Theory of protein folding: the energy landscape perspective

Protein conformational ensembles in function: roles and mechanisms

The sequence-structure-function paradigm has dominated twentieth century molecular biology. The paradigm tacitly stipulated that for each sequence there exists a single, well-organized protein structure. Yet, to sustain cell life, function requires (i) that there be more than a single structure, (ii) that there be switching between the structures, and (iii) that the structures be incompletely organized. These fundamental tenets called for an updated sequence-conformational ensemble-function paradigm. The powerful energy landscape idea, which is the foundation of modernized molecular biology, imported the conformational ensemble framework from physics and chemistry. This framework embraces the recognition that proteins are dynamic and are always interconverting between conformational states with varying energies. The more stable the conformation the more populated it is. The changes in the populations of the states are required for cell life. As an example, in vivo, under physiological conditions, wild type kinases commonly populate their more stable "closed", inactive, conformations. However, there are minor populations of the "open", ligand-free states. Upon their stabilization, e.g., by high affinity interactions or mutations, their ensembles shift to occupy the active states. Here we discuss the role of conformational propensities in function. We provide multiple examples of diverse systems, including protein kinases, lipid kinases, and Ras GTPases, discuss diverse conformational mechanisms, and provide a broad outlook on protein ensembles in the cell. We propose that the number of molecules in the active state (inactive for repressors), determine protein function, and that the dynamic, relative conformational propensities, rather than the rigid structures, are the hallmark of cell life.

Signature of functional enzyme dynamics in quasielastic neutron scattering spectra: The case of phosphoglycerate kinase

We present an analysis of high-resolution quasi-elastic neutron scattering spectra of phosphoglycerate kinase which elucidates the influence of the enzymatic activity on the dynamics of the protein. We show that in the active state the inter-domain motions are amplified and the intra-domain asymptotic power-law relaxation ∝t-α is accelerated, with a reduced coefficient α. Employing an energy landscape picture of protein dynamics, this observation can be translated into a widening of the distribution of energy barriers separating conformational substates of the protein.

Multibody Terms in Protein Coarse-Grained Models: A Top-Down Perspective

Coarse-grained models allow computational investigation of biomolecular processes occurring on long time and length scales, intractable with atomistic simulation. Traditionally, many coarse-grained models rely mostly on pairwise interaction potentials. However, the decimation of degrees of freedom should, in principle, lead to a complex many-body effective interaction potential. In this work, we use experimental data on mutant stability to parametrize coarse-grained models for two proteins with and without many-body terms. We demonstrate that many-body terms are necessary to reproduce quantitatively the effects of point mutations on protein stability, particularly to implicitly take into account the effect of the solvent.

Dynamics of chromosome organization in a minimal bacterial cell

Computational models of cells cannot be considered complete unless they include the most fundamental process of life, the replication and inheritance of genetic material. By creating a computational framework to model systems of replicating bacterial chromosomes as polymers at 10 bp resolution with Brownian dynamics, we investigate changes in chromosome organization during replication and extend the applicability of an existing whole-cell model (WCM) for a genetically minimal bacterium, JCVI-syn3A, to the entire cell-cycle. To achieve cell-scale chromosome structures that are realistic, we model the chromosome as a self-avoiding homopolymer with bending and torsional stiffnesses that capture the essential mechanical properties of dsDNA in Syn3A. In addition, the conformations of the circular DNA must avoid overlapping with ribosomes identitied in cryo-electron tomograms. While Syn3A lacks the complex regulatory systems known to orchestrate chromosome segregation in other bacteria, its minimized genome retains essential loop-extruding structural maintenance of chromosomes (SMC) protein complexes (SMC-scpAB) and topoisomerases. Through implementing the effects of these proteins in our simulations of replicating chromosomes, we find that they alone are sufficient for simultaneous chromosome segregation across all generations within nested theta structures. This supports previous studies suggesting loop-extrusion serves as a near-universal mechanism for chromosome organization within bacterial and eukaryotic cells. Furthermore, we analyze ribosome diffusion under the influence of the chromosome and calculate in silico chromosome contact maps that capture inter-daughter interactions. Finally, we present a methodology to map the polymer model of the chromosome to a Martini coarse-grained representation to prepare molecular dynamics models of entire Syn3A cells, which serves as an ultimate means of validation for cell states predicted by the WCM.

