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The warming climate is causing livestock to experience heat stress at an increasing frequency. Holstein cows are particularly susceptible to heat stress because of their high metabolic rate. Heat stress negatively affects immune function, particularly with respect to the cell-mediated immune response, which leads to increased susceptibility to disease. Cattle identified as having enhanced immune response have lower incidence of disease. Therefore, the objective of this study was to evaluate the impact of in vitro heat challenge on blood mononuclear cells from dairy cattle, that had previously been ranked for immune response, in terms of heat shock protein 70 concentration, nitric oxide production, and cell proliferation. Bovine blood mononuclear cells, from Holstein dairy cattle previously ranked for immune response based on their estimated breeding values, were subjected to three heat treatments: thermoneutral, heat stress 1 and heat stress 2. Cells of each treatment were evaluated for heat shock protein 70, cell proliferation and nitric oxide production. Blood mononuclear cells from dairy cattle classified as high immune responders, based on their estimated breeding values for antibody and cell-mediated responses, produced a significantly greater concentration of heat shock protein 70 under most heat stress treatments compared to average and low responders, and greater cell-proliferation across all treatments. Similarly, a trend was observed where high responders displayed greater nitric oxide production compared to average and low responders across heat treatments. Overall, these results suggest that blood mononuclear cells from high immune responder dairy cows are more thermotolerant compared to average and low immune responders, Comment: 37 pages, 3 figures, submitted to BMC Journal of Veterinary Research

Cancer cell migration between different body parts is the driving force behind cancer metastasis, which is the main cause of mortality of patients. Migration of cancer cells often proceeds by penetration through narrow cavities in locally stiff, yet flexible tissues. In our previous work, we developed a model for cell geometry evolution during invasion, which we extend here to investigate whether leader and follower (cancer) cells that only interact mechanically can benefit from sequential transmigration through narrow micro-channels and cavities. We consider two cases of cells sequentially migrating through a flexible channel: leader and follower cells being closely adjacent or distant. Using Wilcoxon's signed-rank test on the data collected from Monte Carlo simulations, we conclude that the modelled transmigration speed for the follower cell is significantly larger than for the leader cell when cells are distant, i.e. follower cells transmigrate after the leader has completed the crossing. Furthermore, it appears that there exists an optimum with respect to the width of the channel such that cell moves fastest. On the other hand, in the case of closely adjacent cells, effectively performing collective migration, the leader cell moves 12% faster since the follower cell pushes it. This work shows that mechanical interactions between cells can increase the net transmigration speed of cancer cells, resulting in increased invasiveness. In other words, interaction between cancer cells can accelerate metastatic invasion. The work was partially supported by the Israeli Ministry of Science and Technology (MOST) Medical Devices Program (Grant no. 3-17427 awarded to Prof. Daphne Weihs), by the Gerald O. Mann and the Frank and Dolores Corbett Charitable Foundations, and by the Applebaum Foundation (All granted to DW).

The spongy mesophyll is a complex, porous tissue found in plant leaves that enables carbon capture and provides mechanical stability. Unlike many other biological tissues, which remain confluent throughout development, the spongy mesophyll must develop from an initially confluent tissue into a tortuous network of cells with a large proportion of intercellular airspace. How the airspace in the spongy mesophyll develops while the cells remain mechanically stable remains unknown. Here, we used computer simulations of deformable particles to develop a purely mechanical model for the development of the spongy mesophyll tissue. By stipulating that (1) cell perimeter grows only near voids, (2) cells both form and break adhesive bonds, and (3) the tissue pressure remains constant, the computational model was able to recapitulate the developmental trajectory of the microstructure of the spongy mesophyll observed in Arabidopsis thaliana leaves. Robust generation of pore space in the spongy mesophyll requires a balance of cell growth, adhesion, stiffness and tissue pressure to ensure cell networks remain both porous yet mechanically robust. The success of this mechanical model of tissue growth and porosity evolution suggests that simple physical principles can coordinate and drive the development of complex plant tissues like the spongy mesophyll., 28 pages, 6 figures, 1 table, 9 pages of supplementary information

In this paper, we address the modeling issues of cell movement and division with a special focus on the phenomenon of volume exclusion in a lattice-based, exact stochastic simulation framework. We propose a new exact method, called Reduced Rate Method -- RRM, that is substantially quicker than the previously used exclusion method, for large number of cells. In addition, we introduce three novel reaction types: the contact-inhibited, the contact-promoted, and the spontaneous reactions. To the best of our knowledge, these reaction types have not been taken into account in lattice-based stochastic simulations of cell cultures. These new types of events may be easily applied to complicated systems, enabling the generation of biologically feasible stochastic cell culture simulations. Furthermore, we show that the exclusion algorithm and our RRM algorithm are mathematically equivalent in the sense that the next reaction to be realized and the corresponding sojourn time both belong to the same reaction and time distributions in the two approaches -- even with the newly introduced reaction types. Exact, agent-based, stochastic methods of cell culture simulations seem to be undervalued and are mostly used as benchmarking tools to validate deterministic approximations of the corresponding stochastic models. Our proposed methods are exact, they are easy to implement, have a high predictive value, and can be conveniently extended with new features. Therefore, these approaches promise a great potential., 22 pages, 6 figures

To understand cell migration, it is crucial to gain knowledge on how cells exert and integrate forces on/from their environment. A quantity of prime interest for biophysicists interested in cell movements modeling is the intracellular stresses. Up to now, three different methods have been proposed to calculate it, they are all in the regime of the thin plate approximation. Two are based on solving the mechanical equilibrium equation inside the cell material (Monolayer Stress Microscopy, and Bayesian Inference Stress Microscopy) and one is based on the continuity of displacement at the cell/substrate interface (Intracellular Stress Microscopy). We show here using 3D FEM modeling that these techniques do not calculate the same quantities (as was previously assumed), the first techniques calculate the sum of the active and resistive stresses within the cell, whereas the last one only calculate the resistive component. Combining these techniques should in principle permit to get access to the active stress alone., Comment: 7 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:2105.05792

