Sub-group minisymposia (9:30-11:00am)

CDEV: Subgroup Contributed Talks (9:30-11:00am)

Andrew Krause University of Oxford
"Matching Theory to Real Biology: Recent Progress and Open Questions in Turing's Theory of Morphogenesis"

Turing's reaction-diffusion theory of morphogenesis has been enormously well-studied from a variety of perspectives. While incredibly successful in motivating enormous theoretical and experimental work, there are many open questions in elucidating specific aspects of Turing-type morphogenesis in real developmental settings. I will present recent work on developing new tools and perspectives on matching Turing's idealized theory with the complexity of real biological development. This includes recent extensions to the classical theory of linear instability analysis to account for heterogeneity in space and time, curvature, growth, as well as open boundary conditions combining Turing's theory with other ideas in understanding spatial pattern formation, such as positional information. While this extends and confirms intuitive insights gained from experiments and simulations over the past few decades, it raises an enormous number of questions regarding how far we can push such extensions. I will briefly mention some of these, hopefully stimulating broader perspectives on how to develop simple yet physically interpretable theories of pattern formation.

Daniel Lobo University of Maryland, Baltimore County
"A Turing system explains regeneration patterning and fission behavior in planaria"

Planarian worms have the extraordinary ability to regenerate any body part after an amputation. This ability allows them to reproduce asexually by fission, cutting themselves to produce two separated pieces each repatterning and regenerating a complete animal. The induction of this process is known to be dependent on the size of the worm as well as on environmental factors such as population density, temperature, and light intensity. Models based on Turing systems can explain the self-regulation of many biological mechanisms, from skin patterns to digit formation. Here, we combine experimental evidence with a modeling approach to show how a cross-inhibited Turing system can explain at once both the signaling mechanism of regeneration and fission in planaria. The model explains in a growing domain the precise signals that control the regeneration of the different body parts after amputations as well as when and where planaria fission, and its dependence on the worm length. We provide molecular implementations of the proposed model, which also explains the effects of environmental factors in the signaling of fission. In summary, the proposed controlled cross-inhibited Turing system represents a completely self-regulated model of the whole-body regeneration and fission signaling in planaria.

Jason Ko University of Maryland, Baltimore County
"Regulated Cell Adhesion Dynamics in a Continuous Model: Sorting, Intercalation, and Involution"

Cell-cell adhesion can dictate tissue growth and multicellular pattern formation and it is crucial for the cellular dynamics during embryogenesis and cancer progression. While it is known that these adhesive forces are generated by cell adhesion molecules (CAMs), the regulation of CAMs is not well understood due to complex nonlinear interactions that span multiple levels of biological organization–from genetic regulation to whole-organism shape formation. We present a novel continuous model using partial differential equations that can explain the dynamic relationships between genetic regulation, CAM expression, and differential adhesion. This approach can demonstrate the mechanisms responsible for cell-sorting behaviors, cell intercalation in proliferating populations, and the involution of zebrafish germ layer cells during gastrulation. The model can predict the physical parameters controlling the amplitude and wavelength of a cellular intercalation interface as shown in vitro. We demonstrate the crucial role of N-cadherin regulation for the involution and migration of cells beyond the gradient of the morphogen Nodal during zebrafish gastrulation. Integrating the emergent spatial tissue behaviors with the regulation of genes responsible for essential cellular properties such as adhesion will pave the way toward understanding the genetic regulation of large-scale complex patterns and shapes formation in developmental, regenerative, and cancer biology.

Timothy Ostler Cardiff University
"Choosing the best embryo in In-Vitro Fertilization"

We aim to characterise the shape and size of thawing embryos after they have been cryopreserved during In-Vitro Fertilization (IVF). Through image segmentation techniques and data analysis, we seek to determine appropriate metrics that can predict pregnancy. We also model the increasing temperature of thawing embryos, determining the conditions that will prevent damage. This is work undertaken through an academia-industry grant at Cardiff University in collaboration with the London Women's Clinic. Joint work with: Katerina Kaouri, Thomas Woolley, Karl Swann (Cardiff University), Andrew Thompson, Giles Palmer (London Women’s Clinic), with funding from the KESS2 Scholarship. Knowledge Economy Skills Scholarships (KESS 2) is a pan-Wales higher level skills initiative led by Bangor University on behalf of the HE sector in Wales. It is part funded by the Welsh Government’s European Social Fund (ESF) convergence programme for West Wales and the Valleys.sector in Wales. It is part funded by the Welsh Government’s European Social Fund (ESF) convergence programme for West Wales and the Valleys.

Maria Abou Chakra University of Toronto
"Control of tissue development by cell-cycle dependent transcriptional filtering"

A fundamental question in biology is how a single eukaryotic cell produces the complexity required to develop into an organism. Cell cycle duration changes dramatically during development, starting out fast to generate cells quickly and slowing down over time as the organism matures. The cell cycle may also act as a transcriptional filter to control the expression of long genes which can’t be completely transcribed in short cycles. Using mathematical simulations, we discovered an inherent trade-off where fast cycling cells serve to increase cell number while slower cycling cells contribute to cell diversity by introducing genes in a controlled manner. Simulations show that cell-cycle duration can fine tune cell number, cell diversity and cell proportions in a tissue. Our predictions are supported by comparison to single-cell RNA-seq data captured over embryonic development. Our results support the idea that cell-cycle dynamics may be important for controlling gene expression and cell fate.

MEPI: Modeling COVID-19 to inform control efforts, Part I (9:30-11:00am)

Jonathan Read Lancatser University
"Modelling early transmission of Covid-19 within China"

In this talk, I will describe rapid modelling work conducted between 20-27 January 2020 to estimate key epidemiological parameters during the early stages of the Covid-19 outbreak in China. Key uncertain- ties at the time were the transmission potential of the new virus as well as the case ascertainment ratio and likely full size of the epidemic. We fitted a deterministic metapopulation SEIR model of transmission to reported case information across Chinese cities as well as in other locations around the world, up until large-scale movement restrictions were imposed on 23 January. We estimated that the R0 in China was 3.11 (95%CI, 2.39-4.13) and the case ascertainment ratio in Wuhan, the center of the outbreak at the time, was only 5.0% (3.6-7.4), demonstrating the potential for sizable epidemics that may be difficult to control.

Yanni Xiao Xi'an Jiaotang Univeresity
"Modeling COVID-19 epidemic in mainland China based on multi-source data"

Since December 2019, the outbreak of new coronavirus in Wuhan has continued to spread, which has attracted worldwide attention. It is essential to effectively predict the development trend of the epidemic, including when the 2019-nCoV infection will peak, what are the specific peak value and the final size, etc. How do the large-scale directional movement of the national population and random movement of individuals influence on the national epidemic during the Spring Festival, and what is the role of the control strategies on the epidemic? Address these questions fall within the the scope of this talk. We develop a novel modeling approach with multiple control measures and parameterize the model based on a small amount of constantly updated data to quick predict the development trend and transmission risk of the disease, to reveal the development trend of the new coronavirus. We develop spatial network model to study the influences of population movement, information transmission, enhanced prevention and control measures on epidemic transmission, to identify the key factors that significantly affect the spread of disease, and to analyze the effectiveness of prevention and control measures of 2019-nCoV in- fection. The findings provide quantitative decision basis for national epidemic prevention and control.

Julien Riou University of Bern
"Early transmission pattern and severity of COVID-19 in China"

The coronavirus disease 2019 (COVID-19) epidemic that originated in Wuhan, China, has spread globally. Early in the epidemic, we estimated the basic reproduction number R0 of 2019-nCoV to be around 2.2 (1.43.8), indicating the potential for sustained human-to-human transmission. As more data was becoming available, we estimated the age-specific case fatality ratio (CFR) by fitting a transmis- sion model to data from China, accounting for underreporting and the time delay to death. Overall CFR among all infections was 1.6% (1.4-1.8) and increased considerably for the elderly, highlighting the expected burden for healthcare systems with further expansion of the COVID-19 epidemic around the globe. This presentation aims to highlight methods that can be used to inform public health authorities in real time in situations of disease emergence, with a particular focus on how to handle uncertainty.

Zhilan Feng Purdue University
"Staggered Release Policies for COVID-19 Control: Costs and Benefits of Relaxing Restrictions by Age and Risk"

Lockdown and social distancing restrictions have been widely used as part of policy efforts aimed at controlling the ongoing COVID-19 pandemic. Since these restrictions have a negative impact on the economy, there exists a strong incentive to relax these policies while protecting public health. Using a multigroup SEIR epidemiological model, we explore the costs and benefits associated with the sequential release of specific groups based on age and risk from isolation. The results suggest that properly designed staggered-release policies can do better than simultaneous-release policies in terms of protecting the most vulnerable members of a population, reducing health risks overall, and increasing economic activity.

