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arXiv2009

Actin based propulsion: Intriguing interplay between material properties and growth processes

Eukaryotic cells and intracellular pathogens such as bacteria or viruses utilize the actin polymerization machinery to propel themselves forward. Thereby, the onset of motion and choice of direction may be the result of a spontaneous symmetry-breaking or might be triggered by external signals and preexisting asymmetries, e.g. through a previous septation in bacteria. Although very complex, a key feature of cellular motility is the ability of actin to form dense polymeric networks, whose microstructure is tightly regulated by the cell. These polar actin networks produce the forces necessary for propulsion but may also be at the origin of a spontaneous symmetry-breaking. Understanding the exact role of actin dynamics in cell motility requires multiscale approaches which capture at the same time the polymer network structure and dynamics on the scale of a few nanometers and the macroscopic distribution of elastic stresses on the scale of the whole cell. In this chapter we review a selection of theories on how mechanical material properties and growth processes interact to induce the onset of actin based motion.

cond-mat.soft↗
arXiv2009

A mathematical model of intercellular signaling during epithelial wound healing

Recent experiments in epithelial wound healing have demonstrated the necessity of Mitogen-activated protein kinase (MAPK) for coordinated cell movement after damage. This MAPK activity is characterized by two wave-like phenomena. One MAPK "wave" that originates immediately after injury, propagates deep into the cell layer, and then rebounds back to the wound interface. After this initial MAPK activity has largely disappeared, a second MAPK front propagates slowly from the wound interface and continues into the tissue, maintaining a sustained level of MAPK activity throughout the cell layer. It has been suggested that the first wave is initiated by reactive oxygen species (ROS) generated at the time of injury. In this paper, we develop a minimal mechanistic diffusion-convection model that reproduces the observed behavior. The main ingredients of our model are a competition between ligand (e.g., Epithelial Growth Factor) and ROS for the activation of Epithelial Growth Factor Receptor (EGFR) and a second MAPK wave that is sustained by stresses induced by the slow cell movement that closes the wound. We explore the mathematical properties of the model in connection with the bistability of the MAPK cascade and look for traveling wave solutions consistent with the experimentally observed MAPK activity patterns.

q-bio.CB↗
arXiv2009

Theoretical analyses predict A20 regulates period of NF-kB oscillation

The nuclear-cytoplasmic shuttling of NF-kB is characterized by damped oscillations of the nuclear concentration with a time period of around 1-2 hours. The NF-kB network contains several feedback loops modulating the overall response of NF-kB activity. While IkBa is known to drive and IkBe is known to dampen the oscillations, the precise role of A20 negative feedback remains to be elucidated. Here we propose a model of the NF-kB system focusing on three negative feedback loops (IkBa, IkBe and A20) which capture the experimentally observed responses in wild-type and knockout cells. We find that A20, like IkBe, efficiently dampens the oscillations albeit through a distinct mechanism. In addition, however, we have discovered a new functional role of A20 by which it controls the oscillation period of nuclear NF-kB. The design based on three nested feedback loops allows independent control of period and amplitude decay in the oscillatory response. Based on these results we predict that adjusting the expression level of A20, e.g. by siRNA, the period can be changed by up to a factor 2.

physics.bio-ph↗
arXiv2009

Influence of Protein Electromagnetic Field on Hydrogen Bonding

The quantum-mechanical mechanisms by which the enzymes catalyze the hydrogen transfer in biochemical reactions are considered. Up to date it was established both experimentally and theoretically that in many cases the proton tunnelling through the intermolecular potential barrier is essential. We argue that in this case the enzyme excitation and internal motion facilitate proton transfer between reactants by squeezing the potential barrier which otherwise is practically impenetrable. In the similar fashion, the enzymes can facilitate the formation of hydrogen (H) bonds between the molecules. By means of barrier squeezing, the enzymes not only facilitate such reactions but also can control their rate and their final outcome, depending of enzyme excitation. In particular, such effects can play the major role in DNA polymerization reactions where preliminary DNTP selection is quite important.

