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arXiv2008

Cancer Cell Motility: Optimizing Spatial Search Strategies

Aberrantly regulated cell motility is a hallmark of cancer cells. A hybrid agent-based model has been developed to investigate the synergistic and antagonistic cell motility-impacting effects of three microenvironment variables simultaneously: chemoattraction, haptotactic permission, and biomechanical constraint or resistance. Reflecting distinct cell-specific intracellular machinery, the cancer cells are modelled as processing a variety of spatial search strategies that respond to these three influencing factors with differential weights attached to each. While responding exclusively to chemoattraction optimizes cell displacement effectiveness, incorporating permission and resistance components becomes increasingly important with greater distance to the chemoattractant source and/or after reducing the ligand's effective diffusion coefficient. Extending this to a heterogeneous population of cells shows that displacement effectiveness increases with clonal diversity as characterized by the Shannon index. However, the resulting data can be fit best to an exponential function, suggesting that there is a level of population heterogeneity beyond which its added value to the cancer system becomes minimal as directionality ceases to increase. Possible experimental extensions and potential clinical implications are discussed.

q-bio.CB↗

arXiv2008

From differential equations to Boolean networks: A Case Study in modeling regulatory networks

Methods of modeling cellular regulatory networks as diverse as differential equations and Boolean networks co-exist, however, without any closer correspondence to each other. With the example system of the fission yeast cell cycle control network, we here set the two approaches in relation to each other. We find that the Boolean network can be formulated as a specific coarse-grained limit of the more detailed differential network model for this system. This lays the mathematical foundation on which Boolean networks can be applied to biological regulatory networks in a controlled way.

q-bio.MN↗

arXiv2008

Shoot regeneration seedlings from transverse thin cell layer explants excised from cotyledon, petiole, hypocotyl of [{Brassica juncea} L. Czern.] in the presence of CdCl$_2$

The present work describes a novel neoformation process of \textit{Brassica juncea} (L.) Czern. seedlings from transverse thin cell layers in the presence of CdCl$_2$. In order to investigate the regeneration ability of this crop, the effect of CdCl$_2$ on shoot regeneration (frequency of regeneration and bud number per tTCL) was examined. The tTCL explants were excised from cotyledon, petiole and hypocotyl of 7 day-old \textit{B. juncea} seedlings and cultivated on a solid basal MS medium supplemented with $α$-naphtalenacetic acid (NAA : 3.22 $μ$M), 6-benzylamino-purine (BAP : 26.6 $μ$M), sucrose (2 %, w/v), silver nitrate (AgNO3 : 10 $μ$M) and various concentrations of CdCl$_2$ (0 - 250 $μ$M). A concentration of CdCl$_2$ of 5 $μ$M is enough to reduce significantly the percentage of regenerated tTCL from 95-100 % to 77-86 % for all organs tested. In addition, 5 $μ$M of CdCl$_2$ reduces the bud number from 4.5 to 2.98 and 3.2 to 2.02 of hypocotyl and petiole tTCLs, but not for cotyledon tTCLs. Besides, 250 $μ$M of CdCl$_2$ is lethal for all tTCLs whatever the organ, and 200 $μ$M is lethal only for cotyledon and petiole tTCLs but not for hypocotyl explants which had 3.6 % of frequency of shoot regeneration. Plantlets regenerated from all shoots, whatever the treatment, developed and flowered normally 6 weeks after the transfer to pots. The regenerated plants were fertile and identical to source plants.

q-bio.CB↗

arXiv2012

A Markovian growth dynamics on rooted binary trees evolving according to the Gompertz curve

Inspired by biological dynamics, we consider a growth Markov process taking values on the space of rooted binary trees, similar to the Aldous-Shields model. Fix $n\ge 1$ and $β>0$. We start at time 0 with the tree composed of a root only. At any time, each node with no descendants, independently from the other nodes, produces two successors at rate $β(n-k)/n$, where $k$ is the distance from the node to the root. Denote by $Z_n(t)$ the number of nodes with no descendants at time $t$ and let $T_n = β^{-1} n \ln(n /\ln 4) + (\ln 2)/(2 β)$. We prove that $2^{-n} Z_n(T_n + n τ)$, $τ\in\bb R$, converges to the Gompertz curve $\exp (- (\ln 2) e^{-βτ})$. We also prove a central limit theorem for the martingale associated to $Z_n(t)$.