MFBM: Simulations and Experiments in Small Scale Bio-Locomotion (9:30-11:00am)

Orrin Shindell Trinity University, United States, oshindel@trinity.edu
"Rigid Body Dynamics of Motile Bacteria near Surfaces"

Bacteria in their natural environment switch between living as free-swimming individual cells and living as members of surface-aggregated communities. To perform this transition, individual cells must contend with the hydrodynamic force interactions between them and the surface. In our work, we determine these interactions by combining experiments and numerical simulations. Using total internal reflection microscopy, we acquire time lapse images of fluorescent bacteria swimming near a surface. By analyzing the intensity profiles, we reconstruct the three-dimensional trajectories of the bacteria. We then input the measured trajectories into a computational fluid dynamics model – the method of images for regularized Stokeslets – and calculate the force and torque exerted on the bacteria when they swim near the surface. In this talk, we will present the technical details of the experiment, show the resulting measurements, and discuss the computational approach.

Meuriq Galagher University of Birmingham, United Kingdom, m.t.gallagher@bham.ac.uk
"FAST: Automated Flagellar Capture as a Research and Clinical Tool"

In an age where huge amounts of imaging data can be readily produced it is increasingly important to be able to accurately and efficiently this information, and to be able to use these analyses as a marker for clinical outcome. However, semen analysis in the human is currently limited to methods such as sperm counting and analysis of fixed cells. To address this, we have developed and released FAST, a free-to-use package for the high-throughput detection and tracking of large numbers of beating flagella in experimental microscopy videos. In this talk we will discuss how the combination of experimental data analysis, integrated with mathematical and numerical modelling of the elastohydrodynamic environment, can be utilised to understand the characteristics of flagellar motility in a semen sample. We will focus on what this means in the context of using clinical data from Birmingham Women’s Hospital, and international partners, in order to improve outcomes from assisted reproductive technologies.

Suzanne Jacobs UT Austin, United States, sjacobs@chaos.utexas.edu
"To Swarm or to Slide? Understanding the Mechanics of Bacterial Colony Expansion"

Whether in our guts or on our skin, on our medical devices or along the roots of our crops, microbes have always been an invisible part of human life. Now, thanks to advances in genomics technology, we can identify which microbes are where and understand how they influence human and environmental health. But to ever effectively manipulate these microbial ecosystems to our benefit, we must understand not only their composition, but also the physics of microbial surface colonization. In this talk, I will describe how colonies of the common soil bacteria Bacillus subtilis swarm and slide along surfaces and what we know about the forces that individual bacteria experience during these processes. Understanding such forces will be crucial to identifying the physical triggers that promote or inhibit various modes of surface colonization.

Bruce Rodenborn Centre College, United States, bruce.rodenborn@centre.edu
"Life at Low Reynolds Number in a Macroscopic Lab"

The swimming of microorganisms is typically analyzed using biological experiments or numerical simulations because of the difficulty of making microscopic measurements of forces and torques. Our research group uses model macroscopic experiments with typical length scales of ≈ 10 cm, but match the low Reynolds number of microoganisms by using a highly viscous silicone oil that is 105 more viscous than water but with approximately the same density. We can build laboratory scale robotic swimmers and model microorganisms that are typically ≈ 10 µm, while keeping the Reynolds much less than unity. We also explore fundamental theories such as building a laboratory scale three-link swimmer (Purcell 1977). We compare our laboratory experiments of helical flagella with complimentary numerical simulations and find good agreement. We also compare our results with theory from geometric mechanics, which predicts the translation and rotation of a three-link swimmer for a given gate.

ONCO: Frontiers in MathOnco, Part 1 (9:30-11:00am)

Morgan L. Craig Université de Montréal, Canada
"Leveraging patient-specific heterogeneity to establish effective immunotherapeutic protocols"

Cancer is an intrinsically heterogeneous disease distinguished by disparate outcomes based on cancer types, patient-specific characteristics, and treatment modalities. Further complicating this picture, therapeutic resistance poses a major challenge to the design and implementation of effective cancer treatments. To overcome these hurdles, it is crucial to characterize heterogeneity within and around the tumour and to quantify the effects that neighbouring tumour and immune cells have on therapeutic success. In contrast to generalized and cytotoxic chemotherapies, immunotherapies aim to harness an individual’s immune system to elicit a targeted immune response and hopefully provide durable therapeutic benefits. Unfortunately, recent disappointing trial results for a variety of immunotherapies stress the need for a more tailored approach to immunotherapeutic scheduling that takes into account patient-specific heterogeneity and the potential for developing resistance. In response, quantitative approaches provide a way to test therapeutic protocols before they are used in patients, ultimately reducing bottlenecks along the drug development pipeline, rationalizing therapeutic scheduling, and improving patient outcomes. Here I will discuss two recent projects focused on establishing effective therapeutic protocols for mono- and poly-oncolytic virus treatments. Using mathematical and computational modelling, we constructed models that recapitulated realistic patient cohorts to study combined vaccinia and vesicular stomatitis oncolytic viruses, and to understand the impact of the tumour microenvironment in glioblastoma multiforme (a deadly central nervous system tumour) on oncolytic virotherapy penetration and efficacy. In both cases, we showed that therapeutic success was principally determined by tailoring treatment to underlying patient characteristics, including tumour aggressivity and spatial structure. Our results highlight the relevance of quantitative approaches to pre-clinical development and therapeutic design, and underline the impact of inter- and intra-individual variability on treatment outcomes.

David Basanta Moffitt Cancer Center, Tampa, USA
"Innocent bystander? The role of stromal cells in cancer evolution and treatment resistance"

Much work on cancer’s evolutionary dynamics is focused on the genetic mutations that characterize the different stages of cancer progression or the competition between different clones as the tumor grows and copes with different treatment options and schedules. Those evolutionary dynamics are shaped by the tumor ecosystem that, in the context of skeletal cancers, include cells such as osteoclasts, osteoblasts, macrophages and mesenchymal stem cells. Those cells perform a variety of roles in a normal bone and also have an impact on cancer. In this talk I will describe mathematical models that allow us to understand the role of those cells in the normal bone, which is a key step to uncover how they can be co-opted by a tumor and what role do they play as the tumor grows and undergoes treatment.

Kaitlyn Johnson University of Texas at Austin, USA
"Towards an integrated framework for incorporating multimodal data sets into mechanistic models of treatment response dynamics in cancer"

In the field of mathematical oncology, we commonly look to longitudinal data to calibrate and validate models of tumor progression. Longitudinal data allow for precise model fitting and parameter estimation which can be used to predict tumor behavior. However, molecular level data, although often available at few snapshots in time, is what biologists and clinicians typically use to better understand underlying disease biology in both experimental and clinical settings. While the quantitative nature of these snapshot data sets has vastly improved with technologies such as single cell RNA sequencing (scRNAseq), there exists a need for integrating snapshot and longitudinal data into mathematical frameworks in order to develop the most informed models to describe and predict cancer progression. In this work, we integrate longitudinal drug-response data with snapshot scRNAseq data at just three times points, thus calibrating model outputs to experimental data for two distinct modes of data. We demonstrate that direct incorporation of high-resolution scRNAseq snapshot data into the parameter estimation improves the identifiability of the mathematical model and its predictive power. We present this work as an example of how mathematical oncology can develop novel workflows for incorporating the available biological data to better understand cancer treatment response.

Khaphetsi Joseph Mahasa Lesotho
"Mesenchymal stem cells used as carrier cells of oncolytic adenovirus results in enhanced oncolytic virotherapy"

Mesenchymal stem cells (MSCs) loaded with oncolytic viruses are presently being investigated as a new modality of advanced/metastatic tumors treatment and enhancement of virotherapy. MSCs can, however, either promote or suppress tumor growth. To address the critical question of how MSCs loaded with oncolytic viruses affect virotherapy outcomes and tumor growth patterns in a tumor microenvironment, we developed and analyzed an integrated mathematical-experimental model. We used the model to describe both the growth dynamics in our experiments of firefly luciferase-expressing Hep3B tumor xenografts and the effects of the immune response during the MSCs-based virotherapy. We further employed it to explore the conceptual clinical feasibility, particularly, in evaluating the relative significance of potential immune promotive/suppressive mechanisms induced by MSCs loaded with oncolytic viruses. We were able to delineate conditions which may significantly contribute to the success or failure of MSC-based virotherapy as well as generate new hypotheses. In fact, one of the most impactful outcomes shown by this investigation, not inferred from the experiments alone, was the initially counter-intuitive fact that using tumor-promoting MSCs as carriers is not only helpful but necessary in achieving tumor control. Considering the fact that it is still currently a controversial debate whether MSCs exert a pro- or anti-tumor action, mathematical models such as this one help to quantitatively predict the consequences of using MSCs for delivering virotherapeutic agents in vivo. Taken together, our results show that MSC-mediated systemic delivery of oncolytic viruses is a promising strategy for achieving synergistic anti-tumor efficacy with improved safety profiles.