q-bio.BM↗
arXiv2009

Chemical and Mechanical Signaling in Epithelial Spreading

We propose a minimal mathematical model to explain long-range coordination of dynamics of multiple cells in epithelial spreading, which may be induced, under different conditions, by a chemical signal, or mechanical stress, or both. The model is based on chemo-mechanical interactions including a chemical effect of stress and concentration-dependent traction. The results, showing kinase concentration distribution and cell displacement, allow us to reproduce two activation waves on different time scales observed in the experiment, and distinguish between distinct dynamical patterns observed under conditions of injury or unconstraining.

physics.bio-ph↗
arXiv2009

A Biomechanical Model for Dictyostelium Motility

The crawling motion of Dictyostelium discoideum on substrata involves a number of coordinated events including cell contractions and cell protrusions. The mechanical forces exerted on the substratum during these contractions have recently been quantified using traction force experiments. Based on the results from these experiments, we present a biomechanical model of Dictyostelium discoideum motility with an emphasis on the adhesive properties of the cell-substratum contact. Our model assumes that the cell contracts at a constant rate and is bound to the substratum by adhesive bridges which are modeled as elastic springs. These bridges are established at a spatially uniform rate while detachment occurs at a spatially varying, load-dependent rate. Using Monte-Carlo simulations and assuming a rigid substratum, we find that the cell speed depends only weakly on the adhesive properties of the cell-substratum, in agreement with experimental data. Varying the parameters that control the adhesive and contractile properties of the cell we are able to make testable predictions. We also extend our model to include a flexible substrate and show that our model is able to produce substratum deformations and force patterns that are quantitatively and qualitatively in agreement with experimental data.

physics.bio-ph↗
arXiv2009

Mathematical description of bacterial traveling pulses

The Keller-Segel system has been widely proposed as a model for bacterial waves driven by chemotactic processes. Current experiments on {\em E. coli} have shown precise structure of traveling pulses. We present here an alternative mathematical description of traveling pulses at a macroscopic scale. This modeling task is complemented with numerical simulations in accordance with the experimental observations. Our model is derived from an accurate kinetic description of the mesoscopic run-and-tumble process performed by bacteria. This model can account for recent experimental observations with {\em E. coli}. Qualitative agreements include the asymmetry of the pulse and transition in the collective behaviour (clustered motion versus dispersion). In addition we can capture quantitatively the main characteristics of the pulse such as the speed and the relative size of tails. This work opens several experimental and theoretical perspectives. Coefficients at the macroscopic level are derived from considerations at the cellular scale. For instance the stiffness of the signal integration process turns out to have a strong effect on collective motion. Furthermore the bottom-up scaling allows to perform preliminary mathematical analysis and write efficient numerical schemes. This model is intended as a predictive tool for the investigation of bacterial collective motion.

math.AP↗
arXiv2009

Scale-free dynamics of somatic adaptability in immune system

The long-time dynamics of somatic adaptability in immune system is simulated by a simple physical model. The immune system described by the model exhibits a scale free behavior as is observed in living systems. The balance between the positive and negative feedbacks of the model leads to a robust immune system where the positive one corresponds to the formation of memory cells and the negative one to immunosuppression. Also the immunosenescence of the system is discussed based on the time-dependence of the epigenetic landscape of the adaptive immune cells in the shape space.

physics.bio-ph↗
arXiv2009

Human cell recovery after microwave irradiation

Cells of human buccal epithelium of 6 male donors were exposed to microwave radiation (frequency f=36,64 GHz, power density E = 10, 100, and 400 mcW/cm^2). Exposure time in all experiments was 10 seconds. Heterochromatin was stained by 2% orcein in 45 % acetic acid. The stainability of cells with trypan blue (0,5 %) and indigocarmine (5 mM) after 5 min of staining was investigated. Irradiation induced chromatin condensation (increase of number of heterochromatin granules) and increase of membrane permeability to vital dyes trypan blue and indigocarmine. Isolated human buccal cells had shown the ability to recover these changes. Number of heterochromatin granules lowered to initial level after 0,5 hour (E = 10 mcW/cm^2) and 2 hours (E = 100, and 400 mcW/cm^2) after irradiation. Cell plasma membrane permeability recovered a bit later, in correspondence, after 1 hour and 3 hours after irradiation.

q-bio.CB↗
arXiv2009

Inspiration from genetics to promote recognition and protection within ad hoc sensor networks

