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Motile human-skin fibroblasts form macroscopic swirling patterns when grown to confluence on a culture dish. In this paper, we investigate the effect of coating the culture-dish surface with collagen on the resulting pattern, using human-skin fibroblast NB1RGB cells as the model system. The presence of the collagen coating is expected to enhance the adherence of the fibroblasts to the dish surface, and thereby also enhance the traction that the fibroblasts have as they move. We find that, contrary to our initial expectation, the coating does not significantly affect the motility of the fibroblasts. Their eventual number density at confluence is also unaffected. However, the coherence length of cell orientation in the swirling pattern is diminished. We also find that the fibroblasts cultured in a collagen-coated dish are rounder in shape and shorter in perimeter, compared to those cultured in an uncoated dish. We hypothesize that the rounder cell-shape which weakens the cell-cell nematic contact interaction is responsible for the change in coherence length. A simple mathematical model of the migrating fibroblasts is constructed, which demonstrates that constant motility with weaker nematic interaction strength does indeed lead to the shortening of the coherence length., to appear in J. of Biological Physics

A recent experimental study found that the binding affinity between the cellular receptor human angiotensin converting enzyme 2 (ACE2) and receptor-binding domain (RBD) in spike (S) protein of novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is more than 10-fold higher than that of the original severe acute respiratory syndrome coronavirus (SARS-CoV). However, main-chain structures of the SARS-CoV-2 RBD are almost the same with that of the SARS-CoV RBD. Understanding physical mechanism responsible for the outstanding affinity between the SARS-CoV-2 S and ACE2 is the "urgent challenge" for developing blockers, vaccines and therapeutic antibodies against the coronavirus disease 2019 (COVID-19) pandemic. Considering the mechanisms of hydrophobic interaction, hydration shell, surface tension, and the shielding effect of water molecules, this study reveals a hydrophobic-interaction-based mechanism by means of which SARS-CoV-2 S and ACE2 bind together in an aqueous environment. The hydrophobic interaction between the SARS-CoV-2 S and ACE2 protein is found to be significantly greater than that between SARS-CoV S and ACE2. At the docking site, the hydrophobic portions of the hydrophilic side chains of SARS-CoV-2 S are found to be involved in the hydrophobic interaction between SARS-CoV-2 S and ACE2. We propose a method to design live attenuated viruses by mutating several key amino acid residues of the spike protein to decrease the hydrophobic surface areas at the docking site. Mutation of a small amount of residues can greatly reduce the hydrophobic binding of the coronavirus to the receptor, which may be significant reduce infectivity and transmissibility of the virus.

We perform a bidimensional Stokes experiment in an active cellular material: an autonomously migrating monolayer of Madin-Darby Canine Kidney (MDCK) epithelial cells flows around a circular obstacle within a long and narrow channel, involving an interplay between cell shape changes and neighbour rearrangements. Based on image analysis of tissue flow and coarse-grained cell anisotropy, we determine the tissue strain rate, cell deformation and rearrangement rate fields, which are spatially heterogeneous. We find that the cell deformation and rearrangement rate fields correlate strongly, which is compatible with a Maxwell viscoelastic liquid behaviour (and not with a Kelvin-Voigt viscoelastic solid behaviour). The value of the associated relaxation time is measured as $\tau = 70 \pm 15$~min, is observed to be independent of obstacle size and division rate, and is increased by inhibiting myosin activity. In this experiment, the monolayer behaves as a flowing material with a Weissenberg number close to one which shows that both elastic and viscous effects can have comparable contributions in the process of collective cell migration., Comment: 17 pages, 15 figures

Stem cells can precisely and robustly undergo cellular differentiation and lineage commitment, referred to as stemness. However, how the gene network underlying stemness regulation reliably specifies cell fates is not well understood. To address this question, we applied a recently developed computational method, Random Circuit Perturbation (RACIPE), to a nine-component gene regulatory network (GRN) governing stemness, from which we identified fifteen robust gene states. Among them, four out of the five most probable gene states exhibit gene expression patterns observed in single mouse embryonic cells at 32-cell and 64-cell stages. These gene states can be robustly predicted by the stemness GRN but not by randomized versions of the stemness GRN. Strikingly, we found a hierarchical structure of the GRN with the Oct4/Cdx2 motif functioning as the first decision-making module followed by Gata6/Nanog. We propose that stem cell populations, instead of being viewed as all having a specific cellular state, can be regarded as a heterogeneous mixture including cells in various states. Upon perturbations by external signals, stem cells lose the capacity to access certain cellular states, thereby becoming differentiated. The findings demonstrate that the functions of the stemness GRN is mainly determined by its well-evolved network topology rather than by detailed kinetic parameters., Comment: 28 pages, 8 figures

Many complex systems, ranging from migrating cells to animal groups, exhibit stochastic dynamics described by the underdamped Langevin equation. Inferring such an equation of motion from experimental data can provide profound insight into the physical laws governing the system. Here, we derive a principled framework to infer the dynamics of underdamped stochastic systems from realistic experimental trajectories, sampled at discrete times and subject to measurement errors. This framework yields an operational method, Underdamped Langevin Inference, which performs well on experimental trajectories of single migrating cells and in complex high-dimensional systems, including flocks with Viscek-like alignment interactions. Our method is robust to experimental measurement errors, and includes a self-consistent estimate of the inference error.

An aster of microtubules is a set of flexible polar filaments with dynamic plus-ends, which irradiate from a common location at which the minus ends of the filaments are found. Processive soluble oligomeric motor complexes can bind simultaneously to two microtubules, and thus exert forces between two asters. Using computer simulations, I have explored systematically the possible steady-state regimes reached by two asters under the action of various kinds of oligomeric motors. As expected, motor complexes can induce the asters to fuse, for example when the complexes consist only of minus-end directed motors, or to fully separate, when the motors are plus-end directed. More surprisingly, complexes made of two motors of opposite directionalities can also lead to anti-parallel interactions between overlapping microtubules that are stable and sustained, like those seen in mitotic spindle structures. This suggests that such hetero-complexes could have significant biological role, if they exist in the cell., Comment: 26 pages, The final formated version can be downloaded at www.jcb.org

