arXiv subjects

D. Hansmann

Publications and source records attributed to D. Hansmann.

5 recordsLinked to original sources

arXiv2019

Stochastic model for the CheY-P molarity in the neighbourhood of E. coli flagella motors

E.coli serves as prototype for the study of peritrichous enteric bacteria that perform runs and tumbles alternately. Bacteria run forward as a result of the counterclockwise (CCW) rotation of their flagella bundle and perform tumbles when at least one of their flagella rotates clockwise (CW), moving away from the bundle. The flagella are hooked to molecular rotary motors of nanometric diameter able to make transitions between CCW and CW rotations that last up to one hundredth of a second. At the same time, flagella move or rotate the bacteria's body microscopically during lapses that range between a tenth and ten seconds. We assume that the transitions between CCW and CW rotations occur solely by fluctuations of CheY-P molarity in the presence of two threshold values, and that a veto rule selects the run or tumble motions. We present Langevin eqs for the CheY-P molarity in the vicinity of each molecular motor. This model allows to obtain the run- or tumble-time distribution as a linear combination of decreasing exponentials that is a function of the steady molarity of CheY-P in the neighbourhood of the molecular motor, which fits experimental data. In turn, if the internal signaling system is unstimulated, we show that the runtime distributions reach power-law behaviour, a characteristic of self-organized systems, in some time range and, afterwards, exponential cutoff. In addition, our model explains without any fitting parameters the ultrasensitivity of the flagella motors as a function of the steady state of CheY-P molarity. In addition, we show that the tumble bias for peritrichous bacterium has a similar sigmoid-shape to the CW bias, although shifted to lower concentrations when the flagella number increases. Thus, the increment in the flagella number allows lower operational values for each motor increasing amplification and robustness of the chemotatic pathway.

physics.bio-ph↗

arXiv2018

Langevin equations for the run-and-tumble of swimming bacteria

The run and tumble motions of a swimming bacterium are well characterized by two stochastic variables: the speed $v(t)$ and the change of direction or deflection \mbox{$x(t)=\cos\varphi(t)$}, where $\varphi(t)$ is the turning angle at time $t$. Recently, we have introduced [Soft Matter {\bf 13}, 3385 (2017)] a single stochastic model for the deflection $x(t)$ of an {\sl E. coli} bacterium performing both types of movement in isotropic media without taxis, based on available experimental data. In this work we introduce Langevin equations for the variables $(v,x)$, which for particular values of a control parameter $\beta$ correspond to run and tumble motions, respectively. These Langevin equations have analytical solutions, which make it possible to calculate the statistical properties of both movements in detail. Assuming that the stochastic processes $x$ and $v$ are not independent during the tumble, we show that there are small displacements of the center of mass along the normal direction to the axis of the bacterial body, a consequence of the flagellar unbundling during the run-to-tumble transition. Regarding the tumble we show, by means of the directional correlation, that the process is not stationary for tumble-times of the order of experimentally measured characteristic tumble-time. The mean square displacement is studied in detail for both movements even in the non-stationary regime. We determine the diffusion and ballistic coefficients for tumble- and run-times, establishing their properties and relationships.

cond-mat.soft↗

arXiv2016

A stochastic model for directional changes of swimming bacteria

In this work we introduce a stochastic model to describe directional changes in the movement of swimming bacteria. We use the probability density function (PDF) of turn angles, measured on tumbling wild-type {\it E. coli}, to build a Langevin equation for the deflection of the bacterial body swimming in isotropic media. We have solved this equation analytically by means of the Green function method and shown that three parameters are sufficient to describe the movement: the characteristic time, the steady-state solution and the control parameter. We conclude that the tumble motion, which is manifested as abrupt turns, is primarily caused by the rotational boost generated by the flagellar motor and complementarily by the rotational diffusion introduced by noise. We show that in the tumble motion the deflection is a non-stationary stochastic process during times at which the tumbling occurs. By tuning the control parameter our model is able to explain small turns of the bacteria around their centres of mass along the run. We show that the deflection during the run is an OrnsteinUhlenbeck process, which for typical run times is stationary. We conclude that, along the run, the rotational boosts do not exist and that only the rotational diffusion remains. Thus we have a single model to explain the turns of through a critical value that can explain the transition between the two turn behaviours. This model is the bacterium during the run or tumble movements, through a control parameter that can be tuned also able to explain in a very satisfactory way all available statistical experimental data, such as PDFs and average values of turning angles times, of both run and tumble motions.

cond-mat.soft↗

arXiv2014

Revisiting random deposition with surface relaxation: approaches from growth rules to Edwards-Wilkinson equation

We present several approaches for deriving the coarse-grained continuous Langevin equation (or Edwards-Wilkinson equation) from a random deposition with surface relaxation (RDSR) model. First we introduce a novel procedure to divide the first transition moment into the three fundamental processes involved: deposition, diffusion and volume conservation. We show how the diffusion process is related to antisymmetric contribution and the volume conservation process is related to symmetric contribution, which renormalizes to zero in the coarse-grained limit. In another approach, we find the coefficients of the continuous Langevin equation, by regularizing the discrete Langevin equation. Finally, in a third approach, we derive these coefficients from the set of test functions supported by the stationary probability density function (SPDF) of the discrete model. The applicability of the used approaches to other discrete random deposition models with instantaneous relaxation to a neighboring site is discussed.

cond-mat.stat-mech↗

arXiv2012

Coarse grained approach for universality classification of discrete models

Discrete and continuous models belonging to a universality class share the same linearities and (or) nonlinearities. In this work, we propose a new approach to calculate coarse grained coefficients of the continuous differential equation from discrete models. We apply small constant translations in a test space and show how to obtain these coefficients from the transformed average interface growth velocity. Using the examples of the ballistic deposition (BD) model and the restricted solid-on-solid (RSOS) model, both belonging to the Kardar-Parisi-Zhang (KPZ) universality class, we demonstrate how to apply our approach to calculate analytically the corresponding coefficients of the KPZ equation. Our analytical nonlinear coefficients are in agreement with numerical results obtained by Monte Carlo tilted simulations. In addition to the BD and the RSOS we study a competitive RSOS model that shows crossover between the KPZ and Edwards-Wilkinson universality classes.

cond-mat.stat-mech↗