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.

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.

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.

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.

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.

DynamicBind: predicting ligand-specific protein-ligand complex structure with a deep equivariant generative model.

While significant advances have been made in predicting static protein structures, the inherent dynamics of proteins, modulated by ligands, are crucial for understanding protein function and facilitating drug discovery. Traditional docking methods, frequently used in studying protein-ligand interactions, typically treat proteins as rigid. While molecular dynamics simulations can propose appropriate protein conformations, they're computationally demanding due to rare transitions between biologically relevant equilibrium states. In this study, we present DynamicBind, a deep learning method that employs equivariant geometric diffusion networks to construct a smooth energy landscape, promoting efficient transitions between different equilibrium states. DynamicBind accurately recovers ligand-specific conformations from unbound protein structures without the need for holo-structures or extensive sampling. Remarkably, it demonstrates state-of-the-art performance in docking and virtual screening benchmarks. Our experiments reveal that DynamicBind can accommodate a wide range of large protein conformational changes and identify cryptic pockets in unseen protein targets. As a result, DynamicBind shows potential in accelerating the development of small molecules for previously undruggable targets and expanding the horizons of computational drug discovery.

Local energetic frustration conservation in protein families and superfamilies.

Energetic local frustration offers a biophysical perspective to interpret the effects of sequence variability on protein families. Here we present a methodology to analyze local frustration patterns within protein families and superfamilies that allows us to uncover constraints related to stability and function, and identify differential frustration patterns in families with a common ancestry. We analyze these signals in very well studied protein families such as PDZ, SH3, ɑ and ß globins and RAS families. Recent advances in protein structure prediction make it possible to analyze a vast majority of the protein space. An automatic and unsupervised proteome-wide analysis on the SARS-CoV-2 virus demonstrates the potential of our approach to enhance our understanding of the natural phenotypic diversity of protein families beyond single protein instances. We apply our method to modify biophysical properties of natural proteins based on their family properties, as well as perform unsupervised analysis of large datasets to shed light on the physicochemical signatures of poorly characterized proteins such as the ones belonging to emergent pathogens.

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.

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.

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.

Interphase chromosomes of the Aedes aegypti mosquito are liquid crystalline and can sense mechanical cues.

We use data-driven physical simulations to study the three-dimensional architecture of the Aedes aegypti genome. Hi-C maps exhibit both a broad diagonal and compartmentalization with telomeres and centromeres clustering together. Physical modeling reveals that these observations correspond to an ensemble of 3D chromosomal structures that are folded over and partially condensed. Clustering of the centromeres and telomeres near the nuclear lamina appears to be a necessary condition for the formation of the observed structures. Further analysis of the mechanical properties of the genome reveals that the chromosomes of Aedes aegypti, by virtue of their atypical structural organization, are highly sensitive to the deformation of the nuclei. This last finding provides a possible physical mechanism linking mechanical cues to gene regulation.

Time-Resolved In Situ AFM Measurement of Growth Rates of Aß40 Fibrils.

We employ time-resolved in situ atomic force microcopy to monitor the growth of individual Aß40 fibrils and thereby directly measure the fibril growth rates. We describe procedures to express and purify the Aß peptide and verify its identity, prepare solutions and seeds, quantify the displacements of the growing tips of individual fibrils, and determine their respective growth rates. We discuss approaches to evaluate and minimize the impact of the scanning tip on the monitored processes. We use the distribution of fibril thickness to characterize approximately the fibril structure. The ability to quantify faithfully the growth kinetics of amyloid fibrils empowers exploration of the molecular-level processes of fibril growth that relate to behaviors of amyloid species of laboratory and clinical interest.

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.

Unleashing the potential of noncanonical amino acid biosynthesis to create cells with precision tyrosine sulfation.