Despite the molecular evidence that the nearly linear steady-state current-voltage relationship in mammalian astrocytes reflects a total current resulting from more than one differently regulated K+ conductances, detailed ODE models of membrane voltage Vm are still lacking. Repeated experimental results of deregulated expressions of major K+ channels in glia, Kir4.1, in models of neurodegenerative disease, as well as their altered rectification when assembling heteromeric Kir4.1/Kir5.1 channels have motivated us to attempt a detailed model incorporating the weaker potassium K2P-TREK1 current, in addition to Kir4.1, and study the stability of the resting state Vr. The main question is whether with a deregulated Kir conductivity the nominal resting state Vr remains stable, and the cell retains a trivial, potassium electrode behavior with Vm following EK. The minimal 2-dimensional model near Vr showed that certain alterations of Kir4.1 current may result in multistability of Vm if the typically observed K+ currents - Kir, K2P, and non-specific potassium leak are present. More specifically, a decrease or loss of outward Kir4.1 conductance (turning the channels into inwardly rectifying) introduces instability of Vr, near EK. That happens through robustly observed fold bifurcation giving birth to a second, much more depolarized stable resting state Vdr > −10 mV. Realistic time series were used to perturb the membrane model, from recordings of glial Vm during electrographic seizures. Simulations of the perturbed system by constant currents through gap-junctions and transient seizure-like discharges as local field potentials led to depolarization of the astrocyte and switching of Vm between the two stable states, in a downstate – upstate manner. If the prolonged depolarizations near Vdr prove experimentally plausible, such catastrophic instability would impact all aspects of the glial function, from metabolic support to membrane transport and practically all neuromodulatory roles assigned to glia.Statement of SignificanceThe almost linear current-voltage relationship of most glial membranes results from multiple non-linear potassium leaky-pore, or background conductances. The corresponding channel types develop and deregulate independently, some of them asymmetrically – deregulate differently in different Vm ranges. Effect of those deregulations on whole-cell voltage responses has not been treated. We developed a minimal ODE model of voltage dynamics incorporating detailed models of the different potassium currents based on electrophysiological recordings. Parametrically inducing some of the reported deregulations of Kir current in glia resulted in instability of the nominal resting membrane potential and appearence of a second much more depolarized resting state. If prolonged glial depolarizations prove plausible such bistability would change the present beliefs about glial Vm dynamics.

A fundamental issue in biology is the nature of evolutionary transitions from unicellular to multicellular organisms. Volvocine algae are models for this transition, as they span from the unicellular biflagellate Chlamydomonas to multicellular species of Volvox with up to 50,000 Chlamydomonas-like cells on the surface of a spherical extracellular matrix. The mechanism of phototaxis in these species is of particular interest since they lack a nervous system and intercellular connections; steering is a consequence of the response of individual cells to light. Studies of Volvox and Gonium, a 16-cell organism with a plate-like structure, have shown that the flagellar response to changing illumination of the cellular photosensor is adaptive, with a recovery time tuned to the rotation period of the colony around its primary axis. Here, combining high-resolution studies of the flagellar photoresponse with 3D tracking of freely-swimming cells, we show that such tuning also underlies phototaxis of Chlamydomonas. A mathematical model is developed based on the rotations around an axis perpendicular to the flagellar beat plane that occur through the adaptive response to oscillating light levels as the organism spins. Exploiting a separation of time scales between the flagellar photoresponse and phototurning, we develop an equation of motion that accurately describes the observed photoalignment. In showing that the adaptive time scale is tuned to the organisms' rotational period across three orders of magnitude in cell number, our results suggest a unified picture of phototaxis in green algae in which the asymmetry in torques that produce phototurns arise from the individual flagella of Chlamydomonas, the flagellated edges of Gonium and the flagellated hemispheres of Volvox., 24 pages, 21 figures, 3 supplementary videos (available from REG)

Advances in science and engineering often reveal the limitations of classical approaches initially used to understand, predict, and control phenomena. With progress, conceptual categories must often be re-evaluated to better track recently discovered invariants across disciplines. It is essential to refine frameworks and resolve conflicting boundaries between disciplines such that they better facilitate, not restrict, experimental approaches and capabilities. In this essay, we discuss issues at the intersection of developmental biology, computer science, and robotics. In the context of biological robots, we explore changes across concepts and previously distinct fields that are driven by recent advances in materials, information, and life sciences. Herein, each author provides their own perspective on the subject, framed by their own disciplinary training. We argue that as with computation, certain aspects of developmental biology and robotics are not tied to specific materials; rather, the consilience of these fields can help to shed light on issues of multi-scale control, self-assembly, and relationships between form and function. We hope new fields can emerge as boundaries arising from technological limitations are overcome, furthering practical applications from regenerative medicine to useful synthetic living machines., 21 pages, 3 figures

The growth of a tissue, which depends on cell-cell interactions and biologically relevant process such as cell division and apoptosis, is regulated by a mechanical feedback mechanism. We account for these effects in a minimal two-dimensional model in order to investigate the consequences of mechanical feedback, which is controlled by a critical pressure, $p_c$. A cell can only grow and divide if the pressure it experiences, due to interaction with its neighbors, is less than $p_c$. Because temperature is an irrelevant variable in the model, the cell dynamics is driven by self-generated active forces (SGAFs) that are created by cell division. It is shown that even in the absence of intercellular interactions, cells undergo diffusive behavior. The SGAF driven diffusion is indistinguishable from the well-known dynamics of a free Brownian particle at a fixed finite temperature. When intercellular interactions are taken into account, we find persistent temporal correlations in the force-force autocorrelation function ($FAF$) that extends over timescale of several cell division times. The time-dependence of the $FAF$ reveals memory effects, which increases as pc increases. The observed non-Markovian effects emerge due to the interplay of cell division and mechanical feedback, and is inherently a non-equilibrium phenomenon., 6 pages, 4 figures

Funding: F.R.M. gratefully acknowledges support from the RSE Saltire Early Career Fellowship ‘Multiscale mathematical modelling of spatial eco-evolutionary cancer dynamics’ (Fellowship No. 1879). T.L. gratefully acknowledges support from the Italian Ministry of University and Research (MUR) through the grant “Dipartimenti di Eccellenza 2018–2022” (Project no. E11G18000350001) and the PRIN 2020 project (No. 2020JLWP23) “Integrated Mathematical Approaches to Socio-Epidemiological Dynamics” (CUP: E15F21005420006). K.J.P. acknowledges “MIUR-Dipartimento di Eccellenza” funding to the Dipartimento Interateneo di Scienze, Progetto e Politiche del Territorio (DIST). The capacity to aggregate through chemosensitive movement forms a paradigm of self-organisation, with examples spanning cellular and animal systems. A basic mechanism assumes a phenotypically homogeneous population that secretes its own attractant, with the well known system introduced more than five decades ago by Keller and Segel proving resolutely popular in modelling studies. The typical assumption of population phenotypic homogeneity, however, often lies at odds with the heterogeneity of natural systems, where populations may comprise distinct phenotypes that vary according to their chemotactic ability, attractant secretion, etc. To initiate an understanding into how this diversity can impact on autoaggregation, we propose a simple extension to the classical Keller and Segel model, in which the population is divided into two distinct phenotypes: those performing chemotaxis and those producing attractant. Using a combination of linear stability analysis and numerical simulations, we demonstrate that switching between these phenotypic states alters the capacity of a population to self-aggregate. Further, we show that switching based on the local environment (population density or chemoattractant level) leads to diverse patterning and provides a route through which a population can effectively curb the size and density of an aggregate. We discuss the results in the context of real world examples of chemotactic aggregation, as well as theoretical aspects of the model such as global existence and blow-up of solutions. Publisher PDF

Cell-cell adhesion is one the most fundamental mechanisms regulating collective cell migration during tissue development, homeostasis, and repair, allowing cell populations to self-organize and eventually form and maintain complex tissue shapes. Cells interact with each other via the formation of protrusions or filopodia and they adhere to other cells through binding of cell surface proteins. The resulting adhesive forces are then related to cell size and shape and, often, continuum models represent them by nonlocal attractive interactions. In this paper, we present a new continuum model of cell-cell adhesion which can be derived from a general nonlocal model in the limit of short-range interactions. This new model is local, resembling a system of thin-film type equations, with the various model parameters playing the role of surface tensions between different cell populations. Numerical simulations in one and two dimensions reveal that the local model maintains the diversity of cell sorting patterns observed both in experiments and in previously used nonlocal models. In addition, it also has the advantage of having explicit stationary solutions, which provides a direct link between the model parameters and the differential adhesion hypothesis.

