UV levels for most of the nodes is similar to the predictions of the existing model. The greater complexity allows investigation of the sensitivity of melanin to additional nodes. We carried out perturbation analysis of the network through node deletion and constitutive activation to identify the sensitivity of outcomes, and compared the nodes identified as sensitive to previous reports
Prachi Bisht
(MFBM)
"Interface growth driven by a single active particle"
We study pattern formation, fluctuations, and scaling induced by a growth-promoting active walker on an otherwise static interface. Active particles on an interface define a simple model for energy-consuming proteins embedded in the plasma membrane, responsible for membrane deformation and cell movement. In our model, the active particle overturns local valleys of the interface into hills, simulating growth, while itself sliding and seeking new valleys. In one dimension, this “overturn-slide-search” dynamics of the active particle causes it to move superdiffusively in the transverse direction while pulling the immobile interface upward. Using Monte Carlo simulations, we find an emerging tentlike mean profile developing with time, despite large fluctuations. The roughness of the interface follows scaling with the growth, dynamic, and roughness exponents, derived using simple arguments as beta = 2/3, z = 3/2, and alpha = 1/2, respectively, implying a breakdown of the usual scaling law beta = alpha/z, due to very local growth of the interface. The transverse displacement of the puller on the interface scales as~t^{2/3} and the probability distribution of its displacement is bimodal, with an unusual linear cusp at the origin. Both the mean interface pattern and probability distribution display scaling. A puller on a static two-dimensional interface also displays aspects of scaling in the mean profile and probability distribution. We also show that a pusher on a fluctuating interface moves subdiffusively leading to a separation of timescale in pusher motion and interface response.
PHYSICAL REVIEW E 100, 052120 (2019)
Pranav Khade
(MFBM)
Iowa State University
"Using alpha shapes to characterize protein flexibility"
There are only limited methods available to study the global motions of the protein such as their hinge motions and shear motions. These motions take place over a broad range of time scales, from microseconds to seconds; however, molecular dynamics methods can only model easily the motions occurring on the time scale from picoseconds to microseconds, and in addition, such simulations require that replicas be run. Thus, extracting the meaningful slow motions is difficult. Hence, there is a need to model the global motions of the protein. The important motions depend on a multiscale phenomenon known as protein packing. In this study, we have explored alpha shapes (a subset of Delaunay tessellations) for the protein backbone coordinates as a model of protein packing. We demonstrate that the method can predict the protein hinges which are responsible for the global motions of the proteins.
Quan Anh Hoang
(MFBM)
Vietnam National University
"Analyzing Bacterial Motility Near a Smooth Surface"
Motile bacteria play a pivotal role for life on Earth and studying them has many real-world applications. In particular, studying how motile bacteria interact with a smooth surface provides fundamental understanding about their transition from living as free-swimmers in the fluid to being a part of a surface aggregated community. Such knowledge can be useful in the resolution of medical problems like infections in the lungs of cystic fibrosis patients.
In this work, we report the reconstructed three-dimensional motion of a motile bacterium from its two-dimensional images generated by total internal reflection fluorescence microscopy. First, the Trackpy package keeps track of the bacterium's position on a plane parallel to the surface at each time step. Then, our in-house Ellipsoid Fitting Algorithm analyzes the intensity profile of the bacterium to reconstruct its three-dimensional position and orientation relative to the surface. From these parameters, we further extract the velocity and the localized turning radii of the bacterium's trajectory in space.
Rey Audie Escosio
(MFBM)
University of the Philippines Diliman
"Parameter Estimation of the Fitzhugh-Nagumo Model via a Perturbed Accelerated Gradient Descent Algorithm with an n-Dimensional Golden Section Search Method"
The Fitzhugh-Nagumo equations is a system of first-order nonlinear ordinary differential equations based on the researches of Fitzhugh and Nagumo et al. This reduced model captures the simplistic essence of neuronal spiking dependent on two variables, the membrane potential and the recovery variable.