POPD: Stochastic Population Dynamics (9:30-11:00am)

Fima C. Klebaner Monash University
"Appearance of random initial conditions in the Wright-Fisher model"

We consider the Wright-Fisher model with a positive selection parameter and a small di↵usion co- e cient. When the starting point is near zero, and the time goes to infinity appropriately as the noise goes to zero, we show that the approximating solution follows the logistic equation with a random initial condition. This condition has the form H(W), where H(x) is the scaled limit of the deterministic flow, and W is the long time limit of the approximating Feller di↵usion. This is joint work with J. Baker and K. Hamza (Monash University) and P. Chigansky (Hebrew University). More general results appeared in the paper “Persistance of small noise and random initial conditions” Adv. Appl. Probab. 2018, 50(A).

Sophie Hautphenne Univeristy of Melbourne
"Inference in population-size-dependent branching processes"

Population-size-dependent branching processes (PSDBPs) are models which describe the evolution of populations where individuals in the same generation give birth independently according to a probability distribution which depends on the current population size. One important class of PSDBPs are branching processes with a carrying capacity; these are appropriate for modelling populations that exhibit logistic growth, where the population size tends to fluctuate, for a long period of time, around a threshold value corresponding to the maximum number of individuals that an ecosystem can support. We propose an estimator for the mean of the o↵spring distribution at each population size in a discrete- time PSDBP, based on the observation of the total population sizes up to some generation. Our main challenge is the fact that branching processes with a carrying capacity eventually become extinct with probability one (after a long time). We propose a way to derive asymptotic properties of the estimator in this setting. This leads to a number of questions about desired properties of estimators in branching processes that almost surely become extinct. (Joint work with Peter Braunsteins and Carmen Minuesa Abril.)

Carmen Minuesa Abril Autonomous University of Madrid
"Estimation of the carrying capacity in a population-size-dependent branching process"

In this talk we deal with the estimation of the parameters of branching processes with a carrying capacity, which is the maximum population size of the species that the environment can sustain given the resources available in the environment. In these processes, the population size grows logistically and lingers for a long period of time around the carrying capacity before eventually becoming extinct. We consider discrete-time branching processes with a carrying capacity and assume that the offspring distributions belong to some parametric family with unknown parameter. Based on the observation of the population sizes, we propose several estimators for the target parameters, and in particular, for the carrying capacity. Finally, we illustrate the properties of these estimators via some examples. (Joint work with Peter Braunsteins and Sophie Hautphenne.)

Göran Högnäs Åbo Akademi University
"Exit times of some nonlinear autoregressive processes"

We know from Klebaner and Nerman that certain size-dependent branching processes are well approximated by autoregressive processes, at least in the short run. Our aim is to estimate the exit time of some nonlinear autoregressive processes and hereby gain insight into the problem of determining the expected life time of the corresponding size-dependent branching process. Let {Xn}, n = 0, 1, 2, . . ., be a stochastic process defined by the recursion formula Xn+1 = f(Xn)+ e C n+1, X0 = 0 in Rd where f is a mapping from Rd to itself and the C’s are a sequence of i.i.d. normal random variables. e is a small nonnegative parameter. We assume that f(0) = 0 and that f is in some sense contracting so that the resulting Markov chain is positive recurrent. In the one-dimensional case we take f to be, for example, a piecewise linear function or a piecewise polynomial. The aim is to investigate, asymptotically as e goes to 0, the expected time until the process exits from the interval [-1,1]. In the case of linear autoregressive processes the asymptotics of the expected exit times was treated in Jung. (Joint work with Brita Jung.)

15 minute break (11:00-11:15am)

Sub-group minisymposia (11:15am)

CDEV: Modeling dynamics in single-cell biology (11:15am-12:45pm)

Laleh Haghverdi Max Delbruck Center for Molecular Medicine, Berlin
"Cell lineage trajectories and pseudotime reconstruction from single-cell transcriptomics"

The reconstruction of cell lineage trajectories from single-cell transcriptomics allows us to resolve temporal expression dynamics of several genes from snapshot collected data. The temporal order of gene activities in return, can provide new insights into the gene regulatory networks governing cell differentiation. We adapted a dimension-reduction technique called “diffusion maps” for the analysis and reconstruction of cell differentiation trajectories. We perceived cell differentiation as a diffusion-like process, where cells are gradually and to some extent stochastically changing their gene expression profiles as they proceed to more differentiated molecular states. Thus, cell differentiation dynamics can (in discrete form) be described by: p(t) = p(t − 1) * T. That is, the probability distribution at the position of each sampled cell at time t, p(t) is given by the probability distributions at time (t − 1) multiplied by the cells’ pairwise transition probabilities matrix T. Thus, p(t) and p(t − 1) are vectors of length N (number of cells) and T is an N by N matrix which accommodates: 1) transition probabilities which are purely based on geometrical distances between the cells, 2) directional transition probabilities towards more differentiated cell states and 3) source/sink probabilities for accounting for cell’s prolifereation/death rates. Considering purely geometrical transition probabilities, Tgeom is a row-normalised positive-definite matrix which characterises the manifold on which cell differentiation is taking place in the high-dimensional gene expression space. The complete process (i.e., including directional and source/sink diffusion terms) thus, describes different dynamics taking place on that same manifold. Because of this resemblance to a diffusion process, we introduced an adaptation of diffusion maps for data embedding and differentiation trajectories reconstruction from single-cell data. In a simple form, data embedding by diffusion maps is given by the first eigenvectors of Tgeom corresponding to it largest eigenvalues. We extended the diffusion map’s framework to define “pseudotime” quantifying the differentiation stage of each cell based on on-manifold diffusion distances from the root (pluripotent) cell state. Fur- thermore, we showed that differentiation branching events can be identified by application of the triangle inequality to the on-manifold distances. The diffusion metrics with new approaches for inclusion of directional and source/sink probabilities (infered from biologically known differentiation terminal points, spliced/unspliced mRNA comparisons, time-lapse measurements for a few genes) has been used in several trajectory reconstruction methods on exceedingly complex manifolds which I will briefly discuss in my presentation.

Adam MacLean University of Southern California
"Inferring the structure and parameters of cell lineage models from single-cell data"

Since single-cell RNA sequencing technologies have become widespread, great efforts have been made to develop appropriate statistical methods to learn biological features from high dimensional data. Lag- ging behind are efforts to combine dynamical systems models with single-cell data. The existence of transient or intermediate cell states – corresponding to shallow attractor states on a potential landscape – further confounds the development of simple models. Here we present new approaches to address these challenges. We propose methods to infer both model structure and model parameters of cell lineage models using single-cell RNA-sequencing data. We fit model structure by assuming a core set of cell population dynamic processes, i.e. a general system described by ẋ(t) = (αf (x) − δ)x(t), where x(t) is a vector of cell states, α and δ are cell state-specific proliferation and death rates, and f (x) is a feedback function. We use methods for trajectory and cell-cell communication inference to infer lineage relationships and feedback interactions. Taking advantage of the information present in the pseudotemporal ordering of cells, we perform Bayesian parameter inference: that is we fit the model to “pseudo-dynamics” to constrain the parameters. With application to hematopoiesis, we demonstrate the ability to select between models and predict future cell differentiation dynamics. We will discuss how this model inference framework can also be applied to gene regulatory network dynamics, enabling not only the simulation of single-cell data-derived models, but also the characterization of their stable steady states and bifurcations.

Caleb Weinreb Harvard University
"Limits on dynamic inference from single-cell RNA-seq and the case for additional measurements"

For decades, biologists have dreamed of building dynamical systems models of gene expression that could be used to understand and predict cell state. High-throughput single-cell analysis has brought the dream closer. It is now possible to sample cell states in high-dimension and to map trajectories through continuous gene expression space. Using prior knowledge or measurements of RNA maturity, the general direction of cell progression along these trajectories can be inferred. Yet it remains unclear to what extent single-cell RNA-seq encodes a unique dynamical system over cell state. Here, I will discuss two key obstacles to inferring cell state dynamics from single-cell RNA seq data, and how additional types single-cell measurements might overcome them. First, applying the principle of population reveals the importance of measuring cell proliferation and death rates for accurately inferring cell dynamics. Second, clonal tracing using DNA barcoding reveals that RNA-seq alone cannot distinguish cells with different cell-autonomous fate biases, emphasizing the need to measure other variables such as chromatin state.

