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.
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