Biological nanopore sensors are widely used for genetic sequencing as nucleic acids and other molecules translocate through them across membranes. Recent studies have shown that the transport of these polymers through nanopores is strongly influenced by macromolecular bulk crowders. By using poly(ethylene glycol) (PEG) molecules as crowders, experiments have shown an increase in the capture rates and translocation times of polymers through an α-hemolysin (αHL) nanopore, which provides high-throughput signals and accurate sensing. A clear molecular-level understanding of how the presence of PEGs offers such desirable outcomes in nanopore sensing is still missing. In this work, we present a new theoretical approach to probe the effect of PEG crowders on DNA capture and translocation through the αHL nanopore. We develop an exactly solvable discrete-state stochastic model based on the cooperative partitioning of individual polycationic PEGs within the cavity of the αHL nanopore. It is argued that the apparent electrostatic interactions between the DNA and PEGs control all of the dynamic processes. Our analytical predictions find excellent agreements with existing experiments, thereby strongly supporting our theory.

Catalysis is a method of accelerating chemical reactions that is critically important for fundamental research as well as for industrial applications. It has been recently discovered that catalytic reactions on metal nanoparticles exhibit cooperative effects. The mechanism of these observations, however, remains not well understood. In this work, we present a theoretical investigation on possible microscopic origin of cooperative communications in nanocatalysts. In our approach, the main role is played by positively charged holes on metal surfaces. A corresponding discrete-state stochastic model for the dynamics of holes is developed and explicitly solved. It is shown that the observed spatial correlation lengths are given by the average distances migrated by the holes before they disappear, while the temporal memory is determined by their lifetimes. Our theoretical approach is able to explain the universality of cooperative communications as well as the effect of external electric fields. Theoretical predictions are in agreement with experimental observations. The proposed theoretical framework quantitatively clarifies some important aspects of the microscopic mechanisms of heterogeneous catalysis.

Single-molecule microscopic techniques allow the counting of successive turnover events and the study of the time-dependent fluctuations of the catalytic activities of individual enzymes and different sites on a single heterogeneous nanocatalyst. It is important to establish theoretical methods to obtain the statistical measurements of such stochastic fluctuations that provide insight into the catalytic mechanism. In this review, we discuss a few theoretical frameworks for evaluating the first passage time distribution functions using a self-consistent pathway approach and chemical master equations, to establish a connection with experimental observables. The measurable probability distribution functions and their moments depend on the molecular details of the reaction and provide a way to quantify the molecular mechanisms of the reaction process. The statistical measurements of these fluctuations should provide insight into the enzymatic mechanism.

Recent experimental advances on investigating nanoparticle catalysts with multiple active sites provided a large amount of quantitative information on catalytic processes. These observations stimulated significant theoretical efforts, but the underlying molecular mechanisms are still not well-understood. We introduce a simple theoretical method to analyze the reaction dynamics on catalysts with multiple active sites based on a discrete-state stochastic description and obtain a comprehensive description of the dynamics of chemical reactions on such catalysts. We explicitly determine how the dynamics of catalyzed chemical reactions depend on the number of active sites, on the number of intermediate chemical transitions, and on the topology of underlying chemical reactions. It is argued that the theory provides quantitative bounds for realistic dynamic properties of catalytic processes that can be directly applied to analyze the experimental observations. In addition, this theoretical approach clarifies several important aspects of the molecular mechanisms of chemical reactions on catalysts.

The facilitated diffusion mechanism that involves the combination of one-dimensional and three-dimensional (3D) diffusion for recognition of a DNA target site by its protein is affected by the crowded cellular environment. Dynamic crowders can provide a better description of real processes in living cells. We develop a theoretical method based on a discrete state stochastic approach to understand the mechanism of the protein search on DNA in the presence of crowders that are moving around in the cellular medium. We obtain approximate analytical expressions for all dynamic properties. Our theoretical findings show that macromolecules present in the cellular volume and acting as dynamic crowders can influence 3D diffusion. The target search dynamics of proteins on DNA in the crowded cellular medium depend on the size and mobility of the macromolecular crowders. Highly mobile crowders do not affect the search dynamics, while slow moving crowders can significantly slow down the search process. Our theoretical results are discussed using physical explanations and they are also tested with extensive Monte Carlo computer simulations. Our theoretical predictions provide a physical understanding of the experimental observations and simulation results.