Simonbolton3358

Our work may unveil the underlying mechanism of several synchronization phenomena that exist in a network of oscillators having a mixed type of coupling.When two macromolecules come very near in a fluid, the surrounding molecules, having finite volume, are less likely to get in between. This leads to a pressure difference manifesting as an entropic attraction, called depletion force. Akt inhibitor Here we calculate the density profile of liquid molecules surrounding a disordered rigid macromolecules modeled as a random arrangement of hard spheres on a linear backbone. We analytically determine the position dependence of the depletion force between two such disordered molecules by calculating the free energy of the system. We then use molecular dynamics simulations to obtain the depletion force between stiff disordered polymers as well as flexible ones and compare the two against each other. We also show how the disorder averaging can be handled starting from the inhomogenous reference interaction site model equations.Previous work has introduced scale-split energy density ψ_l,L(x,t)=1/2B_l·B_L for vector field B(x,t) coarse grained at scales l and L, in order to quantify the field stochasticity or spatial complexity. In this formalism, the L_p norms S_p(t)=1/2||1-B[over ̂]_l·B[over ̂]_L||_p, pth-order stochasticity level, and E_p(t)=1/2||B_lB_L||_p, pth order mean cross energy density, are used to analyze the evolution of the stochastic field B(x,t). Application to turbulent magnetic fields leads to the prediction that turbulence in general tends to tangle an initially smooth magnetic field increasing the magnetic stochasticity level, ∂_tS_p>0. An increasing magnetic stochasticity in turn leads to disalignments of the coarse-grained fields B_d at smaller scales, d≪L, thus they average to weaker fields B_L at larger scales upon coarse graining, i.e., ∂_tE_p0 with s_p(t)=1/2||1-u[over ̂]_l.u[over ̂]_L||_p, which may correspond to fluid jets spontaneously driven by sudden field-flu.The diffusion in two dimensions of noninteracting active particles that follow an arbitrary motility pattern is considered for analysis. A Fokker-Planck-like equation is generalized to take into account an arbitrary distribution of scattered angles of the swimming direction, which encompasses the pattern of active motion of particles that move at constant speed. An exact analytical expression for the marginal probability density of finding a particle on a given position at a given instant, independently of its direction of motion, is provided, and a connection with a generalized diffusion equation is unveiled. Exact analytical expressions for the time dependence of the mean-square displacement and of the kurtosis of the distribution of the particle positions are presented. The analysis is focused in the intermediate-time regime, where the effects of the specific pattern of active motion are conspicuous. For this, it is shown that only the expectation value of the first two harmonics of the scattering angle of the direction of motion are needed. The effects of persistence and of circular motion are discussed for different families of distributions of the scattered direction of motion.The formation of biomolecular condensates inside cells often involve intrinsically disordered proteins (IDPs), and several of these IDPs are also capable of forming dropletlike dense assemblies on their own, through liquid-liquid phase separation. When modeling thermodynamic phase changes, it is well known that finite-size scaling analysis can be a valuable tool. However, to our knowledge, this approach has not been applied before to the computationally challenging problem of modeling sequence-dependent biomolecular phase separation. Here we implement finite-size scaling methods to investigate the phase behavior of two 10-bead sequences in a continuous hydrophobic-polar protein model. Combined with reversible explicit-chain Monte Carlo simulations of these sequences, finite-size scaling analysis turns out to be both feasible and rewarding, despite relying on theoretical results for asymptotically large systems. While both sequences form dense clusters at low temperature, this analysis shows that only one of them undergoes liquid-liquid phase separation. Furthermore, the transition temperature at which droplet formation sets in is observed to converge slowly with system size, so that even for our largest systems the transition is shifted by about 8%. Using finite-size scaling analysis, this shift can be estimated and corrected for.The formation of protein patterns inside cells is generically described by reaction-diffusion models. The study of such systems goes back to Turing, who showed how patterns can emerge from a homogenous steady state when two reactive components have different diffusivities (e.g., membrane-bound and cytosolic states). However, in nature, systems typically develop in a heterogeneous environment, where upstream protein patterns affect the formation of protein patterns downstream. Examples for this are the polarization of Cdc42 adjacent to the previous bud site in budding yeast and the formation of an actin-recruiter ring that forms around a PIP3 domain in macropinocytosis. This suggests that previously established protein patterns can serve as a template for downstream proteins and that these downstream proteins can "sense" the edge of the template. A mechanism for how this edge sensing may work remains elusive. Here we demonstrate and analyze a generic and robust edge-sensing mechanism, based on a two-component mass-conserving reaction-diffusion (McRD) model. Our analysis is rooted in a recently developed theoretical framework for McRD systems, termed local equilibria theory. We extend this framework to capture the spatially heterogeneous reaction kinetics due to the template. This enables us to graphically construct the stationary patterns in the phase space of the reaction kinetics. Furthermore, we show that the protein template can trigger a regional mass-redistribution instability near the template edge, leading to the accumulation of protein mass, which eventually results in a stationary peak at the template edge. We show that simple geometric criteria on the reactive nullcline's shape predict when this edge-sensing mechanism is operational. Thus, our results provide guidance for future studies of biological systems and for the design of synthetic pattern forming systems.