Motorized chain models of the ideal chromosome.

An array of motor proteins consumes chemical energy in setting up the architectures of chromosomes. Here, we explore how the structure of ideal polymer chains is influenced by two classes of motors. The first class which we call "swimming motors" acts to propel the chromatin fiber through three-dimensional space. They represent a caricature of motors such as RNA polymerases. Previously, they have often been described by adding a persistent flow onto Brownian diffusion of the chain. The second class of motors, which we call "grappling motors" caricatures the loop extrusion processes in which segments of chromatin fibers some distance apart are brought together. We analyze these models using a self-consistent variational phonon approximation to a many-body Master equation incorporating motor activities. We show that whether the swimming motors lead to contraction or expansion depends on the susceptibility of the motors, that is, how their activity depends on the forces they must exert. Grappling motors in contrast to swimming motors lead to long-ranged correlations that resemble those first suggested for fractal globules and that are consistent with the effective interactions inferred by energy landscape analyses of Hi-C data on the interphase chromosome.

Quantum information scrambling and chemical reactions.

The ultimate regularity of quantum mechanics creates a tension with the assumption of classical chaos used in many of our pictures of chemical reaction dynamics. Out-of-time-order correlators (OTOCs) provide a quantum analog to the Lyapunov exponents that characterize classical chaotic motion. Maldacena, Shenker, and Stanford have suggested a fundamental quantum bound for the rate of information scrambling, which resembles a limit suggested by Herzfeld for chemical reaction rates. Here, we use OTOCs to study model reactions based on a double-well reaction coordinate coupled to anharmonic oscillators or to a continuum oscillator bath. Upon cooling, as one enters the tunneling regime where the reaction rate does not strongly depend on temperature, the quantum Lyapunov exponent can approach the scrambling bound and the effective reaction rate obtained from a population correlation function can approach the Herzfeld limit on reaction rates: Tunneling increases scrambling by expanding the state space available to the system. The coupling of a dissipative continuum bath to the reaction coordinate reduces the scrambling rate obtained from the early-time OTOC, thus making the scrambling bound harder to reach, in the same way that friction is known to lower the temperature at which thermally activated barrier crossing goes over to the low-temperature activationless tunneling regime. Thus, chemical reactions entering the tunneling regime can be information scramblers as powerful as the black holes to which the quantum Lyapunov exponent bound has usually been applied.

The physical and evolutionary energy landscapes of devolved protein sequences corresponding to pseudogenes.

Protein evolution is guided by structural, functional, and dynamical constraints ensuring organismal viability. Pseudogenes are genomic sequences identified in many eukaryotes that lack translational activity due to sequence degradation and thus over time have undergone "devolution." Previously pseudogenized genes sometimes regain their protein-coding function, suggesting they may still encode robust folding energy landscapes despite multiple mutations. We study both the physical folding landscapes of protein sequences corresponding to human pseudogenes using the Associative Memory, Water Mediated, Structure and Energy Model, and the evolutionary energy landscapes obtained using direct coupling analysis (DCA) on their parent protein families. We found that generally mutations that have occurred in pseudogene sequences have disrupted their native global network of stabilizing residue interactions, making it harder for them to fold if they were translated. In some cases, however, energetic frustration has apparently decreased when the functional constraints were removed. We analyzed this unexpected situation for Cyclophilin A, Profilin-1, and Small Ubiquitin-like Modifier 2 Protein. Our analysis reveals that when such mutations in the pseudogene ultimately stabilize folding, at the same time, they likely alter the pseudogenes' former biological activity, as estimated by DCA. We localize most of these stabilizing mutations generally to normally frustrated regions required for binding to other partners.

Reassessing the exon-foldon correspondence using frustration analysis.