The cytoskeleton is essential for the maintenance of cell morphology in eukaryotes. In fission yeast for example, polarized growth sites are organized by actin whereas microtubules (MT) acting upstream control where growth occurs (La Carbona et al, 2006). Growth is limited to the cell poles when MTs undergo catastrophes there and not elsewhere on the cortex (Brunner and Nurse, 2000). Here we report that the modulation of MT dynamics by forces as observed in vitro (Dogterom and Yurke, 1997; Janson et al, 2003) can quantitatively explain the localization of MT catastro-phes in S. pombe. However, we found that it is necessary to add length-dependent catastrophe rates to make the model fully consistent with other measured traits of MTs. This result demonstrates the possibility that MTs together with associated proteins such as kinesins having a depolymerization activity can reliably mark the tips of the cell., 25 pages, 3 figures

Experimental results on the immune response to cancer indicate that activation of cytotoxic T lymphocytes (CTLs) through interactions with dendritic cells (DCs) can trigger a change in CTL migration patterns. In particular, while CTLs in the pre-activation state move in a non-local search pattern, the search pattern of activated CTLs is more localised. In this paper, we develop a kinetic model for such a switch in CTL migration modes. The model is formulated as a coupled system of balance equations for the one-particle distribution functions of CTLs in the pre-activation state, activated CTLs and DCs. CTL activation is modelled via binary interactions between CTLs in the pre-activation state and DCs. Moreover, cell motion is represented as a velocity-jump process, with the running time of CTLs in the pre-activation state following a long-tailed distribution, which is consistent with a L\'evy walk, and the running time of activated CTLs following a Poisson distribution, which corresponds to Brownian motion. We formally show that the macroscopic limit of the model comprises a coupled system of balance equations for the cell densities whereby activated CTL movement is described via a classical diffusion term, whilst a fractional diffusion term describes the movement of CTLs in the pre-activation state. The modelling approach presented here and its possible generalisations are expected to find applications in the study of the immune response to cancer and in other biological contexts in which switch from non-local to localised migration patterns occurs., Comment: 24 pages, 2 figures

We present a method for automatic cell classification in tissue samples using an automated training set from multiplexed immunofluorescence images. The method utilizes multiple markers stained in situ on a single tissue section on a robust hyperplex immunofluorescence platform (Cell DIVE, GE Healthcare) that provides multi-channel images allowing analysis at single cell/sub-cellular levels. The cell classification method consists of two steps: first, an automated training set from every image is generated using marker-to-cell staining information. This mimics how a pathologist would select samples from a very large cohort at the image level. In the second step, a probability model is inferred from the automated training set. The probabilistic model captures staining patterns in mutually exclusive cell types and builds a single probability model for the data cohort. We have evaluated the proposed approach to classify: i) immune cells in cancer and ii) brain cells in neurological degenerative diseased tissue with average accuracies above 95%., 2019 IEEE International Conference on Bioinformatics and Biomedicine (BIBM)

We study the chemotaxis of a population of genetically identical swimming bacteria undergoing run and tumble dynamics driven by stochastic switching between clockwise and counterclockwise rotation of the flagellar rotary system. Understanding chemotaxis quantitatively requires that one links the switching rate of the rotary system in a gradient of chemoattractant/repellant to experimental measures of the efficiency of a population of bacteria in moving up/down the gradient. Here we achieve this by using a probabilistic model and show that the response of a population to the gradient is complex. We find the changes to a phenotype (the steady state switching rate in the absence of gradients) affects the average speed of the response as well as the width of the distribution and both must be taken into account to optimise the overall response of the population in complex environments. This is due to the behaviour of individuals in the 'tails' of the distribution. Hence we show that for chemotaxis, the behaviour of atypical individuals can have a significant impact on the fitness of a population.

This paper proposes the use of Eukaryotic cells, namely astrocytes, to develop logic gates. The logic gates are achieved by manipulating the threshold of Ca$^{2+}$ ion flows between the cells, based on the input signals. Through wet-lab experiments that engineer the astrocytes cells with pcDNA3.1-hGPR17 genes, we show that both AND and OR gates can be implemented by controlling Ca$^{2+}$ signals that flow through the population. A reinforced learning platform is also presented in the paper to optimize two main parameters, which are the Ca$^{2+}$ activation threshold and time slot of input signals $T_b$ into the gate. This design platform caters for any size and connectivity of the cell population, by taking into consideration the delay and noise produced from the signalling between the cells, in order to fine-tune the activation threshold and input signal time slot parameters. To validate the effectiveness of the reinforced learning platform, a Ca$^{2+}$ Signalling-based Molecular Communications Simulator was used to simulate the signalling between the astrocyte cells. The results from the simulation showed that an optimum value for both the Ca$^{2+}$ activation threshold and time slot of input signals $T_b$ is required to achieve optimal computation accuracy, where up to 90\% accuracy for both the AND and OR gates can be achieved with the right combination of values. The reinforced learning platform for the engineered astrocytes to create digital logic gates can be used for future Neural-Molecular Computing chip, which can revolutionize brain implants that are constructed from engineered biological cells., Submitted to journal publication

Nematode species are well-known for their invariant cell lineage pattern during development. Combining knowledge about the fate specification induced by asymmetric division and the anti-correlation between cell cycle length and cell volume in Caenorhabditis elegans, we propose a model to simulate lineage initiation by altering cell volume segregation ratio in each division, and quantify the derived pattern's performance in proliferation speed, fate diversity and space robustness. The stereotypic pattern in C. elegans embryo is found to be one of the most optimal solutions taking minimum time to achieve the cell number before gastrulation, by programming asymmetric division as a strategy., 7 pages, 5 figures, 4 supplemental figures, 2 supplemental tables

Modeling cell interactions such as co-attraction and contact-inhibition of locomotion is essential for understanding collective cell migration. Here, we propose a novel deep reinforcement learning model for collective neural crest cell migration. We apply the deep deterministic policy gradient algorithm in association with a particle dynamics simulation environment to train agents to determine the migration path. Because of the different migration mechanisms of leader and follower neural crest cells, we train two types of agents (leaders and followers) to learn the collective cell migration behavior. For a leader agent, we consider a linear combination of a global task, resulting in the shortest path to the target source, and a local task, resulting in a coordinated motion along the local chemoattractant gradient. For a follower agent, we consider only the local task. First, we show that the self-driven forces learned by the leader cell point approximately to the placode, which means that the agent is able to learn to follow the shortest path to the target. To validate our method, we compare the total time elapsed for agents to reach the placode computed using the proposed method and the time computed using an agent-based model. The distributions of the migration time intervals calculated using the two methods are shown to not differ significantly. We then study the effect of co-attraction and contact-inhibition of locomotion to the collective leader cell migration. We show that the overall leader cell migration for the case with co-attraction is slower because the co-attraction mitigates the source-driven effect. In addition, we find that the leader and follower agents learn to follow a similar migration behavior as in experimental observations. Overall, our proposed method provides useful insight on how to apply reinforcement learning techniques to simulate collective cell migration.