Coordinated and cooperative motion of cells is essential for embryonic development, tissue morphogenesis, wound healing and cancer invasion. A predictive understanding of the emergent mechanical behaviors in collective cell motion is challenging due to the complex interplay between cell-cell interactions, cell-matrix adhesions and active cell behaviors. To overcome this challenge, we develop a predictive cellular vertex model that can delineate the relative roles of substrate rigidity, tissue mechanics and active cell properties on the movement of cell collectives. We apply the model to the specific case of collective motion in cell aggregates as they spread into a two-dimensional cell monolayer adherent to a soft elastic matrix. Consistent with recent experiments, we find that substrate stiffness regulates the driving forces for the spreading of cellular monolayer, which can be pressure-driven or crawling-based depending on substrate rigidity. On soft substrates, cell monolayer spreading is driven by an active pressure due to the influx of cells coming from the aggregate, whereas on stiff substrates, cell spreading is driven primarily by active crawling forces. Our model predicts that cooperation of cell crawling and tissue pressure drives faster spreading, while the spreading rate is sensitive to the mechanical properties of the tissue. We find that solid tissues spread faster on stiff substrates, with spreading rate increasing with tissue tension. By contrast, the spreading of fluid tissues is independent of substrate stiffness and is slower than solid tissues. We compare our theoretical results with experimental results on traction force generation and spreading kinetics of cell monolayers, and provide new predictions on the role of tissue fluidity and substrate rigidity on collective cell motion., revised paper title, more references added

We provide a short review of existing models with multiple taxis performed by (at least) one species and consider a new mathematical model for tumor invasion featuring two mutually exclusive cell phenotypes (migrating and proliferating). The migrating cells perform nonlinear diffusion and two types of taxis in response to non-diffusing cues: away from proliferating cells and up the gradient of surrounding tissue. Transitions between the two cell subpopulations are influenced by subcellular (receptor binding) dynamics, thus conferring the setting a multiscale character. We prove global existence of weak solutions to a simplified model version and perform numerical simulations for the full setting under several phenotype switching and motility scenarios. We also compare (via simulations) this model with the corresponding haptotaxis-chemotaxis one featuring indirect chemorepellent production and provide a discussion about possible model extensions and mathematical challenges., Comment: 43 pages, 15 figures

Many cytoskeletal systems are now sufficiently well known to permit their precise quantitative modelling. Microtubule and actin filaments are well characterized, and the associated proteins are often known, as well as their abundance and the interactions between these elements. Thus, computer simulations can be used to investigate the collective behavior of the system precisely, in a way that is complementary to experiments. Cytosim is an Open Source cytoskeleton simulation suite designed to handle large systems of flexible filaments with associated proteins such as molecular motors. It also offers the possibility to simulate passive crosslinkers, diffusible crosslinkers, nucleators, cutters and discrete versions of the motors that only step on unoccupied lattice sites on a filament. Other objects complement the filaments by offering spherical or more complicated geometry that can be used to represent chromosomes, nucleus or vesicles in the cell. Cytosim offers simple command-line tools for running a simulation and displaying its results, that are versatile and do not require programming skills. In this workflow, step-by-step instructions are given to: i) install the necessary environment on a new computer, ii) configure Cytosim to simulate the contraction of a 2D actomyosin network, iii) produce a visual representation of the system. Next, the system is probed by systematically varying a key parameter: the number of crosslinkers. Finally, the visual representation of the system is complemented by a numerical quantification of contractility to view, in a graph, how contractility depends on the composition of the system. Overall, these different steps constitute a typical workflow that can be applied with few modifications, to tackle many other problems in the cytoskeletal field.

In multicellular systems, the single-cell behaviors should be coordinated consistently with the overall population dynamics and functions. However, the interrelation between single-cell rules and the population-level goal is still elusive. In this work, we reveal that these two levels are naturally connected via a gradient flow structure of the heterogeneous cellular population and that biologically prevalent single-cell rules such as unidirectional type-switching and hierarchical order in types emerge from this structure. We also demonstrate the gradient flow structure in a standard model of the T-cell immune response. This theoretical framework works as a basis for understanding multicellular dynamics and functions.

Cells rely on the ability to sense and respond to small spatial differences in chemoattractant concentrations for survival. There is growing evidence that this is accomplished by setting the signaling system near the threshold for activation in an excitable system and using the spatial heterogeneities to alter the threshold thereby biasing cell activity in the direction of the gradient. Here we consider a scheme by which the set point is adaptively set near the bifurcation point, but without explicit knowledge of this point. Through simulation, we show that the method would improve chemotactic efficiency of cells. The results of this paper are based on pioneering work by Eduardo Sontag and coworkers, to whom this paper is dedicated in honor of his 70th birthday.

In this paper, we examine the emergence of cell flow induced by a tension gradient on a tissue interface as in the case of the Marangoni flow on liquid interface. We consider the molecule density polarity of the heterophilic adhesion between tissues as the origin of the tension gradient. By applying the cellular Potts model, we demonstrate that polarization in concentration (i.e., intracellular localization) of heterophilic adhesion molecules can induce a cell flow similar to the Marangoni flow. In contrast to the ordinary Marangoni flow, this flow is oriented in the opposite direction to that of the tension gradient. The optimal range of adhesion strength is also identified for the existence of this flow., 10 pages, 7 figures

Atherosclerotic plaques are fatty growths in artery walls that cause heart attacks and strokes. Plaque formation is orchestrated by macrophages that are recruited to the artery wall to consume and remove blood-derived lipids, such as low-density lipoprotein (LDL). Ineffective lipid removal, due to macrophage death and other factors, leads to the accumulation of lipid-loaded macrophages and formation of a necrotic core. Experimental observations suggest that macrophage functionality varies with the extent of lipid loading. However, little is known about the resultant influence on plaque fate. Extending work by Ford et al. (2019) and Chambers et al. (2022), we develop a plaque model in which macrophages are classified by their ingested lipid content and behave in a lipid-dependent manner. The model, a system of partial-integro differential equations, considers several macrophage behaviours. These include: recruitment to the artery wall; proliferation and apoptosis; ingestion of LDL, apoptotic cells and necrotic lipid; emigration from the artery wall; and necrosis of apoptotic cells. Here, we consider apoptosis, emigration and proliferation to be lipid-dependent. We model lipid-dependence in these behaviours with experimentally-informed functions of the internalised lipid load. Our results demonstrate that lipid-dependent macrophage behaviour can substantially alter plaque fate by changing both the total quantity of lipid in the plaque and the distribution of lipid between the live cells, dead cells and necrotic core. For lipid-dependent apoptosis and lipid-dependent emigration simulations, we find significant differences in outcomes for cases that ultimately converge on the same net rate of apoptosis or emigration.