Protein folding and evolution are intimately linked phenomena. Here, we revisit the concept of exons as potential protein folding modules across a set of 38 abundant and conserved protein families. Taking advantage of genomic exon-intron organization and extensive protein sequence data, we explore exon boundary conservation and assess the foldon-like behavior of exons using energy landscape theoretic measurements. We found deviations in the exon size distribution from exponential decay indicating selection in evolution. We show that when taken together there is a pronounced tendency to independent foldability for segments corresponding to the more conserved exons, supporting the idea of exon-foldon correspondence. While 45% of the families follow this general trend when analyzed individually, there are some families for which other stronger functional determinants, such as preserving frustrated active sites, may be acting. We further develop a systematic partitioning of protein domains using exon boundary hotspots, showing that minimal common exons correspond with uninterrupted alpha and/or beta elements for the majority of the families but not for all of them.

Predicting protein conformational motions using energetic frustration analysis and AlphaFold2.

Proteins perform their biological functions through motion. Although high throughput prediction of the three-dimensional static structures of proteins has proved feasible using deep-learning-based methods, predicting the conformational motions remains a challenge. Purely data-driven machine learning methods encounter difficulty for addressing such motions because available laboratory data on conformational motions are still limited. In this work, we develop a method for generating protein allosteric motions by integrating physical energy landscape information into deep-learning-based methods. We show that local energetic frustration, which represents a quantification of the local features of the energy landscape governing protein allosteric dynamics, can be utilized to empower AlphaFold2 (AF2) to predict protein conformational motions. Starting from ground state static structures, this integrative method generates alternative structures as well as pathways of protein conformational motions, using a progressive enhancement of the energetic frustration features in the input multiple sequence alignment sequences. For a model protein adenylate kinase, we show that the generated conformational motions are consistent with available experimental and molecular dynamics simulation data. Applying the method to another two proteins KaiB and ribose-binding protein, which involve large-amplitude conformational changes, can also successfully generate the alternative conformations. We also show how to extract overall features of the AF2 energy landscape topography, which has been considered by many to be black box. Incorporating physical knowledge into deep-learning-based structure prediction algorithms provides a useful strategy to address the challenges of dynamic structure prediction of allosteric proteins.

Frustraevo: a web server to localize and quantify the conservation of local energetic frustration in protein families.

According to the Principle of Minimal Frustration, folded proteins can only have a minimal number of strong energetic conflicts in their native states. However, not all interactions are energetically optimized for folding but some remain in energetic conflict, i.e. they are highly frustrated. This remaining local energetic frustration has been shown to be statistically correlated with distinct functional aspects such as protein-protein interaction sites, allosterism and catalysis. Fuelled by the recent breakthroughs in efficient protein structure prediction that have made available good quality models for most proteins, we have developed a strategy to calculate local energetic frustration within large protein families and quantify its conservation over evolutionary time. Based on this evolutionary information we can identify how stability and functional constraints have appeared at the common ancestor of the family and have been maintained over the course of evolution. Here, we present FrustraEvo, a web server tool to calculate and quantify the conservation of local energetic frustration in protein families.

The marionette mechanism of domain-domain communication in the antagonist, agonist, and coactivator responses of the estrogen receptor.

The human estrogen receptor α (hERα) is involved in the regulation of growth, development, and tissue homeostasis. Agonists that bind to the receptor's ligand-binding domain (LBD) lead to recruitment of coactivators and the enhancement of gene expression. In contrast, antagonists bind to the LBD and block the binding of coactivators thus decreasing gene expressions. In this work, we carry out simulations using the AWSEM (Associative memory, Water mediated, Structure and Energy Model)-Suite force field along with the 3SPN.2C force field for DNA to predict the structure of hERα and study its dynamics when binding to DNA and coactivators. Using simulations of antagonist-bound hERα and agonist-bound hERα by themselves and also along with bound DNA and coactivators, principal component analyses and free energy landscape analyses capture the pathway of domain-domain communication for agonist-bound hERα. This communication is mediated through the hinge domains that are ordinarily intrinsically disordered. These disordered segments manipulate the hinge domains much like the strings of a marionette as they twist in different ways when antagonists or agonists are bound to the ligand-binding domain.