RNA folding pathways from all-atom simulations with a variationally improved history-dependent bias

Atomically detailed simulations of RNA folding have proven very challenging in view of the difficulties of developing realistic force fields and the intrinsic computational complexity of sampling rare conformational transitions. As a step forward in tackling these issues, we extend to RNA an enhanced path-sampling method previously successfully applied to proteins. In this scheme, the information about the RNA's native structure is harnessed by a soft history-dependent biasing force promoting the generation of productive folding trajectories in an all-atom force field with explicit solvent. A rigorous variational principle is then applied to minimize the effect of the bias. Here, we report on an application of this method to RNA molecules from 20 to 47 nucleotides long and increasing topological complexity. By comparison with analog simulations performed on small proteins with similar size and architecture, we show that the RNA folding landscape is significantly more frustrated, even for relatively small chains with a simple topology. The predicted RNA folding mechanisms are found to be consistent with the available experiments and some of the existing coarse-grained models. Due to its computational performance, this scheme provides a promising platform to efficiently gather atomistic RNA folding trajectories, thus retain the information about the chemical composition of the sequence.

How can we discover developable antibody-based biotherapeutics?

Antibody-based biotherapeutics have emerged as a successful class of pharmaceuticals despite significant challenges and risks to their discovery and development. This review discusses the most frequently encountered hurdles in the research and development (R&D) of antibody-based biotherapeutics and proposes a conceptual framework called biopharmaceutical informatics. Our vision advocates for the syncretic use of computation and experimentation at every stage of biologic drug discovery, considering developability (manufacturability, safety, efficacy, and pharmacology) of potential drug candidates from the earliest stages of the drug discovery phase. The computational advances in recent years allow for more precise formulation of disease concepts, rapid identification, and validation of targets suitable for therapeutic intervention and discovery of potential biotherapeutics that can agonize or antagonize them. Furthermore, computational methods for de novo and epitope-specific antibody design are increasingly being developed, opening novel computationally driven opportunities for biologic drug discovery. Here, we review the opportunities and limitations of emerging computational approaches for optimizing antigens to generate robust immune responses, in silico generation of antibody sequences, discovery of potential antibody binders through virtual screening, assessment of hits, identification of lead drug candidates and their affinity maturation, and optimization for developability. The adoption of biopharmaceutical informatics across all aspects of drug discovery and development cycles should help bring affordable and effective biotherapeutics to patients more quickly.

De novo design of protein structure and function with RFdiffusion

There has been considerable recent progress in designing new proteins using deep-learning methods1-9. Despite this progress, a general deep-learning framework for protein design that enables solution of a wide range of design challenges, including de novo binder design and design of higher-order symmetric architectures, has yet to be described. Diffusion models10,11 have had considerable success in image and language generative modelling but limited success when applied to protein modelling, probably due to the complexity of protein backbone geometry and sequence-structure relationships. Here we show that by fine-tuning the RoseTTAFold structure prediction network on protein structure denoising tasks, we obtain a generative model of protein backbones that achieves outstanding performance on unconditional and topology-constrained protein monomer design, protein binder design, symmetric oligomer design, enzyme active site scaffolding and symmetric motif scaffolding for therapeutic and metal-binding protein design. We demonstrate the power and generality of the method, called RoseTTAFold diffusion (RFdiffusion), by experimentally characterizing the structures and functions of hundreds of designed symmetric assemblies, metal-binding proteins and protein binders. The accuracy of RFdiffusion is confirmed by the cryogenic electron microscopy structure of a designed binder in complex with influenza haemagglutinin that is nearly identical to the design model. In a manner analogous to networks that produce images from user-specified inputs, RFdiffusion enables the design of diverse functional proteins from simple molecular specifications.

