| Be'er, Shay | Arrival in groups drastically decreases establishment time of a stochastic population | Abstract |
| Cairoli, Andrea | Anomalous processes with general waiting times: functionals and multi-point structure | Abstract |
| Ghosh, Anandamohan | Nonequilibrium dynamics of stochastic gene transcription | Abstract |
| Hafner, Anne | Anomalous transport in complex dendrites – geometrical considerations | Abstract |
| Klages, Rainer | Anomalous fluctuation relations and application to biological cell migration | Abstract |
| Klindt, Gary | Flow Signatures of Miscroswimmers with Active Flagella | Abstract |
| Knoops, Gert | Anomalous motion of molecular motors in a viscoelastic medium | Abstract |
| Lancaster, Gemma | Chronotaxic dynamics of cell metabolic oscillations | Abstract |
| Lapeyre, John | Brownian motion and weak ergodicity breaking | Abstract |
| Levke, Ortlieb | Brownian and non-Brownian properties of passive particles in an active fluid - Experimental details. | Abstract |
| Madhikar, Pranav | Accelerated Cell Dynamics | Abstract |
| Manzo, Carlo | Heterogeneous diffusion on living cell membranes leads to ergodicity breaking and correlates with receptor function | Abstract |
| Meylahn, Janusz | Biofilament interacting with molecular motors | Abstract |
| Midtvedt, Daniel | Cytosolic pH regulates cytoplasmic material properties | Abstract |
| Najafi, Javad | Swimming characteristics of bacillus subtilis with different number of flagella | Abstract |
| Novotný, Tomáš | Loop exponent in DNA bubble dynamics | Abstract |
| Pönisch, Wolfram | Neisseria gonorrhoeae microcolony merging is driven by pili-mediated interactions | Abstract |
| Ritter, Christine M | Migration of differentiating cells to culture periphery | Abstract |
| Teuerle, Marek | Scaling limits and numerical simulations of multidimensional Levy walks | Abstract |
| Tkachenko, Olena | Non-equlibrium states in finite-popualtion game dynamics | Abstract |
| Tuval, Idan | Moving to the light | Abstract |
| Voigt, Axel | tba | Abstract |
| Volkov, Evgeny | Multi-stable dynamics of non-adiabatic genetic Repressilator | Abstract |
| Wu, Hao | Amoeboid swimming in a confined geometry | Abstract |
| Ślęzak, Jakub | Generalised Langevin equation and random walks | Abstract |
| Arrival in groups drastically decreases establishment time of a stochastic population Be'er, Shay (The Hebrew University of Jerusalem, Racah Institute of Physics, physics, Tel-Aviv, Israel) |
When the mRNA lifetime is short compared to the cell cycle, proteins are produced in bursts which are geometrically distributed. This has a profound effect on the cellular switching dynamics between different metastable phenotypic states. Motivated by this scenario, we study a general problem of establishment of a stochastic population when immigration occurs in groups or bursts. We consider a simple unlimited growth model which includes immigration, binary reproduction, and death, where rather than a constant influx of individuals, immigration occurs via arrival in groups that are sampled from a given distribution. In the deterministic level, the model exhibits a lower stable and a higher unstable fixed points, where the latter can be viewed as the critical threshold for establishment. Employing the probability generating function technique in conjunction with Hamiltonian formulation, we are able to map the problem in the leading order onto solving a stationary Hamilton-Jacobi equation with an effective Hamiltonian that takes into account the bursty nature of the immigration. We show that arrival in groups exponentially decreases the mean switching time compared to the usual case of arrival in ones. In particular, close to the bifurcation limit we find a simple analytical expression for the mean switching time, which depends solely on the mean and variance of the group size distribution. Our results are demonstrated on several biologically relevant distributions such as the geometric and negative-binomial distributions, and compare well with numerical Monte-Carlo simulations. |
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| Anomalous processes with general waiting times: functionals and multi-point structure Cairoli, Andrea (Queen Mary, University of London, School of Mathematical Sciences, London, United Kingdom) |
Many transport processes in nature exhibit anomalous diffusive properties with non-trivial scaling of the mean square displacement, e.g., diffusion of cells or of chromosomes inside the cell nucleus, where typically a crossover between different scaling regimes appears over time. Here, we investigate a class of anomalous diffusion processes that is able to capture such complex dynamics by virtue of a general waiting time distribution. We obtain a complete characterization of such generalized anomalous processes, including their functionals and multi-point structure, using a representation in terms of a normal diffusive process plus a stochastic time change. A generalized Feynman- Kac formula is derived, where the non-Markovian features are manifest in a memory kernel that is naturally related to the characteristic functional of the waiting times. In the special case of power law distributed waiting times we recover well-known results from the theory of continuous time random walks. Our results are readily applicable to joint velocity-position data of anomalous diffusive systems, for which a consistent underlying stochastic process can often not be identified among conventional models. |