Surface crossing and energy flow in many-dimensional quantum systems.

Energy flow in molecules, like the dynamics of other many-dimensional finite systems, involves quantum transport across a dense network of near-resonant states. For molecules in their electronic ground state, the network is ordinarily provided by anharmonic vibrational Fermi resonances. Surface crossing between different electronic states provides another route to chaotic motion and energy redistribution. We show that nonadiabatic coupling between electronic energy surfaces facilitates vibrational energy flow and, conversely, anharmonic vibrational couplings facilitate nonadiabatic electronic state mixing. A generalization of the Logan-Wolynes theory of quantum energy flow in many-dimensional Fermi resonance systems to the two-surface case gives a phase diagram describing the boundary between localized quantum dynamics and global energy flow. We explore these predictions and test them using a model inspired by the problem of electronic excitation energy transfer in the photosynthetic reaction center. Using an explicit numerical solution of the time-dependent Schrödinger equation for this ten-dimensional model, we find quite good agreement with the expectations from the approximate analytical theory.

Computationally exploring the mechanism of bacteriophage T7 gp4 helicase translocating along ssDNA.

Bacteriophage T7 gp4 helicase has served as a model system for understanding mechanisms of hexameric replicative helicase translocation. The mechanistic basis of how nucleoside 5'-triphosphate hydrolysis and translocation of gp4 helicase are coupled is not fully resolved. Here, we used a thermodynamically benchmarked coarse-grained protein force field, Associative memory, Water mediated, Structure and Energy Model (AWSEM), with the single-stranded DNA (ssDNA) force field 3SPN.2C to investigate gp4 translocation. We found that the adenosine 5'-triphosphate (ATP) at the subunit interface stabilizes the subunit-subunit interaction and inhibits subunit translocation. Hydrolysis of ATP to adenosine 5'-diphosphate enables the translocation of one subunit, and new ATP binding at the new subunit interface finalizes the subunit translocation. The LoopD2 and the N-terminal primase domain provide transient protein-protein and protein-DNA interactions that facilitate the large-scale subunit movement. The simulations of gp4 helicase both validate our coarse-grained protein-ssDNA force field and elucidate the molecular basis of replicative helicase translocation.

Vectorial channeling as a mechanism for translational control by functional prions and condensates.

Translation of messenger RNA (mRNA) is regulated through a diverse set of RNA-binding proteins. A significant fraction of RNA-binding proteins contains prion-like domains which form functional prions. This raises the question of how prions can play a role in translational control. Local control of translation in dendritic spines by prions has been invoked in the mechanism of synaptic plasticity and memory. We show how channeling through diffusion and processive translation cooperate in highly ordered mRNA/prion aggregates as well as in less ordered mRNA/protein condensates depending on their substructure. We show that the direction of translational control, whether it is repressive or activating, depends on the polarity of the mRNA distribution in mRNA/prion assemblies which determines whether vectorial channeling can enhance recycling of ribosomes. Our model also addresses the effect of changes of substrate concentration in assemblies that have been suggested previously to explain translational control by assemblies through the introduction of a potential of mean force biasing diffusion of ribosomes inside the assemblies. The results from the model are compared with the experimental data on translational control by two functional RNA-binding prions, CPEB involved in memory and Rim4 involved in gametogenesis.

Frustrated peptide chains at the fibril tip control the kinetics of growth of amyloid-ß fibrils.