We found evidence of dynamic scaling in the spreading of MDCK monolayer, which can be characterized by the Hurst exponent ${\alpha} = 0.86$ and the growth exponent ${\beta} = 0.73$, and theoretically and experimentally clarified the mechanism that governs the contour shape dynamics. During the spreading of the monolayer, it is known that so-called "leader cells" generate the driving force and lead the other cells. Our time-lapse observations of cell behavior showed that these leader cells appeared at the early stage of the spreading, and formed the monolayer protrusion. Informed by these observations, we developed a simple mathematical model that included differences in cell motility, cell-cell adhesion, and random cell movement. The model reproduced the quantitative characteristics obtained from the experiment, such as the spreading speed, the distribution of the increment, and the dynamic scaling law. Analysis of the model equation revealed that the model could reproduce the different scaling law from ${\alpha} = 0.5, {\beta} = 0.25$ to ${\alpha} = 0.9, {\beta} = 0.75$, and the exponents ${\alpha}, {\beta}$ were determined by the two indices: $\rho t$ and $c$. Based on the analytical result, parameter estimation from the experimental results was achieved. The monolayer on the collagen-coated dishes showed a different scaling law ${\alpha} = 0.74, {\beta} = 0.68$, suggesting that cell motility increased by 9 folds. This result was consistent with the assay of the single-cell motility. Our study demonstrated that the dynamics of the contour of the monolayer were explained by the simple model, and proposed a new mechanism that exhibits the dynamic scaling property., Comment: 11 pages, 6 figures, and supplemental materials

Bacteria evolve resistance to antibiotics by a multitude of mechanisms. A central, yet unsolved question is how resistance evolution affects cell growth at different drug levels. Here we develop a fitness model that predicts growth rates of common resistance mutants from their effects on cell metabolism. We map metabolic effects of resistance mutations in drug-free environments and under drug challenge; the resulting fitness trade-off defines a Pareto surface of resistance evolution. We predict evolutionary trajectories of dosage-dependent growth rates and resistance levels, as well as the prevalent resistance mechanism depending on drug and nutrient levels. These predictions are confirmed by empirical growth curves and genomic data of E. coli populations. Our results show that resistance evolution, by coupling major metabolic pathways, is strongly intertwined with systems biology and ecology of microbial populations., joint first authors: Fernanda Pinheiro, Omar Warsi; corresponding authors: Dan I. Andersson, Michael L\"assig

One of the characteristic features of many marine dinoflagellates is their bioluminescence, which lights up nighttime breaking waves or seawater sliced by a ship's prow. While the internal biochemistry of light production by these microorganisms is well established, the manner by which fluid shear or mechanical forces trigger bioluminescence is still poorly understood. We report controlled measurements of the relation between mechanical stress and light production at the single-cell level, using high-speed imaging of micropipette-held cells of the marine dinoflagellate $Pyrocystis~lunula$ subjected to localized fluid flows or direct indentation. We find a viscoelastic response in which light intensity depends on both the amplitude and rate of deformation, consistent with the action of stretch-activated ion channels. A phenomenological model captures the experimental observations., Comment: 6 pages, 5 figures plus 4 pages of Supplementary Material with 4 figures; videos available on website of REG

The emergence of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) disease (COVID-19) has posed a serious threat to global health. As no specific therapeutics are yet available to control disease evolution, more in-depth understanding of the pathogenic mechanisms induced by SARS-CoV-2 will help to characterize new targets for the management of COVID-19. The present study identified a specific set of biological pathways altered in primary human lung epithelium upon SARS-CoV-2 infection, and a comparison with SARS-CoV from the 2003 pandemic was studied. The transcriptomic profiles were also exploited as possible novel therapeutic targets, and anti-signature perturbation analysis predicted potential drugs to control disease progression. Among them, Mitogen-activated protein kinase kinase (MEK), serine-threonine kinase (AKT), mammalian target of rapamycin (mTOR) and I kappa B Kinase (IKK) inhibitors emerged as candidate drugs. Finally, sex-specific differences that may underlie the higher COVID-19 mortality in men are proposed.

Titanium surface treated with titanium oxide nanotubes was used in many studies to quantify the effect of surface topography on cell fate. However, the predicted optimal diameter of nanotubes considerably differs among studies. We propose a model that explain cell adhesion to nanostructured surface by considering deformation energy of cell protrusions into titanium nanotubes and adhesion to surface. The optimal surface topology is defined as a geometry that gives membrane a minimum energy shape. A dimensionless parameter, the cell interaction index, was proposed to describe interplay between the cell membrane bending, intrinsic curvature and strength of cell adhesion. Model simulation show that optimal nanotube diameter ranging from 20 nm to 100 nm (cell interaction index between 0.2 and 1, respectively) is feasible within certain range of parameters describing adhesion and bending energy. The results indicates a possibility to tune the topology of nanostructural surface in order to enhance proliferation and differentation of cells mechanically compatible with given surface geometry while suppress the growth of other mechanically incompatible cells.

