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arXiv2016

Shape dynamics of growing cell walls

We introduce a general theoretical framework to study the shape dynamics of actively growing and remodeling surfaces. Using this framework we develop a physical model for growing bacterial cell walls and study the interplay of cell shape with the dynamics of growth and constriction. The model allows us to derive constraints on cell wall mechanical energy based on the observed dynamics of cell shape. We predict that exponential growth in cell size requires a constant amount of cell wall energy to be dissipated per unit volume. We use the model to understand and contrast growth in bacteria with different shapes such as spherical, ellipsoidal, cylindrical and toroidal morphologies. Coupling growth to cell wall constriction, we predict a discontinuous shape transformation, from partial constriction to cell division, as a function of the chemical potential driving cell-wall synthesis. Our model for cell wall energy and shape dynamics relates growth kinetics with cell geometry, and provides a unified framework to describe the interplay between shape, growth and division in bacterial cells.

physics.bio-ph↗

arXiv2015

A stochastic model for tumor heterogeneity

Phenotype variations define heterogeneity of biological and molecular systems, which play a crucial role in several mechanisms. Heterogeneity has been demonstrated in tumor cells. Here, samples from blood of patients affected from colon tumor were analyzed and fished with a microfluidic assay based on galactose active moieties, and incubated, for culturing, in SCID mice. Following the experimental investigation, a model based on Markov theory was implemented and discussed to explain the equilibrium existing between phenotypes of subpopulations of cells sorted using the microfluidic assay. The model in combination with the experimental results had many implications for tumor heterogeneity. It displayed interconversion of phenotypes, as observed after experiments. The interconversion generates of metastatic cells and implies that targeting the CTCs will be not an efficient method to prevent tumor recurrence. Most importantly, understanding the transitions between cell phenotypes in cell population can boost the understanding of tumor generation and growth.

physics.bio-ph↗

arXiv2015

Dynamic curvature regulation accounts for the symmetric and asymmetric beats of Chlamydomonas flagella

Axonemal dyneins are the molecular motors responsible for the beating of cilia and flagella. These motors generate sliding forces between adjacent microtubule doublets within the axoneme, the motile cytoskeletal structure inside the flagellum. To create regular, oscillatory beating patterns, the activities of the axonemal dyneins must be coordinated both spatially and temporally. It is thought that coordination is mediated by stresses or strains that build up within the moving axoneme, but it is not known which components of stress or strain are involved, nor how they feed back on the dyneins. To answer this question, we used isolated, reactivate axonemes of the unicellular alga Chlamydomonas as a model system. We derived a theory for beat regulation in a two-dimensional model of the axoneme. We then tested the theory by measuring the beat waveforms of wild type axonemes, which have asymmetric beats, and mutant axonemes, in which the beat is nearly symmetric, using high-precision spatial and temporal imaging. We found that regulation by sliding forces fails to account for the measured beat, due to the short lengths of Chlamydomonas cilia. We found that regulation by normal forces (which tend to separate adjacent doublets) cannot satisfactorily account for the symmetric waveforms of the mbo2 mutants. This is due to the model's failure to produce reciprocal inhibition across the axes of the symmetrically beating axonemes. Finally, we show that regulation by curvature accords with the measurements. Unexpectedly, we found that the phase of the curvature feedback indicates that the dyneins are regulated by the dynamic (i.e. time-varying) component of axonemal curvature, but not by the static one. We conclude that a high-pass filtered curvature signal is a good candidate for the signal that feeds back to coordinate motor activity in the axoneme.

physics.bio-ph↗

arXiv2015

Modeling the Multiple Myeloma Vicious Cycle: Signaling Across the Bone Marrow Microenvironment

Multiple myeloma is a plasma cell cancer that leads to a dysregulated bone remodeling process. We present a partial differential equation model describing the dynamics of bone remodeling with the presence of myeloma tumor cells. The model explicitly takes into account the roles of osteoclasts, osteoblasts, precursor cells, stromal cells, osteocytes, and tumor cells. Previous models based on ordinary differential equations make the simplifying assumption that the bone and tumor cells are adjacent to each other. However, in actuality, these cell populations are separated by the bone marrow. Our model takes this separation into account by including the diffusion of chemical factors across the marrow, which can be viewed as communication between the tumor and bone. Additionally, this model incorporates the growth of the tumor and the diminishing bone mass by utilizing a ``moving boundary.'' We present numerical simulations that qualitatively validate our model's description of the cell population dynamics.