This work illustrates potentials for recognition within {\em ad hoc} sensor networks if their nodes possess individual inter-related biologically inspired genetic codes. The work takes ideas from natural immune systems protecting organisms from infection. Nodes in the present proposal have individual gene sets fitting into a self organised phylogenetic tree. Members of this population are genetically ''relatives''. Outsiders cannot easily copy or introduce a new node in the network without going through a process of conception between two nodes in the population. Related nodes can locally decide to check each other for their genetic relation without directly revealing their gene sets. A copy/clone of a gene sequence or a random gene set will appear as alien. Nodes go through a cycle of introduction (conception or ''birth'') with parents in the network and later exit from it (''death''). Hence the phylogenetic tree is dynamic or possesses a genetic drift. Typical lifetimes of gene sets and number of offspring from different parents affect this genetic drift and the level of correlation between gene sets. The frequency of mutations similarly affects the gene pool. Correlation between genes of the nodes implies a common secret for cryptographic material for communication and consistency check facilitating intrusion detection and tracing of events. A node can by itself (non-specifically) recognise an adversary if it does not respond properly according to its genes. Nodes can also collaborate to recognise adversaries by communicating response from intruders to check for consistency with the whole gene pool (phylogenetic tree).

cs.CR↗
arXiv2010

Epigenetic Tracking: Implementation Details

"Epigenetic Tracking" is the name of a model of cellular development that, coupled with an evolutionary technique, becomes an evo-devo (or "artificial embryology", or "computational development") method to generate 2d or 3d sets of artificial cells arbitrarily shaped. 'In silico' experiments have proved the effectiveness of the method in devo-evolving any kind of shape, of any complexity (in terms of number of cells, number of colours, etc.); being shape complexity a metaphor for organismal complexity, such simulations established its potential to generate the complexity typical of biological systems. Moreover, it has also been shown how the underlying model of cellular development is able to produce the artificial version of key biological phenomena such as embryogenesis, the presence of "junk DNA", the phenomenon of ageing and the process of carcinogenesis. The objective of this document is not to provide new material (most of the material presented here has already been published elsewhere): rather, it is to provide all details that, for lack of space, could not be provided in the published papers and in particular to give all technical details necessary to re-implement the method.

nlin.AO↗
arXiv2010

Switch and template pattern formation in a discrete reaction diffusion system inspired by the Drosophila eye

We examine a spatially discrete reaction diffusion model based on the interactions that create a periodic pattern in the Drosophila eye imaginal disc. This model is capable of generating a regular hexagonal pattern of gene expression behind a moving front, as observed in the fly system. In order to better understand the novel switch and template mechanism behind this pattern formation, we present here a detailed study of the model's behavior in one dimension, using a combination of analytic methods and numerical searches of parameter space. We find that patterns are created robustly provided that there is an appropriate separation of timescales and that self-activation is sufficiently strong, and we derive expressions in this limit for the front speed and the pattern wavelength. Moving fronts in pattern-forming systems near an initial linear instability generically select a unique pattern, but our model operates in a strongly nonlinear regime where the final pattern depends on the initial conditions as well as on parameter values. Our work highlights the important role that cellularization and cell-autonomous feedback can play in biological pattern formation.

q-bio.MN↗
arXiv2011

The mechanical creep compliance of tissue cells is gamma distributed

Investigations of natural variation among cells within a population are essential for understanding the stochastic nature of tissue cell deformation under applied load. In the existing literature, the population variation of single-cell creep compliance has so far been modeled universally by using a log-normal distribution. Here we use optical stretching, a non-contact and relatively high-throughput technique for probing cell mechanics, to accumulate a sufficient data set that demonstrates robustly that cell compliance varies according to the similar but distinct gamma distribution. Additionally, we re-examine existing simulations that were originally proposed to justify a log-normal fit, and show that in fact these simulation data also correspond to the gamma distribution. Finally, we propose a general stochastic differential equation that analytically predicts a gamma distribution of creep compliance during cell stretching, as well as the Gaussian distribution of cell recovery that we observe experimentally upon removal of applied load. The population variation is well characterized by just a single parameter in each of the creep and recovery regimes. We expect our correction of a phenomenological distribution fit, enabled by an expansive data set for mesenchymal stem cells, to enable the development of more accurate constitutive laws to describe cytoskeletal deformation. These findings thus serve to replace an empirical distribution with a better-fitting model that rests on a more solid experimental and theoretical foundation, and also provides a basis to predict and understand the stochastic nature of the mechanical response of individual cells within populations.