AGF was supported by a Vice-Chancellor's Fellowship from the University of Sheffield, LJS was supported by a Chancellor's Fellowship from the University of Edinburgh. The deluge of single-cell data obtained by sequencing, imaging and epigenetic markers has led to an increasingly detailed description of cell state. However, it remains challenging to identify how cells transition between different states, in part because data are typically limited to snapshots in time. A prerequisite for inferring cell state transitions from such snapshots is to distinguish whether transitions are coupled to cell divisions. To address this, we present two minimal branching process models of cell division and differentiation in a well-mixed population. These models describe dynamics where differentiation and division are coupled or uncoupled. For each model, we derive analytic expressions for each subpopulation's mean and variance and for the likelihood, allowing exact Bayesian parameter inference and model selection in the idealised case of fully observed trajectories of differentiation and division events. In the case of snapshots, we present a sample path algorithm and use this to predict optimal temporal spacing of measurements for experimental design. We then apply this methodology to an in vitro dataset assaying the clonal growth of epiblast stem cells in culture conditions promoting self-renewal or differentiation. Here, the larger number of cell states necessitates approximate Bayesian computation. For both culture conditions, our inference supports the model where cell state transitions are coupled to division. For culture conditions promoting differentiation, our analysis indicates a possible shift in dynamics, with these processes becoming more coupled over time. Publisher PDF

Multicellular tissues are the building blocks of many biological systems and organs. These tissues are not static, but dynamically change over time. Even if the overall structure remains the same there is a turnover of cells within the tissue. This dynamic homeostasis is maintained by numerous governing mechanisms which are finely tuned in such a way that the tissue remains in a homeostatic state, even across large timescales. Some of these governing mechanisms include cell motion, and cell fate selection through inter cellular signalling. However, it is not yet clear how to link these two processes, or how they may affect one another across the tissue. In this paper, we present a multicellular, multiscale model, which brings together the two phenomena of cell motility, and inter cellular signalling, to describe cell fate selection on a dynamic tissue. We find that the affinity for cellular signalling to occur greatly influences a cells ability to differentiate. We also find that our results support claims that cell differentiation is a finely tuned process within dynamic tissues at homeostasis, with excessive cell turnover rates leading to unhealthy (undifferentiated and unpatterned) tissues.

We investigate Turing pattern formation in a stochastic and spatially discretized version of a reaction diffusion advection (RDA) equation, which was previously introduced to model synaptogenesis in \textit{C. elegans}. The model describes the interactions between a passively diffusing molecular species and an advecting species that switches between anterograde and retrograde motor-driven transport (bidirectional transport). Within the context of synaptogenesis, the diffusing molecules can be identified with the protein kinase CaMKII and the advecting molecules as glutamate receptors. The stochastic dynamics evolves according to an RDA master equation, in which advection and diffusion are both modeled as hopping reactions along a one-dimensional array of chemical compartments. Carrying out a linear noise approximation of the RDA master equation leads to an effective Langevin equation, whose power spectrum provides a means of extending the definition of a Turing instability to stochastic systems, namely, in terms of the existence of a peak in the power spectrum at a non-zero spatial frequency. We thus show how noise can significantly extend the range over which spontaneous patterns occur, which is consistent with previous studies of RD systems., Comment: 26 pages, 8 figures

Here we report on the viscosity of eukaryotic living cells as a function of the time, and on the application of stochastic models to analyze its temporal fluctuations. The viscoelastic properties of NIH/3T3 fibroblastic cells are investigated using an active microrheological technique, where magnetic wires, embedded into cells, are being actuated remotely. The data reveal anomalous transient responses characterized by intermittent phases of slow and fast rotation, revealing significant fluctuations. The time dependent viscosity is analyzed from a time series perspective by computing the autocorrelation functions and the variograms, two functions used to describe stochastic processes in mathematical finance. The resulting analysis gives evidence of a sub-diffusive mean-reverting process characterized by an autoregressive coefficient lower than 1. It also shows the existence of specific cellular times in the ranges 1 - 10 s and 100 - 200 s, not previously disclosed. The shorter time is found being related to the internal relaxation time of the cytoplasm. To our knowledge, this is the first time that similarities are established between the properties of time series describing the intracellular metabolism and statistical results from mathematical finance. The current approach could be exploited to reveal hidden features from biological complex systems, or determine new biomarkers of cellular metabolism., Comment: 19 pages, 8 figures, 3 tables

Cells perform directed motion in response to external stimuli that they detect by sensing the environment with their membrane protrusions. In particular, several biochemical and biophysical cues give rise to tactic migration in the direction of their specific targets. This defines a multi-cue environment in which cells have to sort and combine different, and potentially competitive, stimuli. We propose a non-local kinetic model for cell migration in presence of two external factors both influencing cell polarization: contact guidance and chemotaxis. We propose two different sensing strategies and we analyze the two resulting models by recovering the appropriate macroscopic limit in different regimes, in order to see how the size of the cell, with respect to the variation of both external fields, influences the overall behavior. Moreover, we integrate numerically the kinetic transport equation in a two-dimensional setting in order to investigate qualitatively various scenarios., 34 pages, 10 figures. References added

Microtubule (MT) radial arrays or asters establish the internal topology of a cell by interacting with organelles and molecular motors. We proceed to understand the general pattern forming potential of aster-motor systems using a computational model of multiple MT asters interacting with motors in a cellular confinement. In this model dynein motors are attached to the cell cortex and plus-ended motors resembling kinesin-5 diffuse in the cell interior. The introduction of 'noise' in the form of MT length fluctuations spontaneously results in the emergence of coordinated, achiral vortex-like rotation of asters. The coherence and persistence of rotation requires a threshold density of both cortical dyneins and coupling kinesins, while the onset of rotation if diffusion-limited with relation to cortical dynein mobility. The coordinated rotational motion arises due to the resolution of the 'tug-of-war' of the rotational component due to cortical motors by 'noise' in the form of MT dynamic instability, and such transient symmetry breaking is amplified by local coupling by kinesin-5 complexes. The lack of widespread aster rotation across cell types suggests biophysical mechanisms that suppress such intrinsic dynamics may have evolved. This model is analogous to more general models of locally coupled self-propelled particles (SPP) that spontaneously undergo collective transport in presence of 'noise' that have been invoked to explain swarming in birds and fish. However, the aster-motor system is distinct from SPP models with regard to particle density and 'noise' dependence, providing a set of experimentally testable predictions for a novel sub-cellular pattern forming system.

The motion of cells in tissues is an ubiquitous phenomenon. In particular, in monolayered cell colonies in vitro, pronounced collective behavior with swirl-like motion has been observed deep within a cell colony, while at the same time, the colony remains cohesive, with not a single cell escaping at the edge. Thus, the colony displays liquid-like properties inside, in coexistence with a cell-free "vacuum" outside. How can adhesion be strong enough to keep cells together, while at the same time not jam the system in a glassy state? What kind of minimal model can describe such a behavior? Which other signatures of activity arise from the internal fluidity? We propose a novel active Brownian particle model with attraction, in which the interaction potential has a broad minimum to give particles enough wiggling space to be collectively in the fluid state. We demonstrate that for moderate propulsion, this model can generate the fluid-vacuum coexistence described above. In addition, the combination of the fluid nature of the colony with cohesion leads to preferred orientation of the cell polarity, pointing outward, at the edge, which in turn gives rise to a tensile stress in the colony -- as observed experimentally for epithelial sheets. For stronger propulsion, collective detachment of cell clusters is predicted. Further addition of an alignment preference of cell polarity and velocity direction results in enhanced coordinated, swirl-like motion, increased tensile stress and cell-cluster detachment.