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| Nonequilibrium dynamics of stochastic gene transcription Ghosh, Anandamohan (Indian Institute of Science Education and Research - Kolkata, Department of Physics, Pune, India) |
The process of gene transcription is the response of a cell to fluctuating environmental conditions and is an intrinsically random process resulting in large cell-to-cell variability in mRNA numbers. An interesting experimental observation is that the mRNA distribution is non-Poissonian i.e. they are produced in bursts and can be theoretically explained by an ON-OFF model. The out-of-equilibrium transcriptional dynamics satisfies the fluctuation theorem and the key finding is that the reaction parameters that maximize the mRNA bursts simultaneously maximize the entropy production rate. A generic stochastic model can be constructed where environmental fluctuations are encoded in transcription rates. Our exact calculation and numerical simulations indicate transcription essentially acts as a low-pass filter. We find that the mRNA levels in a cell population can exhibit synchronous/asynchronous behavior resulting in deviations from Poisson distributions. |
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| Anomalous transport in complex dendrites – geometrical considerations Hafner, Anne (Universität des Saarlandes, Fachrichtung Theoretische Physik, Saarbrücken, Germany) |
Anne E. Hafner, M. Reza Shaebani, Heiko Rieger, Ludger Santen Dendritic spines, which are membranous protrusions of dendrites, serve as the main recipients of excitatory inputs in the mammalian brain. They exhibit dynamic structural changes, which form the regulatory basis of neural functions such as cognition, memory, and learning. The density, morphology, and spatial distribution of spines vary at different cortical areas or due to neurodegenerative diseases or aging [1]. Since cargo particles are frequently trapped by spines, alterations of their structure influence the transport features in dendrites. For instance, anomalous diffusion is reported to be strongly dependent on the morphology of the spines [2]. Here we analytically study a diffusive motion composed of two different modes of motility, a motion and a waiting mode. We investigate how the overall transport properties depend on the structural characteristics of dendrites and spines, and on the fraction of time spent in each state of motility. The analytical predictions are in agreement with available experimental data as well as the results of extensive Monte Carlo simulations [3]. [1] Chia-Chien Chen, Ju Lu, and Yi Zuo. Spatiotemporal dynamics of dendritic spines in the living brain. Front. Neuroanat., 8:1, 2014. [2] Fidel Santamaria, Stefan Wils, Erik De Schutter, and George J. Augustine. Anomalous diffusion in purkinje cell dendrites caused by spines. Neuron, 52(4):635, 2006. [3] M. Reza Shaebani, Anne E. Hafner, Ludger Santen. Geometrical Considerations for Anomalous Transport in Complex Dendrites. To be submitted. |
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| Anomalous fluctuation relations and application to biological cell migration Klages, Rainer (Queen Mary University of London, School of Mathematical Sciences, London, United Kingdom) |
Aleksei V. Chechkin (1), Peter Dieterich (2), Rainer Klages (3)
(1) Institute for Theoretical Physics NSC KIPT, Kharkov, Ukraine
(2) Institut fuer Physiologie, Medizinische Fakultaet Carl Gustav Carus, Dresden, Germany
(3) Queen Mary University of London, School of Mathematical Sciences, London, UK
Fluctuation Relations (FRs) generalise the second law of
thermodynamics to small systems far from equilibrium [1]. A prominent
example are transient (work) fluctuation relations (TFRs). They have
been verified by a number of experiments and have been derived
theoretically for many different models exhibiting normal diffusion
where the mean square displacement grows linearly in time. In this
talk we briefly review the concept of TFRs before testing them for a
number of stochastic models generating anomalous diffusion where the
mean square displacement grows nonlinearly in time. Our models are
motivated by experimental results and theoretical modeling of
biologial cell migration that for certain cell types was found to
exhibit anomalous diffusion and power law correlation decay [2]. Here
we study both generalized Langevin equations with power law memory
kernels as well as time-fractional Fokker-Planck equations, both with
or without breaking of fluctuation-dissipation relations (FDRs)
[3,4]. We find that conventional TFRs are recovered when FDRs hold
while breaking FDRs leads to interesting variations of the
conventional TFR form. We argue that our theoretical results are
important to understand biological cell migration under chemical
gradients and more generally systems exhibiting glassy dynamics.
