arXiv subjects

M. Majka

Publications and source records attributed to M. Majka.

8 recordsLinked to original sources

arXiv2023

Stability of pattern formation in systems with dynamic source regions

We explain the principles of gene expression pattern stabilization in systems of interacting, diffusible morphogens, with dynamically established source regions. Using a reaction-diffusion model with step-function production term, we identify the phase transition between low-precision indeterminate patterning and the phase in which a traveling, well-defined contact zone between two domains is formed. Our model analytically explains single- and two-gene domain dynamics and provides pattern stability conditions for all possible two-gene regulatory network motifs.

physics.bio-ph↗

arXiv2019

Effective one-component model of binary mixture: molecular arrest induced by the spatially correlated stochastic dynamics

Spatially correlated noise (SCN), i.e. the thermal noise that affects neighbouring particles in a similar manner, is ubiquitous in soft matter systems. In this work, we apply the over-damped SCN-driven Langevin equations as an effective, one-component model of the dynamics in dense binary mixtures. We derive the thermodynamically consistent fluctuation-dissipation relation for SCN to show that it predicts the molecular arrest resembling the glass transition, i.e. the critical slow-down of dynamics in the disordered phases. We show that the mechanism of singular dissipation is embedded in the dissipation matrix, accompanying SCN. We are also able to identify the characteristic length of collective dissipation, which diverges at critical packing. This novel physical quantity conveniently describes the difference between the ergodic and non-ergodic dynamics. The model is fully analytically solvable, one-dimensional and admits arbitrary interactions between the particles. It qualitatively reproduces several different modes of arrested disorder encountered in binary mixtures, including e.g. the re-entrant arrest. The model can be effectively compared to the mode coupling theory.

cond-mat.soft↗

arXiv2018

The effects of subdiffusion on the NTA size measurements of extracellular vesicles in biological samples

The interest in the extracellular vesicles (EVs) is rapidly growing as they became reliable biomarkers for many diseases. For this reason, fast and accurate techniques of EVs size characterization are the matter of utmost importance. One increasingly popular technique is the Nanoparticle Tracking Analysis (NTA), in which the diameters of EVs are calculated from their diffusion constants. The crucial assumption here is that the diffusion in NTA follows the Stokes-Einstein relation, i.e. that the Mean Square Displacement (MSD) of a particle grows linearly in time (MSD $\propto t$). However, we show that NTA violates this assumption in both artificial and biological samples, i.e. a large population of particles show a strongly sub-diffusive behaviour (MSD $\propto t^α$, $0<α<1$). To support this observation we present a range of experimental results for both polystyrene beads and EVs. This is also related to another problem: for the same samples there exists a huge discrepancy (by the factor of 2-4) between the sizes measured with NTA and with the direct imaging methods, such as AFM. This can be remedied by e.g. the Finite Track Length Adjustment (FTLA) method in NTA, but its applicability is limited in the biological and poly-disperse samples. On the other hand, the models of sub-diffusion rarely provide the direct relation between the size of a particle and the generalized diffusion constant. However, we solve this last problem by introducing the logarithmic model of sub-diffusion, aimed at retrieving the size data. In result, we propose a novel protocol of NTA data analysis. The accuracy of our method is on par with FTLA for small ($\simeq$200nm) particles. We apply our method to study the EVs samples and corroborate the results with AFM.

physics.bio-ph↗

arXiv2016

Collectivity in diffusion of colloidal particles: from effective interactions to spatially correlated noise

The collectivity in the simultaneous diffusion of many particles, i.e. the interdependence of stochastic forces affecting different particles in the same solution, is a largely overlooked phenomenon with no well-established theory. Recently, we have proposed a novel type of thermodynamically consistent Langevin dynamics driven by the Spatially Correlated Noise (SCN) that can contribute to the understanding of this problem. This model draws a link between the theory of effective interactions in binary colloidal mixtures and the properties of SCN. In the current article we review this model from the perspective of collective diffusion and generalize it to the case of multiple ($N>2$) particles. Since our theory of SCN-driven Langevin dynamics has certain issues that could not be resolved within its framework, in this article we also provide another approach to the problem of collectivity. We discuss the multi-particle Mori-Zwanzig model, which is fully microscopically consistent. Indeed, we show that this model supplies many information, complementary to the SCN-based approach, e.g. it predicts the deterministic dynamics of the relative distance between the particles, it provides the approximation for non-equilibrium effective interactions and predicts the collective subdiffusion of tracers in group. These results provide the short-range, inertial limit of the earlier model and agree with its predictions under some general conditions. In this article we also review the origin of SCN and its consequences for the variety of physical systems, with emphasis on the colloids.