Amyloid fibrillization is an exceedingly complex process in which incoming peptide chains bind to the fibril while concertedly folding. The coupling between folding and binding is not fully understood. We explore the molecular pathways of association of Aß40 monomers to fibril tips by combining time-resolved in situ scanning probe microscopy with molecular modeling. The comparison between experimental and simulation results shows that a complex supported by nonnative contacts is present in the equilibrium structure of the fibril tip and impedes fibril growth in a supersaturated solution. The unraveling of this frustrated state determines the rate of fibril growth. The kinetics of growth of freshly cut fibrils, in which the bulk fibril structure persists at the tip, complemented by molecular simulations, indicate that this frustrated complex comprises three or four monomers in nonnative conformations and likely is contained on the top of a single stack of peptide chains in the fibril structure. This pathway of fibril growth strongly deviates from the common view that the conformational transformation of each captured peptide chain is templated by the previously arrived peptide. The insights into the ensemble structure of the frustrated complex may guide the search for suppressors of Aß fibrillization. The uncovered dynamics of coupled structuring and assembly during fibril growth are more complex than during the folding of most globular proteins, as they involve the collective motions of several peptide chains that are not guided by a funneled energy landscape.

An intrinsically disordered transcription activation domain increases the DNA binding affinity and reduces the specificity of NFκB p50/RelA.

Many transcription factors contain intrinsically disordered transcription activation domains (TADs), which mediate interactions with coactivators to activate transcription. Historically, DNA-binding domains and TADs have been considered as modular units, but recent studies have shown that TADs can influence DNA binding. Whether these results can be generalized to more TADs is not clear. Here, we biophysically characterized the NFκB p50/RelA heterodimer including the RelA TAD and investigated the TAD's influence on NFκB-DNA interactions. In solution, we show the RelA TAD is disordered but compact, with helical tendency in two regions that interact with coactivators. We determined that the presence of the TAD increased the stoichiometry of NFκB-DNA complexes containing promoter DNA sequences with tandem κB recognition motifs by promoting the binding of NFκB dimers in excess of the number of κB sites. In addition, we measured the binding affinity of p50/RelA for DNA containing tandem κB sites and single κB sites. While the presence of the TAD enhanced the binding affinity of p50/RelA for all κB sequences tested, it also increased the affinity for nonspecific DNA sequences by over 10-fold, leading to an overall decrease in specificity for κB DNA sequences. In contrast, previous studies have generally reported that TADs decrease DNA-binding affinity and increase sequence specificity. Our results reveal a novel function of the RelA TAD in promoting binding to nonconsensus DNA, which sheds light on previous observations of extensive nonconsensus DNA binding by NFκB in vivo in response to strong inflammatory signals.

Mass Spectrometry of RNA-Binding Proteins during Liquid-Liquid Phase Separation Reveals Distinct Assembly Mechanisms and Droplet Architectures.

Liquid-liquid phase separation (LLPS) of heterogeneous ribonucleoproteins (hnRNPs) drives the formation of membraneless organelles, but structural information about their assembled states is still lacking. Here, we address this challenge through a combination of protein engineering, native ion mobility mass spectrometry, and molecular dynamics simulations. We used an LLPS-compatible spider silk domain and pH changes to control the self-assembly of the hnRNPs FUS, TDP-43, and hCPEB3, which are implicated in neurodegeneration, cancer, and memory storage. By releasing the proteins inside the mass spectrometer from their native assemblies, we could monitor conformational changes associated with liquid-liquid phase separation. We find that FUS monomers undergo an unfolded-to-globular transition, whereas TDP-43 oligomerizes into partially disordered dimers and trimers. hCPEB3, on the other hand, remains fully disordered with a preference for fibrillar aggregation over LLPS. The divergent assembly mechanisms revealed by ion mobility mass spectrometry of soluble protein species that exist under LLPS conditions suggest structurally distinct complexes inside liquid droplets that may impact RNA processing and translation depending on biological context.

A structural dynamics model for how CPEB3 binding to SUMO2 can regulate translational control in dendritic spines.