We extend the lipid-structured model for atherosclerotic plaque development of Ford et al. (2019) to account for macrophage proliferation. Proliferation is modelled as a non-local decrease in the lipid structural variable that is similar to the treatment of cell division in size-structured models (e.g. Efendiev et al. (2018)). Steady state analysis indicates that proliferation assists in reducing eventual necrotic core size and acts to spread the lipid load of the macrophage population amongst the cells. The relative contribution of plaque macrophages by proliferation and recruitment from the bloodstream is also examined. The model suggests that a more proliferative plaque differs from an equivalent (same lipid content and cell count) recruitment-dominant plaque only in the way lipid is distributed amongst the macrophages., 29 pages, 8 figures

Tissue mechanical properties such as rigidity and fluidity, and changes in these properties driven by jamming-unjamming transitions (UJT), have come under recent highlight as mechanical markers of health and disease in various biological processes including cancer. However, most analysis of these mechanical properties and UJT have sidestepped the effect of cellular death and division in these systems. Cellular apoptosis (programmed cell death) and mitosis (cell division) can drive significant changes in tissue properties. The balance between the two is crucial in maintaining tissue function, and an imbalance between the two is seen in situations such as cancer progression, wound healing and necrosis. In this work we investigate the impact of cell death and division on tissue mechanical properties, by incorporating specific mechanosensitive triggers of cell death and division based on the size and geometry of the cell within in silico models of tissue dynamics. Specifically, we look at cell migration, tissue response to external stress, tissue extrusion propensity and self-organization of different cell types within the tissue, as a function of cell death and division and the rules that trigger these events. We find that not only do cell death and division events significantly alter tissue mechanics when compared to systems without these events, but that the choice of triggers driving these cell death and division events also alter the predicted tissue mechanics and overall system behavior.

Bacteria often form surface-bound communities, embedded in a self-produced extracellular matrix, called biofilms. Quantitative studies of their growth have typically focused on unconfined expansion above solid or semi-solid surfaces, leading to exponential radial growth. This geometry does not accurately reflect the natural or biomedical contexts in which biofilms grow in confined spaces. Here we consider one of the simplest confined geometries: a biofilm growing laterally in the space between a solid surface and an overlying elastic sheet. A poroelastic framework is utilised to derive the radial growth rate of the biofilm; it reveals an additional self-similar expansion regime, governed by the stiffness of the matrix, leading to a finite maximum radius, consistent with our experimental observations of growing $Bacillus~subtilis$ biofilms confined by PDMS., 5 pages, 3 figures plus Supplementary Material

Mounting evidence shows that oscillatory activity is widespread in cell signaling. Here we review some of this recent evidence, focusing on both the molecular mechanisms that potentially underlie such dynamical behavior, and the potential advantages that signaling oscillations might have in cell function. The biological processes considered include tissue maintenance, embryonic development and wound healing. With the aid of mathematical modeling, we show that a common principle, namely delayed negative feedback, underpins this wide variety of phenomena., 6 pages, 4 figures

Ordinary differential equations (ODEs) can model the transition of cell states over time. Bifurcation theory is a branch of dynamical systems which studies changes in the behavior of an ODE system while one or more parameters are varied. We have found that concepts in bifurcation theory may be applied to model metastatic cell behavior. Our results show how a specific phenomenon called a cusp bifurcation describes metastatic cell state transitions, separating two qualitatively different transition modalities. Moreover, we show how the cusp bifurcation models other genetic networks, and we relate the dynamics after the bifurcation to observed phenomena in commitment to enter the cell cycle., 57 pages, 22 figures, code included

International audience; To model the morphogenesis of rod-shaped bacterial micro-colony, several individual-based models have been proposed in the biophysical literature. When studying the shape of micro-colonies, most models present interaction forces such as attraction or filial link. In this article, we propose a model where the bacteria interact only through non-overlapping constraints. We consider the asymmetry of the bacteria, and its influence on the friction with the substrate. Besides, we consider asymmetry in the mass distribution of the bacteria along their length. These two new modelling assumptions allow us to retrieve mechanical behaviours of micro-colony growth without the need of interaction such as attraction. We compare our model to various sets of experiments, discuss our results, and propose several quantifiers to compare model to data in a systematic way.

Inflammatory breast cancer (IBC), a rare form of breast cancer associated with increased angiogenesis and metastasis, is largely driven by tumor-stromal interactions with the vasculature and the extracellular matrix (ECM). However, there is currently a lack of understanding of the role these interactions play in initiation and progression of the disease. In this study, we developed the first three-dimensional, in vitro, vascularized, microfluidic IBC platform to quantify the spatial and temporal dynamics of tumor-vasculature and tumor-ECM interactions specific to IBC. Platforms consisting of collagen type 1 ECM with an endothelialized blood vessel were cultured with IBC cells, MDA-IBC3 (HER2+) or SUM149 (triple negative), and for comparison to non-IBC cells, MDA-MB-231 (triple negative). Acellular collagen platforms with endothelialized blood vessels served as controls. SUM149 and MDA-MB-231 platforms exhibited a significantly (p < .05) higher vessel permeability and decreased endothelial coverage of the vessel lumen compared to the control. Both IBC platforms, MDA-IBC3 and SUM149, expressed higher levels of vascular endothelial growth factor (p < .05) and increased collagen ECM porosity compared to non-IBCMDA-MB-231 (p < .05) and control (p < .01) platforms. Additionally, unique to the MDA-IBC3 platform, we observed progressive sprouting of the endothelium over time resulting in viable vessels with lumen. The newly sprouted vessels encircled clusters of MDA-IBC3 cells replicating a key feature of in vivo IBC. The IBC in vitro vascularized platforms introduced in this study model well-described in vivo and clinical IBC phenotypes and provide an adaptable, high throughput tool for systematically and quantitatively investigating tumor-stromal mechanisms and dynamics of tumor progression.