We analyze oscillatory instabilities for a coupled PDE-ODE system modeling the communication between localized spatially segregated dynamically active signaling compartments that are coupled through a passive extracellular bulk diffusion field in a bounded 2-D domain. Each signaling compartment is assumed to secrete a chemical into the extracellular medium (bulk region) and it can also sense the concentration of this chemical in the region around its boundary. This feedback from the bulk region, resulting from the entire collection of cells, in turn modifies the intracellular dynamics within each cell. In the limit where the signaling compartments are circular disks with a small common radius $\epsilon \ll 1$ and where the bulk diffusivity is asymptotically large, a matched asymptotic analysis is used to reduce the dimensionless PDE-ODE system into a nonlinear ODE system with global coupling. For Sel'kov reaction kinetics, this ODE system for the intracellular dynamics and the spatial average of the bulk diffusion field is then used to investigate oscillatory instabilities in the dynamics of the cells that are triggered due to the global coupling. In particular, numerical bifurcation software on the ODEs is used to study the overall effect of coupling defective cells (cells that behave differently from the remaining cells) to a group of identical cells. Moreover, when the number of cells is large, the Kuramoto order parameter is computed to predict the degree of phase synchronization of the intracellular dynamics. Quorum sensing behavior, characterized by the onset of collective behavior in the intracellular dynamics as the number of cells increases above a threshold, is also studied. Our analysis shows that the cell population density plays a dual role of triggering and then quenching synchronous oscillations in the intracellular dynamics., Comment: 25 pages, 68 figures

In December 2019, a newly discovered SARS-CoV-2 virus was emerged from China and propagated worldwide as a pandemic. In the absence of preventive medicine or a ready to use vaccine, mathematical models can provide useful scientific insights about transmission patterns and targets for drug development. In this study, we propose a within-host mathematical model of SARS-CoV-2 infection considering innate and adaptive immune responses. We analyze the equilibrium points of the proposed model and obtain an expression of the basic reproduction number. We then numerically show the existence of a transcritical bifurcation. The proposed model is calibrated to real viral load data of two COVID-19 patients. Using the estimated parameters, we perform global sensitivity analysis with respect to the peak of viral load. Finally, we study the efficacy of antiviral drugs and vaccination on the dynamics of SARS-CoV-2 infection. Our results suggest that blocking the production of the virus by infected cells decreases the viral load more than reducing the infection rate of healthy cells. Vaccination is also found useful but during the vaccine development phase, blocking virus production from infected cells can be targeted for antiviral drug development., 19 pages, 1 table, 7 figures

The chemotactic network of Escherichia coli has been studied extensively both biophysically and information theoretically. Nevertheless, connection between these two aspects is still elusive. In this work, we report such a connection. We derive an optimal filtering dynamics under the assumption that E. coli's sensory system optimally infers the binary information whether it is swimming up or down along an exponential ligand gradient from noisy sensory signals. Then we show that a standard biochemical model of the chemotactic network is mathematically equivalent to this information-theoretically optimal dynamics. Moreover, we demonstrate that an experimentally observed nonlinear response relation can be reproduced from the optimal dynamics. These results suggest that the biochemical network of E. coli chemotaxis is designed to optimally extract the binary information along an exponential gradient in a noisy condition.

Cell crawling requires the generation of intracellular forces by the cytoskeleton and their transmission to an extracellular substrate through specific adhesion molecules. Crawling cells show many features of excitable systems, such as spontaneous symmetry breaking and crawling in the absence of external cues, and periodic and propagating waves of activity. Mechanical instabilities in the active cytoskeleton network and feedback loops in the biochemical network of activators and repressors of cytoskeleton dynamics have been invoked to explain these dynamical features. Here, we show that the interplay between the dynamics of cell-substrate adhesion and linear cellular mechanics is sufficient to reproduce many non-linear dynamical patterns observed in spreading and crawling cells. Using an analytical formalism of the molecular clutch model of cell adhesion, regulated by local mechanical forces, we show that cellular traction forces exhibit a stick-slip dynamics resulting in periodic waves of protrusion/retraction and propagating waves along the cell edge. This can explain spontaneous symmetry breaking and polarisation of spreading cells, leading to steady crawling or bipedal motion, and bistability, where persistent cell motion requires a sufficiently strong transient external stimulus. The model also highlight the role of membrane tension in providing the long-range mechanical communication across the cell required for symmetry breaking., 12 pages, 5 figures

Partial hepatectomy (PHx) is a surgical intervention where a part of the liver is removed. Due to its extraordinary capacity to regenerate, the liver is able to regenerate about two-thirds of its mass within a few weeks. Nevertheless, in some patients regeneration fails. Understanding the principles and limitations underlying regeneration may permit to control this process and prospectively improve the regeneration. Here, we established a simulation model to mimic the process of regeneration in the liver lobe of a mouse. This model represents each hepatocyte individually and builds upon a previous computational model of regeneration of drug induced damage in a single liver lobule. The present study simulates entire liver lobes that consist of hundreds to thousands of lobules. It accounts for biomechanical control of cell cycle progression (Biomechanical Growth Control), which has not been considered in that previous work. The model reproduced the available experimental observations only if BGC was taken into account. Interestingly, the model predicted that BGC minimizes the number of proliferating neighbor cells of a proliferating cell resulting in a checkerboard-like proliferation pattern. Moreover, the model predicted different cell proliferation patterns in pigs and mice that corresponded to data obtained from regenerating tissue of the two species. In conclusion, the here established model suggest that biomechanical control mechanisms may play a significant role in liver regeneration after PHx.

