Organized by: Lei Zhang (Peking University, China)
Note: this minisymposia has multiple sessions. The second session is MS09-CBBS.

• Lei Zhang (Peking University, China)
  "Computable Early C. elegans Embryo with a Data-driven Phase Field Model"
Morphogenesis is a precise and robust dynamic process during metazoan embryogenesis consisting of both cell proliferation and cell migration. However, unlike the progress in discovering molecular activity that regulate morphogenesis, general and extensible in silico model based on cell-level interaction has not been well established yet, especially for comprehensive reconstruction and prediction on morphological features observed in live embryo (e.g., cell shape, cell-cell contact relationship). In this talk, using Caenorhabditis elegans as model animal, we present a data-driven phase field model to simulate the morphogenesis procedure within a confined compressed eggshell. We first collected three-dimensional time-lapse (4D) cellular morphological information from the in vivo imaging experiments. Based on the developmental properties obtained, we not only successfully reconstructed the evolution of cell location, cell morphology and cell-cell contact relationship observed in real embryo, but also provided mechanical perspectives on several significant developmental events such as Wnt signaling from P2 to EMS, establishment of the three orthogonal body axes and spatial robustness against external compression.
• Masakazu Akiyama (Meiji University, Japan)
  "A three-dimensional vertex dynamics model for understanding the twisting phenomenon of the hindgut of Drosophila"
Epithelial tissue morphogenesis requires morphologic changes such as migration or deformation of individual epithelial cells constituting the tissue. To reveal 3D morphologic changes of the cells contributing to the tissue deformation, we constructed a 3D vertex dynamics model in which the hindgut epithelial cells were represented by hexagonal cylinders. Numerical simulations suggested that twisting of individual cells along apico-basal axes can induce the directional tube twist. To see whether the cell twisting predicted by the simulation occurs in vivo, we quantified the cell shape change using time-lapse imaging of the whole hindgut. As a result, the hindgut epithelial cells directionally twist before and during the twisting.
• Chunhe Li (Fudan University, China)
  "A Dimension Reduction Approach for Energy Landscape"
Dimension reduction is a challenging problem in complex dynamical systems. We propose a dimension reduction approach of landscape (DRL) for complex dynamical systems, by mapping a high-dimensional system on a low-dimensional energy landscape. The DRL approach is applied to three biological networks, which validates that new reduced dimensions preserve the major information of stability and transition of original high-dimensional systems. The consistency of barrier heights calculated from the low-dimensional landscape and transition actions calculated from the high-dimensional system further shows that the landscape after dimension reduction can quantify the global stability of the system. The epithelial-mesenchymal transitions (EMT) and abnormal metabolism are two hallmarks of cancers. With the DRL approach, a quadrastable landscape for EMT-metabolism network is identified, including epithelial (E), abnormal metabolic (A), hybrid E/M (H), and mesenchymal (M) cell states. The quantified energy landscape and kinetic transition paths suggest that for the EMT process the cells at E state need to first change their metabolism, then enter the M state. This work proposes a general framework for the dimension reduction of a stochastic dynamical system, and advances the mechanistic understanding of the underlying relationship between EMT and cellular metabolism.
• Chansoo Kim (Korea Institute of Science and Technology, Korea)
  "Kinetic Monte Carlo and the infectious disease dynamics with age and region"

Organized by: Tae-Soo Chon (Pusan National University/Ecology and Future Research Association, Republic of Korea), Fugo Takasu (Nara Women’s University, Japan)
Note: this minisymposia has multiple sessions. The second session is MS09-ECOP.