cond-mat.stat-mech↗

arXiv2016

Thermodynamically consistent Langevin dynamics with spatially correlated noise predicts frictionless regime and transient attraction effect

While the origin of temporal correlations in Langevin dynamics have been thoroughly researched, the understanding of Spatially Correlated Noise (SCN) is rather incomplete. In particular, very little is known about the relation between friction and SCN. In this article, we derive the formal formula for the spatial correlation function in the particle-bath interactions. This expression shows that SCN is the inherent component of binary mixtures, originating from the effective (entropic) interactions. Further, employing this spatial correlation function, we postulate the thermodynamically consistent Langevin equation driven by SCN and the adequate Fluctuation-Dissipation Relation. The thermodynamical consistency is achieved by introducing the spatially variant friction coefficient, which can be also derived analytically. This coefficient exhibits a number of intriguing properties, e.g. the singular behavior for certain interaction types. Eventually, we apply this new theory to the system of two charged particles in the presence of counter-ions. Such particles interact via the screened-charge Yukawa potential and the inclusion of SCN leads to the emergence of the anomalous frictionless regime. In this regime the particles can experience active propulsion leading to the transient attraction effect. This effect suggests a non-equilibrium mechanism facilitating the molecular binding of the like-charged particles.

cond-mat.stat-mech↗

arXiv2015

Non-Gaussian polymers described by alpha-stable chain statistics: model, applications and effective interactions in binary mixtures

The Gaussian chain model is the classical description of a polymeric chain, which provides the analytical results regarding end-to-end distance, the distribution of segments around the mass center of a chain, coarse grained interactions between two chains and effective interactions in binary mixtures. This hierarchy of results can be calculated thanks to the alpha stability of the Gaussian distribution. In this paper we show that it is possible to generalize the model of Gaussian chain to the entire class of alpha stable distributions, obtaining the analogous hierarchy of results expressed by the analytical closed-form formulas in the Fourier space. This allows us to establish the alpha-stable chain model. We begin with reviewing the applications of Levy flights in the context of polymer sciences, which include: chains with heavy-tailed distributions of persistence length, polymers adsorbed to the surface and the chains driven by a noise with power-law spatial correlations. Further, we derive the distribution of segments around the mass center of the alpha-stable chain and the coarse-grained interaction potential between two chains is constructed. These results are employed to discuss the model of binary mixture consisting of the alpha-stable chains. On what follows, we establish the spinodal decomposition condition generalized to the particles described by the shape of alpha-stable distributions. This condition is finally applied to analyze the on-surface phase separation of adsorbed polymers, which are known to be described with heavy tailed statistics.

cond-mat.soft↗

arXiv2014

A model for effective interactions in binary colloidal systems of soft particles

While the density functional theory with integral equations techniques are very efficient tools in numerical analysis of complex fluids, an analytical insight into the phenomenon of effective interactions is still limited. In this paper we propose a theory of binary systems which results in a relatively simple analytical expression combining arbitrary microscopic potentials into the effective interaction. The derivation is based on translating many particle Hamiltonian including particle-depletant and depletant-depletant interactions into the occupation field language. Such transformation turns the partition function into multiple Gaussian integrals, regardless of what microscopic potentials are chosen. In result, we calculate the effective Hamiltonian and discuss when our formula is a dominant contribution to the effective interactions. Our theory allows us to analytically reproduce several important characteristics of systems under scrutiny. In particular, we analyze the effective attraction as a demixing factor in the binary systems of Gaussian particles, effective interactions in the binary mixtures of Yukawa particles and the system of particles consisting of both repulsive core and attractive/repulsive Yukawa interaction tail, for which we reproduce the 'attraction-through-repulsion' and 'repulsion-through-attraction' effects.

cond-mat.soft↗

arXiv2012

Polymer unfolding and motion synchronization induced by spatially correlated noise

The problem of a spatially correlated noise affecting a complex system is studied in this paper. We present a comprehensive analysis of a 2D model polymer chain, driven by the spatially correlated Gaussian noise, for which we have varied the amplitude and the correlation length. The chain model is based on a bead-spring approach, enriched with a global Lennard-Jones potential and angular interactions. We show that spatial correlations in the noise inhibit the chain geometry dynamics, enhancing the preservation of the polymer shape. This is supported by the analysis of correlation functions of both the module length and angles between neighboring modules, which have been measured for the noise amplitude ranging over 3 orders of magnitude. Moreover, we have observed the correlation length dependent beads motion synchronization, and the spontaneous polymer unfolding, resulting from an interplay between chain potentials and the spatially structured noise.

cond-mat.stat-mech↗