Heyrim Cho University of California at Riverside
"Modeling cell state dynamics of Hematopoiesis from single-cell gene sequencing data"

Recent advances in single-cell gene sequencing data and high-dimensional data analysis techniques are bringing new opportunities in modeling biological systems. In this talk, I will discuss different approaches to develop mathematical models from high-dimensional single-cell data. In particular, single-cell RNA sequencing data is challenging due to its high-dimensionality, and dimension reduction techniques are essential in finding the trajectories of cell states in the reduced differentiation space. We develop models using differential equations that describe the cell differentiation as directed and random movement on the abstracted graph or on the multi-dimensional reduced space. Normal hematopoiesis differentiation and abnormal processes of acute myeloid leukemia (AML) progression are simulated. We show that the model can predict the emergence of cells in novel intermediate states of differentiation consistent with immunophenotypic characterizations of AML, and compare the pros and cons of the models on the graph and on the multi-dimensional reduced space.

MEPI: COVID-19 Contributed Talks I (11:15am-12:45pm)

Alun Lloyd North Carolina State University
"Bidirectional contact tracing dramatically improves COVID-19 control"

Contact tracing is critical to controlling COVID-19, but most protocols only “forward-trace” to notify people who were recently exposed. Using a stochastic branching-process model, we show that “bidirectional” tracing to identify infector individuals and their other infectees robustly improves outbreak control, reducing the effective reproduction number (Reff) by at least ~0.3 while dramatically increasing resilience to low case ascertainment and test sensitivity. Adding smartphone-based exposure notification can further reduce Reff by 0.25, but only if nearly all smartphones can detect exposure events. Our results suggest that with or without digital approaches, implementing bidirectional tracing will enable health agencies to control COVID-19 more effectively without requiring high-cost interventions.

Grzegorz Rempala Ohio State University
"Dynamical Survival Analysis for COVID-19 Predictions in Ohio"

Over the last several weeks many mathematicians, statisticians and data scientists have found themselves involved with various efforts in response to the public health crisis caused by the COVID-19 pandemic. Did predictive modeling really help with COVID preparedness and decision making? Following up on my earlier lectures on the topic over the summer, I will try to give a perspective of how various mathematical methods turned out to work (or not) in practical settings of the daily predictions of the pandemic size in Ohio. In particular, I will briefly outline some new ideas and possible improvements in the methodology of 'dynamic survival analysis' developed by the OSU COVID response team to help predict COVID hospital burden.

Adeshina Adekunle James Cook University
"Delaying the COVID-19 epidemic in Australia: Evaluating the effectiveness of international travel bans"

Following the outbreak of novel Severe Acute Respiratory Syndrome Coronavirus-2 (SARS-CoV-2), and the disease named COVID-19, in Wuhan, China in late 2019, countries have implemented different interventions such as travel bans to slow the spread of this novel virus. This brief report evaluates the effect of travel bans imposed to prevent COVID-19 importation in the Australian context. We developed a stochastic meta-population model to capture the global dynamics and spread of COVID-19. By adjusting our model to capture the travel bans imposed globally and in Australia, the predicted COVID-19 cases imported to Australia were evaluated in comparison to observed imported cases. Our modelling results closely aligned with observed cases in Australia and elsewhere. We observed a 79% reduction in COVID-19 importation and a delay of the COVID-19 outbreak in Australia by approximately one month. Further projection of COVID-19 to May 2020 showed spread patterns depending on the basic reproduction number. Imposing the travel ban was effective in delaying widespread transmission of COVID-19. However, strengthening of the domestic control measures is needed to prevent Australia from becoming another epicentre.This report has shown the importance of border closure to pandemic control.

David JD Earn McMaster University
"1918 vs 2020: Influenza vs COVID-19"

Comparisons are constantly being made between the 1918 influenza pandemic and the present COVID-19 pandemic. I will discuss our previous work on influenza pandemics, and and the tools we have used to understand the temporal patterns of those outbreaks. Applying similar tools to the COVID-19 pandemic is easier in some respects and harder in others. I will describe our current approach to modelling the spread of COVID-19, and some of the challenges and limitations of epidemic forecasting.

MFBM: Simulations and Experiments in Small Scale Bio-Locomotion (11:15am-12:45pm)

Madeleine Hall Imperial College London, United Kingdom, madeleine.hall17@imperial.ac.uk
"Optimal Turning Gaits for Undulators"

An organism’s ability to efficiently traverse and search their surroundings can be important to its survival. This has inspired the study of optimal gaits and locomotion strategies, in particular for the case of undulatory movement of slender bodies. The primary focus has been on finding optimal waveforms for moving forwards along straight paths. However, the ability to turn and manoeuvre is also relevant to survival. We revisit this problem in the context of low Reynolds number hydrodynamics and obtain the optimal waveforms for undulators along curved trajectories. For shallow turning angles, we obtain small perturbations of a travelling wave as optimal. For larger turning angles, however, the optimal gait can be radically different, with the undulator abruptly curling and uncurling itself. We believe that these results can lend insight into the search behaviours of simple organisms, such as C. elegans, as well as be a tool for phenotyping their behaviour across mutant strains and under different environmental conditions.

David Smith University of Birmingham, United Kingdom, D.J.Smith@bham.ac.uk
"Algorithmic Developments in the Method of Regularized Stokeslets for the Study of Micro-Locomotion"

Microscopic swimming and propulsion due to cilia and flagella are characterised by complex shaped moving boundaries, and for Newtonian fluids, the linear Stokes flow equations. These features of the problem have motivated the development of methods based on singularity distributions (Stokeslets/Oseen tensors). In recent years the methods of regularized Stokeslets has become widely used in biological fluid dynamics; this technique avoids the need for generation of a connected surface mesh, removes the need to compute singular integrals, and therefore is very convenient and accessible. This talk focuses on some algorithmic refinements to the method of regularized Stokeslets aimed at improving the efficiency of the method while retaining the convenience and accessibility of the method. We discuss (1) the use of meshless interpolation, in particular the nearest-neighbour discretisation, (2) exploitation of graphical processing unit computing to handle relatively large problems through built-in linear algebra routines in Matlab, (3) the NEAREST software package in Matlab, and benchmarking against a compiled Fortran code. The focus will be on providing practical and reliable tools for the quantitative biology of microscopic motility.

Hoa Nguyen Trinity University, United States, hnguyen5@trinity.edu
"Effects of Cell Morphology, Attachment to a Surface, and Colony Formation on the Hydrodynamic Performance of Choanoflagellates"

Choanoflagellates, eukaryotes that are important predators on bacteria in aquatic ecosystems, share a common ancestor with sponges and are used as a model system to study the evolution of animals from protozoan ancestors. The choanoflagellate Salpingoeca rosetta, which has a complex life cycle that includes unicellular and multicellular stages, provides a model system to study within one species the functional consequences of: 1) different cell morphologies (swimming cell with a collar of prey- capturing microvilli surrounding a single flagellum; dispersal-stage cell with a slender body, long flagellum, and short collar), 2) being free-swimming vs. sessile (thecate cell attached to a surface), and 3) being a single cell vs. a multicellular colony. For model organisms of different life stages, we use the method of regularized Stokeslets to examine the effects of different morphological features on swimming and feeding performance. We compare the model predictions with lab experiments that used high-speed microvideography to measure swimming and feeding currents produced by different life stages. We find that a longer flagellum increases swimming speed, longer microvilli reduce speed, and cell shape only affects speed when the collar is very short. The flux of prey-carrying water into the collar capture zone is greater for swimming than sessile cells, but this advantage decreases with collar size. Stalk length has little effect on flux for sessile cells.

Genevieve O' Brien Johns Hopkins University, United States, gsteinobrien@jhmi.edu
"Decomposing cell identity for transfer learning across cellular measurements, platforms, tissues, and species"

Single cell RNA sequencing (scRNAseq) has lead to the discovery of new cell types. Thus, it is important to have methods to determine the identifying and consequential features of cells. To this end, we developed scCoGAPS to learn robust feature dimensions from scRNAseq and projectR to investigate these, or other continuous valued, feature dimensions in biologically related data across technologies, omics, and species. We demonstrate how this implementation of transfer learning via dimension reduction represent a platform for in silico experimentation and hypothesis generation where knowledge from multiple data sets is leveraged for selection of meaningful feature dimensions for validation.

ONCO: Frontiers in MathOnco, Part 2 (11:15am-12:45pm)

Mohit Kumar Jolly Indian Institute of Science, India
"Integrating mechanism-based and data-based approaches to identify hybrid epithelial/mesenchymal phenotypes"

Epithelial–mesenchymal transition (EMT) is a key driver of metastasis and therapy resistance. During EMT, cells lose their epithelial traits and acquire mesenchymal ones to varying degrees. Recent evidence has suggested that cells need not necessarily display 'pure' epithelial or mesenchymal states, but can stably acquire one or more hybrid epithelial/mesenchymal (E/M) ones. In silico, in vitro and in vivo analysis indicates that these hybrid E/M states can be more aggressive and perhaps the 'fittest' for metastasis, thus identifying mechanisms enabling these hybrid E/M states is crucial for decoding tumor aggressiveness. Using an integrative approach involving mechanism-based models to identify master regulators of such hybrid E/M phenotypes, data-based models to decipher transcriptomics signatures specific to the hybrid E/M phenotypes, and experiments to test our predictions, we have identified how these hybrid E/M cell states may be maintained via cell-autonomous and non-cell autonomous mechanisms. Our work also highlights that the hybrid E/M specific signatures associate with worse clinicopathological traits, thus offering a mechanistic basis for its aggressiveness and pinpointing novel putative targets.

