Optimal transition paths of phenotypic switching in a non-Markovian self-regulation gene expression

Escape from a metastable state in non-Markovian population dynamics

We study the long-time dynamics in non-Markovian single-population stochastic models, where one or more reactions are modeled as a stochastic process with a fat-tailed nonexponential distribution of waiting times, mimicking long-term memory. We focus on three prototypical examples: genetic switching, population establishment, and population extinction, all with nonexponential production rates. The system is studied in two regimes. In the first, the distribution of waiting times has a finite mean. Here, the system approaches a (quasi)stationary steady state at long times, and we develop a general Wentzel-Kramers-Brillouin approach for these non-Markovian systems. We derive explicit results for the mean population size and mean escape time from the metastable state of the stochastic dynamics. In this realm, we reveal that for sufficiently strong memory, a memory-induced (meta)stable state can emerge in the system. In the second regime, the waiting time distribution is assumed to have an infinite mean. Here, for bistable systems we find two distinct scaling regimes, separated by an exponentially long time which may strongly depend on the initial conditions of the system.

Late stage of the formation of a protein corona around nanoparticles in biofluids

In biofluids containing various proteins, nanoparticles rapidly come to be surrounded by a nanometer-thick protein layer referred to as a protein corona. The late stage of this process occurs via replacement of proteins already bound to a nanoparticle by new ones. In the available kinetic models, this process is considered to include independent acts of protein detachment and attachment. It can, however, occur also at the level of protein pairs via exchange, i.e., concerted replacement of an attached protein by a newly arrived one. I argue that the exchange channel can be more important than the conventional one. To illustrate the likely specifics of the exchange channel, I present a kinetic model focused exclusively on this channel and based on the Evans-Polanyi-type relation between the activation energies of the protein-exchange steps and the protein binding energies. The corresponding kinetics were calculated for three qualitatively different distributions of proteins in solution over binding energy (with a maximum or monotonously decreasing or increasing, respectively) and are found to be similar, with relatively rapid replacement of weakly bound proteins and slow redistribution of strongly bound proteins. The ratio of the timescales characterizing the evolution of weakly and strongly bound proteins is found to depend on the type of the binding-energy distribution.