Quantitative Biology

A one-dimensional continuum-mechanical model of axonal elongation due to assembly of tubulin dimers in the growth cone is presented. The conservation of mass leads to a coupled system of three differential equations. A partial differential equation models the dynamic and spatial behaviour of the concentration of tubulin that is transported along the axon from the soma to the growth cone. Two ordinary differential equations describe the time-variation of the concentration of free tubulin in the growth cone and the speed of elongation, respectively. All steady-state solutions of the model are categorized. Given a set of the biological parameter values, it is shown how one easily can infer whether there exist zero, one or two steady-state solutions and directly determine the possible steady-state lengths of the axon. Explicit expressions are given for each stationary concentration distribution. It is thereby easy to examine the influence of each biological parameter on a steady state. Numerical simulations indicate that when there exist two steady states, the one with shorter axon length is unstable and the longer is stable. Another result is that, for nominal parameter values extracted from literature, in a large portion of a fully grown axon the concentration of free tubulin is lower than both concentrations in the soma and in the growth cone.

A pathway-based mean-field theory (PBMFT) was recently proposed for E. coli chemotaxis in [G. Si, T. Wu, Q. Quyang and Y. Tu, Phys. Rev. Lett., 109 (2012), 048101]. In this paper, we derived a new moment system of PBMFT by using the moment closure technique in kinetic theory under the assumption that the methylation level is locally concentrated. The new system is hyperbolic with linear convection terms. Under certain assumptions, the new system can recover the original model. Especially the assumption on the methylation difference made there can be understood explicitly in this new moment system. We obtain the Keller-Segel limit by taking into account the different physical time scales of tumbling, adaptation and the experimental observations. We also present numerical evidence to show the quantitative agreement of the moment system with the individual based E. coli chemotaxis simulator.

We discuss several continuum cell-cell adhesion models based on the underlying microscopic assumptions. We propose an improvement on these models leading to sharp fronts and intermingling invasion fronts between different cell type populations. The model is based on basic principles of localized repulsion and nonlocal attraction due to adhesion forces at the microscopic level. The new model is able to capture both qualitatively and quantitatively experiments by Katsunuma et al. (2016) [J. Cell Biol. 212(5), pp. 561--575]. We also review some of the applications of these models in other areas of tissue growth in developmental biology. We finally explore the resulting qualitative behavior due to cell-cell repulsion.

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

Bacteria live in environments that are continuously fluctuating and changing. Exploiting any predictability of such fluctuations can lead to an increased fitness. On longer timescales bacteria can "learn" the structure of these fluctuations through evolution. However, on shorter timescales, inferring the statistics of the environment and acting upon this information would need to be accomplished by physiological mechanisms. Here, we use a model of metabolism to show that a simple generalization of a common regulatory motif (end-product inhibition) is sufficient both for learning continuous-valued features of the statistical structure of the environment and for translating this information into predictive behavior; moreover, it accomplishes these tasks near-optimally. We discuss plausible genetic circuits that could instantiate the mechanism we describe, including one similar to the architecture of two-component signaling, and argue that the key ingredients required for such predictive behavior are readily accessible to bacteria.

Migration of cells can be characterized by two, prototypical types of motion: individual and collective migration. We propose a statistical-inference approach designed to detect the presence of cell-cell interactions that give rise to collective behaviors in cell-motility experiments. Such inference method has been first successfully tested on synthetic motional data, and then applied to two experiments. In the first experiment, cell migrate in a wound-healing model: when applied to this experiment, the inference method predicts the existence of cell-cell interactions, correctly mirroring the strong intercellular contacts which are present in the experiment. In the second experiment, dendritic cells migrate in a chemokine gradient. Our inference analysis does not provide evidence for interactions, indicating that cells migrate by sensing independently the chemokine source. According to this prediction, we speculate that mature dendritic cells disregard inter-cellular signals that could otherwise delay their arrival to lymph vessels.

Spatial interactions between cancer and immune cells, as well as the recognition of tumour antigens by cells of the immune system, play a key role in the immune response against solid tumours. The existing mathematical models generally focus only on one of these key aspects. We present here a spatial stochastic individual-based model that explicitly captures antigen expression and recognition. In our model, each cancer cell is characterised by an antigen profile which can change over time due to either epimutations or mutations. The immune response against the cancer cells is initiated by the dendritic cells that recognise the tumour antigens and present them to the cytotoxic T cells. Consequently, T cells become activated against the tumour cells expressing such antigens. Moreover, the differences in movement between inactive and active immune cells are explicitly taken into account by the model. Computational simulations of our model clarify the conditions for the emergence of tumour clearance, dormancy or escape, and allow us to assess the impact of antigenic heterogeneity of cancer cells on the efficacy of immune action. Ultimately, our results highlight the complex interplay between spatial interactions and adaptive mechanisms that underpins the immune response against solid tumours, and suggest how this may be exploited to further develop cancer immunotherapies.

In this work we approach cell migration under a large-scale assumption, so that the system reduces to a particle in motion. Unlike classical particle models, the cell displacement results from its internal activity: the cell velocity is a function of the (discrete) protrusive forces exerted by filopodia on the substrate. Cell polarisation ability is modeled in the feedback that the cell motion exerts on the protrusion rates: faster cells form preferentially protrusions in the direction of motion. By using the mathematical framework of structured population processes previously developed to study population dynamics [Fournier and M{é}l{é}ard, 2004], we introduce rigorously the mathematical model and we derive some of its fundamental properties. We perform numerical simulations on this model showing that different types of trajectories may be obtained: Brownian-like, persistent, or intermittent when the cell switches between both previous regimes. We find back the trajectories usually described in the literature for cell migration.

Transposable elements are DNA sequences that can move around to different positions in the genome. During this process, they can cause mutations, and lead to an increase in genome size. Despite representing a large genomic fraction, transposable elements have no clear biological function. This work builds upon a previous model, to propose a new concept of natural selection which combines Lamarckian and Darwinian elements. Transposable elements are hypothesised to be the vector of a flow of genetic information from soma to germline, that shapes gene regulatory regions across the genome. The paper introduces the concept, presents and discusses the body of evidence in support of this hypothesis, and suggests an experiment to test it.

Background: AQP1 belongs to aquaporins family, water-specific, membrane-channel proteins expressed in diverse tissues. Recent papers showed that during angiogenesis, AQP1 is expressed preferentially by microvessels, favoring angiogenesis via the increase of permeability In particular, in AQP1 null mice, endothelial cell migration is impaired without altering their proliferation or adhesion. Therefore, AQP1 has been proposed as a novel promoter of tumor angiogenesis. Methods/Findings: Using targeted silencing of AQP1 gene expression, an impairment in the organization of F-actin and a reduced migration capacity was demonstrated in human endothelial and melanoma cell lines. Interestingly, we showed, for the first time, that AQP1 co-immunoprecipitated with Lin-7. Lin7-GFP experiments confirmed co-immunoprecipitation. In addition, the knock down of AQP1 decreased the level of expression of Lin-7 and b-catenin and the inhibition of proteasome contrasted partially such a decrease. Conclusions/Significance: All together, our findings show that AQP1 plays a role inside the cells through Lin-7/b-catenin interaction. Such a role of AQP1 is the same in human melanoma and endothelial cells, suggesting that AQP1 plays a global physiological role. A model is presented.