Despite the great promise of genetic code expansion technology to modulate structures and functions of proteins, external addition of ncAAs is required in most cases and it often limits the utility of genetic code expansion technology, especially to noncanonical amino acids (ncAAs) with poor membrane internalization. Here, we report the creation of autonomous cells, both prokaryotic and eukaryotic, with the ability to biosynthesize and genetically encode sulfotyrosine (sTyr), an important protein post-translational modification with low membrane permeability. These engineered cells can produce site-specifically sulfated proteins at a higher yield than cells fed exogenously with the highest level of sTyr reported in the literature. We use these autonomous cells to prepare highly potent thrombin inhibitors with site-specific sulfation. By enhancing ncAA incorporation efficiency, this added ability of cells to biosynthesize ncAAs and genetically incorporate them into proteins greatly extends the utility of genetic code expansion methods.

Frustration and the Kinetic Repartitioning Mechanism of Substrate Inhibition in Enzyme Catalysis.

Substrate inhibition, whereby enzymatic activity decreases with excess substrate after reaching a maximum turnover rate, is among the most elusive phenomena in enzymatic catalysis. Here, based on a dynamic energy landscape model, we investigate the underlying mechanism by performing molecular simulations and frustration analysis for a model enzyme adenylate kinase (AdK), which catalyzes the phosphoryl transfer reaction ATP + AMP ⇋ ADP + ADP. Intriguingly, these reveal a kinetic repartitioning mechanism of substrate inhibition, whereby excess substrate AMP suppresses the population of an energetically frustrated, but kinetically activated, catalytic pathway going through a substrate (ATP)-product (ADP) cobound complex with steric incompatibility. Such a frustrated pathway plays a crucial role in facilitating the bottleneck product ADP release, and its suppression by excess substrate AMP leads to a slow down of product release and overall turnover. The simulation results directly demonstrate that substrate inhibition arises from the rate-limiting product-release step, instead of the steps for populating the catalytically competent complex as often suggested in previous works. Furthermore, there is a tight interplay between the enzyme conformational equilibrium and the extent of substrate inhibition. Mutations biasing to more closed conformations tend to enhance substrate inhibition. We also characterized the key features of single-molecule enzyme kinetics with substrate inhibition effect. We propose that the above molecular mechanism of substrate inhibition may be relevant to other multisubstrate enzymes in which product release is the bottleneck step.

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.

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.

Exploring the Interplay between Disordered and Ordered Oligomer Channels on the Aggregation Energy Landscapes of α-Synuclein.

The abnormal aggregation of α-synulcein is associated with multiple neurodegenerative diseases such as Parkinson's disease. The hydrophobic non-amyloid component (NAC) region of α-synuclein comprises the core of the fibril in vitro and in vivo. In this work, we study the aggregation landscape of the hydrophobic NAC region of α-synuclein using a transferrable coarse-grained force field, the associative memory water-mediated structure, and energy model (AWSEM). Using structural similarity, we can group metastable states on the free energy landscape of aggregation into three types of oligomers: disordered oligomers, prefibrillar oligomers with disordered tips, and ordered prefibrillar oligomers. The prefibrillar oligomers with disordered tips have more in-register parallel ß strands than do the fully disordered oligomers but have fewer in-register parallel ß strands than the ordered prefibrillar oligomers. Along with the ordered prefibrillar species, the disordered oligomeric states dominate at small oligomer sizes while the prefibrillar species with disordered tips thermodynamically dominate with the growth of oligomers. The topology of the aggregation landscape and observations in simulations suggest there is backtracking between ordered prefibrillar oligomers and other kinds of oligomers as the aggregation proceeds. The significant structural differences between the ordered prefibrillar oligomers and the disordered oligomers support the idea that the growth of these two kinds of oligomers involves kinetically independent parallel pathways. In contrast, the overall structural similarity between the fully ordered prefibrillar oligomers and the prefibrillar oligomers with disordered tips implies that two channels can interconvert on slower time scales. We also evaluate the effects of phosphorylation on the aggregation free energy landscape using statistical mechanical perturbation theory.

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.