Graphene conductive properties have been long exploited in the field of organic photovoltaics and optoelectronics by the scientific community worldwide. We engineered and characterized a hybrid biointerface in which graphene is coupled with photosensitive polymers, and tested its ability to elicit lighttriggered neural activity modulation in primary neurons and blind retina explants. We designed such a graphene-based device by modifying a photoactive P3HT-based retinal interface, previously reported to rescue light sensitivity in blind rodents, with a CVD graphene layer replacing the conductive PEDOT:PSS layer to enhance charge separation. The new graphene-based device was characterized for its electrochemical features and for the ability to photostimulate primary neurons and blind retina explants, while preserving biocompatibility. Light-triggered responses, recorded by patch-clamp in vitro or MEA ex vivo, show a stronger light-transduction efficiency when the neurons are interfaced with the graphene-based device with respect to the PEDOT:PSS-based one. The possibility to ameliorate flexible photo-stimulating devices via the insertion of graphene, paves the way for potential biomedical applications of graphenebased neuronal interfaces in the context of retinal implants., Comment: 10 pages, 5 figures

A two-dimensional mathematical model for cells migrating without adhesion capabilities is presented and analyzed. Cells are represented by their cortex, which is modelled as an elastic curve, subject to an internal pressure force. Net polymerization or depolymerization in the cortex is modelled via local addition or removal of material, driving a cortical flow. The model takes the form of a fully nonlinear degenerate parabolic system. An existence analysis is carried out by adapting ideas from the theory of gradient flows. Numerical simulations show that these simple rules can account for the behavior observed in experiments, suggesting a possible mechanical mechanism for adhesion-independent motility., Comment: 22 pages and 9 figures

Cell division is a process that involves many biochemical steps and complex biophysical mechanisms. To simplify the understanding of what triggers cell division, three basic models that subsume more microscopic cellular processes associated with cell division have been proposed. Cells can divide based on the time elapsed since their birth, their size, and/or the volume added since their birth -- the timer, sizer, and adder models, respectively. Here, we propose unified adder-sizer models and investigate some of the properties of different adder processes arising in cellular proliferation. Although the adder-sizer model provides a direct way to model cell population structure, we illustrate how it is mathematically related to the well-known model in which cell division depends on age and size. Existence and uniqueness of weak solutions to our 2+1-dimensional PDE model are proved, leading to the convergence of the discretized numerical solutions and allowing us to numerically compute the dynamics of cell population densities. We then generalize our PDE model to incorporate recent experimental findings of a system exhibiting mother-daughter correlations in cellular growth rates. Numerical experiments illustrating possible average cell volume blowup and the dynamical behavior of cell populations with mother-daughter correlated growth rates are carried out. Finally, motivated by new experimental findings, we extend our adder model cases where the controlling variable is the added size between DNA replication initiation points in the cell cycle., Comment: 23 pages, 8 figures

Gene expression time delays, modelling the complex biological processes of gene transcription and translation, have been shown to play an important role in cellular dynamics. Time delays, motivated by the gene expression process, can also greatly affect the behaviour of reaction-diffusion systems. In this dissertation, we explore their effects on Turing pattern mechanisms. By incorporating time delays, modelled as both a fixed parameter and as a continuous distribution, into classical reaction-diffusion systems that exhibit Turing instabilities, we investigate the changing behaviour of these systems. We find that an introduction of increasing time delay increases the time taken for spatially inhomogeneous patterns to stabilise, and the two are related linearly. We also present results to show, through a linear stability analysis, that an increasing time delay can act both to expand or shrink the Turing space of a certain reaction-diffusion mechanism, depending on the placement of time-delayed terms. Significantly, we find that modelling time delays as a continuous distribution has a negligible impact on qualitative or quantitative aspects of the results seen compared with a fixed time delay of the mean of the distribution. These findings serve to highlight the importance of considering gene expression time delays when modelling biological patterning events, as well as requiring a complete understanding of the cellular dynamics before attempting to apply Turing mechanisms to explain biological phenomena. The results also suggest, at least for the distributions considered in this dissertation, that fixed delay and distributed delay models have almost identical dynamics. This allows one to use simpler fixed delay models rather than the more complicated distributed delay variants., 81 pages, 64 figures, MSc Thesis

Biological membranes are host to proteins and molecules which may form domain-like structures resulting in spatially-varying material properties. Vesicles with such heterogeneous membranes can exhibit intricate shapes at equilibrium and rich dynamics when placed into a flow. Under the assumption of small deformations we develop a reduced order model to describe the fluid-structure interaction between a viscous background shear flow and an inextensible membrane in two dimensions with spatially varying bending stiffness and spontaneous curvature. Material property variations of a critical magnitude, relative to the flow rate and internal/external viscosity contrast, can set off a qualitative change in the vesicle dynamics. A membrane of nearly constant bending stiffness or spontaneous curvature undergoes a small amplitude swinging motion (which includes tangential tank-treading), while for large enough material variations the dynamics pass through a regime featuring tumbling and periodic phase-lagging of the membrane material, and ultimately for very large material variation to a rigid body tumbling behavior. Distinct differences are found for even and odd spatial modes of domain distribution. Full numerical simulations are used to probe the theoretical predictions, which appear valid even when studying substantially deformed membranes., Comment: 26 pages, 6 figures

The coupling of the internal mechanisms of cell polarization to cell shape deformations and subsequent cell crawling poses many interdisciplinary scientific challenges. Several mathematical approaches have been proposed to model the coupling of both processes, where one of the most successful methods relies on a phase field that encodes the morphology of the cell, together with the integration of partial differential equations that account for the polarization mechanism inside the cell domain as defined by the phase field. This approach has been previously employed to model the motion of single cells of the social amoeba Dictyostelium discoideum, a widely used model organism to study actin-driven motility and chemotaxis of eukaryotic cells. Besides single cell motility, Dictyostelium discoideum is also well-known for its collective behavior. Here, we extend the previously introduced model for single cell motility to describe the collective motion of large populations of interacting amoebae by including repulsive interactions between the cells. We performed numerical simulations of this model, first characterizing the motion of single cells in terms of their polarity and velocity vectors. We then systematically studied the collisions between two cells that provided the basic interaction scenarios also observed in larger ensembles of interacting amoebae. Finally, the relevance of the cell density was analyzed, revealing a systematic decrease of the motility with density, associated with the formation of transient cell clusters that emerge in this system. This model is a prototypical active matter system for the investigation of the emergent collective dynamics of deformable, self-driven cells with a highly complex, nonlinear coupling of cell shape deformations, self-propulsion and repulsive cell-cell interactions., Comment: 25 pages, 12 Figures and 1 Table

Within the human respiratory tract (HRT), virus diffuses through the periciliary fluid (PCF) bathing the epithelium. But virus also undergoes advection: as the mucus layer sitting atop the PCF is pushed along by the ciliated cell’s beating cilia, the PCF and its virus content are also pushed along, upwards towards the nose and mouth. While many mathematical models (MMs) have described the course of influenza A virus (IAV) infections in vivo, none have considered the impact of both diffusion and advection on the kinetics and localization of the infection. The MM herein represents the HRT as a one-dimensional track extending from the nose down towards the lower HRT, wherein stationary cells interact with IAV which moves within (diffusion) and along with (advection) the PCF. Diffusion was found to be negligible in the presence of advection which effectively sweeps away IAV, preventing infection from disseminating below the depth at which virus first deposits. Higher virus production rates (10-fold) are required at higher advection speeds (40 μm/s) to maintain equivalent infection severity and timing. Because virus is entrained upwards, upper parts of the HRT see more virus than lower parts. As such, infection peaks and resolves faster in the upper than in the lower HRT, making it appear as though infection progresses from the upper towards the lower HRT, as reported in mice. When the spatial MM is expanded to include cellular regeneration and an immune response, it reproduces tissue damage levels reported in patients. It also captures the kinetics of seasonal and avian IAV infections, via parameter changes consistent with reported differences between these strains, enabling comparison of their treatment with antivirals. This new MM offers a convenient and unique platform from which to study the localization and spread of respiratory viral infections within the HRT., Author summary This work proposes a new way to think about and model the dissemination of an influenza A virus (IAV) infection within the human respiratory tract (HRT). The computational model takes into account the physiological environment in which the infection takes place by representing the HRT spatially in one dimension (depth), and by incorporating the effect of virion diffusion within the periciliary fluid that bathes infectable cells, and the remarkable physiological barrier that is the mucus escalator, sweeping virus upwards. Cell regeneration, the immune response, and infection with human vs avian IAV strains are explored in this spatial context. The numerical efficiency of this model, compared to agent-based models, makes it an attractive alternative to model respiratory virus infections in vivo.

