Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation–dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production. (Some figures may appear in colour only in the online journal) This article was invited by Erwin Frey.

/pdf/stochastic-thermodynamics-fluctuation-theorems-and-molecular-2epwyvmpf0.pdf

Stochastic thermodynamics, fluctuation theorems and molecular machines

The past five years have seen many scientific and biological discoveries made through the experimental design of genome-wide association studies (GWASs). These studies were aimed at detecting variants at genomic loci that are associated with complex traits in the population and, in particular, at detecting associations between common single-nucleotide polymorphisms (SNPs) and common diseases such as heart disease, diabetes, auto-immune diseases, and psychiatric disorders. We start by giving a number of quotes from scientists and journalists about perceived problems with GWASs. We will then briefly give the history of GWASs and focus on the discoveries made through this experimental design, what those discoveries tell us and do not tell us about the genetics and biology of complex traits, and what immediate utility has come out of these studies. Rather than giving an exhaustive review of all reported findings for all diseases and other complex traits, we focus on the results for auto-immune diseases and metabolic diseases. We return to the perceived failure or disappointment about GWASs in the concluding section.

Five years of GWAS discovery

‡We describe the use of singular value decomposition in transforming genome-wide expression data from genes 3 arrays space to reduced diagonalized ‘‘eigengenes’’ 3 ‘‘eigenarrays’’ space, where the eigengenes (or eigenarrays) are unique orthonormal superpositions of the genes (or arrays). Normalizing the data by filtering out the eigengenes (and eigenarrays) that are inferred to represent noise or experimental artifacts enables meaningful comparison of the expression of different genes across different arrays in different experiments. Sorting the data according to the eigengenes and eigenarrays gives a global picture of the dynamics of gene expression, in which individual genes and arrays appear to be classified into groups of similar regulation and function, or similar cellular state and biological phenotype, respectively. After normalization and sorting, the significant eigengenes and eigenarrays can be associated with observed genome-wide effects of regulators, or with measured samples, in which these regulators are overactive or underactive, respectively.

Singular Value Decomposition for Genome-Wide Expression Data Processing and Modeling

The Strategy of the Genes

Protein phosphorylation is estimated to affect 30% of the proteome and is a major regulatory mechanism that controls many basic cellular processes. Until recently, our biochemical understanding of protein phosphorylation on a global scale has been extremely limited; only one half of the yeast kinases have known in vivo substrates and the phosphorylating kinase is known for less than 160 phosphoproteins. Here we describe, with the use of proteome chip technology, the in vitro substrates recognized by most yeast protein kinases: we identified over 4,000 phosphorylation events involving 1,325 different proteins. These substrates represent a broad spectrum of different biochemical functions and cellular roles. Distinct sets of substrates were recognized by each protein kinase, including closely related kinases of the protein kinase A family and four cyclin-dependent kinases that vary only in their cyclin subunits. Although many substrates reside in the same cellular compartment or belong to the same functional category as their phosphorylating kinase, many others do not, indicating possible new roles for several kinases. Furthermore, integration of the phosphorylation results with protein-protein interaction and transcription factor binding data revealed novel regulatory modules. Our phosphorylation results have been assembled into a first-generation phosphorylation map for yeast. Because many yeast proteins and pathways are conserved, these results will provide insights into the mechanisms and roles of protein phosphorylation in many eukaryotes.

Global Analysis of Protein Phosphorylation in Yeast

Mathematical Theory of Nonequilibrium Steady States

Preface.- Introduction.- Circulation Distribution, Entropy Production and Irreversibility of Denumerable Markov Chains.- Circulation Distribution, Entropy Production and Irreversibility of Finite Markov Chains with Continuous Parameter.- General Minimal Diffusion Process: its Construction, Invariant Measure, Entropy Production and Irreversibility.- Measure-theoretic Discussion on Entropy Production of Diffusion Processes and Fluctuation-dissipation Theorem.- Entropy Production, Rotation Numbers and Irreversibility of Diffusion Processes on Manifolds.- On a System of Hyperstable Frequency Locking Persistence under White Noise.- Entropy Production and Information Gain in Axiom A Systems.- Lyapunov Exponents of Hyperbolic Attractors.- Entropy Production, Information Gain and Lyapunov Exponents of Random Hyperbolic Dynamical Systems.- References.- Index.