[1] R.Klages, W.Just, C.Jarzynski (Eds.), {em Nonequilibrium
Statistical Physics of Small Systems}, Wiley-VCH, Weinheim (2013)
[2] P.Dieterich, R.Klages, R.Preuss, A.Schwab, PNAS 105, 459 (2008)
[3] A.V.Chechkin, R.Klages, J.Stat.Mech. L03002 (2009)
[4] A.V.Chechkin, F.Lenz, R.Klages, J.Stat.Mech. L11001 (2012)
|
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| Flow Signatures of Miscroswimmers with Active Flagella Klindt, Gary (Max Planck Institute for the Physics of Complex Systems, Biological Physics, Dresden, Germany) |
Many eukaryotic cells are propelled in a liquid by regular bending waves of whip-like appendages, termed cilia and flagella. Flagellar oscillations drive a range of physical phenomena including fluid transport, self-propulsion, navigation, synchronization. We seek to understand the motility of cells, due to nonlinear, stochastic dynamics of flagellar oscillations, using hydrodynamic simulations parametrized by experimental data that account for flagellar noise. Beside a thorough investigation of emergent flow signatures, we report recent measurements of active, non-thermal fluctuations and active mechano-responses of the flagellar beat, and discuss their impact on flagellar swimming and synchronization. |
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| Anomalous motion of molecular motors in a viscoelastic medium Knoops, Gert (Uhasselt, Universiteit Hasselt, theoretical physics, Opglabbeek, Belgium) |
The movement of a molecular motor can be described by considering cyclic steps which correspond to internal and external changes in the motor. The external steps which involve motion in a viscoelastic medium can not be described by Kramer's theory. We suggest a semi-Markov approach with non-exponential waiting times with an infinite average to represent the motion within a cell. With this approach anomalous diffusion is observed in analytical calculation as well as in dynamical simulations. |
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| Chronotaxic dynamics of cell metabolic oscillations Lancaster, Gemma (Lancaster University, Department of Physics, United Kingdom) |
G. Lancaster, Y. F. Suprunenko, K. Jenkins, and A. Stefanovska
A living cell is a thermodynamically open system characterised by a continuously varying energy. This variation arises mainly through fluctuations in rates of adenosine triphosphate (ATP) production and use. Attempts to model ATP production include both stochastic and deterministic approaches. However, there has been no direct consideration of the driving-driven relationships within the cell that result from its continuous exchange of substances and energy with the environment. The resulting time-variability as well as the oscillatory nature of this exchange lead naturally to the nonautonomous dynamics system approach to cell energy metabolism, introduced here.