Multicellular collective migration is a ubiquitous strategy of cells to translocate spatially in diverse tissue environments to accomplish a wide variety of biological phenomena, viz. embryonic development, wound healing, and tumor progression. Diverse cellular functions and behaviors, for instance, cell protrusions, active contractions, cell-cell adhesion, biochemical signaling, remodeling of tissue micro-environment, etc., play their own role concomitantly to have a single concerted consequence of multicellular migration. Thus unveiling the driving principles, both biochemical and biophysical, of the inherently complex process of collective cell migration is an insurmountable task. Mathematical and computational models, in tandem with experimental data, help in shedding some light on it. Here we review different factors influencing Collective Cell Migration and then focus on different mathematical and computational models - discrete, hybrid, and continuum - which helps in revealing different aspects of multicellular migration. Finally, we discuss the applications of these modeling frameworks specific to cancer, 27 pages, 2 figures, book chapter

Phagocytosis is the process of engulfment and internalization of comparatively large particles by the cell, that plays a central role in the functioning of our immune system. We study the process of phagocytosis by considering a simplified coarse grained model of a three-dimensional vesicle, having uniform adhesion interaction with a rigid particle, in the presence of curved membrane proteins and active cytoskeletal forces. Complete engulfment is achieved when the bending energy cost of the vesicle is balanced by the gain in the adhesion energy. The presence of curved (convex) proteins reduces the bending energy cost by self-organizing with higher density at the highly curved leading edge of the engulfing membrane, which forms the circular rim of the phagocytic cup that wraps around the particle. This allows the engulfment to occur at much smaller adhesion strength. When the curved proteins exert outwards protrusive forces, representing actin polymerization, at the leading edge, we find that engulfment is achieved more quickly and at lower protein density. We consider spherical as well as non-spherical particles, and find that non-spherical particles are more difficult to engulf in comparison to the spherical particles of the same surface area. For non-spherical particles, the engulfment time crucially depends upon the initial orientation of the particles with respect to the vesicle. Our model offers a mechanism for the spontaneous self-organization of the actin cytoskeleton at the phagocytic cup, in good agreement with recent high-resolution experimental observations., 27 pages, 23 figures

Atherosclerotic plaques form in artery walls due to a chronic inflammatory response driven by lipid accumulation. A key component of the inflammatory response is the interaction between monocyte-derived macrophages and extracellular lipid. Although concentrations of low-density lipoprotein (LDL) and high-density lipoprotein (HDL) particles in the blood are known to affect plaque progression, their impact on the lipid load of plaque macrophages remains unexplored. In this paper, we develop a lipid-structured mathematical model to investigate the impact of blood LDL/HDL levels on plaque composition, and lipid distribution in plaque macrophages. A reduced subsystem, derived by summing the equations of the full model, describes the dynamics of biophysical quantities relating to plaque composition (e.g. total number of macrophages, total amount of intracellular lipid). We also derive a continuum approximation of the model to facilitate analysis of the macrophage lipid distribution. The results, which include time-dependent numerical solutions and asymptotic analysis of the unique steady state solution, indicate that plaque lipid content is sensitive to the influx of LDL relative to HDL capacity. The macrophage lipid distribution evolves in a wave-like manner towards an equilibrium profile which may be monotone decreasing, quasi-uniform or unimodal, attaining its maximum value at a non-zero lipid level. Our model also reveals that macrophage uptake may be severely impaired by lipid accumulation. We conclude that lipid accumulation in plaque macrophages may serve as a partial explanation for the defective uptake of apoptotic cells (efferocytosis) often reported in atherosclerotic plaques., Comment: 44 pages, 13 figures

A model for the mathematical study of immune response to breast cancer is proposed and studied, both analytically and numerically. It is a simplification of a complex one, recently introduced by two of the present authors. It serves for a compact study of the dynamical role in cancer promotion of a relatively recently described subgroup of regulatory B cells, which are evoked by the tumour.

It has recently been discovered that the viscoelastic properties of cells are inherent markers reflecting the complex biological states, functions and malfunctions of the cells. Although the extraction of model parameters from the viscoelasticity data of many cell types has been done successfully using integer order mechanical and power-law viscoelastic models, there are some cell types and conditions where the goodness of fits falls behind. Thus, fractional order viscoelastic models have been proposed as more general and better suited for such modeling. In this work, we test such proposed generality using published data already fitted by integer order models. We find that cell viscoelasticity data can be fitted using fractional order viscoelastic models in more situations than integer order. For macrophages, which are among the white blood cells that function in the immune system, the fractional order Kelvin-Voigt model best captures pharmacological interventions and maturation of the cells. The steady state viscosity of macrophages decreases following depolymerization of F-actin using the drug cytochalasin D, and also decreases following myosin II breakdown using Blebbistatin. When macrophages are treated with a bacterium-derived chemoattractant, the steady state viscosity decreases. Interestingly, both the steady state viscosity and elastic modulus are progressively altered as the cells become mature and approach senescence. Taken together, these results show that fractional viscoelastic modeling, more robustly than integer order modeling, enables the further quantification of cell function and malfunction, with potential diagnostic and therapeutic applications especially in cases of cancer and immune system dysfunctions., Comment: 20 pages, 6 figures

Amoeboid cell motility is relevant in a wide variety of biomedical applications such as wound healing, cancer metastasis, and embryonic morphogenesis. It is characterized by pronounced changes of the cell shape associated with expansions and retractions of the cell membrane, which result in a crawling kind of locomotion. Despite existing computational models of amoeboid motion, the inference of expansion and retraction components of individual cells, the corresponding classification of cells, and the a priori specification of the parameter regime to achieve a specific motility behavior remain challenging open problems. We propose a novel model of the spatio-temporal evolution of two-dimensional cell contours comprising three biophysiologically motivated components: a stochastic term accounting for membrane protrusions and two deterministic terms accounting for membrane retractions by regularizing the shape and area of the contour. Mathematically, these correspond to the intensity of a self-exciting Poisson point process, the area-preserving curve-shortening flow, and an area adjustment flow. The model is used to generate contour data for a variety of qualitatively different, e.g., polarized and non-polarized, cell tracks that are hardly distinguishable from experimental data. In application to experimental cell tracks, we inferred the protrusion component and examined its correlation to commonly used biomarkers: the actin concentration close to the membrane and its local motion. Due to the low model complexity, parameter estimation is fast, straightforward and offers a simple way to classify contour dynamics based on two locomotion types: the amoeboid and a so-called fan-shaped type. For both types, we use cell tracks segmented from fluorescence imaging data of the model organism D. discoideum. An implementation of the model is provided within the open-source software package AmoePy., Comment: 32 pages, 7 figures, for supporting information, see https://doi.org/10.5281/zenodo.7243416, for software and data publication, see https://doi.org/10.5281/zenodo.3982371