We propose a model of antibiotic diffusion through a bacterial biofilm when diffusion and/or absorption barriers develop in the biofilm. The idea of this model is: We deduce details of the diffusion process in a medium in which direct experimental study is difficult, based on probing diffusion in external regions. Since a biofilm has a gel-like consistency, we suppose that subdiffusion of particles in the biofilm may occur. To describe this process we use a fractional subdiffusion-absorption equation with an adjustable anomalous diffusion exponent. The boundary conditions at the boundaries of the biofilm are derived by means of a particle random walk model on a discrete lattice leading to an expression involving a fractional time derivative. We show that the temporal evolution of the total amount of substance that has diffused through the biofilm explicitly depends on whether there is antibiotic absorption in the biofilm. This fact is used to experimentally check for antibiotic absorption in the biofilm and if the biofilm parameters change over time. We propose a four-stage model of antibiotic diffusion in biofilm based on the mentioned above physical characteristics. The biological interpretation of the stages, in particular their relation with the bacterial defence mechanisms, is discussed. Theoretical results are compared with empirical results of ciprofloxacin diffusion through Pseudomonas aeruginosa biofilm, and ciprofloxacin and gentamicin diffusion through Proteus mirabilis biofilm., 11 pages, 6 figures

Cells are known to sense and respond to their mechanical microenvironment in profound ways. Various evidence has implicated the adhesome, a body of adhesion associated proteins, in several cell fate decisions, including differentiation and proliferation. Furthermore, recent work has demonstrated that substrate topography can modulate the epigenetic state of fibroblasts, facilitate cell reprogramming, and temper inflammation. However, the effectors responsible for such phenomena remain poorly understood. Here we explore the effect of biomaterial design, adhesion, and intracellular forces of the epigenetic and transcriptional regulation of cell state during macrophage activation and somatic cell reprogramming., PhD thesis (2019)

Collective cell migration is crucial in many biological processes such as wound healing, tissue morphogenesis, and tumor progression. The leading front of a collective migrating epithelial cell layer often destabilizes into multicellular finger-like protrusions, each of which is guided by a leader cell at the fingertip. Here, we develop a subcellular-element-based model of this fingering instability, which incorporates leader cells and other related properties of a monolayer of epithelial cells. Our model recovers multiple aspects of the dynamics, especially the traction force patterns and velocity fields, observed in experiments on Madin-Darby canine kidney cells. Our model predicts the necessity of the leader cell and its minimal functions for the formation and maintenance of a stable finger pattern. Meanwhile, our model allows for an analysis of the role of supracellular actin cable on the leading front, predicting that while this observed structure helps maintain the shape of the finger, it is not required in order to form a finger. In addition, we also study the driving instability in the context of continuum active fluid model, which justifies some of our assumptions in the computational approach. In particular, we show that in our model no finger protrusions would emerge in a phenotypically homogenous active fluid and hence the role of the leader cell and its followers are often critical.

It is difficult to predict how antibodies will behave when mixed together, even after each has been independently characterized. Here, we present a statistical mechanical model for the activity of antibody mixtures that accounts for whether pairs of antibodies bind to distinct or overlapping epitopes. This model requires measuring n individual antibodies and their n(n-1)2 pairwise interactions to predict the 2n potential combinations. We apply this model to epidermal growth factor receptor (EGFR) antibodies and find that the activity of antibody mixtures can be predicted without positing synergy at the molecular level. In addition, we demonstrate how the model can be used in reverse, where straightforward experiments measuring the activity of antibody mixtures can be used to infer the molecular interactions between antibodies. Lastly, we generalize this model to analyze engineered multidomain antibodies, where components of different antibodies are tethered together to form novel amalgams, and characterize how well it predicts recently designed influenza antibodies., Author summary With the rise of new antibody combinations in therapeutic regimens, it is important to understand how antibodies work together as well as individually. Here, we investigate the specific case of monoclonal antibodies targeting a cancer-causing receptor or the influenza virus and develop a statistical mechanical framework that predicts the effectiveness of a mixture of antibodies. The power of this model lies in its ability to make a large number of predictions based on a limited amount of data. For example, once 10 antibodies have been individually characterized and their epitopes have been mapped, our model can predict how any of the 210 = 1024 combinations will behave. This predictive power can aid therapeutic efforts by assessing which combinations of antibodies will elicit the most effective response.

Cells are constantly exposed to DNA damaging insults. To protect the organism, cells developed a complex molecular response coordinated by P53, the master regulator of DNA repair, cell division and cell fate. DNA damage accumulation and abnormal cell fate decision may represent a pathomechanism shared by aging-associated disorders such as cancer and neurodegeneration. Here, we examined this hypothesis in the context of tauopathies, a neurodegenerative disorder group characterized by Tau protein deposition. For this, the response to an acute DNA damage was studied in neuroblastoma cells with depleted Tau, as a model of loss-of-function. Under these conditions, altered P53 stability and activity result in reduced cell death and increased cell senescence. This newly discovered function of Tau involves abnormal modification of P53 and its E3 ubiquitin ligase MDM2. Considering the medical need with vast social implications caused by neurodegeneration and cancer, our study may reform our approach to disease-modifying therapies., Comment: 36 pages, 8 figures, 11 supplementary figures

We present a minimal driven lattice gas model which generates the morphological characteristics associated with single colony mycelium arising from the growth and branching process of fungal hyphae, which is fed by a single source of nutrients. We first analyze the growth and transport process in the primary hypha modeled as a growing 1-d lattice, which is subject to particle (vesicle) loss due to presence of dynamically created branching sites. We show that the spatial profile of vesicles along the growing lattice is an exponential distribution, while the length grows logarithmically with time. We also find that the probability distribution of length of the hypha tends to a Gaussian distribution function at late times. In contrast, the probability distribution function of the time required for growth to a specific length tends to a broad log-normal distribution. We simulate the resultant 2-d morphology generated by the growing primary hypha, quantifying the motility behavior and morphological characteristics of the colony. Analysis of the temporal behavior and morphological characteristics of the resultant 2-d morphology reveals a wide variability of these characteristics which depend on the input parameters which characterize the branching and elongation dynamics of the hyphae. By calibrating the input parameters for our model, we make some quantitative comparison of the predictions of our model with the observed experimental growth characteristics of fungal hyphae and the morphological characteristics of single colony fungal mycelium., Comment: 12 pages, 10 figures

As zebrafish develop, black and gold stripes form across their skin due to the interactions of brightly colored pigment cells. These characteristic patterns emerge on the growing fish body, as well as on the anal and caudal fins. While wild-type stripes form parallel to a horizontal marker on the body, patterns on the tailfin gradually extend distally outward. Interestingly, several mutations lead to altered body patterns without affecting fin stripes. Through an exploratory modeling approach, our goal is to help better understand these differences between body and fin patterns. By adapting a prior agent-based model of cell interactions on the fish body, we present an in silico study of stripe development on tailfins. Our main result is a demonstration that two cell types can produce stripes on the caudal fin. We highlight several ways that bone rays, growth, and the body-fin interface may be involved in patterning, and we raise questions for future work related to pattern robustness.

