Recent advances in non-equilibrium statistical mechanics and single molecule technologies make it possible to extract free energy differences from irreversible work measurements in pulling experiments. To date, free energy recovery has been focused on native or equilibrium molecular states, whereas free energy measurements of kinetic states (i.e. finite lifetime states that are generated dynamically and are metastable) have remained unexplored. Kinetic states can play an important role in various domains of physics, such as nanotechnology or condensed matter physics. In biophysics, there are many examples where they determine the fate of molecular reactions: protein and peptide-nucleic acid binding, specific cation binding, antigen-antibody interactions, transient states in enzymatic reactions or the formation of transient intermediates and non-native structures in molecular folders. Here we demonstrate that it is possible to obtain free energies of kinetic states by applying extended fluctuation relations. This is shown by using optical tweezers to mechanically unfold and refold DNA structures exhibiting intermediate and misfolded kinetic states.Kinetic states are observed under non-equilibrium conditions and have higher free energies than native states. Yet, they can be crucial, as shown by the role that misfolded proteins play in numerous severe diseases [1]. The measurement of the free energy of formation of kinetic states is therefore a central question in biophysics. Recent theoretical developments known as fluctuation relations [13, 12, 4, 5, 6] have been applied to extract free energy differences of equilibrium states from irreversible work measurements. Applications include the measurement of the free energy of formation of RNA and DNA hairpins [7]; the determination of the stability of native domains in proteins [8]; the measurement of mechanical torque in rotary motors [9]; the conversion of information into work in systems under feedback control [10]; or the recovery of free energy landscapes from unidirectional work measurements [11, 12].The characterization of kinetic states under non-equilibrium conditions remains a challenging problem. Here we use a recently introduced extended fluctuation relation (EFR) to extract free energies of kinetic states and thermodynamic branches using irreversible work measurements [13, 10]. In the EFR, a kinetic state is a partially equilibrated region of configurational space, meaning that during a finite timescale the system is confined and thermalized within that region [15]. This is mathematically described by a Boltzmann-Gibbs distribution restricted to configurations contained in that region ( Fig. 1a).Let A, B denote any two kinetic states and λ a control parameter. We consider a forward (F) non-equilibrium process, where the system starts in partial equilibrium in A at λ 0 , and its time-reversed (R), where the partial equilibrium condition is required over B at λ 1 . In the F process λ varies from λ 0 to λ 1 during a time τ according to a predetermined proto...

Restraint-based modeling of genomes has been recently explored with the advent of Chromosome Conformation Capture (3C-based) experiments. We previously developed a reconstruction method to resolve the 3D architecture of both prokaryotic and eukaryotic genomes using 3C-based data. These models were congruent with fluorescent imaging validation. However, the limits of such methods have not systematically been assessed. Here we propose the first evaluation of a mean-field restraint-based reconstruction of genomes by considering diverse chromosome architectures and different levels of data noise and structural variability. The results show that: first, current scoring functions for 3D reconstruction correlate with the accuracy of the models; second, reconstructed models are robust to noise but sensitive to structural variability; third, the local structure organization of genomes, such as Topologically Associating Domains, results in more accurate models; fourth, to a certain extent, the models capture the intrinsic structural variability in the input matrices and fifth, the accuracy of the models can be a priori predicted by analyzing the properties of the interaction matrices. In summary, our work provides a systematic analysis of the limitations of a mean-field restrain-based method, which could be taken into consideration in further development of methods as well as their applications.

We present a method for determining the free energy of coexisting states from irreversible work measurements. Our approach is based on a fluctuation relation that is valid for dissipative transformations in partially equilibrated systems. To illustrate the validity and usefulness of the approach, we use optical tweezers to determine the free energy branches of the native and unfolded states of a two-state molecule as a function of the pulling control parameter. We determine, within 0:6k B T accuracy, the transition point where the free energies of the native and the unfolded states are equal.

