Internal friction, which reflects the "roughness" of the energy landscape, plays an important role for proteins by modulating the dynamics of their folding and other conformational changes. However, the experimental quantification of internal friction and its contribution to folding dynamics has remained challenging. Here we use the combination of single-molecule Förster resonance energy transfer, nanosecond fluorescence correlation spectroscopy, and microfluidic mixing to determine the reconfiguration times of unfolded proteins and investigate the mechanisms of internal friction contributing to their dynamics. Using concepts from polymer dynamics, we determine internal friction with three complementary, largely independent, and consistent approaches as an additive contribution to the reconfiguration time of the unfolded state. We find that the magnitude of internal friction correlates with the compactness of the unfolded protein: its contribution dominates the reconfiguration time of approximately 100 ns of the compact unfolded state of a small cold shock protein under native conditions, but decreases for more expanded chains, and approaches zero both at high denaturant concentrations and in intrinsically disordered proteins that are expanded due to intramolecular charge repulsion. Our results suggest that internal friction in the unfolded state will be particularly relevant for the kinetics of proteins that fold in the microsecond range or faster. The low internal friction in expanded intrinsically disordered proteins may have implications for the dynamics of their interactions with cellular binding partners.energetic roughness | Kramers theory | protein folding | Rouse model | single-molecule FRET C onformational changes in proteins, including those involved in protein folding, are driven by thermal fluctuations. In the dense environment of an aqueous solution, these processes thus typically exhibit diffusive dynamics (1-4). A theoretical framework for describing such diffusive processes in the condensed phase is provided by Kramers-type theories, which have been successful in quantifying key properties of protein folding reactions (5-12). These theories predict the rate of folding to depend exponentially on the height of the folding free energy barrier, with a prefactor representing the "attempt frequency" of crossing the barrier. The latter is related to the inherent timescale at which the protein can diffusively explore its conformational space. As a result, the reaction rate is expected to depend on the friction (13). For simple reactions, only solvent friction may need to be taken into account, but in proteins, where the amino acid residues are only partially exposed to solvent, other dissipative, "internal friction" mechanisms are possible and result in a slowdown of the conformational dynamics. In particular, intrachain collisions, dihedral angle rotation, and other interactions within the polypeptide chain (1, 14, 15) lead to an increased "roughness" of the underlying energy landscape, thereby slowing...

Cohesin extrusion is thought to play a central role in establishing the architecture of mammalian genomes. However, extrusion has not been visualized in vivo, and thus, its functional impact and energetics are unknown. Using ultra-deep Hi-C, we show that loop domains form by a process that requires cohesin ATPases. Once formed, however, loops and compartments are maintained for hours without energy input. Strikingly, without ATP, we observe the emergence of hundreds of CTCF-independent loops that link regulatory DNA. We also identify architectural "stripes," where a loop anchor interacts with entire domains at high frequency. Stripes often tether super-enhancers to cognate promoters, and in B cells, they facilitate Igh transcription and recombination. Stripe anchors represent major hotspots for topoisomerase-mediated lesions, which promote chromosomal translocations and cancer. In plasmacytomas, stripes can deregulate Igh-translocated oncogenes. We propose that higher organisms have coopted cohesin extrusion to enhance transcription and recombination, with implications for tumor development.