Metastatic cancer cells detect the direction of lymphatic flow by self-communication: they secrete and detect a chemical which, due to the flow, returns to the cell surface anisotropically. The secretion rate is low, meaning detection noise may play an important role, but the sensory precision of this mechanism has not been explored. Here we derive the precision of flow sensing for two ubiquitous detection methods: absorption vs.\ reversible binding to surface receptors. We find that binding is more precise due to the fact that absorption distorts the signal that the cell aims to detect. Comparing to experiments, our results suggest that the cancer cells operate remarkably close to the physical detection limit. Our prediction that cells should bind the chemical reversibly, not absorb it, is supported by endocytosis data for this ligand-receptor pair., 27 pages, 6 figures

International audience; Reduced blood flow, as occurring in ischemia or resulting from exposure to microgravity such as encountered in space flights, induces a decrease in the level of shear stress sensed by the endothelial cells forming the inner part of blood vessels. In the present study, we use a microvasculature-on-a-chip device in order to investigate in vitro the effect of such a reduction in shear stress on shear-adapted endothelial cells. We find that, within one hour of exposition to reduced wall shear stress, human umbilical vein endothelial cells undergo a reorganization of their actin skeleton, with a decrease in the number of stress fibers and actin being recruited into the cells' peripheral band, indicating a fairly fast change in cells' phenotype due to altered flow.

The improved in vitro regulation of human embryonic stem cell (hESC) pluripotency and differentiation trajectories is required for their promising clinical applications. The temporal and spatial quantification of the molecular interactions controlling pluripotency is also necessary for the development of successful mathematical and computational models. Here we use time-lapse experimental data of OCT4-mCherry fluorescence intensity to quantify the temporal and spatial dynamics of the pluripotency transcription factor OCT4 in a growing hESC colony in the presence and absence of BMP4. We characterise the internal self-regulation of OCT4 using the Hurst exponent and autocorrelation analysis, quantify the intra-cellular fluctuations and consider the diffusive nature of OCT4 evolution for individual cells and pairs of their descendants. We find that OCT4 abundance in the daughter cells fluctuates sub-diffusively, showing anti-persistent self-regulation. We obtain the stationary probability distributions governing hESC transitions amongst the different cell states and establish the times at which pro-fate cells (which later give rise to pluripotent or differentiated cells) cluster in the colony. By quantifying the similarities between the OCT4 expression amongst neighbouring cells, we show that hESCs express similar OCT4 to cells within their local neighbourhood within the first two days of the experiment and before BMP4 treatment. Our framework allows us to quantify the relevant properties of proliferating hESC colonies and the procedure is widely applicable to other transcription factors and cell populations.

Induced pluripotent stem cells (iPSCs) provide a great model to study the process of reprogramming and differentiation of stem cells. Single-cell RNA sequencing (scRNA-seq) enables us to investigate the reprogramming process at single-cell level. Here, we introduce single-cell entropy (scEntropy) as a macroscopic variable to quantify the cellular transcriptome from scRNA-seq data during reprogramming and differentiation of iPSCs. scEntropy measures the relative order parameter of genomic transcriptions at single cell level during the cell fate change process, which shows increasing during differentiation, and decreasing upon reprogramming. Moreover, based on the scEntropy dynamics, we construct a phenomenological stochastic differential equation model and the corresponding Fokker-Plank equation for cell state transitions during iPSC differentiation, which provide insights to infer cell fates changes and stem cell differentiation. This study is the first to introduce the novel concept of scEntropy to the biological process of iPSC, and suggests that the scEntropy can provide a suitable quantify to describe cell fate transition in differentiation and reprogramming of stem cells., 12 pages, 5 figures

In stable environments, cell size fluctuations are thought to be governed by simple physical principles, as suggested by recent findings of scaling properties. Here, by developing a microfluidic device and using E. coli, we investigate the response of cell size fluctuations against starvation. By abruptly switching to non-nutritious medium, we find that the cell size distribution changes but satisfies scale invariance: the rescaled distribution is kept unchanged and determined by the growth condition before starvation. These findings are underpinned by a model based on cell growth and cell cycle. Further, we numerically determine the range of validity of the scale invariance over various characteristic times of the starvation process, and find the violation of the scale invariance for slow starvation. Our results, combined with theoretical arguments, suggest the relevance of the multifork replication, which helps retaining information of cell cycle states and may thus result in the scale invariance., 15+23 pages, 5+11 figures and 2 tables

There is no vaccine or specific antiviral treatment for COVID-19. One current focus is drug repurposing research, but those drugs have limited therapeutic efficacies and known adverse effects. The pathology of COVID-19 is essentially unknown. It is therefore challenging to discover a successful treatment to be approved for clinical use. This paper addresses several key biological processes of reactive oxygen, halogen and nitrogen species (ROS, RHS and RNS) that play crucial physiological roles in organisms from plants to humans. These include why superoxide dismutases, the enzymes to catalyze the formation of H2O2, are required for protecting ROS-induced injury in cell metabolism, why the amount of ROS/RNS produced by ionizing radiation at clinically relevant doses is ~1000 fold lower than the endogenous ROS/RNS level routinely produced in the cell and why a low level of endogenous RHS plays a crucial role in phagocytosis for immune defense. Herein we propose a plausible amplification mechanism in immune defense: ozone-depleting-like halogen cyclic reactions enhancing RHS effects are responsible for all the mentioned physiological functions, which are activated by H2O2 and deactivated by NO signaling molecule. Our results show that the reaction cycles can be repeated thousands of times and amplify the RHS pathogen-killing (defense) effects by 100,000 fold in phagocytosis, resembling the cyclic ozone-depleting reactions in the stratosphere. It is unraveled that H2O2 is a required protective signaling molecule (angel) in the defense system for human health and its dysfunction can cause many diseases or conditions such as autoimmune disorders, aging and cancer. We also identify a class of potent drugs for effective treatment of invading pathogens such as HIV and SARS-CoV-2 (COVID-19), cancer and other diseases, and provide a molecular mechanism of action of the drugs or candidates., 18 pages, 4 figures, 1 table