q-bio.CB↗

arXiv2015

Mathematical Modeling of Myosin Induced Bistability of Lamellipodial Fragments

For various cell types and for lamellipodial fragments on flat surfaces, externally induced and spontaneous transitions between symmetric nonmoving states and polarized migration have been observed. This behavior is indicative of bistability of the cytoskeleton dynamics. In this work, the Filament Based Lamellipodium Model (FBLM), a two-dimensional, anisotropic, two-phase continuum model for the dynamics of the actin filament network in lamellipodia, is extended by a new description of actin-myosin interaction. For appropriately chosen parameter values, the resulting model has bistable dynamics with stable states showing the qualitative features observed in experiments. This is demonstrated by numerical simulations and by an analysis of a strongly simplified version of the FBLM with rigid filaments and planar lamellipodia at the cell front and rear.

q-bio.CB↗

arXiv2016

Optimal Strategies for Virus Propagation

This paper explores a number of questions regarding optimal strategies evolved by viruses upon entry into a vertebrate host. The infected cell life cycle consists of a non-productively infected stage in which it is producing virions but not releasing them and of a productively infected stage in which it is just releasing virions. The study explores why the infected cell cycle should be so delineated, something which is akin to a classic bang-bang control or all-or-none principle. The times spent in each of these stages represent a viral strategy to optimize peak viral load. Increasing the time spent in the non-productively infected phase (τ1) would lead to a concomitant increase in peak viremia. However increasing this time would also invite a more vigorous response from Cytotoxic T-Lymphocytes (CTLs). Simultaneously, if there is a vigorous antibody response, then we might expect τ1 to be high, in order that the virus builds up its population and conversely if there is a weak antibody response, τ1 might be small. These tradeoffs are explored using a mathematical model of virus propagation using Ordinary Differential Equations (ODEs). The study raises questions about whether common viruses have actually settled into an optimum, the role for reliability and whether experimental infections of hosts with non-endemic strains could help elicit answers about viral progression.

q-bio.CB↗

arXiv2015

Bacterial chemotaxis: information processing, thermodynamics, and behavior

Escherichia coli has long been used as a model organism due to the extensive experimental characterization of its pathways and molecular components. Take chemotaxis as an example, which allows bacteria to sense and swim in response to chemicals, such as nutrients and toxins. Many of the pathway's remarkable sensing and signaling properties are now concisely summarized in terms of design (or engineering) principles. More recently, new approaches from information theory and stochastic thermodynamics have begun to address how pathways process environmental stimuli and what the limiting factors are. However, to fully capitalize on these theoretical advances, a closer connection with single-cell experiments will be required.

q-bio.CB↗

arXiv2015

Modelling axon growing using CTRW

The main goal of this study is to propose a mathematical model describing paths of the axon growth cones and differences in the behavior of normal and mutant axons. We introduce a probabilistic model for axon growing, such that each family of axons is described as an ensemble of trajectories of a continuous time random walk (CTRW) model under different parameters in the case of normal and mutant axons. We describe different regimes in the model and conclude how the behavior of axons depends on the parameters of the model. Biological observations of the axonal growth process say us that the guiding development of axons to their targets is operated by chemical signals from the cellular environment. To simulate this control mechanism we propose the CTRW model, where a random waiting time reflects a reaction time of the growth cones on the neighboring chemical environment.

q-bio.NC↗

arXiv2015

Multiscale modelling of tumour growth induced by circadian rhythm disruption in epithelial tissue

We propose a multiscale chemo-mechanical model of cancer tumour development in an epithelial tissue. The model is based on transformation of normal cells into the cancerous state triggered by a local failure of spatial synchronisation of the circadian rhythm. The model includes mechanical interactions and chemical signal exchange between neighbouring cells, as well as division of cells and intercalation, and allows for modification of the respective parameters following transformation into the cancerous state. The numerical simulations reproduce different dephasing patterns - spiral waves and quasistationary clustering, with the latter being conducive to cancer formation. Modification of mechanical properties reproduces distinct behaviour of invasive and localised carcinoma.

q-bio.CB↗

arXiv2015

The cell cycle related rhythms, cells' states correlation and the cancer

We consider the decision making by mammalian cells, looking them as dynamic systems with rhythms. We calculate the effective dimension of the cell division model of the healthy mammalian cells consistent with the data: it is described via a four dimensional dynamic system. We assume that the cell's decision making property is strongly affected by the cells rhythms, their causal relations, and by the correlation between internal states of different cells in tissue. There is a strong correlation between the states of different healthy cells (verified partially experimentally), and we assume that there is no such a correlation between internal states of the healthy and cancer cells. The origins of the cancer are just the disruption of this correlation (self-identification of the cells) and the change of the causal relations between the Circadian and cell cycle rhythms. Assuming the Gaussian channel version of the cell-cell communications and a key role of public goods for the cancer cells, we get a strong correlation between the states of different cancer cells.