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arXiv2008

Consistency Principle in Biological Dynamical Systems

We propose a principle of consistency between different hierarchical levels of biological systems. Given a consistency between molecule replication and cell reproduction, universal statistical laws on cellular chemical abundances are derived and confirmed experimentally. They include a power law distribution of gene expressions, a lognormal distribution of cellular chemical abundances over cells, and embedding of the power law into the network connectivity distribution. Second, given a consistency between genotype and phenotype, a general relationship between phenotype fluctuations by genetic variation and isogenic phenotypic fluctuation by developmental noise is derived. Third, we discuss the chaos mechanism for stem cell differentiation with autonomous regulation, resulting from a consistency between cell reproduction and growth of the cell ensemble.

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arXiv2008

Dynamics of gene expression under feedback

Gene expression is a stochastic process governed by the presence of specific transcription factors. Here we study the dynamics of gene expression in the presence of feedback, where a gene regulates its own expression. The nonlinear coupling between input and output of gene expression can generate a dynamics different from simple scenarios such as the Poisson process. This is exemplified by our findings for the time intervals over which genes are transcriptionally active and inactive. We apply our results to the lac system in E. coli, where parametric inference on experimental data results in a broad distribution of gene activity intervals.

q-bio.CB↗

arXiv2008

A Theoretical Model of Chaotic Attractor in Tumor Growth and Metastasis

This paper proposes a novel chaotic reaction-diffusion model of cellular tumor growth and metastasis. The model is based on the multiscale diffusion cancer-invasion model (MDCM) and formulated by introducing strong nonlinear coupling into the MDCM. The new model exhibits temporal chaotic behavior (which resembles the classical Lorenz strange attractor) and yet retains all the characteristics of the MDCM diffusion model. It mathematically describes both the processes of carcinogenesis and metastasis, as well as the sensitive dependence of cancer evolution on initial conditions and parameters. On the basis of this chaotic tumor-growth model, a generic concept of carcinogenesis and metastasis is formulated. Keywords: reaction-diffusion tumor growth model, chaotic attractor, sensitive dependence on initial tumor characteristics

q-bio.CB↗

arXiv2009

ODE, RDE and SDE Models of Cell Cycle Dynamics and Clustering in Yeast

Biologists have long observed periodic-like oxygen consumption oscillations in yeast populations under certain conditions and several unsatisfactory explanations for this phenomenon have been proposed. These "autonomous oscillations" have often appeared with periods that are nearly integer divisors of the calculated doubling time of the culture. We hypothesize that these oscillations could be caused by a weak form of cell cycle synchronization that we call clustering. We develop some novel ordinary differential equation models of the cell cycle. For these models, and for random and stochastic perturbations, we give both rigorous proofs and simulations showing that both positive and negative growth rate feedback within the cell cycle are possible agents that can cause clustering of populations within the cell cycle. It occurs for a variety of models and for a broad selection of parameter values. These results suggest that the clustering phenomenon is robust and is likely to be observed in nature. Since there are necessarily an integer number of clusters, clustering would lead to periodic-like behavior with periods that are nearly integer divisors of the period of the cell cycle.

math.DS↗

arXiv2008

Power-law scaling in protein synthesis of a stochastic regulon

We investigate the protein expression pattern of the lamB gene in Escherichia coli LE392. The gene product LamB is an important membrane protein for maltose transport into cells but it is also exploited by bacteriophage lambda for infection. Although our bacterial population is clonal, stochastic gene expression leads to a majority population with a large receptor number and a minority population with a small receptor number. We find that the LamB receptor distribution p(n) of the small-n population is scale invariant with the exponent depending on growth conditions. A heuristic model is proposed that relates the observed exponent to the protein production rate.