Heterologous gene expression draws resources from host cells. These resources include vital components to sustain growth and replication, and the resulting cellular burden is a widely recognised bottleneck in the design of robust circuits. In this tutorial we discuss the use of computational models that integrate gene circuits and the physiology of host cells. Through various use cases, we illustrate the power of host-circuit models to predict the impact of design parameters on both burden and circuit functionality. Our approach relies on a new generation of computational models for microbial growth that can flexibly accommodate resource bottlenecks encountered in gene circuit design. Adoption of this modelling paradigm can facilitate fast and robust design cycles in synthetic biology.

Cell detection and segmentation is fundamental for all downstream analysis of digital pathology images. However, obtaining the pixel-level ground truth for single cell segmentation is extremely labor intensive. To overcome this challenge, we developed an end-to-end deep learning algorithm to perform both single cell detection and segmentation using only point labels. This is achieved through the combination of different task orientated point label encoding methods and a multi-task scheduler for training. We apply and validate our algorithm on PMS2 stained colon rectal cancer and tonsil tissue images. Compared to the state-of-the-art, our algorithm shows significant improvement in cell detection and segmentation without increasing the annotation efforts.

We present ESCELL, a method for developing an emergent symbolic language of communication between multiple agents reasoning about cells. We show how agents are able to cooperate and communicate successfully in the form of symbols similar to human language to accomplish a task in the form of a referential game (Lewis' signaling game). In one form of the game, a sender and a receiver observe a set of cells from 5 different cell phenotypes. The sender is told one cell is a target and is allowed to send one symbol to the receiver from a fixed arbitrary vocabulary size. The receiver relies on the information in the symbol to identify the target cell. We train the sender and receiver networks to develop an innate emergent language between themselves to accomplish this task. We observe that the networks are able to successfully identify cells from 5 different phenotypes with an accuracy of 93.2%. We also introduce a new form of the signaling game where the sender is shown one image instead of all the images that the receiver sees. The networks successfully develop an emergent language to get an identification accuracy of 77.8%., IEEE International Symposium on Biomedical Imaging (IEEE ISBI 2020)

Unraveling bacterial strategies for spatial exploration is crucial for understanding the complexity in the organization of life. Bacterial motility determines the spatio-temporal structure of microbial communities, controls infection spreading and the microbiota organization in guts or in soils. Most theoretical approaches for modeling bacterial transport rely on their run-and-tumble motion. For Escherichia coli, the run time distribution was reported to follow a Poisson process with a single characteristic time related to the rotational switching of the flagellar motors. However, direct measurements on flagellar motors show heavy-tailed distributions of rotation times stemming from the intrinsic noise in the chemotactic mechanism. Currently, there is no direct experimental evidence that the stochasticity in the chemotactic machinery affect the macroscopic motility of bacteria. In stark contrast with the accepted vision of run-and-tumble, here we report a large behavioral variability of wild-type \emph{E. coli}, revealed in their three-dimensional trajectories. At short observation times, a large distribution of run times is measured on a population and attributed to the slow fluctuations of a signaling protein triggering the flagellar motor reversal. Over long times, individual bacteria undergo significant changes in motility. We demonstrate that such a large distribution of run times introduces measurement biases in most practical situations. Our results reconcile the notorious conundrum between run time observations and motor switching statistics. We finally propose that statistical modeling of transport properties currently undertaken in the emerging framework of active matter studies, should be reconsidered under the scope of this large variability of motility features., 12 pages, 7 figures, Supplementary information included

Phase-field models have recently had great success in describing the dynamic morphologies and motility of eukaryotic cells. In this work we investigate the minimal phase-field model introduced in [Berlyand, Potomkin, Rybalko (2017)]. Rigorous analysis of its sharp interface limit dynamics was completed in [Mizuhara, Berlyand, Rybalko, Zhang (2016); Mizuhara, Zhang (2019)], where it was observed that persistent cell motion was not stable. In this work we numerically study the pre-limiting phase-field model near the sharp interface limit, to better understand this lack of persistent motion. We find that immobile, persistent, and rotating states are all exhibited in this minimal model, and investigate the loss of persistent motion in the sharp interface limit. In addition we study cell speed as a function of biophysical parameters., 18 pages, 5 figures

By embedding inert tracer particles (TPs) in a growing multicellular spheroid the local stresses on the cancer cells (CCs) can be measured. In order for this technique to be effective the unknown effect of the dynamics of the TPs on the CCs has to be elucidated to ensure that the TPs do not greatly alter the local stresses on the CCs. We show, using theory and simulations, that the self-generated (active) forces arising from proliferation and apoptosis of the CCs drive the dynamics of the TPs far from equilibrium. On time scales less than the division times of the CCs, the TPs exhibit sub-diffusive dynamics (the mean square displacement, $\Delta_{TP}(t) \sim t^{\beta_{TP}}$ with $\beta_{TP}2$) due to persistent directed motion for long times. In comparison, proliferation of the CCs randomizes their motion leading to superdiffusive behavior with $\alpha_{CC}$ exceeding unity. Most importantly, $\alpha_{CC}$ is not significantly affected by the TPs. Our predictions could be tested using \textit{in vitro} imaging methods where the motion of the TPs and the CCs can be tracked., Comment: 5 pages, 5 figures

Gene expression and chromatin conformation reliably distinguish cell types, enabling equation-free control of human cells., The relationship between microscopic observations and macroscopic behavior is a fundamental open question in biophysical systems. Here, we develop a unified approach that—in contrast with existing methods—predicts cell type from macromolecular data even when accounting for the scale of human tissue diversity and limitations in the available data. We achieve these benefits by applying a k-nearest-neighbors algorithm after projecting our data onto the eigenvectors of the correlation matrix inferred from many observations of gene expression or chromatin conformation. Our approach identifies variations in epigenotype that affect cell type, thereby supporting the cell-type attractor hypothesis and representing the first step toward model-independent control strategies in biological systems.