A prion-like RNA-binding protein, CPEB3, can regulate local translation in dendritic spines. CPEB3 monomers repress translation, whereas CPEB3 aggregates activate translation of its target mRNAs. However, the CPEB3 aggregates, as long-lasting prions, may raise the problem of unregulated translational activation. Here, we propose a computational model of the complex structure between CPEB3 RNA-binding domain (CPEB3-RBD) and small ubiquitin-like modifier protein 2 (SUMO2). Free energy calculations suggest that the allosteric effect of CPEB3-RBD/SUMO2 interaction can amplify the RNA-binding affinity of CPEB3. Combining with previous experimental observations on the SUMOylation mode of CPEB3, this model suggests an equilibrium shift of mRNA from binding to deSUMOylated CPEB3 aggregates to binding to SUMOylated CPEB3 monomers in basal synapses. This work shows how a burst of local translation in synapses can be silenced following a stimulation pulse, and explores the CPEB3/SUMO2 interplay underlying the structural change of synapses and the formation of long-term memories.

A generalized Flory-Stockmayer kinetic theory of connectivity percolation and rigidity percolation of cytoskeletal networks.

Actin networks are essential for living cells to move, reproduce, and sense their environments. The dynamic and rheological behavior of actin networks is modulated by actin-binding proteins such as α-actinin, Arp2/3, and myosin. There is experimental evidence that actin-binding proteins modulate the cooperation of myosin motors by connecting the actin network. In this work, we present an analytical mean field model, using the Flory-Stockmayer theory of gelation, to understand how different actin-binding proteins change the connectivity of the actin filaments as the networks are formed. We follow the kinetics of the networks and estimate the concentrations of actin-binding proteins that are needed to reach connectivity percolation as well as to reach rigidity percolation. We find that Arp2/3 increases the actomyosin connectivity in the network in a non-monotonic way. We also describe how changing the connectivity of actomyosin networks modulates the ability of motors to exert forces, leading to three possible phases of the networks with distinctive dynamical characteristics: a sol phase, a gel phase, and an active phase. Thus, changes in the concentration and activity of actin-binding proteins in cells lead to a phase transition of the actin network, allowing the cells to perform active contraction and change their rheological properties.

Single-molecule conformational dynamics of a transcription factor reveals a continuum of binding modes controlling association and dissociation.

Binding and unbinding of transcription factors to DNA are kinetically controlled to regulate the transcriptional outcome. Control of the release of the transcription factor NF-κB from DNA is achieved through accelerated dissociation by the inhibitor protein IκBα. Using single-molecule FRET, we observed a continuum of conformations of NF-κB in free and DNA-bound states interconverting on the subseconds to minutes timescale, comparable to in vivo binding on the seconds timescale, suggesting that structural dynamics directly control binding kinetics. Much of the DNA-bound NF-κB is partially bound, allowing IκBα invasion to facilitate DNA dissociation. IκBα induces a locked conformation where the DNA-binding domains of NF-κB are too far apart to bind DNA, whereas a loss-of-function IκBα mutant retains the NF-κB conformational ensemble. Overall, our results suggest a novel mechanism with a continuum of binding modes for controlling association and dissociation of transcription factors.

The Nucleome Data Bank: web-based resources to simulate and analyze the three-dimensional genome.

We introduce the Nucleome Data Bank (NDB), a web-based platform to simulate and analyze the three-dimensional (3D) organization of genomes. The NDB enables physics-based simulation of chromosomal structural dynamics through the MEGABASE + MiChroM computational pipeline. The input of the pipeline consists of epigenetic information sourced from the Encode database; the output consists of the trajectories of chromosomal motions that accurately predict Hi-C and fluorescence insitu hybridization data, as well as multiple observations of chromosomal dynamics in vivo. As an intermediate step, users can also generate chromosomal sub-compartment annotations directly from the same epigenetic input, without the use of any DNA-DNA proximity ligation data. Additionally, the NDB freely hosts both experimental and computational structural genomics data. Besides being able to perform their own genome simulations and download the hosted data, users can also analyze and visualize the same data through custom-designed web-based tools. In particular, the one-dimensional genetic and epigenetic data can be overlaid onto accurate 3D structures of chromosomes, to study the spatial distribution of genetic and epigenetic features. The NDB aims to be a shared resource to biologists, biophysicists and all genome scientists. The NDB is available at https://ndb.rice.edu.

