Since the universal acceptance of atoms and molecules as the fundamental constituents of
matter in the early-twentieth century, molecular physics, chemistry, and molecular biology …

This article studies the estimation of a stepwise signal. To determine the number and
locations of change-points of the stepwise signal, we formulate a maximum marginal …

The Michaelis–Menten (MM) fundamental formula describes how the rate of enzyme
catalysis depends on substrate concentration. The familiar hyperbolic relationship was …

Toward the last quarter of the 20th century, the emergence of single-molecule experiments
enabled scientists to track and study individual molecules' dynamic properties in real time …

Single turnover measurements of a fluorogenic reaction at the surface of a nanoparticle
provide a detailed view of reaction dynamics at a catalyst with multiple heterogeneous active …

Single enzyme molecules display inevitable, stochastic fluctuations in their catalytic activity.
In metabolism, for instance, the stochastic activity of individual enzymes is averaged out due …

Markov chain is a random process with Markov characteristics, which exists in the discrete
index set and state space in probability theory and mathematical statistics. Markov chains …

We consider two different ways of representing stochastic matrices by bi-stochastic ones
acting on a larger probability space, referred to as``dilation by uniform coarse graining" …

In this Supporting Information, we first provide background on the linear framework and then
restate and give full proofs of Props. 1-4 from the main text. We also state and prove Prop …

Optically detected single-turnover measurements of biological and inorganic catalysts
provide a detailed picture of structural and dynamical influences on catalytic activity …