Genome-wide measurements of transcriptional activity in bacteria indicate that the transcription of successive genes is strongly correlated beyond the scale of operons. Here, we analyze hundreds of bacterial genomes to identify supra-operonic segments of genes that are proximal in a large number of genomes. We show that these synteny segments correspond to genomic units of strong transcriptional co-expression. Structurally, the segments contain operons with specific relative orientations (co-directional or divergent) and nucleoid-associated proteins are found to bind at their boundaries. Functionally, operons inside a same segment are highly co-expressed even in the apparent absence of regulatory factors at their promoter regions. Remote operons along DNA can also be co-expressed if their corresponding segments share a transcriptional or sigma factor, without requiring these factors to bind directly to the promoters of the operons. As evidence that these results apply across the bacterial kingdom, we demonstrate them both in the Gram-negative bacterium Escherichia coli and in the Gram-positive bacterium Bacillus subtilis. The underlying process that we propose involves only RNA-polymerases and DNA: it implies that the transcription of an operon mechanically enhances the transcription of adjacent operons. In support of a primary role of this regulation by facilitated co-transcription, we show that the transcription en bloc of successive operons as a result of transcriptional read-through is strongly and specifically enhanced in synteny segments. Finally, our analysis indicates that facilitated co-transcription may be evolutionary primitive and may apply beyond bacteria.

Transcriptional activity has been shown to relate to the organization of chromosomes in the eukaryotic nucleus and in the bacterial nucleoid. In particular, highly transcribed genes, RNA polymerases and transcription factors gather into discrete spatial foci called transcription factories. However, the mechanisms underlying the formation of these foci and the resulting topological order of the chromosome remain to be elucidated. Here we consider a thermodynamic framework based on a worm-like chain model of chromosomes where sparse designated sites along the DNA are able to interact whenever they are spatially close by. This is motivated by recurrent evidence that there exist physical interactions between genes that operate together. Three important results come out of this simple framework. First, the resulting formation of transcription foci can be viewed as a micro-phase separation of the interacting sites from the rest of the DNA. In this respect, a thermodynamic analysis suggests transcription factors to be appropriate candidates for mediating the physical interactions between genes. Next, numerical simulations of the polymer reveal a rich variety of phases that are associated with different topological orderings, each providing a way to increase the local concentrations of the interacting sites. Finally, the numerical results show that both one-dimensional clustering and periodic location of the binding sites along the DNA, which have been observed in several organisms, make the spatial co-localization of multiple families of genes particularly efficient.

UQ, a key molecule for cellular bioenergetics that is conserved from proteobacteria to humans, appeared in an ancestral proteobacterium more than 2 billion years ago. UQ biosynthesis has been studied only in a few model organisms, and thus, the diversity of UQ biosynthesis pathways is largely unknown. In the work reported here, we conducted a phylogenomic analysis of hydroxylases involved in UQ biosynthesis. Our results support the existence of at least two UQ hydroxylases in the proteobacterial ancestor, and yet, we show that their number varies from one to four in extant proteobacterial species. Our biochemical experiments demonstrated that bacteria containing only one or two UQ hydroxylases have developed generalist enzymes that are able to catalyze several steps of UQ biosynthesis. Our study documents a rare case where evolution favored the broadening of an enzyme’s regioselectivity, which resulted in gene loss in several proteobacterial species with small genomes.

The mechanisms that control chromosome conformation and segregation in bacteria have not yet been elucidated. In Escherichia coli, the mere presence of an active process remains an open question. Here, we investigate the conformation and segregation pattern of the E. coli genome by performing numerical simulations on a polymer model of the chromosome. We analyze the roles of the intrinsic structuring of chromosomes and the forced localization of specific loci, which are observed in vivo. Specifically, we examine the segregation pattern of a chromosome that is divided into four structured macrodomains (MDs) and two non-structured regions. We find that strong osmotic-like organizational forces, which stem from the differential condensation levels of the chromosome regions, dictate the cellular disposition of the chromosome. Strikingly, the comparison of our in silico results with fluorescent imaging of the chromosome choreography in vivo reveals that in the presence of MDs the targeting of the origin and terminus regions to specific positions are sufficient to generate a segregation pattern that is indistinguishable from experimentally observed patterns.

Bacteria of the genus Streptomyces are prolific producers of specialized metabolites, including antibiotics. The linear chromosome includes a central region harboring core genes, as well as extremities enriched in specialized metabolite biosynthetic gene clusters. Here, we show that chromosome structure in Streptomyces ambofaciens correlates with genetic compartmentalization during exponential phase. Conserved, large and highly transcribed genes form boundaries that segment the central part of the chromosome into domains, whereas the terminal ends tend to be transcriptionally quiescent compartments with different structural features. The onset of metabolic differentiation is accompanied by a rearrangement of chromosome architecture, from a rather ‘open’ to a ‘closed’ conformation, in which highly expressed specialized metabolite biosynthetic genes form new boundaries. Thus, our results indicate that the linear chromosome of S. ambofaciens is partitioned into structurally distinct entities, suggesting a link between chromosome folding, gene expression and genome evolution.