From a collection of data points, the three parameters can be determined using the process of parameter estimation. This method minimizes the mean-squared difference between the data points and the solutions of the system. Researches by Ramsay et al. have shown the complexity and computational cost of this problem. The minimization may not converge properly using classic algorithms such as gradient descent and conjugate gradient. Hence, we propose a deterministic method that employs an accelerated gradient descent for iterating on the function surface and activates the local search to escape saddle points and local minima.
We apply the n-dimensional golden section search as the deterministic local search. It is a novel generalized technique for convex optimization by subsequently enclosing this optimum until convergence. Furthermore, partitioned n-spherical coordinate system is used which creates an adjusted smaller search
spaces as an equidistant ball centered on the iterate.
For the parameter estimation, the data points used is generated by applying noise to the deterministic solution of the system. The proposed algorithm, in comparison with other gradient-based methods such as the conjugate gradient and the steepest descent, highly performed in terms of its convergence, accuracy, and precision to the true value of the parameters amidst increasing noise level.
Rhudaina Z. Mohammad
(MFBM)
University of the Philippines Diliman
"Cellular patterning in sensory systems: An interface evolution problem"
This work in collaboration with Karel Svadlenka (Kyoto University), Hideru Togashi (Kobe University), and Hideki Murakawa (Ryukoku University) focuses on modeling cellular rearrangements in tissue morphogenesis, with emphasis on observed cellular pattern formations in sensory epithelia. Adopting the viewpoint of free energy minimization principle, we focus on the energy associated with cell-cell junction, an interface between cells. We take cellular rearrangement as an $L^2$-gradient flow of a weighted interfacial energy constrained by each cell's preferred volume, where the weights are related to physical parameters of the cells, for example, cell-cell adhesion and cell contractility. Unlike existing models such as vertex dynamics model and cellular Potts model, which are also based on free energy minimization, we propose a level set-based approach which allows for cell-cell junctions with nonzero curvatures, realizes the correct cell contact angles, has minimal possible number of parameters, and naturally handles topological changes, e.g., cell intercalation, without relying on ad hoc algorithms that inevitably involve unnatural parameters. This model successfully reproduces the development of cellular patterns in embryonic auditory and olfactory epithelial tissues.
Sayan Biswas
(MFBM)
Institute for Stem Cell Science & Regenerative Medicine
"Predicting mitochondrial functional state : An imaging based SVM tool"
Mitochondria are dynamic organelles, shown to provide signatures of onset of diseases or cellular stresses. In this work we attempt to probe whether specific patterns exist for stress in mitochondria which is assessed though quantitative imaging followed by machine learning. Feature extraction is performed to assess mitochondrial morphology, intensity and intra-mitochondrial structural heterogeneity features from confocal micrographs of mitochondria stained with micro-viscosity sensing and potentiometric dyes. These features examined from the acquired con-focal images of cells with mitochondria in apriori known perturbed (or stress) or unperturbed functional state. Perturbation dependent signatures in these assessed features were studied by employing supervised learning - Support Vector Machine. The classification between perturbed and unperturbed states was performed with an accuracy of nearly 93%. Furthermore, accuracy improvement methods were engineered by optimising the feature space through which an optimal classification accuracy of 98% was achieved and accounted the importance of intra mitochondrial heterogeneity. Overall, the derived features showed the presence of computationally identifiable unique functional state dependent patterns strengthening the way for assembling predictive models for assaying mitochondrial functional states. This could assist in developing less resource-intensive method to classify and study stress conditions. This tool provides a promising application of mathematics in biology that could be applied to characterize stress conditions, drug screening to aid the identification of functional stress state.