The energy landscape used by nature over evolutionary timescales to select protein sequences is essentially the same as the one that folds these sequences into functioning proteins, sometimes in microseconds. We show that genomic data, physical coarse-grained free energy functions, and family-specific information theoretic models can be combined to give consistent estimates of energy landscape characteristics of natural proteins. One such characteristic is the effective temperature T sel at which these foldable sequences have been selected in sequence space by evolution. T sel quantifies the importance of folded-state energetics and structural specificity for molecular evolution. Across all protein families studied, our estimates for T sel are well below the experimental folding temperatures, indicating that the energy landscapes of natural foldable proteins are strongly funneled toward the native state.energy landscape theory | information theory | selection temperature | funneled landscapes | elastic effects T he physics and natural history of proteins are inextricably intertwined (1, 2). The cooperative manner in which proteins find their way to a folded structure is the result of proteins having undergone natural selection and not typical of random polymers (3, 4). Likewise, the requirement that most proteins must fold to function is a strong constraint on their phylogeny. The unavoidable random mutation events that proteins have undergone throughout their evolution have provided countless numbers of physicochemical experiments on folding landscapes. Thus, the evolutionary patterns of proteins found through comparative sequence analysis can be used to understand protein structure and energetics. In this paper, we compare the information content in the correlated changes that have occurred in protein sequences of common ancestry with energies from a transferable energy function to quantify the influence of maintaining foldability on molecular evolution. Funneled Folding Landscapes from Evolution in Sequence SpaceThe key to our analysis is the principle of minimal frustration (3, 5), which states that, for quick and robust folding, the energy landscape of a protein must be dominated by interactions found in the native conformation. This native conformation is, therefore, separated by an energy gap from other compact structures that otherwise might act as kinetic traps (6, 7). These kinetic traps might appear on the folding landscape during evolution if a random mutation was to stabilize a conformation distinct from the functional one, leading to unviability. In this way, evolution and physical dynamics are coupled. A funneled, minimally frustrated landscape can be achieved if the sequence of the protein evolves to stabilize the native state while not increasing the landscape ruggedness.If folding were the only physicochemical constraint on evolution, the ensemble of naturally observed sequences would correspond to the set of sequences that has a solvent-averaged free energy for the native conformation below a ...

The effects of aggregate formation on the photophysical properties of oligomers of MEH-PPV were studied in bulk solution to better understand the effects of aggregation on the emission properties of the polymer. Nanoaggregates of oligomers from 3 to 17 repeat units in length were formed using a solvent reprecipitation method. The spectra are not readily modeled using the classical dipole-dipole coupling picture of interchain interactions. A strong dependence of the photophysics on the oligomer chain length is also observed. Shortchain oligomers produce nanoaggregates with absorption and emission spectra essentially identical to those of the monomer. Long-chain oligomers form aggregates having more strongly perturbed absorption and fluorescence spectra and decreased emission yields. In these aggregates, the size of the 0-0 band relative to that of the vibronic replicates is a sensitive function of aggregate size and solvent precipitation conditions. Their fluorescence lifetimes are also strongly wavelength dependent. These trends are explained in terms of a core-shell model that postulates the existence of "single-chain-like" and "aggregate-like" emitters within a single aggregate.

A challenge in molecular biology is to distinguish the key subset of residues that allow two-component signaling (TCS) proteins to recognize their correct signaling partner such that they can transiently bind and transfer signal, i.e., phosphoryl group. Detailed knowledge of this information would allow one to search sequence space for mutations that can be used to systematically tune the signal transmission between TCS partners as well as potentially encode a TCS protein to preferentially transfer signals to a nonpartner. Motivated by the notion that this detailed information is found in sequence data, we explore the sequence coevolution between signaling partners to better understand how mutations can positively or negatively alter their ability to transfer signal. Using direct coupling analysis for determining evolutionarily conserved protein-protein interactions, we apply a metric called the direct information score to quantify mutational changes in the interaction between TCS proteins and demonstrate that it accurately correlates with experimental mutagenesis studies probing the mutational change in measured in vitro phosphotransfer. Furthermore, by subtracting from our metric an appropriate null model corresponding to generic, conserved features in TCS signaling pairs, we can isolate the determinants that give rise to interaction specificity and recognition, which are variable among different TCS partners. Our methodology forms a potential framework for the rational design of TCS systems by allowing one to quickly search sequence space for mutations or even entirely new sequences that can increase or decrease our metric, as a proxy for increasing or decreasing phosphotransfer ability between TCS proteins. statistical inference | signal transduction | information theory | covariation | protein recognition