q-bio.CB↗
arXiv2010

Continuum Electrostatics in Cell Biology

Recent experiments revealing possible nanoscale electrostatic interactions in force generation at kinetochores for chromosome motions have prompted speculation regarding possible models for interactions between positively charged molecules in kinetochores and negative charge on C-termini near the plus ends of microtubules. A clear picture of how kinetochores establish and maintain a dynamic coupling to microtubules for force generation during the complex motions of mitosis remains elusive. The current paradigm of molecular cell biology requires that specific molecules, or molecular geometries, for force generation be identified. However, it is possible to account for mitotic motions within a classical electrostatics approach in terms of experimentally known cellular electric charge interacting over nanometer distances. These charges are modeled as bound surface and volume continuum charge distributions. Electrostatic consequences of intracellular pH changes during mitosis may provide a master clock for the events of mitosis.

q-bio.CB↗
arXiv2010

Theoretical results for chemotactic response and drift of E. coli in a weak attractant gradient

The bacterium Escherichia coli (E. coli) moves in its natural environment in a series of straight runs, interrupted by tumbles which cause change of direction. It performs chemotaxis towards chemo-attractants by extending the duration of runs in the direction of the source. When there is a spatial gradient in the attractant concentration, this bias produces a drift velocity directed towards its source, whereas in a uniform concentration, E.coli adapts, almost perfectly in case of methyl aspartate. Recently, microfluidic experiments have measured the drift velocity of E.coli in precisely controlled attractant gradients, but no general theoretical expression for the same exists. With this motivation, we study an analytically soluble model here, based on the Barkai-Leibler model, originally introduced to explain the perfect adaptation. Rigorous mathematical expressions are obtained for the chemotactic response function and the drift velocity in the limit of weak gradients and under the assumption of completely random tumbles. The theoretical predictions compare favorably with experimental results, especially at high concentrations. We further show that the signal transduction network weakens the dependence of the drift on concentration, thus enhancing the range of sensitivity.

q-bio.QM↗
arXiv2010

Monocyte and T-lymphocyte trans-endothelial migration in relation to cardiovascular disease: some alternative boundary conditions in a model recently proposed by Little et al. (PLoS Comput Biol 2009 5(10) e1000539)

We consider a slight modification to the monocyte and T-lymphocyte boundary conditions of Little et al. (PLoS Comput Biol 2009 5(10) e1000539) and derive alternative parameter estimates. No changes to the results and conclusions of the paper of Little et al. (PLoS Comput Biol 2009 5(10) e1000539) are implied.

q-bio.CB↗
arXiv2010

Mathematical Modelling of Allergy and Specific Immunotherapy: Th1-Th2-Treg Interactions

Regulatory T cells (Treg) have recently been identified as playing a central role in allergy and during allergen-specific immunotherapy. We have extended our previous mathematical model describing the nonlinear dynamics of Th1-Th2 regulation by including Treg cells and their major cytokines. We hypothesize that immunotherapy mainly acts on the T cell level and that the decisive process can be regarded as a dynamical phenomenon. The model consists of nonlinear differential equations which describe the proliferation and mutual suppression of different T cell subsets. The old version of the model was based upon the Th1-Th2 paradigm and is successful in describing the "Th1-Th2 switch" which was considered the decisive event during specific immunotherapy. In recent years, however, the Th1-Th2 paradigm has been questioned and therefore, we have investigated a modified model in order to account for the influence of a regulatory T cell type. We examined the extended model by means of numerical simulations and analytical methods. As the modified model is more complex, we had to develop new methods to portray its characteristics. The concept of stable manifolds of fixed points of a stroboscobic map turned out to be especially important. We found that when including regulatory T cells, our model can describe the events in allergen-specific immunotherapy more accurately. Our results suggest that the decisive effect of immunotherapy, the increased proliferation of Treg and suppression of Th2 cells, crucially depends on the administration of high dose injections right before the maintenance phase sets in. Empirical protocols could therefore be improved by optimizing this step of therapy.

q-bio.CB↗