Sebastian Ruhle
(MFBM)
HTW Dresden
"Analysis of cell contact inhibition during growth of epithelial tissue"
The question of dominating mechanisms in the development of healthy epithelial tissue is subject to contemporary research, especially for tumour progression. While experiments suggest, that biomechanical cell-cell-interactions are crucial for the development of the tissue, it is usually oversimplified or neglected in theoretical approaches. For instance, the impact of cell migration, competition or contact inhibition on development of a cell colony is barely quantified. Puliafito et al. performed experiments on MDCK-cells (Madin-Darby-Canine-Kidney-cells) [1] and proposed, that the behaviour of the colony during the growth phase can be solely explained by contact inhibition To test this hypothesis, we develop a cell-based model and compare the numerical results with the experimental data. We introduce a novel cell-based model based on a probabilistic cellular automaton as our basic model and which is capable of emulating single cell behaviour like persistent cell migration, growth or proliferation and cell-cell-interactions like adhesion. The model parameters are calibrated by evaluating experimental single cell tracking measurements. Subsequently, we compare the temporal development of emergent quantities in the model like colony area, density, shape, cell size distribution, effective cell proliferation rate and the characteristic length scale of collective cell motion with the experiment.
Shadi Esmaeili-Wellman
(MFBM)
University of California Davis
"Density Dependent Resource Budget Model for Alternate Bearing"
Alternate bearing is the variability of the fruit and nut production with a strongly biennial pattern and is observed in many types of plants. This phenomenon is observed in collective synchrony among trees that are coupled directly and indirectly in orchards and natural forests and is known as masting. This is a yearly phenomenon so discrete time models, coupled nonlinear difference equations, are the appropriate modeling framework, with alternation between local in space dynamics and exchange between locations. The well-known resource budget model, while proposing a mechanism for alternate bearing behavior, can only model the synchronization observed in systems where the trees are coupled through indirect coupling (pollen coupling). We developed a density-dependent resource budget model based on the balance between photosynthesis and reproduction process. We analyzed the model through examination of the bifurcation structure for the uncoupled (local in space) model and numerically for spatially coupled versions. By addressing some of the shortcomings of the well-known resource budget model, our new approach can model the alternate bearing behavior and the synchronization phenomenon observed in trees coupled through direct coupling mechanism (root grafting).
Shawn Ryan
(MFBM)
Cleveland State University
"Role of Hydrodynamics in Chemotaxis of Bacterial Populations"
How bacteria sense local chemical gradients and decide to move has been a fascinating area of recent study. Chemotaxis of bacterial populations has been traditionally modeled using either individual-based models describing the motion of a single bacterium as a velocity jump process, or macroscopic PDE models that describe the evolution of the bacterial density. In these models, the hydrodynamic interaction between the bacteria is usually ignored. However, hydrodynamic interaction has been shown to induce collective bacterial motion and self-organization resulting in larger mesoscale structures. In this talk, the role of hydrodynamic interactions in bacterial chemotaxis is investigated by extending a hybrid computational model that incorporates hydrodynamic interactions and adding components from a classical velocity jump model. It is shown that by including hydrodynamic interactions, a suspension with a low initial volume fraction can exhibit locally high concentrations in bacterial aggregates. Also, it is shown that hydrodynamic interactions enhance the merging of the small aggregates into larger ones and lead to qualitatively different aggregate behavior than possible with pure chemotaxis models. Namely, differences in the shape, number, and dynamics of these emergent clusters.
Soumen Bera
(MFBM)
Central University of Rajasthan, India
"Biphasic Adaptive Activity of Plant Nitrate Transporter NRT1.1"
Defective nitrate signaling in plants causes disorder in nitrogen metabolism, and it negatively affects nitrate transport systems, which toggle between high- and low-affinity modes in variable soil nitrate conditions. Recent discovery of a plasma membrane nitrate transceptor protein NRT1.1—a transporter cum sensor—provides a clue on this toggling mechanism. However, the general mechanistic description still remains poorly understood. Here, we illustrate adaptive responses and regulation of NRT1.1-mediated nitrate signaling in a wide range of extracellular nitrate concentrations. The results show that the homodimeric structure of NRT1.1 and its dimeric switch play an important role in eliciting specific cytosolic calcium waves sensed by the calcineurin-B-like calcium sensor CBL9, which activates the kinase CIPK23, in low nitrate concentration that is, however, impeded in high nitrate concentration. Nitrate binding at the high-affinity unit initiates NRT1.1 dimer decoupling and priming of the Thr101 site for phosphorylation by CIPK23. This phosphorylation stabilizes the NRT1.1 monomeric state, acting as a high-affinity nitrate transceptor. However, nitrate binding in both monomers, retaining the unmodified NRT1.1 state through dimerization, attenuates CIPK23 activity and thereby maintains the low-affinity mode of nitrate signaling and transport. This phosphorylation-led modulation of NRT1.1 activity shows bistable behavior controlled by an incoherent feedforward loop, which integrates nitrate-induced positive and negative regulatory effects on CIPK23. These results, therefore, advance our molecular understanding of adaptation in fluctuating nutrient availability and are a way forward for improving plant nitrogen use efficiency.