Pamela Jackson Mayo Clinic, Phoenix, USA
"Parameterizing a Brain Tumor Growth Model Using Noisy Simulated MRIs"

Mathematical models of brain tumor growth are commonly parameterized using volumes of abnormal regions segmented from magnetic resonance imaging (MRI). For imaging-level brain tumor growth modeling, such as the Proliferation-Invasion (PI) model and its more complex variants, the abnormality region requires an assumption for the tumor cell density. This assumption is necessary to make estimates regarding the shape of the leading edge, however the use of an assumption can be limiting. Searching across MRI images that have been simulated across the model parameter space could eliminate the need for a cell density assumption, however noisy MRIs will reduce the reliability of such a technique. Our objective is to determine if matching the noise between simulations and MRIs can increase our ability to predict model parameters based on an image's characteristics. We generated phantom brain tumors using the Proliferation-Invasion-Hypoxia-Necrosis-Angiogenesis- Edema (PIHNA-E) model. One hundred unique phantoms were created assuming 10 different rates of migration (D [mm2/year]) and 10 different rates of proliferation ( [1/year])]. PIHNA-E simulations were then passed into a MRI signal model for generating simulated T2-weighted MRIs. We created two independent runs of six sets of 100 simulated MRIs, with each set incorporating a different level noise. The first run represented simulated images with known D and or 'ground truth', while the second run represented candidate 'real-world' noisy images for which we would have not normally known D and . We then compared each noise level from the second 'real-world' run to each noise level from the first 'ground truth' run. Within each set comparison, we calculated the L2-norm of twelve statistical features for each image in the second 'real-world' set relative to the 'ground truth' set of images. The D and of the 'ground truth' image with the lowest L2-norm relative to the 'real-world' image were selected as the predicted parameters. For each noise level, a prediction rate is calculated by assessing the percentage rate that the L2-norm-based selection was correct. As expected, the prediction rates decreased overall as the image noise level increased. For 'real- world' images with limited noise, creating a similar noise level in the 'ground truth' images did enable higher prediction rates of D and . Future directions of this work include repeating these methods across additional replicates and exploring processing steps for reducing MRI noise, which could increase our prediction rate of D.

Jeffrey West Moffitt Cancer Center, Tampa, USA
"Anti-fragile Cancer Therapy"

Herein we present a novel paradigm of evolutionary cancer therapy based on the 'anti-fragility' of the drug dose-response function. Anti-fragility is a situation where the curvature of the dose-response function is convex, mathematically defined as a positive second derivative. This positive curvature is associated with benefits from increased variance or unevenness of a treatment schedule. For example, if the curvature is positive near a dose of ‘x’, continuous administration of x may have a less efficacious response compared to a regimen that switches equally between 120% of x and 80% of x, even though both regimens use the same total drug. Although dose-response data is readily available, such second-order effects are typically ignored. Nonlinear sigmoidal dose-response curves are ubiquitous in medicine and have both convex and concave regions. Selection pressure due to treatment selects for resistant phenotypes over time. In response, the magnitude of dose response curvature and the convex-concave inflection point both decrease in value. The key insight is that dose-response convexity ('anti-fragility') decreases in proportion to the amount of resistance in the tumor population. This provides a time-dependent metric which 1) predicts the emergence of resistance and 2) determines the optimal subsequent dosing strategy. We demonstrate this paradigm using a Hill function model parameterized by in vitro experimental data of H3122 non-small cell lung cancer cell lines confronted to 10 different drugs. Through this dataset, we present antifragility applied to 1) treatment resistance, 2) collateral sensitivity, and 3) combination therapy.

Anna Marciniak-Czochra University of Heidelberg, Germany
"Stem cell niche dynamics in acute leukemia: Insights from mathematical modeling"

Acute myeloid leukemia (AML) is one of the most aggressive blood cancers. The cancer originates from a small population of so called leukemia stem cells (LSC) that survive treatment and trigger re- lapse. During the course of the disease leukemic cells accumulate in the bone marrow and impair healthy blood cell formation. The impact of this interaction on the clinical course of the disease remains not well understood. We develop and validate a mathematical model of stem cell competition in the human hematopoietic stem cell niche. Model simulations predict how processes in the stem cell niche affect the speed of disease progression. Combining the mathematical model with data of individual patients, we quantify the selective pressure LSC exert on HSC and demonstrate model's prognostic significance. We develop a novel model-based risk-stratification approach. This approach allows extracting prognostic information from counts of healthy and malignant cells at the time of diagnosis. We demonstrate its feasibility based on a cohort of ALDH-rare AML patients and show that the model-based risk strati- fication is an independent predictor of disease free and overall survival. This proof of concept study shows how model-based interpretation of patient data can improve prognostic scoring and contribute to personalization of treatment. The talk is based on joint works with Thomas Stiehl (Institute of Applied Mathematics, Heidelberg University), Wenwen Wang and Christoph Lutz (Heidelberg Medical Clinic).

POPD: (11:15am-12:45pm)

Swarnendu Banerjee Indian Statistical Institute, Kolkata
"Chemical contamination mediated regime shifts in planktonic systems"

Increasing chemical contamination is a growing concern worldwide. Although, regime shifts leading to algal blooms are quite well known in aquatic ecosystems, the effect of contamination on such regime shift is not particularly well understood. Motivated by this, we studied the effect of copper enrichment on planktonic system using a minimal phytoplankton-zooplankton model. Interestingly, our results suggest that both the toxic and deficient concentration of copper in water bodies can lead to catastrophic transition of the ecosystem to an alternative stable state. Further, on adding stochasticity to the system the region of bistability is diminished and the system switches from zooplankton dominated state to the phytoplankton dominated state much prior to the tipping point. The bistability is further weakened on increasing noise intensity and redness. However, in case of systems with high nutrient enrichment, the bimodality in the probability density can be very prominent. Nevertheless, generic early warning signals may fails to predict an impending state shift due to contamination. Our study provides important perspective to regime shifts in the context of eco-toxicology.

Jody Reimer University of Utah
"Long transient dynamics in the presence of noise"

Recent theoretical work has highlighted several mechanisms giving rise to so-called ``long transient'' dynamics. These long transients tantalizingly appear to replicate dynamics seen in real systems-with one critical difference: ecological data is noisy, a reality theoretical work often ignores. In general, stochasticity is known to have important consequences: it can qualitatively alter model dynamics as well as impact our ability to infer underlying processes through statistical analysis. To explore the effect of stochasticity on qualitative model behavior and the implications for our ability to infer underlying mechanisms, we generated time series from a simple model of long transient behavior with additive noise. We then examined if noise qualitatively changes the expected dynamics of the system and how well phenomenological and mechanistic statistical models could recover the underlying model. We found that long transients such as those generated by even the simplest stochastic model of a ghost attractor are highly sensitive to noise, and that the mean behavior of the stochastic model differs substantially from that of the deterministic model. In spite of this, we illustrate that statistical inference on a single realization may still provide insight into model parameters, and highlight that inference improves for an increasing number of realizations of the process. All approaches saw improved results with increasing data realizations. We suggest methods to increase our ability to draw inference from real ecological time series with suspected long transient dynamics.

Carlos A. Braumann Universidade de Evora
"General autonomous fishing models with Allee effects in a randomly varying environment"

In a randomly varying environment, a general fishing model is the stochastic differential equation dX(t) = f(X(t))X(t)dt+σX(t)dW(t)−qE(t,X(t))X(t)dt, where X(t) is the fished population size at time t, f (of class C1) is the per capita arithmetic average natural growth rate, σdW(t)/dt describes the effect of environmental fluctuations on the growth rate (with W(t) a standard Wiener process and σ > 0), E(t,X(t)) is the harvesting effort applied and q > 0 is the catchability. Here, we will consider autonomous models for which E(t, X(t)) ≡ E(X(t)) non-negative of class C1. The usual density-dependence case with f strictly decreasing and f(+∞) < 0 was studied in [1] w.r.t. conditions for population extinction or for existence of a stationary density. In [5, 6], for the particular cases of f being logistic or Gompertz, profit optimization was studied comparing variable effort E(t, X(t)) fishing policies with constant effort E(t, X(t)) ≡ E policies. Sometimes, however, the population under fishing is affected by Allee effects, with an unexpected depression (accompanied by growth) of f(x) for small values of x, due, for instance, to the difficulty of finding mating partners or of putting together an effective collective defence from predators. [4] made a comparative study between variable and constant effort policies for the particular case of f being logistic-like with Allee effects. In [2, 3], for populations not subjected to fishing and for general growth models f with Allee effects, conditions for extinction or for existence of a stationary density were studied. We are now generalizing this study, under appopriate conditions, to fished populations with general growth models f(·) with Allee effects and with also general autonomous harvesting efforts E(·). Again, we found out that the deciding factor between extinction or existence of a stationary density is the sign, when the population size is small, of the net (i.e., discounting the mortality rate due to fishing) geometric average per capita growth rate. The cases previously studied, as well as the gear saturation phenomenon, can be treated as particular cases.