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arXiv2008

Stochastic models and numerical algorithms for a class of regulatory gene networks

Regulatory gene networks contain generic modules like those involving feedback loops, which are essential for the regulation of many biological functions. We consider a class of self-regulated genes which are the building blocks of many regulatory gene networks, and study the steady state distributions of the associated Gillespie algorithm by providing efficient numerical algorithms. We also study a regulatory gene network of interest in synthetic biology and in gene therapy, using mean-field models with time delays. Convergence of the related time-nonhomogeneous Markov chain is established for a class of linear catalytic networks with feedback loops

q-bio.SC↗

arXiv2008

A Mathematical Model of Chaotic Attractor in Tumor Growth and Decay

We propose a strange-attractor model of tumor growth and metastasis. It is a 4-dimensional spatio-temporal cancer model with strong nonlinear couplings. Even the same type of tumor is different in every patient both in size and appearance, as well as in temporal behavior. This is clearly a characteristic of dynamical systems sensitive to initial conditions. The new chaotic model of tumor growth and decay is biologically motivated. It has been developed as a live Mathematica demonstration, see Wolfram Demonstrator site: http://demonstrations.wolfram.com/ChaoticAttractorInTumorGrowth/ Key words: Reaction-diffusion tumor growth model, chaotic attractor, sensitive dependence on initial tumor characteristics

q-bio.CB↗

arXiv2008

The Dynamic Replicon: adapting to a changing cellular environment

Eukaryotic cells are often exposed to fluctuations in growth conditions as well as endogenous and exogenous stress-related agents. In addition, during development global patterns of gene transcription change dramatically, and these changes are associated with altered patterns of DNA replication. In metazoan embryos, for example, transcription is repressed globally and any sequence in the genome can serve as a site for the start of DNA synthesis. As transcription is activated and a G1 phase imposed, the pattern of replication adapts to these changes by restricting the sites where DNA synthesis begins. Recent evidence indicates that each unit of replication, or replicon, is specified by two or more potential replication origins, but only one is selected to initiate replication of the replicon. How the cell distinguishes between potential origins, and how it selects a given origin of replication remain unclear. This raises important questions concerning the nature and definition of the eukaryotic replicon. In the following we will review emerging evidence concerning the mechanisms involved in regulating replication origins during both the normal and perturbed eukaryotic cell cycle.

q-bio.GN↗

arXiv2008

From random to directed motion: Understanding chemotaxis in E. Coli within a simplified model

The bacterium E.Coli swims in a zig-zag manner, in a series of straight runs and tumbles occurring alternately, with the run-durations dependent on the local spatial gradient of chemo-attractants/repellants. This enables the organism to move towards nutrient sources and move away from toxins. The signal transduction network of E.Coli has been well-characterized, and theoretical modeling has been used, with some success, in understanding its many remarkable features, including the near-perfect adaptation to spatially uniform stimulus. We study a reduced form of this network, with 3 methylation states for the receptor instead of 5. We derive an analytical form of the response function of the tumbling rate and use it to compute the drift velocity of the bacterium in the presence of a weak spatial attractant gradient.