Inside the cell nucleus, genomes fold into organized structures that are characteristic of cell type. Here, we show that this chromatin architecture can be predicted de novo using epigenetic data derived from chromatin immunoprecipitation-sequencing (ChIP-Seq). We exploit the idea that chromosomes encode a 1D sequence of chromatin structural types. Interactions between these chromatin types determine the 3D structural ensemble of chromosomes through a process similar to phase separation. First, a neural network is used to infer the relation between the epigenetic marks present at a locus, as assayed by ChIP-Seq, and the genomic compartment in which those loci reside, as measured by DNA-DNA proximity ligation (Hi-C). Next, types inferred from this neural network are used as an input to an energy landscape model for chromatin organization [Minimal Chromatin Model (MiChroM)] to generate an ensemble of 3D chromosome conformations at a resolution of 50 kilobases (kb). After training the model, dubbed Maximum Entropy Genomic Annotation from Biomarkers Associated to Structural Ensembles (MEGABASE), on odd-numbered chromosomes, we predict the sequences of chromatin types and the subsequent 3D conformational ensembles for the even chromosomes. We validate these structural ensembles by using ChIP-Seq tracks alone to predict Hi-C maps, as well as distances measured using 3D fluorescence in situ hybridization (FISH) experiments. Both sets of experiments support the hypothesis of phase separation being the driving process behind compartmentalization. These findings strongly suggest that epigenetic marking patterns encode sufficient information to determine the global architecture of chromosomes and that de novo structure prediction for whole genomes may be increasingly possible.epigenetics | machine learning | energy landscape theory | genomic architecture | Hi-C I n the nucleus of eukaryotic cells, the 1D information of the genome is organized in three dimensions (1, 2). It is increasingly evident that genomic spatial organization is a key element of transcriptional regulation (1, 3, 4). During interphase, the 3D arrangement of chromatin brings into close spatial proximity sections of DNA separated by great genomic distance, introducing interactions between genes and regulatory elements. These folding patterns are cell type-specific (5, 6), and their disruption can lead to disease (7-10).The use of high-resolution contact mapping experiments (Hi-C) has revealed that, at the large scale, genome structure is dominated by the segregation of human chromatin into compartments. Initial analysis of Hi-C experiments revealed that loci typically exhibited one of two long-range contact patterns, suggesting the presence of two spatial neighborhoods, dubbed the A and B compartments (11). Subsequently, higher resolution experiments have shown the presence of six distinct long-range patterns, indicating the presence of six subcompartments (A1, A2, B1, B2, B3, and B4) in human lymphoblastoid cells (GM12878) (6). The compartmentalization o...

SignificanceIn the nucleus of eukaryotic cells, the genome is organized in three dimensions in an architecture that depends on cell type. This organization is a key element of transcriptional regulation, and its disruption often leads to disease. We demonstrate that it is possible to predict how a genome will fold based on the epigenetic marks that decorate chromatin. Epigenetic marking patterns are used to predict the corresponding ensemble of 3D structures by leveraging both energy landscape theory and neural network-based machine learning. These predictions are extensively validated by the results of DNA-DNA ligation assays and fluorescence microscopy, which are found to be in exceptionally good agreement with theory.

Recent experiments showed that the reconfiguration dynamics of unfolded proteins are often adequately described by simple polymer models. In particular, the Rouse model with internal friction (RIF) captures internal friction effects as observed in single-molecule fluorescence correlation spectroscopy (FCS) studies of a number of proteins. Here we use RIF, and its non-free draining analog, Zimm model with internal friction, to explore the effect of internal friction on the rate with which intramolecular contacts can be formed within the unfolded chain. Unlike the reconfiguration times inferred from FCS experiments, which depend linearly on the solvent viscosity, the first passage times to form intramolecular contacts are shown to display a more complex viscosity dependence. We further describe scaling relationships obeyed by contact formation times in the limits of high and low internal friction. Our findings provide experimentally testable predictions that can serve as a framework for the analysis of future studies of contact formation in proteins.