Vedang Narain
(MFBM)
Indiana University
"A boids-based model of collective cell migration in wound healing"
The re-epithelialization of a wound is a critical phase in the healing process, the disruption of which can lead to hypertrophic scarring. An accurate simulation of collective eukaryotic cell migration is critical for the development of computational models of wound healing. Using an agent-based model, we explored the feasibility of leveraging modified boids mechanics and adaptive proliferation rules to replicate contact-based locomotion and inhibition. Cells in our centre-based in silico simulation migrated from the edges of the cutaneous wound and successfully restored 'skin' integrity. When compared to simulations incorporating random walk movements, our boids-based model appeared to generate an improved qualitative approximation of in vivo observations. These simple rules may be useful for replicating various instances of collective cell migration.
Vehpi Yildirim
(MFBM)
Erzurum Technical University
"Mathematical Modeling Postprandial Lipoprotein Metabolism and Investigating the Effects of the Bariatric Surgery"
Obesity has become one of the most serious public health issues over the past decades. Dyslipidemia, which is characterized by elevated plasma triglyceride-rich lipoprotein levels and disrupted plasma cholesterol profiles, is a major health risk associated with obesity. Bariatric surgery is one of the most effective methods for treating obesity. In addition to a significant weight loss, surgery induces remarkable improvements in plasma lipid profiles and insulin sensitivity indices. Even though the improving effects of bariatric surgery on the plasma lipid profiles and lipoprotein metabolism are well recognized, due to the complex nature of metabolism, the underlying mechanism is not fully understood. Lipoproteins are complex biochemical assemblies of lipids and apoproteins that transport water-insoluble triglycerides and cholesterol from the liver and intestines to the peripheral tissues. Studies show that lipoprotein metabolism is regulated by insulin and different lipoprotein species compete for the same clearance pathways in the circulation. The complexity induced by these regulatory mechanisms, interactions and feedbacks make computational models very effective for investigating lipoprotein metabolism.
In this study, we introduce a physiologically based multicompartmental model of hepatic and intestinal lipoprotein metabolisms. The model is designed to utilize stable isotopic enrichment and biochemical concentration data that has been collected during a mixed meal test. Hence, unlike several other models in the literature, the current model enables estimating metabolic parameters under non-steady-state conditions. An insulin module has been incorporated into the model to explore insulin-mediated regulations by utilizing available insulin data. The gastrointestinal module is designed to simulate the anatomical changes induced by gastric bypass surgery. This way, the model can comparatively analyze pre and post-surgery data to better understand the improvements induced at each metabolic pathway following the surgery. Finally, we test our model with pre- and post-surgery clinical data that has been collected from patients that went through Roux-en-y gastric bypass surgery. Our results indicate that, after the surgery, postprandial plasma lipoprotein clearance is significantly increased. Another key finding is that insulin-mediated stimulation of lipoprotein clearance is ameliorated. Furthermore, measured insulin responsiveness indices are significantly correlated with model estimates. Work done with
Will Leone
(MFBM)
UTK
"Understanding factors contributing to bacterial burden in granulomas of Mycobacterium tuberculosis-infected monkeys"
Mycobacterium tuberculosis (Mtb) is the bacterium that causes tuberculosis (TB) and kills more people per year than any other infectious agent. Factors that influence the spread of Mtb within individuals are an ongoing topic of investigation. We analyzed novel data from 25 Mtb-infected rhesus macaques on the number of colony forming units (CFUs) in individual granulomas in lungs of the animal. In these experiments, macaques were infected with different initial doses (varying between 1-40 CFUs); animals underwent different Mtb-controlling treatments, and measurement of lung granuloma CFUs were done at different time points after the infection. We found that a higher initial dose resulted in a larger average number of CFUs per granuloma when comparing macaques given an initial dose of 8 or 40 CFUs. The caveat in this comparison, however, is that time since infection and controlling treatments were varied between the doses. Interestingly, we found that variability in CFU/granuloma (estimated using coefficient of variation, CV) is higher among all animals as compared to CV estimated for individual animals. This suggests that infection dynamics in granulomas of a given animal proceeds more similarly than infection between two randomly chosen granulomas in two different animals. This result challenges the commonly stated hypothesis that dynamics of Mtb in individual granulomas in one animal are independent. Our analysis also suggested that the CFU/granuloma in macaques is dependent on a combination of the initial dose of Mtb, treatment, and time since infection. These results lead further research into assessing the relative contributions the dose and time since infection have on TB infection in the lungs of the macaque and is the focus of ongoing research.