In the Age of Machine Learning Cryo-EM Research is Still Necessary: A Path toward Precision Medicine

Machine learning has proven useful in analyzing complex biological data and has greatly influenced the course of research in structural biology and precision medicine. Deep neural network models oftentimes fail to predict the structure of complex proteins and are heavily dependent on experimentally determined structures for their training and validation. Single-particle cryogenic electron microscopy (cryoEM) is also advancing the understanding of biology and will be needed to complement these models by continuously supplying high-quality experimentally validated structures for improvements in prediction quality. In this perspective, the significance of structure prediction methods is highlighted, but the authors also ask, what if these programs cannot accurately predict a protein structure important for preventing disease? The role of cryoEM is discussed to help fill the gaps left by artificial intelligence predictive models in resolving targetable proteins and protein complexes that will pave the way for personalized therapeutics.

EnGens: a computational framework for generation and analysis of representative protein conformational ensembles

Proteins are dynamic macromolecules that perform vital functions in cells. A protein structure determines its function, but this structure is not static, as proteins change their conformation to achieve various functions. Understanding the conformational landscapes of proteins is essential to understand their mechanism of action. Sets of carefully chosen conformations can summarize such complex landscapes and provide better insights into protein function than single conformations. We refer to these sets as representative conformational ensembles. Recent advances in computational methods have led to an increase in the number of available structural datasets spanning conformational landscapes. However, extracting representative conformational ensembles from such datasets is not an easy task and many methods have been developed to tackle it. Our new approach, EnGens (short for ensemble generation), collects these methods into a unified framework for generating and analyzing representative protein conformational ensembles. In this work, we: (1) provide an overview of existing methods and tools for representative protein structural ensemble generation and analysis; (2) unify existing approaches in an open-source Python package, and a portable Docker image, providing interactive visualizations within a Jupyter Notebook pipeline; (3) test our pipeline on a few canonical examples from the literature. Representative ensembles produced by EnGens can be used for many downstream tasks such as protein-ligand ensemble docking, Markov state modeling of protein dynamics and analysis of the effect of single-point mutations.

Benchmarking Molecular Dynamics Force Fields for All-Atom Simulations of Biological Condensates

Proteins containing intrinsically disordered regions are integral parts of the cellular signaling pathways and common components of biological condensates. Point mutations in the protein sequence, genetic at birth or acquired through aging, can alter the properties of the condensates, marking the onset of neurodegenerative diseases such as ALS and dementia. While the all-atom molecular dynamics method can, in principle, elucidate the conformational changes that arise from point mutations, the applications of this method to protein condensate systems is conditioned upon the availability of molecular force fields that can accurately describe both structured and disordered regions of such proteins. Using the special-purpose Anton 2 supercomputer, we benchmarked the efficacy of nine presently available molecular force fields in describing the structure and dynamics of a Fused in sarcoma (FUS) protein. Five-microsecond simulations of the full-length FUS protein characterized the effect of the force field on the global conformation of the protein, self-interactions among its side chains, solvent accessible surface area, and the diffusion constant. Using the results of dynamic light scattering as a benchmark for the FUS radius of gyration, we identified several force fields that produced FUS conformations within the experimental range. Next, we used these force fields to perform ten-microsecond simulations of two structured RNA binding domains of FUS bound to their respective RNA targets, finding the choice of the force field to affect stability of the RNA-FUS complex. Taken together, our data suggest that a combination of protein and RNA force fields sharing a common four-point water model provides an optimal description of proteins containing both disordered and structured regions and RNA-protein interactions. To make simulations of such systems available beyond the Anton 2 machines, we describe and validate implementation of the best performing force fields in a publicly available molecular dynamics program NAMD. Our NAMD implementation enables simulations of large (tens of millions of atoms) biological condensate systems and makes such simulations accessible to a broader scientific community.

In vivo functional phenotypes from a computational epistatic model of evolution

Computational models of evolution are valuable for understanding the dynamics of sequence variation, to infer phylogenetic relationships or potential evolutionary pathways and for biomedical and industrial applications. Despite these benefits, few have validated their propensities to generate outputs with in vivo functionality, which would enhance their value as accurate and interpretable evolutionary algorithms. We demonstrate the power of epistasis inferred from natural protein families to evolve sequence variants in an algorithm we developed called Sequence Evolution with Epistatic Contributions. Utilizing the Hamiltonian of the joint probability of sequences in the family as fitness metric, we sampled and experimentally tested for in vivo β -lactamase activity in E. coli TEM-1 variants. These evolved proteins can have dozens of mutations dispersed across the structure while preserving sites essential for both catalysis and interactions. Remarkably, these variants retain family-like functionality while being more active than their WT predecessor. We found that depending on the inference method used to generate the epistatic constraints, different parameters simulate diverse selection strengths. Under weaker selection, local Hamiltonian fluctuations reliably predict relative changes to variant fitness, recapitulating neutral evolution. SEEC has the potential to explore the dynamics of neofunctionalization, characterize viral fitness landscapes and facilitate vaccine development.

