##### THEORY FOR SINGLE-X SCIENCE

Single-molecule theory of enzymatic inhibition

The classical theory of enzymatic inhibition takes a deterministic, bulk-based, approach to quantitatively describe how inhibitors affect the progression of enzymatic reactions. Catalysis at the single-enzyme level is, however, inherently stochastic which could lead to strong deviations from classical predictions. To study this, we collaborated with Tal Robin and Michael Urbakh. Taking a single-enzyme perspective, we rebuilt the theory of enzymatic inhibition from the bottom up [Nat. Commun. 9(1), 779, 2018]. We discovered that stochastic fluctuations at the single-enzyme level could unexpectedly make inhibitors act as activators, which should fundamentally change the way we think about enzymatic inhibition.

A unified approach to gated reactions on networks

For two molecules to react they must first meet. This condition is, however, insufficient since stochastic transitions between reactive and non-reactive states result in an effective fluctuating molecular “gate” that can prevent reactions from occurring despite the spatial proximity of the reactants involved. To better understand this phenomenon, we developed a general approach to gated reactions on networks [Phys. Rev. Lett. 127, 018301, 2021; J. Chem. Phys. 155, 234112, 2021]. The analysis gives a practical way of calculating the mean and distribution of gated reaction times from the corresponding, and often known, ungated reaction times. The theory also sheds light on universal features of gated reactions, as well as novel and exotic kinetics that arise due to molecular gating.

Inference from gated first-passage times

When does a stochastic time-series cross a predefined threshold for the first time? The answer to this question relies on the first-passage time — a concept that has attracted interdisciplinary research interest for several decades. However, in applications ranging from time-series analysis to chemical reactions, various forms of “gating” prevent first-passage times from being directly observable. The challenge is the to infer the statistics of

first-passage times from the gated observations, i.e., from actual detection times, which can be strikingly different from the true first-passage times. Motivated by this inference challenge, and the complete lack of results on this front, we collaborated with Aanjaneya Kumar and M. S. Santhanam to develop a model-free framework that allows for the reconstruction of first-passage time statistics from observed detection times [Phys. Rev. Research 5, L032043, 2023]. The universality of the proposed framework remarkably allows for the inference of unknown first-passage statistics without needing to know or assume the underlying laws of stochastic motion. In addition, when the underlying laws of motions are known, our framework also provides a way to infer physically meaningful parameters, e.g., diffusion coefficients and gating rates. Being the first of its kind, our approach opens new avenues connecting experimental and theoretical research by allowing practitioners to infer keystone quantities, which are often concealed from direct observation.

Microscopic theory of adsorption kinetics

Adsorption is the accumulation of a solute at an interface that is formed between a solution and an additional gas, liquid, or solid phase. The macroscopic theory of adsorption dates back more than a century and is now well-established. Yet, despite recent advancements, a detailed and self-contained theory of single-particle adsorption is still lacking. We bridge this gap by developing a microscopic theory of adsorption kinetics, from which

macroscopic properties follow directly [J. Chem. Phys. 158, 094107, 2023]. One of our central achievements is the derivation of the microscopic version of the seminal Ward–Tordai relation, which connects the surface and subsurface adsorbate concentrations via a universal equation that holds for arbitrary adsorption dynamics. Furthermore, we present a microscopic interpretation of the Ward–Tordai relation that, in turn, allows us to generalize it to arbitrary dimension, geometry, and initial conditions. The power of our approach is showcased on a set of hitherto unsolved adsorption problems to which we present exact analytical solutions. The developed framework sheds fresh light on the fundamentals of adsorption kinetics, which opens new research avenues in surface science with applications to artificial and biological sensing and to the design of nano-scale devices.

Escape of a sticky particle

Adsorption to a surface, reversible binding, and trapping are all prevalent scenarios where particles exhibit “stickiness.” Escape and first-passage times are known to be drastically affected, but a detailed understanding of this phenomenon remains illusive. To tackle this problem, we collaborated with Denis Grebenkov to develop an

analytical approach to the escape of a diffusing particle from a domain of arbitrary shape, size, and surface reactivity [Phys. Rev. Research 5, 043196, 2023]. We used this approach to elucidate the effect of stickiness on the escape time from a slab domain, revealing how adsorption and desorption rates affect the mean and variance and providing an way to infer these rates from measurements. Moreover, as any smooth boundary is locally flat, slab results are leveraged to devise a numerically efficient scheme for simulating sticky boundaries in arbitrary domains. Generalizing our analysis to higher dimensions reveals that the mean escape time abides a general structure that is independent of the dimensionality of the problem. This paper thus offers a starting point for analytical and numerical studies of stickiness and its role in escape, first-passage, and diffusion-controlled reactions.