Mathematical Theory of Nonequilibrium Steady States: On the Frontier of Probability and Dynamical Systems

Stochastic model of yeast cell-cycle network

A "bidirectional gene pair" is defined as two adjacent genes which are located on opposite strands of DNA with transcription start sites (TSSs) not more than 1000 base pairs apart and the intergenic region between two TSSs is commonly designated as a putative "bidirectional promoter". Individual examples of bidirectional gene pairs have been reported for years, as well as a few genome-wide analyses have been studied in mammalian and human genomes. However, no genome-wide analysis of bidirectional genes for plants has been done. Furthermore, the exact mechanism of this gene organization is still less understood. We conducted comprehensive analysis of bidirectional gene pairs through the whole Arabidopsis thaliana genome and identified 2471 bidirectional gene pairs. The analysis shows that bidirectional genes are often coexpressed and tend to be involved in the same biological function. Furthermore, bidirectional gene pairs associated with similar functions seem to have stronger expression correlation. We pay more attention to the regulatory analysis on the intergenic regions between bidirectional genes. Using a hierarchical stochastic language model (HSL) (which is developed by ourselves), we can identify intergenic regions enriched of regulatory elements which are essential for the initiation of transcription. Finally, we picked 27 functionally associated bidirectional gene pairs with their intergenic regions enriched of regulatory elements and hypothesized them to be regulated by bidirectional promoters, some of which have the same orthologs in ancient organisms. More than half of these bidirectional gene pairs are further supported by sharing similar functional categories as these of handful experimental verified bidirectional genes. Bidirectional gene pairs are concluded also prevalent in plant genome. Promoter analyses of the intergenic regions between bidirectional genes could be a new way to study the bidirectional gene structure, which may provide a important clue for further analysis. Such a method could be applied to other genomes.

https://link.springer.com/content/pdf/10.1186/1471-2105-10-S1-S29.pdf

Searching for bidirectional promoters in Arabidopsis thaliana

DNA methylation is an important defense and regulatory mechanism. In mammals, most DNA methylation occurs at CpG sites, and asymmetric non-CpG methylation has only been detected at appreciable levels in a few cell types. We are the first to systematically study the strand-specific distribution of non-CpG methylation. With the divide-and-compare strategy, we show that CHG and CHH methylation are not intrinsically different in human embryonic stem cells (ESCs) and induced pluripotent stem cells (iPSCs). We also find that non-CpG methylation is skewed between the two strands in introns, especially at intron boundaries and in highly expressed genes. Controlling for the proximal sequences of non-CpG sites, we show that the skew of non-CpG methylation in introns is mainly guided by sequence skew. By studying subgroups of transposable elements, we also found that non-CpG methylation is distributed in a strand-specific manner in both short interspersed nuclear elements (SINE) and long interspersed nuclear elements (LINE), but not in long terminal repeats (LTR). Finally, we show that on the antisense strand of Alus, a non-CpG site just downstream of the A-box is highly methylated. Together, the divide-and-compare strategy leads us to identify regions with strand-specific distributions of non-CpG methylation in humans.

/pdf/characterizing-the-strand-specific-distribution-of-non-cpg-50pl7qurw2.pdf

Minping Qian

Papers

Mathematical Theory of Nonequilibrium Steady States

Mathematical Theory of Nonequilibrium Steady States: On the Frontier of Probability and Dynamical Systems

Stochastic model of yeast cell-cycle network

Searching for bidirectional promoters in Arabidopsis thaliana

Characterizing the strand-specific distribution of non-CpG methylation in human pluripotent cells