A selective view of stochastic inference and modeling problems in nanoscale biophysics

Abstract

Advances in nanotechnology enable scientists for the first time to study biological processes on a nanoscale molecule-by-molecule basis. They also raise challenges and opportunities for statisticians and applied probabilists. To exemplify the stochastic inference and modeling problems in the field, this paper discusses a few selected cases, ranging from likelihood inference, Bayesian data augmentation, and semi-and non-parametric inference of nanometric biochemical systems to the utilization of stochastic integro-differential equations and stochastic networks to model single-molecule biophysical processes. We discuss the statistical and probabilistic issues as well as the biophysical motivation and physical meaning behind the problems, emphasizing the analysis and modeling of real experimental data. Keywords: likelihood analysis, Bayesian data augmentation, semi-and non-parametric inference, single-molecule experiment, subdiffusion, generalized Langevin equation, fractional Brownian motion, stochastic network, enzymatic reaction MSC(2000): 60G35, 62F15, 62G05, 62P10, 92C05, 92C45

Stepwise Signal Extraction via Marginal Likelihood

“…New advances in nanosciences in the last two decades have opened the door for scientists to study such processes on a microscopic molecule-by-molecule basis (Nie and Zare, 1997; Xie and Lu, 1999; Xie and Trautman, 1998; Tamarat et al ., 2000; Weiss, 2000; Moerner, 2002; Kou, 2009; Qian and Kou, 2014). In such experiments, a single enzyme molecule is immobilized and its fluorescence intensity over time is recorded (Lu, Xun and Xie, 1998).…”

Nonparametric inference of doubly stochastic Poisson process data via the kernel method

“…Assumption 1 is particularly relevant for single-molecule biophysical experiments (Kou, 2009) in which the system under study is typically in equilibrium or steady state.…”

“…Stationarity (i.e., the distribution of {λ(t), t ∈ R} is time-shift invariant) and ergodicity (i.e., essentially 1 T T 0 λ(s) ds → E[λ(0)], as T → ∞) are both natural and necessary for making nonparametric inference of λ(t) from a single sequence of arrival data. Assumption 1 is particularly relevant for single-molecule biophysical experiments [Kou (2009)] in which the system under study is typically in equilibrium or steady state.…”

Quantum Monte Carlo simulation

“…While the traditional simulation methods with the aid of classical computers based on transistors are to understand basic properties of materials, many contemporary simulations rely on understanding quantum systems, such as those in bio-chemistry and nanotechnology for the design of nano-materials and novel molecules. See Aspuru-Guzik et al (2005), Kou (2009) and Waldner (2007).…”