Polymer folding through active processes recreates features of genome organization

From proteins to chromosomes, polymers fold into specific conformations that control their biological function. Polymer folding has long been studied with equilibrium thermodynamics, yet intracellular organization and regulation involve energy-consuming, active processes. Signatures of activity have been measured in the context of chromatin motion, which shows spatial correlations and enhanced subdiffusion only in the presence of adenosine triphosphate. Moreover, chromatin motion varies with genomic coordinate, pointing toward a heterogeneous pattern of active processes along the sequence. How do such patterns of activity affect the conformation of a polymer such as chromatin? We address this question by combining analytical theory and simulations to study a polymer subjected to sequence-dependent correlated active forces. Our analysis shows that a local increase in activity (larger active forces) can cause the polymer backbone to bend and expand, while less active segments straighten out and condense. Our simulations further predict that modest activity differences can drive compartmentalization of the polymer consistent with the patterns observed in chromosome conformation capture experiments. Moreover, segments of the polymer that show correlated active (sub)diffusion attract each other through effective long-ranged harmonic interactions, whereas anticorrelations lead to effective repulsions. Thus, our theory offers nonequilibrium mechanisms for forming genomic compartments, which cannot be distinguished from affinity-based folding using structural data alone. As a first step toward exploring whether active mechanisms contribute to shaping genome conformations, we discuss a data-driven approach.

Probing the Protein Folding Energy Landscape: Dissociation of Amyloid-β Fibrils by Laser-Induced Plasmonic Heating

Insoluble amyloid fibrils made from proteins and peptides are difficult to be degraded in both living and artificial systems. The importance of studying their physical stability lies primarily with their association with human neurodegenerative diseases, but also owing to their potential role in multiple bio-nanomaterial applications. Here, gold nanorods (AuNRs) were utilized to investigate the plasmonic heating properties and dissociation of amyloid-β fibrils formed by different peptide fragments (Aβ_16-22/Aβ_25-35/Aβ_1-42) related to the Alzheimer's disease. It is demonstrated that AuNRs were able to break mature amyloid-β fibrils from both the full length (Aβ_1-42) and peptide fragments (Aβ_16-22/Aβ_25-35) within minutes by triggering ultrahigh localized surface plasmon resonance (LSPR) heating. The LSPR energy absorbed by the amyloids to unfold and move to higher levels in the protein folding energy landscape can be measured directly and in situ by luminescence thermometry using lanthanide-based upconverting nanoparticles. We also show that Aβ_16-22 fibrils, with the largest persistence length, displayed the highest resistance to breakage, resulting in a transition from rigid fibrils to short flexible fibrils. These findings are consistent with molecular dynamics simulations indicating that Aβ_16-22 fibrils possess the highest thermostability due to their highly ordered hydrogen bond networks and antiparallel β-sheet orientation, hence affected by an LSPR-induced remodeling rather than melting. The present results introduce original strategies for disassembling amyloid fibrils noninvasively in liquid environment; they also introduce a methodology to probe the positioning of amyloids on the protein folding and aggregation energy landscape via nanoparticle-enabled plasmonic and upconversion nanothermometry.

Crystal Growth Rates from Molecular Liquids: The Kinetics of Entropy Loss

It has been established empirically that the rate of addition of molecules to the crystal during crystal growth from the melt is proportional to exp(-|ΔS_fus|/R), where ΔS_fus is the entropy of fusion. Here we show that this entropic slowdown arises directly from the separation of the entropy loss and energy loss processes associated with the freezing of the liquid. We present a theoretical treatment of the kinetics based on a model flat energy landscape and derive an explicit expression for the coupling magnitude in terms of the crystal-melt interfacial free energy. The implications of our work for nucleation kinetics are also discussed.