Mammalian brains operate in a very special surrounding: to survive they have to react quickly and effectively to the pool of stimuli patterns previously recognized as danger. Many learning tasks often encountered by living organisms involve a specific set-up centered around a relatively small set of patterns presented in a particular environment. For example, at a party, people recognize friends immediately, without deep analysis, just by seeing a fragment of their clothes. This set-up with reduced "ontology" is referred to as a "situation". Situations are usually local in space and time. In this work, we propose that neuron-astrocyte networks provide a network topology that is effectively adapted to accommodate situation-based memory. In order to illustrate this, we numerically simulate and analyze a well-established model of a neuron-astrocyte network, which is subjected to stimuli conforming to the situation-driven environment. Three pools of stimuli patterns are considered: external patterns, patterns from the situation associative pool regularly presented to the network and learned by the network, and patterns already learned and remembered by astrocytes. Patterns from the external world are added to and removed from the associative pool. Then we show that astrocytes are structurally necessary for an effective function in such a learning and testing set-up. To demonstrate this we present a novel neuromorphic model for short-term memory implemented by a two-net spiking neural-astrocytic network. Our results show that such a system tested on synthesized data with selective astrocyte-induced modulation of neuronal activity provides an enhancement of retrieval quality in comparison to standard spiking neural networks trained via Hebbian plasticity only. We argue that the proposed set-up may offer a new way to analyze, model, and understand neuromorphic artificial intelligence systems., Comment: 38 pages, 11 figures, 4 tables

Collective cell migration plays an essential role in vertebrate development, yet the extent to which dynamically changing microenvironments influence this phenomenon remains unclear. Observations of the distribution of the extracellular matrix (ECM) component fibronectin during the migration of loosely connected neural crest cells (NCCs) lead us to hypothesize that NCC remodeling of an initially punctate ECM creates a scaffold for trailing cells, enabling them to form robust and coherent stream patterns. We evaluate this idea in a theoretical setting by developing an individual-based computational model that incorporates reciprocal interactions between NCCs and their ECM. ECM remodeling, haptotaxis, contact guidance, and cell-cell repulsion are sufficient for cells to establish streams in silico, however additional mechanisms, such as chemotaxis, are required to consistently guide cells along the correct target corridor. Further model investigations imply that contact guidance and differential cell-cell repulsion between leader and follower cells are key contributors to robust collective cell migration by preventing stream breakage. Global sensitivity analysis and simulated gain- and loss-of-function experiments suggest that long-distance migration without jamming is most likely to occur when leading cells specialize in creating ECM fibers, and trailing cells specialize in responding to environmental cues by upregulating mechanisms such as contact guidance., Comment: 66 pages, 19 figures (of which 14 are supplementary)

Tumor cells invade individually or in groups, mediated by mechanical interactions between cells and their surrounding matrix. These multicellular dynamics are reminiscent of leader-follower coordination and epithelial-mesenchymal transitions (EMT) in tissue development, which may occur via dysregulation of associated molecular or physical mechanisms. However, it remains challenging to elucidate such phenotypic heterogeneity and plasticity without precision measurements of single cell behavior. The convergence of technological developments in live cell imaging, biophysical measurements, and 3D biomaterials are highly promising to reveal how tumor cells cooperate in aberrant microenvironments. Here, we highlight new results in collective migration from the perspective of cancer biology and bioengineering. First, we review the biology of collective cell migration. Next, we consider physics-inspired analyses based on order parameters and phase transitions. Further, we examine the interplay of metabolism and heterogeneity in collective migration. We then review the extracellular matrix, and new modalities for mechanical characterization of 3D biomaterials. We also explore epithelial-mesenchymal plasticity and implications for tumor progression. Finally, we speculate on future directions for integrating mechanobiology and cancer cell biology to elucidate collective migration.

Predictive modeling is the key factor for saving time and resources with respect to manufacturing processes such as fermentation processes arising e.g.\ in food and chemical manufacturing processes. According to Zhang et al. (2002), the open-loop dynamics of yeast are highly dependent on the initial cell mass distribution. This can be modeled via population balance models describing the single-cell behavior of the yeast cell. There have already been several population balance models for wine fermentation in the literature. However, the new model introduced in this paper is much more detailed than the ones studied previously. This new model for the white wine fermentation process is based on a combination of components previously introduced in literature. It turns it into a system of highly nonlinear weakly hyperbolic partial/ordinary integro-differential equations. This model becomes very challenging from a theoretical and numerical point of view. Existence and uniqueness of solutions to a simplified version of the introduced problem is studied based on semigroup theory. For its numerical solution a numerical methodology based on a finite volume scheme combined with a time implicit scheme is derived. The impact of the initial cell mass distribution on the solution is studied and underlined with numerical results. The detailed model is compared to a simpler model based on ordinary differential equations. The observed differences for different initial distributions and the different models turn out to be smaller than expected. The outcomes of this paper are very interesting and useful for applied mathematicians, winemakers and process engineers., 26 pages, 20 figures

Mathematical models come in many forms across biological applications. In the case of complex, spatial dynamics and pattern formation, stochastic models also face two main challenges: pattern data is largely qualitative, and model realizations may vary significantly. Together these issues make it difficult to relate models and empirical data -- or even models and models -- limiting how different approaches can be combined to offer new insights into biology. These challenges also raise mathematical questions about how models are related, since alternative approaches to the same problem -- e.g., cellular Potts models; off-lattice, agent-based models; on-lattice, cellular automaton models; and continuum approaches -- treat uncertainty and implement cell behavior in different ways. To help open the door to future work on questions like these, here we adapt methods from topological data analysis and computational geometry to quantitatively relate two different models of the same biological process in a fair, comparable way. To center our work and illustrate concrete challenges, we focus on the example of zebrafish-skin pattern formation, and we relate patterns that arise from agent-based and cellular automaton models.