q-bio.CB↗

arXiv2016

Towards a cell-based mechanostat theory of bone: the need to account for osteocyte desensitisation and osteocyte replacement

Bone's mechanostat theory describes the adaptation of bone tissues to their mechanical environment. Many experiments have investigated and observed such structural adaptation. However, there is still much uncertainty about how to define the reference mechanical state at which bone structure is adapted and stable. Clinical and experimental observations show that this reference state varies both in space and in time, over a wide range of timescales. We propose an osteocyte-based mechanostat theory that links various timescales of structural adaptation with various dynamic features of the osteocyte network in bone. This theory assumes that osteocytes are formed adapted to their current local mechanical environment through modulation of morphological and genotypic osteocyte properties involved in mechanical sensitivity. We distinguish two main types of physiological responses by which osteocytes subsequently modify the reference mechanical state. One is the replacement of osteocytes during bone remodelling, which occurs over the long timescales of bone turnover. The other is cell desensitisation responses, which occur more rapidly and reversibly during an osteocyte's lifetime. The novelty of this theory is to propose that long-lasting morphological and genotypic osteocyte properties provide a material basis for a long-term mechanical memory of bone that is gradually reset by bone remodelling. We test this theory by simulating long-term mechanical disuse (modelling spinal cord injury), and short-term mechanical loadings (modelling daily exercises) with a mathematical model. The consideration of osteocyte desensitisation and of osteocyte replacement by remodelling is able to capture the different phenomena and timescales observed during the mechanical adaptation of bone tissues, lending support to this theory.

q-bio.CB↗

arXiv2016

Rhythmomimetic drug delivery: modeling, analysis and numerical simulation

We develop, analyse and numerically simulate a model of a prototype, glucose-driven, rhythmic drug delivery device, aimed at hormone therapies, and based on chemomechanical interaction in a polyelectrolyte gel membrane. The pH-driven interactions trigger volume phase transitions between the swollen and collapsed states of the gel.For a robust set of material parameters, we find a class of solutions of the governing system that oscillate between such states, and cause the membrane to rhythmically swell, allowing for transport of the drug, fuel and reaction products across it, and collapse, hampering all transport across it. The frequency of the oscillations can be adjusted so that it matches the natural frequency of the hormone to be released. The work is linked to extensive laboratory experimental studies of the device built by Siegel's team. The thinness of the membrane and its clamped boundary, together with the homogeneously held conditions in the experimental apparatus, justify neglecting spatial dependence on the fields of the problem. Upon identifying the forces and energy relevant to the system, and taking into account its dissipative properties, we apply Rayleigh's variational principle to obtain the governing equations. The material assumptions guarantee the monotonicity of the system and lead to the existence of a three dimensional limit cycle. By scaling and asymptotic analysis, this limit cycle is found to be related to a two-dimensional one that encodes the volume phase transitions of the model. The identification of the relevant parameter set of the model is aided by a Hopf bifurcation study of steady state solutions.

physics.chem-ph↗

arXiv2015

Embryonic Elongation controlled by Graded Cell Fate: A Molecular Dynamics Approach

Regression of Hensen's node from anterior to posterior is driving the elongation and patterning of avian embryo body. Recent experiments link gradient of presomitic mesoderm cell motility to displacement of the node and body axis elongation. Ingression of new cells into presomitic mesoderm tissue also contributes to the process. At present, movements of presomitic mesoderm can be tracked at single cell precision. Yet, mechanisms that couple these movements to regression and axis elongation are largely unknown. In this work we develop a computational approach to study regression of Hensen's node and the elongation of anterior-posterior body axis. Based on our simulations we propose that regression and the elongation are a result of the influx of new mesoderm cells mediated by cell density gradient. Addition of new cells leads to expansion of tissue in anterior-posterior direction (elongation) and pushes node towards posterior (regression). Motility gradient of cells further aids regression by biasing tissue expansion towards more motile posterior. We show that our model reproduces experimentally observed differences in presomitic mesoderm cell movements and regression of Hensen's node in various embryo phenotypes.