Xinzhe Zuo
(MFBM)
UCLA
"Backtracking in RNA polymerization"
Backtracking of RNA polymerase (RNAP) is an important pausing mechanism during DNA transcription that is part of the error correction process that enhances transcription fidelity. We model the backtracking mechanism of RNA polymerase which usually happens when the polymerase tries to incorporate a mismatched nucleoside triphosphate. Previous models have made assumptions for easier calculations. One of the key assumptions made is that there is no trailing polymerase behind the backtracking polymerase or the trailing polymerase remains stationary when the leading polymerase backtracks. We derive analytic solutions for a stochastic model that allows for locally interacting RNAPs to explicitly show how a trailing RNAP influences the probability that an error is corrected or incorporated by the leading backtracking RNAP. We also provide a related method for computing the statistics of the times to error correction or incorporation given an initial local RNAP configuration. Our model and the associated results provide the components needed in more complete multi-RNAP descriptions. For example, all RNAPs along a transcript may be considered using exclusion processes such as the TASEP model that has been used to describe mRNA. In the many-body picture, one would be able to address multiple, simultaneously stalled RNAPs on how their interactions affect their probabilities of correction or incorporating an error. A competition between transcription fidelity and RNA production rate would be expected to arise
and will be the subject of future investigation.
Yahe Yu
(MFBM)
NC State
"Finding Optimal STI Strategies for HIV Using Fitted Q Algorithm with XGBoost Regression"
We are trying to use the fitted Q algorithm with XGBoost regression to compute the optimal structured treatment interruption strategies for HIV infected patients. By using the combination of these two methods, we showed that this approach is computationally more efficient, at the same time the optimal results were obtained using fewer training data. And the speed of convergence of the optimal strategy is much fast than the Extra-tress regression method used in the fitted Q algorithm.
Yeeren Low
(MFBM)
McGill University
"Data-driven modeling of T cell morphodynamics during migration"
T cells can spontaneously migrate rapidly through the extracellular matrix using an 'amoeboid' mechanism, which is believed to aid their search for antigens. While modeling and experiments have in part addressed motility parameters and the impact of matrix characteristics, the morphodynamics during locomotion remains not well understood. We consider a data-driven approach using low–spatial resolution time-lapse fluorescence microscopy videos of activated T cells migrating in collagen matrix or under agarose gel. We analyze the resulting cell shapes by using an autoencoder to extract a low-dimensional 'shape space'. We find time-irreversible motion in shape space, as expected from Purcell's theorem for a swimmer at low Reynolds number. We also find evidence of distinct signatures of turning behavior as a result of cell–matrix interactions. Our statistical analysis allows us to generate artificial trajectories of cells and their shapes using a coarse-grained morphology. This approach confers the possibility of inferring predictive dynamical laws which would inform biophysical models of cell morphology during migration and interaction with the environment.
Hosted by eSMB2020 Follow
Virtual conference of the Society for Mathematical Biology, 2020.