Toni Klauschies Potsdam University
"Ecological and evolutionary causes of intermittent predator-prey cycles"

The presence of trait variation in prey or predator populations may affect the stability and the shape, i.e. amplitude and phase, of predator-prey dynamics. However, while previous studies have shown how trait variation can alter the overall amplitude of the predator-prey oscillations, this altered amplitude remained constant over time. This strongly contrasts with empirically observed predator-prey dynamics and recent theoretical work, showing that several mechanisms may lead to so called intermittent predator- prey cycles where the amplitude of the predator-prey dynamics varies temporally. For instance, trait differences that determine the functional responses of two predators may provoke temporal fluctuations in the amplitudes of the predator-prey cycles due to recurrent changes in the relative abundance of the two predator types: a predator with a relatively linear functional response promotes small-amplitude oscillations whereas a predator with a more strongly non-linear functional response stimulates larger amplitudes. We analysed various models that incorporate trait variation within prey, predators, or both, and identified three general conditions that are necessary for intermittent cycles to occur. First, the predator-prey system comprises at least two subsystems that exhibit substantial differences in the amplitude of their population dynamics and thus tendency to promote stable or unstable population dynamics. Second, these subsystems recurrently alternate in their dominance, leading to a second “trait” cycle superimposed on the population dynamics. Finally, the time scale of the trait dynamics must be significantly slower than that of the population dynamics. For instance, co-evolution may promote intermittent cycles in predator-prey dynamics by inducing a lag in the predators’ trait adjustment in response to altered trait values of the prey. The resulting temporal variation in the interaction strength between predator and prey is associated with temporal changes in the amplitudes of the population dynamics since e.g., a dominance of defended prey dampens the population dynamics whereas a high abundance of undefended prey enhances it. Our results highlight that intermittent cycles may frequently occur in simple predator-prey systems allowing for trait variation.

Mentoring Luncheon

Sub-group contributed talks (1:30-2:30pm)

CDEV: Subgroup Contributed Talks (1:30-2:30pm)

Nathan Weinstein UNAM
"A computational model of the differentiation of endothelial cells into macrophages"

Endothelial cells (ECs), macrophages (MPs), and pericytes are the main cellular components of microvascular networks. The principal process that allows microvascular network remodeling and adaptation is angiogenesis. Angiogenesis begins when hypoxia or lack of nutrients triggers the release of a vascular endothelial growth factor (VEGF), which is typically VEGFA. The VEGF forms a gradient, and when the concentration of VEGF reaches a threshold around a segment of the blood vessel, it causes the segment to destabilize and to lose its mural cells. During the subsequent stage of sprouting angiogenesis, some of the ECs become tip cells that extend filipodia and migrate following the VEGF gradient. The ECs adjacent to the tip cells become stalk cells that elongate, proliferate, and trail the tip cell. Once the tip cell reaches another tip cell or blood vessel segment, an anastomosis forms establishing a new connection in the microvascular network. During anastomosis formation macrophages act as chaperones for the tip cell. Additionally, macrophages phagocytize the ECs that undergo apoptosis during microvascular pruning. Definitive hematopoiesis occurs first during early embryogenesis when a group of endothelial cells undergo the endothelial-to-hematopoietic transition (EHT) and become hematopoietic stem cells (HSC). Some of the HSCs become granulocyte monocyte precursor cells (GMPs). Certain GMPs differentiate into monocytes, and macrophages differentiate from monocytes. In adult humans, ECs retain the capability to undergo EHT and we aim to study the potential of ECs to differentiate into macrophages and to elucidate the extracellular microenvironmental conditions that promote EC-to-macrophage differentiation. Our approach is to first assemble a molecular regulatory network based on the information available in the literature about the main molecules involved in the regulation of the process and the interactions between them. Then we will transform the model into a dynamic system in the form of a Boolean Network. Then, we simulate and analyze the dynamic behavior of the model. Afterward, we will validate the model by comparing the observed effect of the available relevant mutations with their simulated effect.

Aden Forrow University of Oxford
"Learning developmental trajectories from CRISPR lineage tracing and single-cell gene expression"

Recent research has shown that the mathematical theory of optimal transport can effectively reconstruct developmental trajectories from time courses of single cell gene expression; however, this approach requires expensive experiments with fine time resolution. In this work, we present a novel framework that leverages new types of lineage-tracing information measured simultaneously with gene expression. These experimental techniques use heritable CRISPR-induced genetic barcodes to trace the history of cell divisions over the course of development. Crucially, these barcodes can be measured in the same cells as gene expression. Our method, designed for lineage-tracing time courses, learns from both kinds of information together using mathematical tools from graphical models, structural equation models, and optimal transport. We find that lineage data improves optimal transport’s effectiveness in disentangling complex state transitions with lower temporal resolution, thereby reducing experimental cost. Joint work with Geoffrey Schiebinger (University of British Columbia)

Claus Kadelka Iowa State
"Unraveling the Design Principles of Gene Regulatory Networks: a Meta-Analysis"

Gene regulatory networks (GRNs), frequently modeled using Boolean networks, describe how a collection of genes governs the processes within a cell. Boolean networks are intuitive, simple to describe, and yield qualitative results even when data is limited. This talk will outline a research program aimed at harnessing the collective knowledge contained in hundreds of diverse Boolean GRN models in order to understand the impact of network structure and topology on network dynamics and stability, and in particular the role of canalization in gene regulation. The biological term canalization reflects a cell’s ability to maintain a stable phenotype despite ongoing environmental perturbations. Accordingly, Boolean canalizing functions are functions where the output is already determined if a certain, canalizing variable takes on its canalizing input, regardless of all other inputs. Using text- and data-mining techniques and the PubMed search engine, we generated an expandable database of published, expert-curated Boolean GRN models, and extracted more than 5, 000 rules governing these networks. A meta-analysis of all these rules confirmed a strong overrepresentation of certain types of canalizing functions. We also studied the abundance of small structures within the networks, called network motifs, and found significant differences between published GRNs but also when comparing to random networks. Furthermore, we analyzed the dynamical robustness of GRNs and found most of them to operate at a “critical threshold” between order and chaos. These findings highlight how our continuously-expanding database provides a versatile tool to identify the overarching design principles underlying gene regulation.

MEPI: Subgroup Contributed Talks (1:30-2:30pm)

Vijay Pal Bajiya Rajasthan University
"The Impacts of Awareness and Medical Resources on Multi-group SIR Epidemic Model"

When an infectious disease occurs and spreads in a community, then the government department of disease control tries every conceivable afford to avoid and prevent disease transmission. The treatment of infective individuals is a signficant method to reduce infection risk and control the spreads of infectious diseases. In this work, we propose an SIR multi-group epidemic model with the awareness of susceptible population and saturated treatment function, which describes the effects of the availability of medical resources for treatment. We assume that treatment of the infected individuals of a group is affected by the medical resources for the treatment of each group. The basic reproduction number R0 is computed. The local and global stability of equilibrium has been determined in the term of R0 and availability of medical resources for treatment. The occurrence of backward bifurcation have been discussed at R0 = 1 and the existence of multiple endemic equilibria when R0 < 1: The global stability of unique endemic equilibrium has been showed with help of some graph-theoretic techniques when R0 > 1: Finally, numerical simulations of the system are also presented in various cases to support and counterpart the obtained theoretical results. We discussed the impacts of the awareness of the susceptible population and the availability of medical resources for treatment in every group on the epidemic size of each group.

Evan Mitchell Western University
"The Effect of Host Prophylactic Behaviour on Pathogen Evolution"

Much work has considered the evolution of pathogens, but little is known about how they respond to changes in host behaviour. We build a model of sublethal disease effects where hosts are able to choose to engage in prophylactic measures that reduce the likelihood of disease transmission (e.g., hand washing, social distancing). This choice is mediated by utility costs and benefits associated with prophylaxis, and the fraction of hosts engaged in prophylaxis is also affected by population dynamics. When prophylactic host behaviour occurs, we find that the level of pathogen host exploitation is reduced, by the action of selection, relative to the level that would otherwise be predicted in the absence of prophylaxis. Our work emphasizes the significance of the transmission-recovery trade-off faced by the pathogen and the ability of the pathogen to influence host prophylactic behaviour.