• Hyo Gyeom Kim (Chonnam National Univ, Republic of Korea)
  "Importance of spatial clustering and environmental parameters on classification of the relationships between chemical composition of water body and sediment, and indices of various trophic level biotic communities in river system"
Water and sediment quality influence the biotic communities, and the relationships between the chemical compositions and the communities concurrently give an important information for the regulation and management of river system. Our hypotheses are that the importance of spatial clustering and environmental parameters vary among trophic levels. To address these issues, we applied the clustering results from self-organizing map (SOM) and geo-self-organizing map (Geo-SOM) as a random effect for linear mixed-effect models (LMMs). The datasets were composed of 12 water-quality and 10 sediment variables with indices of benthic diatoms, macroinvertebrates, and fish communities surveyed from 84 stations of rivers of South Korea for 2 years. The SOM proposed 8 clusters based on the relationships between parameters, and the Geo-SOM proposed 13 clusters based on those relationships plus the geographical characteristics. Inclusion of the random effects to SOM and Geo-SOM clustering improved the performance of all the LMMs. In particular, benthic diatom index was best explained with the Geo-SOM clusters, while macroinvertebrate and fish indices were best explained with the SOM clusters. This indicates that benthic diatoms appear to be more affected by spatial heterogeneity caused from the effects of either local pollutant variables or land-use patterns. While the SOM and Geo-SOM suggested that water quality variables were more important than sediment variables, the LMM revealed the importance of Cu for diatom, Cr for macroinvertebrate, and As for fish communities. The parameter for geographical tolerance is useful for determining the necessity of spatial clustering for each trophic level, and the combined method of LMM and SOM provides us an efficient means of establishing target environmental parameters.
• Byungjoon Min (Chungbuk National University, Republic of Korea)
  "Identifying an influential spreader in epidemics on meta-population models"
Identifying the most influential spreaders is one of the most important problems in epidemic modeling. So far, some approaches have attempted to rank the influence of spreaders in meta-population models based on heuristics. Here, we derive a theory for calculating the expected size of epidemic outbreaks originated from a single node in a network with a meta-population model by using a message-passing approach. We also test and validate our theory using real-world airline data. Our study provides an analytical tool to predict the most dangerous city for epidemic spreading.
• KyoungEun Lee (National Institute of Ecology, Republic of Korea)
  "Network analysis for predicting invasive alien species dispersal in a novel cell-based metapopulation model"
We introduce a cell-based metapopulation model for muskrat (Ondatra zibethicus) dispersal dynamics in the Geum River watershed area in Korea. Muskrat dynamics on the cell is described by a phenomenological metapopulation rate equation, including growth rate, carrying capacity, Allee effect, and especially moving tendency as a function of muskrat population and habitat preference. Diffusive spreading of muskrats is proportional to the growing rate and diffusive deviation rate, whereas decreasing with the Allee effect. The dynamical network using causal decomposition methods was effective in addressing key network properties such as hubs and edge strength similarity. Numerical database construction along with simulation-based prediction framework will enable us to identify ecological as well as environmental properties in revealing invasion causality of muskrats in the target area (Geum River, in this study). Network approaches to modelling and analysing the spreading dynamics can be useful for detecting significant habitats and eco-corridors for either survival or management of invasive species. Furthermore, the dynamical network analyses can be applied to the control scenarios of invasive species concurrently with system sensitivity tests.
• Fugo Takasu (Nara Women’s Univ, Japan)
  "Estimation of spatial interaction kernel from time series data - a point pattern approach"
In spatial and invasion ecology, more and more empirical data are available and provided as mapped point pattern; individuals' location in space, status, etc., are recorded as time series data. Examples include spatial expansion of tree diseases such as the pine wilt disease and epidemic/meta-population dynamics, a process made of infection/colonization and recovery/local extinction, etc., over space. Observed time series data as point pattern, however, often contain sampling errors, noises and factors driven by unknown processes, all of which make it difficult to explore true mechanistic processes involved behind the data. In order to explore mechanistic interactions at individual level, we aim to explore methods that better estimate spatial 'interaction kernel'. As an example, in this talk, we extend the classical epidemic models to stochastic point pattern models where infection rate depends on the distance from infectious to susceptible with a certain functional form (infection kernel). We then explore several methods that better estimate the infection kernel based on the time series data generated from the stochastic model. Results of our analyses will be presented and discussed. Our approach is a kind of 'inverse problem' in which we explore methods that better estimate unknowns from data generated from known processes.

Organized by: Chiu-Yen Kao (Claremont McKenna College, United States), Bo Zhang (Oklahoma State University, United States)
Note: this minisymposia has multiple sessions. The second session is MS08-EVOP. The third session is MS09-EVOP.