A novel framework of chronotaxic (from emph{chronos} -- time and emph{taxis} -- order) systems cite{Suprunenko:13,Suprunenko:14b}, which are capable of maintaining their energy balance within prescribed limits despite external perturbations, is used to model the interplay between glycolytic and mitochondrial involvement in ATP production. The model is based on coupled chronotaxic phase oscillators. Through quantification of the chronotaxicity of a single ATP time-series using inverse approach methods cite{Clemson:14b}, dominant metabolic processes can be identified. We show that the transition from a healthy state to a dysfunctional one, such as is observed in cancer cite{Hanahan:11}, can be characterised in terms of inter-oscillator interactions. This could lead to the detection of metabolic alterations corresponding to carcinogenesis at an early stage, opening up the possibility of new diagnostic and therapeutic strategies. |
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| Brownian motion and weak ergodicity breaking Lapeyre, John (ICFO - The Institute of Photonic Sciences, ICFO - The Institute of Photonic Sciences, Quantum optics theory, Castelldefels, Spain) |
Non-ergodicity observed in single-particle tracking experiments is usually modeled by transient trapping rather than spatial disorder. I will talk about our models of a particle diffusing in a medium with inhomogeneous random diffusivities, but no traps. For some values of model parameters, we find that the mean squared displacement displays subdiffusion due to non-ergodicity for both annealed and quenched disorder. I will also discuss recent results on extensions of these models to quenched 2-d disorder. |
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| Brownian and non-Brownian properties of passive particles in an active fluid - Experimental details. Levke, Ortlieb (Universität des Saarlandes, Saarbrücken, Germany) |
This poster is directly related to the oral presentation with the same title. As experimental system we use a suspension of passive tracer particles in a fluid containing alga as microswimmers. The alga used are Chlamydomonas reinhardtii and have a nearly spherical body of 5 to 10 µm diameter and two flagella, which allow them to swims as a puller. As passive tracer particles we used polystyrene particles with diameters of few µm, where sedimentation was not important. To observe the 2D projection of the particle and swimmer positions, a dark field microscope was used. The chamber has an area of approximately one cm^2 and a height of 150 µm. In the middle of the cell, the influence of the boundaries can be neglected. We tracked the position of swimmer and tracers. Our statistical approach focuses on the tracer characteristics, e.g. mean square displacement and probability density function of the displacements as function of different alga concentrations and particle diameters. We find diffusion characteristics which can be interpreted as enhanced Brownian diffusion. But the same trajectories show also non Brownian statistics, like a non-Gaussian probability density function of the displacements. |
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| Accelerated Cell Dynamics Madhikar, Pranav (SoftSImu Group, Technical University of Eindhoven, Mathematics and Computer Science, Eindhoven, Netherlands) |
Cell behaviour has been notoriously difficult to study due to the complexity of the of the system of the cell. An average cell contains many multitudes of different molecules, large and small, that all come with their own particular complex behaviours and interactions. These complex interactions are, of course, all highly interesting on their own, but they unfortunately make studying the cell as a whole an intractable problem. This problem is compounded further when one considers cell-cell interactions. Fortunately, cell-cell interactions can be approximated through a variety of approximations. However, these approximations tend to be ad hoc in the sense that they can only model limited behaviours of cells in certain regimes. For example, a 2D model that can show motility fails to show proliferation and vice versa. A new modelling technique is needed to study cell behaviour more completely. The model presented here aims to build such a model from two angles. The first being the modelling of cells with molecular dynamics, where each cell is modelled as a spherical membrane made of a variable number of particles in a force field. The force field itself includes of models for the surface tension of a cell, the adhesion (or friction) between cells, and the repulsion between cells. This model is actually capable of doing this simulation in 3D which can allow us to study the formation and behaviour 3D systems in living organisms. This model is an extension of an already implemented 2D model (Soft Matter 10, 4332-4339 (2014)), which in turn was based on a more basic model