Jeremy D'Silva University of Michigan / Stanford University
"Identifiability of linear compartmental models of infectious disease transmission"

Successful parameter estimation for mathematical models generally requires that the estimated parameters are unique. The property of unique estimates for a given output trajectory is called structural identifiability: a system is globally (resp. locally) structurally identifiable if the map from parameters to output trajectories is injective (resp. has finite fibers). Identifiability is especially important for infectious diesease models, since the parameter estimates are used for generating predictions and comparing outbreak intervention strategies. In this paper, we apply differential algebra techniques to study the structural identifiability of multistage infectious disease models (generalizations of the $SEIR$ model with multiple $I$ stages). We prove that these models are not structurally identifiable from incidence data, and we determine the rational functions of parameters that can be estimated from incidence data, called identifiable combinations, for the case where each $I$ stage has equal duration. We conjecture the identifiable combinations of the general model; we provide computational evidence for the conjecture and verify it for models with 2 infectious stages.

MFBM: Subgroup Contributed Talks (1:30-2:30pm)

Jinsu Kim University of California, Irvine
"Stochastic epigenome systems under inflammatory signals and its application to study vivo nucleosome accessibility"

In cellular immune responses, inflammatory ligands activate signal-dependent transcription factors (SDTFs), which can display complex temporal profiles. SDTFs are central effectors for inflammatory gene expression, and hence they serve a critical role in immune system. The information contained in SDTF signals must also be decoded by the epigenome to allow controlled plasticity in cellular epigenetic states in response to environmental encounters. The mechanisms and biophysical principles that generate distinct epigenomes in response to different SDTF signaling remain unclear. Here, we develop and analyze stochastic models of nucleosome accessibility to study how SDTF signals alter the epigenome dynamics. Interestingly the response of our epigenome model to SDTF signals helps us to predict the system parameters of genome-scale nucleosome in vivo. On the genome-scale, the relation between the SDTF binding location and nucleosome accessibility plays a role of a parameter predictor since the epigenome dynamics depends on SDTF binding sites differently under various parameter regimes. We could compare our numerical results to experimental measurements to test our prediction. Our work proposes a systematic framework that allows a predictive understanding in vivo nucleosome accessibility.

Alan Rendall Johannes Gutenberg Universitat Mainz
"Autophosphorylation as a source of multistability."

Src kinases, which have many functions in cell biology, are known to undergo autophosphorylation in trans. This means that the phosphorylation of a site on the kinase is catalysed by another molecule of the same enzyme. This type of phosphorylation can lead to new phenomena. The usual model of the phosphorylation of a protein on a single site is known to admit only one steady state. In the work reported on here it is proved that in the case of a site which is subject to autophosphorylation there can be more than one stable steady state. Thus a substance of this type can serve as a switch. Src kinases such as Lck, which is involved in many processes in lymphocytes, have two tyrosine phosphorylation sites but a form of Lck in which one of these sites (Y394) has been knocked out has been studied experimentally. It represents a known substance to which the model we have studied is applicable. This work is intended as a step towards a better understanding of the regulation of the activation of Lck, and thus of the function of lymphocytes. This type of insight has the potential to improve cancer immunotherapy.

Thomas Hillen University of Alberta
"Non-local models for cellular adhesion"

Cellular adhesion is one of the most important interaction forces between cells and other tissue components. In 2006, Armstrong, Painter and Sherratt introduced a non-local PDE model for cellular adhesion, which was able to describe known experimental results on cell sorting and cancer growth. Since then, this model has been the focus of applications and analysis. The analysis becomes challenging through non-local cell-cell interaction and interactions with boundaries. In this talk I will present theoretical results of the adhesion model, such as a random walk derivation, biologically realistic boundary conditions, pattern formation and results on local and global existence of solutions.

ONCO: Subgroup Contributed Talks (1:30-2:30pm)

Adam Malik Chalmers University of Technology, University of Gothenburg
"Modelling glioblastoma growth and invasion using Diffusion Tensor Imaging-data"

Many human cancers are studied using xenograft mouse models, in which human cancer cells are transplanted into mice. This constitutes a versatile tool, where various imaging modalities can reveal the dynamics of tumour progression, and novel drug targets can be investigated. However, this research occurs at expense of animal su ering. With the advent of high-performance computing and increasing knowledge of cellular and physiological processes the opportunity arises to replace in vivo mouse models with computational models that describe the growth of the tumour and its interactions with the host animal. We have developed a computational model of glioblastoma, a malignant form of brain tumour, which utilises data from Di usion Tensor Imaging (DTI) to represent anatomical structures within the model. The model takes into account a DTI-map obtained from adult normal mouse brains. The corresponding di usion tensor encodes information about nerve bre direction and density, and is therefore assumed to in uence cancer cell migration. In contrast to previous DTI-models we consider a cell-based model, where each cancer cell resides within a voxel (of volume 40 x 40 x 40 m3), which, due to volumetric constraints can contain a maximum of K cells. If the local density is below K each cell divides with at a rate α placing the daughter cell in the same voxel. Cell migration occurs with a rate Davg, which is the average value of the diffusion tensor, into one of the 6 neighbouring voxels, where the probability of moving to each neighbouring cell depends on the di usion tensor. A parameter, which ranges from 0 to 1, controls the impact of the di usion tensor, such that q = 0 corresponds to random migration and cells ignoring the anatomical structure, whereas q = 1 results in cells always moving along the direction of largest di usion (i.e. along bres). Simulations are initiated with 10,000 cells at the site of injection and contain approximately 1 million cells upon termination. Our results show that the model can recapitulate both nodal and di use tumours seen in the mouse model depending on the model parameters. Currently we are estimating model parameters from xenograft tumours obtained from di erent patients with the aim of identifying patient-speci c di erences, which, in the future, could inform personalised treatments.

Emma Carrick Smith Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford
"Modelling the Clonal Evolution of Drug-Resistant Cells in Non-Small Cell Lung Carcinoma"

High levels of clonal heterogeneity in non-small cell lung carcinoma (NSCLC) and the selection of drug-resistant cells during treatment drive the evolution to unresponsive tumours to tyrosine kinase inhibitors (TKIs). Cell-autonomous effects such as genetic instability and non-cell-autonomous effects such as cancer therapies and their ability to induce resistance and the local cellular composition of the surrounding microenvironment are key elements promoting high levels of clonal heterogeneity in these evolving ecosystems. To understand the effects such features have on the prevalence of resistance at diagnosis and to predict the impact two-drug treatment protocols have on the level of resistance within the tumour during treatment, we have developed a stochastic Lotka-Volterra model of tumour growth incorporating four cell populations with varying levels of resistance to two drugs. The model incorporates both spontaneous and drug-induced resistance via mutations and employs population-dependent birth rates derived from a recent game-theory study to account for the effects of cellular interactions. The effect of the fitness of drug-resistant cells relative to drug-sensitive cells is also considered by incorporating both advantageous and deleterious mutation cases. We calculated the proportion of resistance in a tumour at diagnosis. The proportion of resistance is an increasing function of the mutation probability and cell turnover ratio with significantly larger proportions when mutations are advantageous as opposed to deleterious. At diagnosis, we introduced four treatment protocols applying either two TKIs with inhibitory effects or two cytotoxic drugs and observed the proportion of resistance in the tumour once it had reached a clinically relevant size. Our model demonstrates the relative fitness of drug-resistant cells to drug-sensitive cells, the ability for the drugs to induce resistance and sequential application of two TKIs results in a notable difference in the level of resistance in the tumour during treatment as opposed to when the drugs are applied simultaneously. These estimates of the size of the drug-resistant tumour cell population prior to and during two-drug treatment protocols can inform treatment strategies when combining two TKIs.

Arturo Araujo University of Roehampton
"Multi-Scale Model of Colorectal Cancer Initiation"

Colorectal cancer (CRC) is currently the fourth leading cause of cancer-related deaths in the world. Development of more effective treatments is hindered by gaps in our understanding of CRC initiation and evolution, as well as the limitations of in vitro and in vivo experimental techniques. Specifically, in CRC we don’t fully understand the role of initiation mutations on the subsequent evolution of the disease, making it unique to each patient and therefore limiting the efficacy of general treatments. To bridge this gap in our knowledge, we use computational techniques such as agent-based modelling, gene regulatory network and continuous mathematical techniques to integrate molecular and cellular scale information to explain tumour growth and evolution. One of the biggest challenges we face is that collecting biological data is not enough. We need to figure out which are the right methods to analyse and utilise the data. Specially in cancer research, there is an abundance of data in many scales, from molecular and cellular to epidemiological; but without the right tools, such as multi-scale models, most of it remains under-utilised. To tackle CRC initiation, where colon epithelium loses its homeostasis, it was important to first have a clear understanding of the normal case. We constructed a cell-based model of a healthy colon crypt, incorporating different biological data and choosing the appropriate modelling abstraction for each one. We decided that agent-based modelling would provide us with the emergent property of homeostasis, common throughout biology. Through the interaction of the elements, cells in this case, a global balance arises which was not programmed into the equation and which was then validated by biological data. We extended this model with gene-regulatory network techniques to create an in silico experimental environment in which the effects of oncogenic mutations can be investigated and analysed with unique granularity. We further incorporated molecular data within the agent-based model to suggest novel therapies that consider not only the tumour, but the complex cross-talk between cancer and the rest of the healthy colon. We are currently working on incorporating data from the impact of current treatments, with the goal of tailoring it to individual patients to help control their specific disease and prolong their life. We envision for multi-scale models in the computational sciences to enable a greater understanding of the dynamics and evolution of diseases such as CRC, helping us explore, understand and harness the complex biological landscape, as well as supporting the development of new clinical prevention and treatment interventions. Further, these techniques can be readily deployed in hospitals, and some of them have already, as an aid for the clinician to help make better decisions, minimise costs and maximise the patients’ quality of life.