• Seyyed Abbas Mohammadi (Yasouj University, Iran)
  "Optimal Chemotherapy for Brain Tumor Growth in a Reaction-Diffusion Model"
We address the question of determining optimal chemotherapy strategies to prevent the growth of brain tumor population. To do so, we consider a reaction-diffusion model which describes the diffusion and proliferation of tumor cells and a minimization problem corresponding to it. It is established that the optimization problem admits a solution and we obtain a necessary condition for the minimizer . In a specific case, the optimizer is calculated explicitly, and we prove that it is unique. Then, a gradient-based efficient numerical algorithm is developed in order to determine the optimizer. Our results suggest a bang-bang chemotherapy strategy in a cycle which starts at the maximum dose and terminates with a rest period. Numerical simulations based upon our algorithm on a real brain image show that this is in line with the maximum tolerated dose (MTD), a standard chemotherapy protocol.
• Daozhou Gao (Shanghai Normal University, China)
  "Effects of asymmetric dispersal on total biomass in a two-patch logistic model"
The impact of animal dispersal on the total population abundance is one of the core issues in theoretical and applied ecology. In this talk, for the two-patch logistic model, we study how dispersal intensity and dispersal asymmetry affects the total population abundance. Two complete classifications of the model parameter space are given: one concerning when dispersal causes smaller or larger total biomass than no dispersal, and the other addressing how the total biomass changes with dispersal intensity and dispersal asymmetry. This improves some existing results, e.g., a recent work of Arditi et al. (Theor. Popul. Biol., 120: 11-15, 2018).
• Alfonso Ruiz-Herrera (University of Oviedo, Spain)
  "Network Topology vs. Spatial Scale of Movement in Trophic Metacommunities"
A central question in spatial ecology is understanding the interplay between the different types of movement and (spatial) network topology in the dynamics of a metacommunity. However, this is not an easy task as most fragmented ecosystems have trophic interactions involving many species and complex path-way structures. Recent attempts to solve this challenge have introduced certain simplifying assumptions or focused on a limited set of examples. However, these results do not cover many real situations. The goal of the talk is to compare the influence of the different topologies for a given configuration of nodes on the population abundances of the species of a trophic metacommunity. In particular, we are able to describe optimal movements/topologies that maximize the total population size of a target species. Regarding methodology, we first distinguish between species with low and high mobility. In the first group, we analyze the role of each path in isolation. In the second, we study the kernel of a matrix obtained from the adjacency matrices. Our main result reveals that the influence of network topologies on the population abundances depends, to a great extent, on the movement time scale. Moreover, we will prove that some directed graphs are useful in maximising the population abundance of a target species. Our framework can be readily used with any metacommunity and, therefore, represents a unification of biological insights. Moreover, we shed light on some folkloric discussions such as the role of the symmetric movement or the number of paths of a landscape.
• Xiaoqing He (East China Normal University, China)
  "On the effects of carrying capacity of intrinsic growth rate on single and multiple species in spatially heterogeneous environments"
We consider a diffusive logistic model of a single species in a heterogeneous environment, with two parameters, r(x) for intrinsic growth rate and K(x) for carrying capacity. When r(x) and K(x) are proportional, i.e., r=cK, it is proved by Prof. Lou Yuan that a population diffusing at any rate will reach a higher total equilibrium biomass than the population in an environment in which the same total resources are distributed homogeneously. In this talk, we study another case when r(x) is a constant, i.e., independent of K(x). In such case, a striking result is that for any dispersal rate, the logistic equation with spatially heterogeneous resources will always support a total population strictly smaller than the total carrying capacity at equilibrium, which is just opposite to the case r = cK. These two cases of single species models also lead to two different forms of Lotka-Volterra competition-diffusion systems. We then report the consequences of the aforementioned difference on the two corresponding forms of the competition systems. Our results indicate that in heterogeneous environments, the correlation between r(x) and K(x) has more profound impacts in population ecology then we had previously expected, at least from a mathematical point of view. This is joint work with Qian Guo and Prof. Wei-Ming Ni.

Organized by: Thomas Hillen (University of Alberta, Canada), Carlos Contreras (University of Alberta, Canada)
Note: this minisymposia has multiple sessions. The second session is MS09-IMMU.

• Suzan Farhang Sardroodi (York University, Canada)
  "Analysis of host immunological response of adenovirus-based Covid-19 vaccines"
The coronavirus disease 2019 (COVID-19) caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) can be mitigated through safe and effective administration of vaccines. In this work, we provide a mathematical framework to investigate the mechanism of vaccine-induced cellular and humoral adaptive immunity. The model uses a system of simple ordinary differential equations to analyze the safety and efficacy of the vaccine. We confront our model to various vaccine doses in an attempt to understand different immunological profiles. An optimum solution is to compute a vaccination strategy of smaller dosage and longer delay that allows the highest efficacy while allowing supply of the vaccine to catch up with the demand. Model parameters are compared to clinical trial data on adenovirus-vectored vaccines against COVID-19 but could be adapted with different vaccine types such as mRNA, protein subunit, or multi-epitope vaccines.
• Dominik Wodarz (UC Irvine, USA)
  "The impact of viral variants on the immune response during COVID-19"
N/A
• Carlos Contreras (University of Alberta, Canada)
  "Personalized Virus Load Curves of SARS-CoV-2 Infection"
We introduce an explicit function that describes virus-load curves on a patient-specific level. This function is based on simple and intuitive model parameters. It allows virus load analysis without solving a full virus load dynamic model. We validate our model on data from influenza A as well as SARS-CoV-2 infection data for Macaque monkeys and humans. Further, we compare the virus load function to an established target model of virus dynamics, which shows an excellent fit. Our virus-load function offers a new way to analyse patient virus load data, and it can be used as input to higher level models for the physiological effects of a virus infection, for models of tissue damage, and to estimate patient risks.
• Jane Heffernan (York University, Canada)
  " A multi-scale model for SARS-CoV-2 infection"
N/A