that was demonstrated earlier (Phys. Rev. E. 73, 062301 (2006)). The second angle is to accelerate this simulation technique to run on devices with a large number of processing cores, such as the Graphics Processing Unit (GPU). Using this device it is possible to greatly reduce simulation run times or to introduce additionally complexities into the model while still keeping run times at acceptable levels. Furthermore, the techniques used by this simulation code can in theory be applied to accelerate any other simulation technique. This Accelerated model has already given us interesting results when it comes to study certain measurable outcomes of the simulation. One is the general Mitotic Index observed in the division or growth rate of cells; a trend comparable to experimental analogs is obtained. The packing and geometries of a variety of cells have been studied experimentally, our simulation is capable of producing similar packing and geometries. |
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| Heterogeneous diffusion on living cell membranes leads to ergodicity breaking and correlates with receptor function Manzo, Carlo (ICFO - The Institute of Photonic Sciences, Single Molecule BioPhotonics, Castelldefels (Barcelona), Spain) |
Receptor diffusion in the plasma membrane of living cells regulates numerous processes underlying biological function and is influenced by the interplay of several mechanisms, such as crowding and molecular interactions. In the last decade, advances in single-molecule techniques have provided novel insights on the dynamics of multiple receptors at unprecedented spatiotemporal resolution. In particular, single particle tracking (SPT) has allowed recording of single receptor motion at video frame rates with nanometer accuracy. These experiments have shown that the complexity of the membrane environment often produces deviation from purely Brownian behavior, leading to anomalous and confined diffusion. Using SPT, we have studied the dynamics of DC-SIGN, a receptor that organizes in a hierarchical fashion on the plasma membrane, facilitating capture and internalization of viral pathogens [1,2]. The analysis of time- and ensemble-averaged mean-square displacement of single receptor trajectories revealed that, besides anomalous diffusion, DC-SIGN dynamics exhibits weak ergodicity breaking and aging [3]. In contrast to other membrane receptors showing analogous behavior, we show that DC-SIGN non-ergodicity is not induced by transient immobilization, but might be interpreted within the framework of inhomogeneous Brownian diffusion [4]. To further investigate the origin of this behavior, we compared the dynamics of DC-SIGN and three mutated forms of the receptor [3] and performed complementary measurements by means of super-resolution imaging (STED) and functional assays[1,2]. These results allow us to correlate receptor motion to its molecular structure, thus establishing a link between nonergodicity and DC-SIGN function in pathogen capture and internalization [3]. As such, our results highlight the fundamental role of disorder in cell membranes, and its connection with function regulation. References: [1] C. Manzo*, J. A. Torreno-Pina*, B. Joosten, I. Reinieren-Beeren, E. J. Gualda, P. Loza-Alvarez, C. G. Figdor, M. F. Garcia-Parajo, A. Cambi The neck region of the C-type lectin DC-SIGN regulates its surface spatiotemporal organization and virus-binding capacity on antigen-presenting cells. Journal of Biological Chemistry (2012) 287(46):38946–38955. [2] J. A. Torreno-Pina*, B. M. Castro*, C. Manzo, S. I. Buschow, A. Cambi, M. F. Garcia-Parajo Enhanced receptor–clathrin interactions induced by n-glycan–mediated membrane micropatterning. PNAS (2014) 111(30):11037–11042. [3] C. Manzo*, J. A. Torreno-Pina*, P. Massignan, G. J. Lapeyre Jr, M. Lewenstein, M. F. Garcia-Parajo Weak ergodicity breaking of receptor motion in living cells stemming from random diffusivity. Physical Review X in press. ArXiv: 1407.2552 (2014). [4] P. Massignan, C. Manzo, J. Torreno-Pina, M. F. García-Parajo, M. Lewenstein, G. J. Lapeyre Jr Nonergodic subdiffusion from brownian motion in an inhomogeneous medium. Physical Review Letters (2014) 112(15):150603. |
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| Biofilament interacting with molecular motors Meylahn, Janusz (Stellenbosch University, Stellenbosch University, Physics, Stellenbosch, South Africa) |
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| Cytosolic pH regulates cytoplasmic material properties Midtvedt, Daniel (Max Planck Institute for the Physics of Complex Systems, Dresden, ) |