q-bio.QM↗

arXiv2015

Evolutionary simulations of autopoietic cells with cognition

The minimal requirements for life are autopoiesis and cognition. We propose autopoietic models with cognition and perform three classes of evolutionary simulation. In our models the plasticity of the metabolic cycle and the regulation function of the membrane are the bases for the cognition. The cognitive cells show the adaptation and the evolution. The environment also shows the evolution via the interaction with the system of cells. This is a prototype of the co-evolution of the living system and its environment.

q-bio.CB↗

arXiv2015

Probing intracellular mass density fluctuation through confocal microscopy: application in cancer diagnostics as a case study

Intracellular structural alterations are hallmark of several disease conditions and treatment modalities. However, robust methods to quantify these changes are scarce. In view of this, we introduce a new method to quantify structural alterations in biological cells through the widely used confocal microscopy. This novel method employs optical eigenfunctions localization properties of cells and quantifies the degree of structural alterations, in terms of nano- to micron scale intracellular mass density fluctuations, in one single parameter. Such approach allows a powerful way to compare changing structures in heterogeneous cellular media irrespective of the origin of the cause. As a case study, we demonstrate its applicability in cancer detection with breast and prostate cancer cases of different tumorigenicity levels. Adding new dimensions to the confocal based studies, this technique has potentially significant applications in areas ranging from disease diagnostics to therapeutic studies, such as patient prognosis and assessing survival potential.

physics.bio-ph↗

arXiv2015

Modelling the Role of Nitric Oxide in Cerebral Autoregulation

Malfunction of the system which regulates the bloodflow in the brain is a major cause of stroke and dementia, costing many lives and many billions of pounds each year in the UK alone. This regulatory system, known as cerebral autoregulation, has been the subject of much experimental and mathematical investigation yet our understanding of it is still quite limited. One area in which our understanding is particularly lacking is that of the role of nitric oxide, understood to be a potent vasodilator. The interactions of nitric oxide with the better understood myogenic response remain un-modelled and poorly understood. In this thesis we present a novel model of the arteriolar control mechanism, comprising a mixture of well-established and new models of individual processes, brought together for the first time. We show that this model is capable of reproducing experimentally observed behaviour very closely and go on to investigate its stability in the context of the vasculature of the whole brain. In conclusion we find that nitric oxide, although it plays a central role in determining equilibrium vessel radius, is unimportant to the dynamics of the system and its responses to variation in arterial blood pressure. We also find that the stability of the system is very sensitive to the dynamics of Ca$^{2+}$ within the muscle cell, and that self-sustaining Ca$^{2+}$ waves are not necessary to cause whole-vessel radius oscillations consistent with vasomotion.

q-bio.TO↗

arXiv2019

Effect of Replication Fork Dynamics on Escherichia coli Cell Size

The variability in cell size of an isogenic population of Escherichia coli has been widely reported in experiment. The probability density function (PDF) of cell lengths has been variously described by exponential and lognormal functions. While temperature, population density and growth rate have all been shown to affect E. coli cell size distributions, and recent models have validated a link between growth rate and cell size through DNA replication, cell size variability is thought to emerge from growth rate variability. A mechanistic link that could distinguish the source of stochasticity, could improve our understanding of cell size regulation. Here, we have developed a population dynamics model of individual cell division based on the BCD, birth, chromosome replication and division model, with DNA replication based on the Cooper and Helmstetter (CH) multi-fork replication. In our model, stochasticity in the model arises solely from the dynamics of DNA replication forks. We model the forks as two-state systems: stalled and recovered. Our model predicts an increase in cell size variability with growth rate, consistent with previous experimental reports. We perturb the model to test the effect of increased replication fork (RF) stalling frequency, or uncoupling RF stalling from the cell-division machinery. Indeed, despite ignoring DNA and protein segregation asymmetry, the model can faithfully reproduce quantitative changes in cell size distributions. In our model, multi-fork replication produces multiplicative 'noise' and provides a mechanism linking growth rate and cell size variability.

q-bio.CB↗

arXiv2016

On the fractional cell kill law governing the lysis of solid tumors

We present in silico simulations and mathematical analyses supporting several hypotheses that explain the saturation expressed in the fractional cell kill law that governs the lysis of tumor cells by cytotoxic CD8 + T cells (CTLs). In order to give insight into the significance of the parameters appearing in such law, a hybrid cellular automaton model describing the spatio-temporal evolution of tumor growth and its interaction with the cell-mediated immune response is used. When the CTLs eradicate efficiently the tumor cells, the model predicts a correlation between the morphology of the tumors and the rate at which they are lysed. As the effectiveness of the effector cells is decreased, the saturation gradually disappears. This limit is thoroughly discussed and a new fractional cell kill is proposed.

q-bio.TO↗