OTHE: Other Contributed Talks (1:30-2:30pm)

Gemma_Massonis CSIS
"Structural Identifiability and Observability of Compartmental Models of the COVID-19 Pandemic"

The recent coronavirus disease (COVID-19) outbreak has dramatically increased the public awareness and appreciation of the utility of dynamic models. At the same time, the dissemination of contradictory model predictions has highlighted their limitations. If some parameters and/or state variables of a model cannot be determined from out-put measurements, its ability to yield correct insights – as well as the possibility of controlling the system – maybe compromised. Epidemic dynamics are commonly analysed using compartmental models, and many variations of such models have been used for analysing and predicting the evolution of the COVID-19 pandemic. In this paper we survey the different models proposed in the literature, assembling a list of 36 model structures and assessing their ability to provide reliable information. We address the problem using the control theoretic concepts of structural identifiability and observability. Since some parameters can vary during the course of an epidemic, we consider boththe constant and time-varying parameter assumptions. We analyse the structural identifiability and observability ofall of the models, considering all plausible choices of outputs and time-varying parameters, which leads us to analyse 255 different model versions. We classify the models according to their structural identifiability and observability under the different assumptions and discuss the implications of the results. We also illustrate with an example several alternative ways of remedying the lack of observability of a model. Our analyses provide guidelines for choosing the most informative model for each purpose, taking into account the available knowledge and measurements.

Cole Zmurchok Vanderbilt
"Mechanosensing can enhance adaptation to maintain polarity of migrating cells"

Migratory cells are known to adapt to environments that contain wide-ranging levels of chemoattractant. While biochemical models of adaptation have been previously proposed, here we discuss a different mechanism based on mechanosensing, where the interaction between biochemical signaling and cell tension facilitates adaptation. In this talk, we develop and analyze a model of mechanochemical-based adaptation consisting of a mechanics-based physical model coupled with the wave-pinning reaction-diffusion model for Rac GTPase activity. We use Local Perturbation Analysis to predict how cells adapt signaling parameters via feedback from mechanics to maintain polarity in response to chemoattractant levels. To confirm this prediction, we simulate the mechanochemical model in moving cells, demonstrating how mechanosensing results in persistent cell polarity when cells are stimulated with wide-ranging levels of chemoattractant in silico. These results demonstrate how mechanosensing may help cells adapt to maintain polarity in variable environments.

Thomas Fai Brandeis University
"Length regulation of multiple flagella that self-assemble from a shared pool of components"

The single cell biflagellate Chlamydomonas reinhardtii has proven to be a very useful model organism for studies of size control. The lengths of its two flagella are tightly regulated. We study a model of flagellar length control whose key assumption is that proteins responsible for the intraflagellar transport (IFT) of tubulin are present in limiting amounts. In the case of two simultaneously assembling flagella, regardless of the details of how the flagella are coupled, we find that the widely-used assumption of a constant disassembly rate is inconsistent with experimental results. We therefore propose a model in which diffusion gives rise to a length-dependent concentration of depolymerizer at the flagellar tip. This model is found to be consistent with experimental results and generalizes to other situations such as arbitrary flagellar number.

POPD: Subgroup Contributed Talks (1:30-2:30pm)

Meike Wittmann Bielefeld University
"A new maximum-likelihood method to infer factors influencing establishment success of introduced species"

One of the most important goals in conservation biology and in the biology of introduced and invasive species is to understand why some small populations persist while others go extinct. Several factors play a potentially important role: 1) demographic and environmental stochasticity, 2) Allee effects, i.e. a reduction in the per-capita growth rate in small populations, for example due to mate-finding difficulties, and 3) propagule size, i.e. the initial number of individuals. It is known that both Allee effects and environmental stochasticity affect the relationship between propagule size and persistence probability in specific ways. Here I propose a new approach for the joint inference of the contributions of these two factors. The approach is based on a Markov chain model for population size with environmental stochasticity and Allee effects. The models without Allee effects or without environmental stochasticity are special cases of the general model. Given a data set for the persistence or extinction of populations of various sizes, the model parameters are estimated using a maximum-likelihood approach and then model choice is performed based on Akaike's information criterion. Using simulation studies, I explore the strengths and weaknesses of this approach. Finally, I apply the approach to published data sets on experimental introductions in the field or laboratory.

Candy Abboud University of Glasgow
"Dating, localizing and predicting invasive-pathogen dynamics"

Prediction of invasive-pathogen dynamics is an essential step towards the assessment of eradication and containment strategies. Such predictions are performed using surveillance data and models grounded on partial differential equations (PDE), which form a framework often exploited to design invasion models. The framework allows the construction of phenomenological but concise models relying on mechanistic hypotheses. However, this may lead to models with overly rigid behaviour, in particular for describing phenomena in population biology. Hence, to avoid drawing a prediction relying on a single PDE-based model that would be prone to errors because of potential data-model mismatch, we propose to apply Bayesian model-averaging (BMA) for handling parameter and model uncertainties. Hence, we combine several competing spatio-temporal models of propagation for inferring parameters and drawing a consensual prediction of certain quantities of interest. This study is applied (i) to date and localize the invasion of Xylella fastidiosa, bacterium detected in Southern Corsica in 2015, France using post-introduction data, and (ii) to predict its future extent.

Bo Zhang Oklahoma State University
"Species competition in heterogeneous environments with directed movement"

Understanding the mechanisms that promote species coexistence is a central topic in ecology. Predicting coexistence in heterogeneous environments where populations are linked by dispersal is a challenge that has attracted attention of ecologists. A particular body of theory, based on Lotka-Volterra-like equations, has focused on the effects of different relative dispersal rates in the absence of other differences in competing species, and has predicted that the slower disperser always outcompetes the faster one in environments where the limiting resources are heterogeneously distributed. However, this theory has never been rigorously tested empirically, and has generally only considered random diffusion. Here, we extended previous theory to include exploitable resources and an additional component of directed movement, proving qualitatively novel results, which we tested experimentally using laboratory populations of C. elegans. We revealed, both theoretically and emperically, that stable coexistence can occur when two competing species have identical directed components but different diffusive components to their movement. Our results advance understanding of coexistence theory and has important ecological implications, such as the essential of individuals obtaining clues of neighboring environments, to determine where to disperse in changing environments.

Poster Session (2:30-3:30pm)

Click to view posters for each subgroup

Sub-group Keynote

3:30pm

Priyanga Amarasekare,
University of California Los Angeles

Population Dynamics, Ecology, & Evolution Subgroup

Effects of climate warming on consumer-resource interactions

There is increasing evidence that climate warming is impacting biodiversity by disrupting species interactions. Trophic (consumer-resource) interactions, which comprise the fundamental units (modules) of food webs, are of particular importance because they have an intrinsic tendency to fluctuate in abundance, thus running to risk of stochastic extinction during periods of low abundances. Here I present a mathematical framework for predicting warming effects on consumer-resource interactions. This work differs from previous theory in two important ways. First, it uses delay differential equations to realistically depict the developmental delays inherent in ectotherm life cycles, and incorporates mechanistic descriptions of phenotypic trait responses, derived from first principles of thermodynamics, into the dynamical delay model. Second, it investigates the recent IPCC predictions on the increase in the number of hotter-than-average days. I report three key results. First, across latitudes (tropical vs. temperate) and feeding strategies (juvenile vs. adult attacked), a greater increase in the maximum temperature compared to the minimum (hotter-than-average summers) is more detrimental to consumer-resource interactions than a greater increase in the minimum temperature (warmer-than-average winters). Second, across latitude and warming scenarios, effects of warming are more detrimental when the consumer attacks the adult stage of the resource. Third, across warming scenarios and feeding strategies, consumer-resource interactions in the tropics are more at risk of species losses due to warming while those in the temperate zone are more at risk of extreme fluctuations in species' abundances. I discuss implications of these results for biodiversity and biological pest control.

Happy hour with friends and colleagues (4:30)

Schedule for Monday, August 17

Opening & Welcome

8:00am

Opening Plenary

8:30am