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arXiv2008

A physical model of nicotinic ACh receptor kinetics

We present a new approach to nicotinic receptor kinetics and a new model explaining random variabilities in the duration of open events. The model gives new interpretation on brief and long receptor openings and predicts (for two identical binding sites) the presence of three components in the open time distribution: two brief and a long. We also present the physical model of the receptor block. This picture naturally and universally explains receptor desensitization, the phenomenon of central importance in cellular signaling. The model is based on single-channel experiments concerning the effects of hydrocortisone (HC) on the kinetics of control wild-type (WT) and mutated alphaD200Q mouse nicotinic acetylcholine receptors (nAChRs), expressed in HEK 293 cells. The appendix contains an original result from probability renewal theory: a derivation of the probability distribution function for the duration of a process performed by two independent servers.

q-bio.NC↗

arXiv2012

The DNA Single-Strand Break Repair Machinery Facilitates CAF-1-Mediated Histone Deposition at Oxidative DNA Strand Breaks

Oxidative DNA single strand breaks arise continuously in cells and defects in their repair have been implicated in neurological disease. While much progress has been made in understanding how chromosomal single strand breaks are repaired little is known about the changes chromatin structure that accompany this process. Here, we show that nascent recombinant histone H3.1 protein accumulates and is deposited into chromatin at sites of DNA strand breakage in quiescent human cells following oxidative stress, and that core components of the single-strand break repair machinery are required for this process. We show that the SSBR sensor and scaffold proteins poly (ADP-ribose) polymerase and XRCC1 facilitate accumulation of chromatin assembly factor-1 (CAF-1) at sites of oxidative DNA strand breakage, which in turn mediates the deposition of Histone H3.1. We also demonstrate that depletion of CAF-1 slows global rates of DNA strand break repair in quiescent cells following oxidative stress, demonstrating that single-strand break repair and histone deposition are tightly coordinated processes. These data describe a novel role for the DNA singlestrand break repair machinery and implicate histone turnover as a core component of the cellular response of quiescent cells to oxidative damage.

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arXiv2012

Changes in chromatin state in donors subjected to physical stress

The purpose of the present study is to evaluate changes in chromatin of human buccal epithelium under the influence of stressing factor - dosed physical activity. Investigations were performed in a group of students (13 men) of age 19-23. Cells were stained on a slide by a 2% orcein solution in 45% acetic acid during 1 h. The following physiological indexes were determined: arterial blood pressure, pulse frequency, and frequency of breathing. The physical stress produced by the dosed physical activity causes the considerable increase of degree of heterochromatinization in the cell nuclei of human buccal epithelium. As a rule, the level of heterochromatinization increases after first stage of training, but in some donors it increases significantly only after the second stage of training.

q-bio.CB↗

arXiv2009

Functional models for large-scale gene regulation networks: realism and fiction

High-throughput experiments are shedding light on the topology of large regulatory networks and at the same time their functional states, namely the states of activation of the nodes (for example transcript or protein levels) in different conditions, times, environments. We now possess a certain amount of information about these two levels of description, stored in libraries, databases and ontologies. A current challenge is to bridge the gap between topology and function, i.e. developing quantitative models aimed at characterizing the expression patterns of large sets of genes. However, approaches that work well for small networks become impossible to master at large scales, mainly because parameters proliferate. In this review we discuss the state of the art of large-scale functional network models, addressing the issue of what can be considered as realistic and what the main limitations may be. We also show some directions for future work, trying to set the goals that future models should try to achieve. Finally, we will emphasize the possible benefits in the understanding of biological mechanisms underlying complex multifactorial diseases, and in the development of novel strategies for the description and the treatment of such pathologies.

q-bio.MN↗

arXiv2009

Cells, cancer, and rare events: homeostatic metastability in stochastic non-linear dynamics models of skin cell proliferation

A recently proposed single progenitor cell model for skin cell proliferation [Clayton et al., Nature v446, 185 (2007)] is extended to incorporate homeostasis as a fixed point of the dynamics. Unlimited cell proliferation in such a model can be viewed as a paradigm for the onset of cancer. A novel way in which this can arise is if the homeostatic fixed point becomes metastable, so that the cell populations can escape from the homeostatic basin of attraction by a large but rare stochastic fluctuation. Such an event can be viewed as the final step in a multi-stage model of carcinogenesis. This offers a possible explanation for the peculiar epidemiology of lung cancer in ex-smokers.

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