Upon sub-optimal growth conditions, many cells enter a quiescent state characterized by lack of cell division, low metabolic activity and decreased intracellular pH. The mechanisms by which cells enter and leave quiescence are as of yet largely unknown. Using single-particle tracking, we investigate the mobility of foreign tracer particles in yeast cells under different cytosolic pH conditions. We find a significant decrease in the mobility of the particles under acidic conditions. Alongside the decreased mobility, acidification causes widespread assembly of macromolecular complexes. Detailed statistical analysis of the single particle trajectories indicate that the cytoplasm undergoes a phase transition, from a viscoelastic fluid to a disordered solid-like state. This transition is reversible, and can be triggered both by energy depleting the cells and by a reduction in cytosolic pH alone. The observed formation of macromolecular complexes is believed to be at the origin of this phase transition. Our findings indicate that cells may use cytosolic pH to regulate the material properties of the cytoplasm. This has broad implications for the understanding of alternative physiological states in cells, and promotes a view on the eukaryotic cytoplasm as a viscoelastic material with widely tunable properties. |
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| Swimming characteristics of bacillus subtilis with different number of flagella Najafi, Javad (Saarland University, Experimental Physics, Saarbruecken, Germany) |
It is well known that bacteria can use flexible appendages called flagella to swim in aqueous environment. Our purpose is to understand the influence of the number of flagella on different behavior of bacteria. We study the wild type and genetically manipulated strains of bacillus subtilis to answer basic questions on their swimming behavior. The wild type strain has about 25 flagella which are distributed all over its surface, and uses run and tumble mechanism to explore its surrounding. The manipulated strains have about 10 and 40 flagella. Using dark field microscopy and tracking of cells, we calculate the statistics of swimming velocity, running and tumbling time, turning angle, diffusion coefficient and correlation in direction. |
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| Loop exponent in DNA bubble dynamics Novotný, Tomáš (Charles University of Prague, Faculty of Mathematics and Physics, Department of Condensed Matter Physics, Praha 2, Czech Republic) |
Dynamics of DNA bubbles are of interest for both statistical physics and biology. We present exact solutions to the Fokker–Planck equation governing bubble dynamics in the presence of a long-range entropic interaction. The complete meeting time and meeting position probability distributions are derived from the solutions. Probability distribution functions (PDFs) reflect the value of the loop exponent of the entropic interaction. Our results extend previous results which concentrated mainly on the tails of the PDFs and open a way to determining the strength of the entropic interaction experimentally which has been a matter of recent discussions. Using numerical integration, we also discuss the influence of the finite size of a DNA chain on the bubble dynamics. Analogous results are obtained also for the case of subdiffusive dynamics of a DNA bubble in a heteropolymer, revealing highly universal asymptotics of meeting time and position probability functions. Ref.: J. Phys. A: Math. Theor 47 (2014) 315003 |
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| Neisseria gonorrhoeae microcolony merging is driven by pili-mediated interactions Pönisch, Wolfram (Max Planck Institute for the Physics of Complex Systems, Biological Physics, Dresden, Germany) |
The sexually transmitted disease gonorrhea is caused by the bacterium Neisseria gonorrhoeae. During the infection the bacteria form microcolonies consisting of a few hundreds to a few thousands of single cells. Type 4 pili, thin and long filaments emerging from the membrane of the cells, are essential for the colony formation process and cause attractive cell-cell-interactions. While the pili-mediated motion of single cells has been extensively studied during the last past years, the assembly and growth of colonies is barely understood. We examine coalescence, a key mechanism of colony formation, by using a theoretical microscopic model where single cells interacting solely by their pili and comparing our results to experimental data. We observe a fast initial approach of two colonies that is followed by a slow relaxation to a spherical shape with a characteristic time of several hours. We suggest that colonies consist of two different domains that can explain this observation: a bulk of cells with a very low motility and a surface layer with cells that are highly motile. |
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| Migration of differentiating cells to culture periphery Ritter, Christine M (University of Copenhagen, Niels Bohr Institute, Copenhagen Ø, Denmark) |