Organized by: Zhiliang Xu (Univeristy of Notre Dame, USA), Giordano Tierra (University of North Texas, USA), Shixin Xu (Duke Kunshan University)
Note: this minisymposia has multiple sessions. The second session is MS16-MMPB.

• Qi Wang (U of South Carolina, USA)
  "A Phase Field Embedding Method for Flow-Active Particle Interactions"
We present a novel computational framework to numerically investigate fluid structure interaction using the phase field embedding. Each solid structure or soft matter structure immersed in the fluid, grossly referred to as the particle in this paper, is represented by a volume preserving phase field. The motion of the active particle is driven by the surrounding fluid velocity and its self-propelling velocity. A repulsive force exists between each pair of particles and between a particle and the boundary. The particle also exerts a drag force to the fluid. When the particle is solid, its state is described by a zero velocity gradient tensor and a phase field that defines its profile. A thermodynamically consistent hydrodynamic model is then derived for the fluid-particle ensemble by the generalized Onsager principle. Structure-preserving numerical algorithms are developed for the thermodynamically consistent model. Numerical tests are carried out to verify the rate of convergence and some numerical examples are given to demonstrate the usefulness of the computational framework for simulating fluid-structure interactions for self-propelling active particles.
• Jia Zhao (Utah State University, USA)
  "Partial demixing of RNA-protein complexes leads to intra-droplet patterning in phase-separated biological condensates"
An emerging mechanism for intracellular organization is liquid-liquid phase separation (LLPS). Found in both the nucleus and the cytoplasm, liquid-like droplets condense to create compartments that are thought to promote and inhibit specific biochemistry. In this work, a multiphase, Cahn-Hilliard diffuse interface model is used to examine RNA-protein interactions driving LLPS. We create a bivalent system that allows for two different species of protein-RNA complexes and model the competition that arises for a shared binding partner, free protein. With this system we demonstrate that the binding and unbinding of distinct RNA-protein complexes leads to diverse spatial pattern formation and dynamics within droplets. Both the initial formation and transient behavior of spatial patterning are subject to the exchange of free proteins between RNA-protein complexes. This study illustrates that spatiotemporal heterogeneity can emerge within phase-separated biological condensates with simple binding reactions and competition. Intra-droplet patterning may influence droplet composition and, subsequently, cellular organization on a larger scale.
• Xinfeng Liu (Department of Mathematics, University of South Carolina, USA)
  "Mathematical modeling and computational investigation of heterogeneity in breast cancer cells"
Solid tumors are heterogeneous in composition. Cancer stem cells (CSCs) are a highly tumorigenic cell type found in developmentally diverse tumors that are believed to be resistant to standard chemotherapeutic drugs and responsible for tumor recurrence. Thus understanding the tumor growth kinetics is critical for development of novel strategies for cancer treatment. For this talk, I shall introduce mathematical modeling to study Her2 signaling for the dynamical interaction between cancer stem cells (CSCs) and non-stem cancer cells, and our findings reveal that two negative feedback loops are critical in controlling the balance between the population of CSCs and that of non-stem cancer cells. Furthermore, the model with negative feedback suggests that over-expression of the oncogene HER2 leads to an increase of CSCs by regulating the division mode or proliferation rate of CSCs.
• Isaac Klapper (Temple University, USA)
  "Modeling Metabolism in Microbial Biofilms"
Outside of laboratories, microbial communities (biofilms and other types) often exist in relatively stable environments where, on average, resource quality and quantity are predictable. Under such conditions, these communities are able to organize into tuned chemical factories, efficiently turning resources into biomass and waste byproducts. To do so, physical, chemical, and biological constraints must be accomodated. Here techniques to model this organization will be discussed. In particular, the importance of coupling microscale metabolic information to community scale transport processes will be emphasized.