Γ-convergence of Onsager–Machlup functionals: II. Infinite product measures on Banach spaces

We derive Onsager–Machlup functionals for countable product measures on weighted ℓ p subspaces of the sequence space R N . Each measure in the product is a shifted and scaled copy of a reference probability measure on R that admits a sufficiently regular Lebesgue density. We study the equicoercivity and Γ-convergence of sequences of Onsager–Machlup functionals associated to convergent sequences of measures within this class. We use these results to establish analogous results for probability measures on separable Banach or Hilbert spaces, including Gaussian, Cauchy, and Besov measures with summability parameter 1 ⩽ p ⩽ 2. Together with part I of this paper, this provides a basis for analysis of the convergence of maximum a posteriori estimators in Bayesian inverse problems and most likely paths in transition path theory.

Transiently increased intercommunity regulation characterizes concerted cell phenotypic transition

Phenotype transition takes place in many biological processes such as differentiation and reprogramming. A fundamental question is how cells coordinate switching of expressions of clusters of genes. Through analyzing single cell RNA sequencing data in the framework of transition path theory, we studied how such a genome-wide expression program switching proceeds in three different cell transition processes. For each process we reconstructed a reaction coordinate describing the transition progression, and inferred the gene regulation network (GRN) along the reaction coordinate. In all three processes we observed common pattern that the effective number and strength of regulation between different communities increase first and then decrease. The change accompanies with similar change of the GRN frustration, defined as overall confliction between the regulation received by genes and their expression states, and GRN heterogeneity. While studies suggest that biological networks are modularized to contain perturbation effects locally, our analyses reveal a general principle that during a cell phenotypic transition intercommunity interactions increase to concertedly coordinate global gene expression reprogramming, and canalize to specific cell phenotype as Waddington visioned.

Statistical analysis of tipping pathways in agent-based models

Agent-based models are a natural choice for modeling complex social systems. In such models simple stochastic interaction rules for a large population of individuals on the microscopic scale can lead to emergent dynamics on the macroscopic scale, for instance a sudden shift of majority opinion or behavior. Here we are introducing a methodology for studying noise-induced tipping between relevant subsets of the agent state space representing characteristic configurations. Due to a large number of interacting individuals, agent-based models are high-dimensional, though usually a lower-dimensional structure of the emerging collective behaviour exists. We therefore apply Diffusion Maps, a non-linear dimension reduction technique, to reveal the intrinsic low-dimensional structure. We characterize the tipping behaviour by means of Transition Path Theory, which helps gaining a statistical understanding of the tipping paths such as their distribution, flux and rate. By systematically studying two agent-based models that exhibit a multitude of tipping pathways and cascading effects, we illustrate the practicability of our approach.

Extending Transition Path Theory: Periodically Driven and Finite-Time Dynamics

Given two distinct subsets A, B in the state space of some dynamical system, transition path theory (TPT) was successfully used to describe the statistical behavior of transitions from A to B in the ergodic limit of the stationary system. We derive generalizations of TPT that remove the requirements of stationarity and of the ergodic limit and provide this powerful tool for the analysis of other dynamical scenarios: periodically forced dynamics and time-dependent finite-time systems. This is partially motivated by studying applications such as climate, ocean, and social dynamics. On simple model examples, we show how the new tools are able to deliver quantitative understanding about the statistical behavior of such systems. We also point out explicit cases where the more general dynamical regimes show different behaviors to their stationary counterparts, linking these tools directly to bifurcations in non-deterministic systems.

Deciphering the Allosteric Process of Phaeodactylum tricornutum Aureochrome 1a LOV Domain

The conformational-driven allosteric protein diatom Phaeodactylum tricornutum aureochrome 1a (PtAu1a) di ers from other light-oxygen-voltage (LOV) proteins for its uncommon structural topology. The mechanism of signaling transduction in PtAu1a LOV domain (AuLOV) including flanking helices remains unclear because of this dissimilarity, which hinders the study of PtAu1a as an optogenetic tool. To clarify this mechanism, we employed a combination of tree-based machine learning models, Markov state models, machine learning based community analysis and transition path theory to quantitatively analyze the allosteric process. Our results are in good agreement with reported experimental findings and revealed a previously overlooked C-alpha helix and linkers as important in promoting the protein conformational change. This integrated approach can be considered as a general workflow and applied on other allosteric proteins to provide detailed information about their allosteric mechanisms.

Deciphering the Allosteric Process of Phaeodactylum tricornutum Aureochrome 1a LOV Domain

The conformational-driven allosteric protein diatom Phaeodactylum tricornutum aureochrome 1a (PtAu1a) di ers from other light-oxygen-voltage (LOV) proteins for its uncommon structural topology. The mechanism of signaling transduction in PtAu1a LOV domain (AuLOV) including flanking helices remains unclear because of this dissimilarity, which hinders the study of PtAu1a as an optogenetic tool. To clarify this mechanism, we employed a combination of tree-based machine learning models, Markov state models, machine learning based community analysis and transition path theory to quantitatively analyze the allosteric process. Our results are in good agreement with reported experimental findings and revealed a previously overlooked C-alpha helix and linkers as important in promoting the protein conformational change. This integrated approach can be considered as a general workflow and applied on other allosteric proteins to provide detailed information about their allosteric mechanisms.

Analyses of Multi-dimensional Single Cell Trajectories Quantify Transition Paths Between Nonequilibrium Steady States

ABSTRACTA problem ubiquitous in almost all scientific areas is escape from a metastable state, or relaxation from one stationary distribution to a new one1. More than a century of studies lead to celebrated theoretical and computational developments such as the transition state theory and reactive flux formulation. Modern transition path sampling and transition path theory focus on an ensemble of trajectories that connect the initial and final states in a state space2, 3. However, it is generally unfeasible to experimentally observe these trajectories in multiple dimensions and compare to theoretical results. Here we report and analyze single cell trajectories of human A549 cells undergoing TGF-β induced epithelial-to-mesenchymal transition (EMT) in a combined morphology and protein texture space obtained through time lapse imaging. From the trajectories we identify parallel reaction paths with corresponding reaction coordinates and quasi-potentials. Studying cell phenotypic transition dynamics will provide testing grounds for nonequilibrium reaction rate theories.