In the early stages of embryonic development, the cells differentiate into extra-embryonic tissue and the embryo itself. 4.5 days after fertilization two different cell lines can be found from which the fetus will develop: the epiblast and the primitive endoderm. The main part of the embryo will develop from the cells of the epiblast, while some of the primitive endodermal cells will contribute to the digestive tract and others will make up an extra-embryonic endoderm layer in the yolk sac. Hence, a correct segregation of epiblast cells from endodermal primed cells is essential for fetal development. In vivo 4.5 days after fertilization, these cell types have separated from each other and the primitive endoderm will be found on the periphery of the epiblast cells. We set out to investigate and quantify this stem cell migration and segregation. The mouse embryonic stem cells used in this study were harvested from the inner cell mass 3.5 days after fertilization and before segregation happens. The cells were modified to express a fluorescent reporter gene, Hhex, which functions as a marker for differentiation into the primitive endoderm. These cells were cultured in LiF (Leukemia inhibitory factor) media, which means that they maintained pluripotency; in other words, they maintained the ability to differentiate into any embryonic tissue type. Confocal microscopy was used to image cell colonies. To quantify cell migration we calculated the second moment of primitive endoderm primed cells with respect to the center of mass of the cell colony. The second moments of 128 primitive endodermal primed cells from 9 independent colonies were found and compared to a randomly generated set of moments. A Student’s t-test was performed and showed that the cell migration was significantly different from random motion (p=0.00024). Hence, we conclude that the primitive endodermal primed cells move in a non-random fashion toward the colony periphery. |
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| Scaling limits and numerical simulations of multidimensional Levy walks Teuerle, Marek (Wrocław University of Technology, Department of Mathematics, Wroclaw, Poland) |
The model of Levy walk (LW) was proposed for the first time by M.F. Shlesinger, J. Klafter and Y.M.Wong (1982). That model assumes that a walker trajectory consists of sum of jumps (or flights), which are characterized by a constant velocity within some heavy-tailed period of time. Moreover after every jumps the walker randomly changes the direction of next jump. Our analysis is based on a model which is very close to the one described above, but not exactly the same. Namely, it arises as a special class of continuous-time random walk (CTRW) which is generated by the sequence of iid heavy-tailed pairs of jumps and respective waiting times. A strong coupling introduced within every pair between the jump and the waiting time implies a finite second moment over whole trajectory [1]. In our work [2, 1] we analyze a multidimensional LW, which is a CTRW process generated by sequence of iid heavy-tailed pairs of jumps and respective waiting times, such that the length of every multidimensional jump is equal to the length of waiting time raised to some fixed positive real power gamma. We investigate the detailed description of the scaling limit by means of their Levy triplet. Another part of our research is devoted to the fractional diffusion equations which governs the pdf of obtained scaling limits. Moreover, we discuss the possible anomalous diffusion regimes (superdiffusion, quasi-normal diffusion and subdiffusion) of the scaling limit, which may be obtained by proper choice of parameter gamma. It worth be noticing that our asymptotical analysis of LW also includes its modification, in which every waiting time is proceeded by a jump leading to so-called ‘jump first’ or ‘jump-wait’ scenario (in contrary to ‘wait first’ or ‘wait-jump’ which arise naturally in CTRW model). The last part of our work describes the algorithm of simulating trajectories of the studied processes and present some Monte Carlo results. [1] M. Teuerle, M. Magdziarz, P. Żebrowski, Multidimensional Levy walk and its scaling limits, J. Phys. A: Math. Theor.2012;45:385002 [2] M. Magdziarz, M. Teuerle, Asymptotic properties and numerical simulation of multidimensional Lévy walks, Commun. Nonlinear. Sci. Numer. Simulat. 2015;20;489–505. |
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| Non-equlibrium states in finite-popualtion game dynamics Tkachenko, Olena (Sumy State University, Sumy State University, General and Theoretical Physics, Sumy, Ukraine) |
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| Moving to the light Tuval, Idan (Mediterranean Institute for Advanced Studies, IMEDEA (UIB-CSIC), Esporles, Spain) |