Braiding topology and the energy landscape of chromosome organization proteins.

Assemblies of structural maintenance of chromosomes (SMC) proteins and kleisin subunits are essential to chromosome organization and segregation across all kingdoms of life. While structural data exist for parts of the SMC-kleisin complexes, complete structures of the entire complexes have yet to be determined, making mechanistic studies difficult. Using an integrative approach that combines crystallographic structural information about the globular subdomains, along with coevolutionary information and an energy landscape optimized force field (AWSEM), we predict atomic-scale structures for several tripartite SMC-kleisin complexes, including prokaryotic condensin, eukaryotic cohesin, and eukaryotic condensin. The molecular dynamics simulations of the SMC-kleisin protein complexes suggest that these complexes exist as a broad conformational ensemble that is made up of different topological isomers. The simulations suggest a critical role for the SMC coiled-coil regions, where the coils intertwine with various linking numbers. The twist and writhe of these braided coils are coupled with the motion of the SMC head domains, suggesting that the complexes may function as topological motors. Opening, closing, and translation along the DNA of the SMC-kleisin protein complexes would allow these motors to couple to the topology of DNA when DNA is entwined with the braided coils.

Exploring the interplay between fibrillization and amorphous aggregation channels on the energy landscapes of tau repeat isoforms.

Filaments made up of different isoforms of tau protein are associated with a variety of neurodegenerative diseases. Filaments made up of the 4R-tau isoform, which has four repeat regions (R1 to R4), are found in patients suffering from Alzheimer's disease, while filaments made of the 3R-tau isoform, which contains only three repeat units (R1, R3, and R4), are found in patients with Pick's disease (frontotemporal dementia). In this work, a predictive coarse-grained protein force field, the associative memory water-mediated structure and energy model (AWSEM), is used to study the energy landscapes of nucleation of the two different fibrils derived from patients with Pick's and Alzheimer's diseases. The landscapes for nucleating both fibril types contain amorphous oligomers leading to branched structures as well as prefibrillar oligomers. These two classes of oligomers differ in their structural details: The prefibrillar oligomers have more parallel in-register ß-strands, which ultimately lead to amyloid fibrils, while the amorphous oligomers are characterized by a near random ß-strand stacking, leading to a distinct amorphous phase. The landscape topography suggests that there must be significant structural reordering, or "backtracking," to transit from the amorphous aggregation channel to the fibrillization channel. Statistical mechanical perturbation theory allows us to evaluate the effects of changing concentration on the aggregation free-energy landscapes and to predict the effects of phosphorylation, which is known to facilitate the aggregation of tau repeats.

Exploring the F-actin/CPEB3 interaction and its possible role in the molecular mechanism of long-term memory.

Dendritic spines are tiny membranous protrusions on the dendrites of neurons. Dendritic spines change shape in response to input signals, thereby strengthening the connections between neurons. The growth and stabilization of dendritic spines is thought to be essential for maintaining long-term memory. Actin cytoskeleton remodeling in spines is a key element of their formation and growth. More speculatively, the aggregation of CPEB3, a functional prion that binds RNA, has been reported to be involved in the maintenance of long-term memory. Here we study the interaction between actin and CPEB3 and propose a molecular model for the complex structure of CPEB3 and an actin filament (F-actin). The results of our computational modeling, including both energetic and structural analyses, are compared with novel data from peptide array experiments. Our model of the CPEB3/F-actin interaction suggests that F-actin potentially triggers the aggregation-prone structural transition of a short CPEB3 sequence by zipping it into a beta-hairpin form. We also propose that the CPEB3/F-actin interaction might be regulated by the SUMOylation of CPEB3, based on bioinformatic searches for potential SUMOylation sites as well as SUMO interacting motifs in CPEB3. On the basis of these results and the existing literature, we put forward a possible molecular mechanism underlying long-term memory that involves CPEB3's binding to actin, its aggregation, and its regulation by SUMOylation.