Modern biology and biomedicine are undergoing a big-data explosion needing advanced computational algorithms to extract mechanistic insights on the physiological state of living cells. We present the motivation for the Cell Physiome: a framework and approach for creating, sharing, and using biophysics-based computational models of single cell physiology. Using examples in calcium signaling, bioenergetics, and endosomal trafficking, we highlight the need for spatially detailed, biophysics-based computational models to uncover new mechanisms underlying cell biology. We review progress and challenges to date towards creating cell physiome models. We then introduce bond graphs as an efficient way to create cell physiome models that integrate chemical, mechanical, electromagnetic, and thermal processes while maintaining mass and energy balance. Bond graphs enhance modularization and re-usability of computational models of cells at scale. We conclude with a look forward into steps that will help fully realize this exciting new field of mechanistic biomedical data science., Comment: Minor text edits to fix minor grammatical errors and figure reference

The severe acute respiratory syndrome coronavirus 2 outbreak in Chinas Hubei area in late 2019 has now created a global pandemic that has spread to over 150 countries. In most people, COVID 19 is a respiratory infection that produces fever, cough, and shortness of breath. Patients with severe COVID 19 may develop ARDS. MSCs can come from a number of places, such as bone marrow, umbilical cord, and adipose tissue. Because of their easy accessibility and low immunogenicity, MSCs were often used in animal and clinical research. In recent studies, MSCs have been shown to decrease inflammation, enhance lung permeability, improve microbial and alveolar fluid clearance, and accelerate lung epithelial and endothelial repair. Furthermore, MSC-based therapy has shown promising outcomes in preclinical studies and phase 1 clinical trials in sepsis and ARDS. In this paper, we posit the therapeutic strategies using MSC and dissect how and why MSC therapy is a potential treatment option for COVID 19 induced ARDS. We cite numerous promising clinical trials, elucidate the potential advantages of MSC therapy for COVID 19 ARDS patients, examine the detriments of this therapeutic strategy and suggest possibilities of subsequent research., Comment: 14 Pages, 6 Figures

Microscopy imaging techniques are instrumental for characterization and analysis of biological structures. As these techniques typically render 3D visualization of cells by stacking 2D projections, issues such as out-of-plane excitation and low resolution in the $z$-axis may pose challenges (even for human experts) to detect individual cells in 3D volumes as these non-overlapping cells may appear as overlapping. In this work, we introduce a comprehensive method for accurate 3D instance segmentation of cells in the brain tissue. The proposed method combines the 2D YOLO detection method with a multi-view fusion algorithm to construct a 3D localization of the cells. Next, the 3D bounding boxes along with the data volume are input to a 3D U-Net network that is designed to segment the primary cell in each 3D bounding box, and in turn, to carry out instance segmentation of cells in the entire volume. The promising performance of the proposed method is shown in comparison with some current deep learning-based 3D instance segmentation methods.

Modeling the ability of multicellular organisms to build and maintain their bodies through local interactions between individual cells (morphogenesis) is a long-standing challenge of developmental biology. Recently, the Neural Cellular Automata (NCA) model was proposed as a way to find local system rules that produce a desired global behaviour, such as growing and persisting a predefined target pattern, by repeatedly applying the same rule over a grid starting from a single cell. In this work, we argue that the original Growing NCA model has an important limitation: anisotropy of the learned update rule. This implies the presence of an external factor that orients the cells in a particular direction. In other words, "physical" rules of the underlying system are not invariant to rotation, thus prohibiting the existence of differently oriented instances of the target pattern on the same grid. We propose a modified Isotropic NCA (IsoNCA) model that does not have this limitation. We demonstrate that such cell systems can be trained to grow accurate asymmetrical patterns through either of two methods: (1) by breaking symmetries using structured seeds or (2) by introducing a rotation-reflection invariant training objective and relying on symmetry-breaking caused by asynchronous cell updates.

Agent-based modeling (ABM) is a well-established paradigm for simulating complex systems via interactions between constituent entities. Machine learning (ML) refers to approaches whereby statistical algorithms 'learn' from data on their own, without imposing a priori theories of system behavior. Biological systems -- from molecules, to cells, to entire organisms -- consist of vast numbers of entities, governed by complex webs of interactions that span many spatiotemporal scales and exhibit nonlinearity, stochasticity and intricate coupling between entities. The macroscopic properties and collective dynamics of such systems are difficult to capture via continuum modelling and mean-field formalisms. ABM takes a 'bottom-up' approach that obviates these difficulties by enabling one to easily propose and test a set of well-defined 'rules' to be applied to the individual entities (agents) in a system. Evaluating a system and propagating its state over discrete time-steps effectively simulates the system, allowing observables to be computed and system properties to be analyzed. Because the rules that govern an ABM can be difficult to abstract and formulate from experimental data, there is an opportunity to use ML to help infer optimal, system-specific ABM rules. Once such rule-sets are devised, ABM calculations can generate a wealth of data, and ML can be applied there too -- e.g., to probe statistical measures that meaningfully describe a system's stochastic properties. As an example of synergy in the other direction (from ABM to ML), ABM simulations can generate realistic datasets for training ML algorithms (e.g., for regularization, to mitigate overfitting). In these ways, one can envision various synergistic ABM$\rightleftharpoons$ML loops. This review summarizes how ABM and ML have been integrated in contexts that span spatiotemporal scales, from cellular to population-level epidemiology., Comment: 32 pages, 1 table, 8 figures

In the brain, both neurons and glial cells work in conjunction with each other during information processing. Stimulation of neurons can cause calcium oscillations in astrocytes which in turn can affect neuronal calcium dynamics. The "glissandi" effect is one such phenomenon, associated with a decrease in infraslow fluctuations, in which synchronized calcium oscillations propagate as a wave in hundreds of astrocytes. Nitric oxide molecules released from the astrocytes contribute to synaptic functions on the basis of the underlying astrocyte-neuron interaction network. In this study, by defining an astrocyte-neuronal (A-N) unit as an integrated circuit of one neuron and one astrocyte, we developed a minimal model of neuronal stimulus-dependent and nitric oxide-mediated emergence of calcium waves in astrocytes. Incorporating inter-unit communication via nitric oxide molecules, a coupled network of 1,000 such A-N units is developed in which multiple stable regimes were found to emerge in astrocytes. We examined the ranges of neuronal stimulus strength and the coupling strength between A-N units that give rise to such dynamical behaviors. We also report that there exists a range of coupling strength, wherein units not receiving stimulus also start showing oscillations and become synchronized. Our results support the hypothesis that glissandi-like phenomena exhibiting synchronized calcium oscillations in astrocytes help in efficient synaptic transmission by reducing the energy demand of the process., Comment: 18 pages, 6 figures, 3 tables

Maintenance and regeneration of adult tissues rely on the self-renewal of stem cells. Regeneration without over-proliferation requires precise regulation of the stem cell proliferation and differentiation rates. The nature of such regulatory mechanisms in different tissues, and how to incorporate them in models of stem cell population dynamics, is incompletely understood. The critical birth-death (CBD) process is widely used to model stem cell populations, capturing key phenomena, such as scaling laws in clone size distributions. However, the CBD process neglects regulatory mechanisms. Here, we propose the birth-death process with volume exclusion (vBD), a variation of the birth-death process that considers crowding effects, such as may arise due to limited space in a stem cell niche. While the deterministic rate equations predict a single non-trivial attracting steady state, the master equation predicts extinction and transient distributions of stem cell numbers with three possible behaviours: long-lived quasi-steady state, and short-lived bimodal or unimodal distributions. In all cases, we approximate solutions to the vBD master equation using a renormalised system-size expansion, quasi-steady state approximation and the WKB method. Our study suggests that the size distribution of a stem cell population bears signatures that are useful to detect negative feedback mediated via volume exclusion., Comment: 23 pages, 5 figures