Photosynthetic microorganisms are fundamental primary producers: they are at the base of major food webs (e.g. in the oceans), and contribute about half of the global oxygen production. Many of these organisms are motile, and adapt their motility in response to light in a poorly understood process known as phototaxis. Phototaxis is a directed motion towards/away from a light source, and as such is completely different from the well known E. coli chemotaxis, based instead on modulating the frequency of random tumblings. It is closer to Dictyostelium and neutrophil chemotaxis, although both the nature of the stimulus (a vector rather than a scalar) and the motility (ciliated swimming rather than crawling) are very different in the two cases. In this talk I will present recent results on the mechanism of light-induced turning in both unicellular and multicellular green algae, and discuss their long-timescale adaptive dynamics. |
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| tba Voigt, Axel (Technische Universität Dresden, Mathematics, Germany) |
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| Multi-stable dynamics of non-adiabatic genetic Repressilator Volkov, Evgeny (Russian Academy of Science, P.N. Lebedev Physical Institute, Theoretical Physics, Moscow, Russian Federation) |
The assumption of the fast binding of transcription factors (TF's) to promoters is a typical point in studies of synthetic genetic circuits functioning in bacteria. Although the assumption is effective for simplifying the models, it becomes questionable in the light of in vivo measurements of the times TF spends searching for its cognate DNA sites. We investigated the dynamics of the full model of the paradigmatic genetic oscillator, Repressilator, using deterministic mathematical modeling and stochastic simulations. We found that decrease in the TF binding rate changes the type of transition between steady state and oscillation. As a result, this gives rise to the hysteresis region in the parameter space, where both the steady state and the oscillation co-exist. We further show that the hysteresis is persistent over considerable range of the parameter values, but presence of the oscillations is limited by the low rate of TF degradation. Finally, the stochastic simulation of the model confirms the hysteresis with switching between the two attractors, resulting in highly skewed period distributions. Moreover, intrinsic noise stipulates trains of large-amplitude modulations around the stable steady state outside the hysteresis region, which makes the period distributions bimodal. |
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| Amoeboid swimming in a confined geometry Wu, Hao (Universite Joseph Fourier GRENOBLE France, Laboratoire interdisciplinaire de Physique - CNRS, Saint Martin d'Hères, France) |
Cells of the immune system, as well as cancer cells, migrating in confined environment of tissues undergo frequent shape changes (described as amoeboid motion) that enable them to move forward through these porous media without the assistance of adhesion sites. In other words, they perform amoeboid swimming (AS) while using extracellular matrices and cells of tissues as support. We introduce a simple model of AS in a confined geometry solved by means of 2D numerical simulations. We find that confinement promotes AS, unless being so strong that it restricts shape change amplitude. A straight AS trajectory in the channel is found to be unstable, and ample lateral excursions of the swimmer prevail. For weak confinement, these excursions are symmetric, while they become asymmetric at stronger confinement, whereby the swimmer is located closer to one of the two walls. This is a spontaneous symmetry-breaking bifurcation. We find that there exists an optimal confinement for migration. We provide numerical results as well as scaling laws. This study raises the question of the relevance of these scenarios to complex situations encountered in vivo. |
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| Generalised Langevin equation and random walks Ślęzak, Jakub (Wroclaw University of Technology, Department of Mathematics, Faculty of Fundamental Problems of Technology, Wroclaw, Poland) |
Generalised Langevin equation is an integro-differential equation describing evolution of coordinates interacting with complex environment. It is derived from Hamilton mechanics of large systems, where influence of almost all but few chosen coordinates can be described using random force process and memory kernel (which are related by the fluctuation-dissipation theorem). This correspondence between mechanical and stochastic systems is exact, but the random force is often approximated by some process with suitable properties and simple analytical properties. It may be surprising, but, in contrary to the integro-differential form of the equation, random walks are also acceptable choices of the random force. Moreover, the solution of such equation is also a random walk with properties that suggest its possible applications in biological subdiffusive environments, such as cellular cytoplasm. |
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