Minimal models of self-propelled particles with short-range volume exclusion interactions have been shown to exhibit signatures of phase separation. Here I show that the observed interfacial stability and fluctuations in motility-induced phase separa
tions (MIPS) can be explained by modeling the microscopic dynamics of the active particles in the interfacial region. In addition, I demonstrate the validity of the Gibbs-Thomson relation in MIPS, which provides a functional relationship between the size of a condensed drop and its surrounding vapor concentration. As a result, the coarsening dynamics of MIPS at vanishing supersaturation follows the classic Lifshitz-Slyozov scaling law at the late stage.
Understanding fluctuation-induced breakages in polymers has important implications for basic and applied sciences. Here I present for the first time an analytical treatment of the thermal breakage problem of a semi-flexible polymer model that is asym
ptotically exact in the low temperature and high friction limits. Specifically, I provide analytical expressions for the breakage propensity and rate, and discuss the generalities of the results and their relevance to biopolymers.
Biological sensory systems react to changes in their surroundings. They are characterized by fast response and slow adaptation to varying environmental cues. Insofar as sensory adaptive systems map environmental changes to changes of their internal d
egrees of freedom, they can be regarded as computational devices manipulating information. Landauer established that information is ultimately physical, and its manipulation subject to the entropic and energetic bounds of thermodynamics. Thus the fundamental costs of biological sensory adaptation can be elucidated by tracking how the information the system has about its environment is altered. These bounds are particularly relevant for small organisms, which unlike everyday computers operate at very low energies. In this paper, we establish a general framework for the thermodynamics of information processing in sensing. With it, we quantify how during sensory adaptation information about the past is erased, while information about the present is gathered. This process produces entropy larger than the amount of old information erased and has an energetic cost bounded by the amount of new information written to memory. We apply these principles to the E. colis chemotaxis pathway during binary ligand concentration changes. In this regime, we quantify the amount of information stored by each methyl group and show that receptors consume energy in the range of the information-theoretic minimum. Our work provides a basis for further inquiries into more complex phenomena, such as gradient sensing and frequency response.
In a reaction-diffusion system, fluctuations in both diffusion and reaction events, have important effects on the steady-state statistics of the system. Here, we argue through extensive lattice simulations, mean-field type arguments, and the Doi-Peli
ti formalism that the collision duration statistics -- i.e., the time two particles stay together in a lattice site -- plays a leading role in determining the steady state of the system. We obtain approximate expressions for the average densities of the chemical species and for the critical diffusion coefficient required to sustain the reaction.
I study the confinement-induced aggregation phenomenon in a minimal model of self-propelled particles inside a channel. Starting from first principles, I derive a set of equations that govern the density profile of such a system at the steady-state,
and calculate analytically how the aggregation at the walls varies with the physical parameters of the system. I also investigate how the gradient of the particle density varies if the inside of the channel is partitioned into two regions within which the active particles exhibit distinct levels of fluctuations in their directions of travel.
We investigate the length distribution of self-assembled, long and stiff polymers at thermal equilibrium. Our analysis is based on calculating the partition functions of stiff polymers of variable lengths in the elastic regime. Our conclusion is that
the length distribution of this self-assembled system follows closely the exponential distribution, except at the short length limit. We then discuss the implications of our results on the experimentally observed length distributions in amyloid fibrils.
In a system of noisy self-propelled particles with interactions that favor directional alignment, collective motion will appear if the density of particles is beyond a critical density. Starting with a reduced model for collective motion, we determin
e how the critical density depends on the form of the initial perturbation. Specifically, we employ a renormalization-group improved perturbative method to analyze the model equations, and show analytically, up to first order in the perturbation parameter, how the critical density is modified by the strength of the initial angular perturbation in the system.
In a well-stirred system undergoing chemical reactions, fluctuations in the reaction propensities are approximately captured by the corresponding chemical Langevin equation. Within this context, we discuss in this work how the Kramers escape theory c
an be used to predict rare events in chemical reactions. As an example, we apply our approach to a recently proposed model on cell proliferation with relevance to skin cancer [P.B. Warren, Phys. Rev. E {bf 80}, 030903 (2009)]. In particular, we provide an analytical explanation for the form of the exponential exponent observed in the onset rate of uncontrolled cell proliferation.
In a system of noisy self-propelled particles with interactions that favor directional alignment, collective motion will appear if the density of particles increases beyond a certain threshold. In this paper, we argue that such a threshold may depend
also on the profiles of the perturbation in the particle directions. Specifically, we perform mean-field, linear stability, perturbative and numerical analyses on an approximated form of the Fokker-Planck equation describing the system. We find that if an angular perturbation to an initially homogeneous system is large in magnitude and highly localized in space, it will be amplified and thus serves as an indication of the onset of collective motion. Our results also demonstrate that high particle speed promotes collective motion.
Protein aggregation in the form of amyloid fibrils has important biological and technological implications. Although the self-assembly process is highly efficient, aggregates not in the fibrillar form would also occur and it is important to include t
hese disordered species when discussing the thermodynamic equilibrium behavior of the system. Here, we initiate such a task by considering a mixture of monomeric proteins and the corresponding aggregates in the disordered form (micelles) and in the fibrillar form (amyloid fibrils). Starting with a model on the respective binding free energies for these species, we calculate their concentrations at thermal equilibrium. We then discuss how the incorporation of the disordered structure furthers our understanding on the various amyloid promoting factors observed empirically, and on the kinetics of fibrilization.