EnGens: a computational framework for generation and analysis of representative protein conformational ensembles

Proteins are dynamic macromolecules that perform vital functions in cells. A protein structure determines its function, but this structure is not static, as proteins change their conformation to achieve various functions. Understanding the conformational landscapes of proteins is essential to understand their mechanism of action. Sets of carefully chosen conformations can summarize such complex landscapes and provide better insights into protein function than single conformations. We refer to these sets as representative conformational ensembles. Recent advances in computational methods have led to an increase in number of available structural datasets spanning conformational landscapes. However, extracting representative conformational ensembles from such datasets is not an easy task and many methods have been developed to tackle it. Our new approach, EnGens (short for ensemble generation), collects these methods into a unified framework for generating and analyzing protein conformational ensembles. In this work we: (1) provide an overview of existing methods and tools for protein structural ensemble generation and analysis; (2) unify existing approaches in an open-source Python package, and a portable Docker image, providing interactive visualizations within a Jupyter Notebook pipeline; (3) test our pipeline on a few canonical examples found in the literature. Representative ensembles produced by EnGens can be used for many downstream tasks such as protein-ligand ensemble docking, Markov state modeling of protein dynamics and analysis of the effect of single-point mutations.

Protein Stability─Analysis of Heat and Cold Denaturation without and with Unfolding Models

Protein stability is important in many areas of life sciences. Thermal protein unfolding is investigated extensively with various spectroscopic techniques. The extraction of thermodynamic properties from these measurements requires the application of models. Differential scanning calorimetry (DSC) is less common, but is unique as it measures directly a thermodynamic property, that is, the heat capacity C_p(T). The analysis of C_p(T) is usually performed with the chemical equilibrium two-state model. This is not necessary and leads to incorrect thermodynamic consequences. Here we demonstrate a straightforward model-independent evaluation of heat capacity experiments in terms of protein unfolding enthalpy ΔH(T), entropy ΔS(T), and free energy ΔG(T)). This now allows the comparison of the experimental thermodynamic data with the predictions of different models. We critically examined the standard chemical equilibrium two-state model, which predicts a positive free energy for the native protein, and diverges distinctly from the experimental temperature profiles. We propose two new models which are equally applicable to spectroscopy and calorimetry. The Θ_U(T)-weighted chemical equilibrium model and the statistical-mechanical two-state model provide excellent fits of the experimental data. They predict sigmoidal temperature profiles for enthalpy and entropy, and a trapezoidal temperature profile for the free energy. This is illustrated with experimental examples for heat and cold denaturation of lysozyme and β-lactoglobulin. We then show that the free energy is not a good criterion to judge protein stability. More useful parameters are discussed, including protein cooperativity. The new parameters are embedded in a well-defined thermodynamic context and are amenable to molecular dynamics calculations.

Machine learned coarse-grained protein force-fields: Are we there yet?

The successful recent application of machine learning methods to scientific problems includes the learning of flexible and accurate atomic-level force-fields for materials and biomolecules from quantum chemical data. In parallel, the machine learning of force-fields at coarser resolutions is rapidly gaining relevance as an efficient way to represent the higher-body interactions needed in coarse-grained force-fields to compensate for the omitted degrees of freedom. Coarse-grained models are important for the study of systems at time and length scales exceeding those of atomistic simulations. However, the development of transferable coarse-grained models via machine learning still presents significant challenges. Here, we discuss recent developments in this field and current efforts to address the remaining challenges.

Origins of life: first came evolutionary dynamics

When life arose from prebiotic molecules 3.5 billion years ago, what came first? Informational molecules (RNA, DNA), functional ones (proteins), or something else? We argue here for a different logic: rather than seeking a molecule type, we seek a dynamical process. Biology required an ability to evolve before it could choose and optimise materials. We hypothesise that the evolution process was rooted in the peptide folding process. Modelling shows how short random peptides can collapse in water and catalyse the elongation of others, powering both increased folding stability and emergent autocatalysis through a disorder-to-order process.

Conformational landscapes of artificial peptides predicted by various force fields: are we ready to simulate β-amino acids?

With the introduction of artificial peptides as antimicrobial agents and organic catalysts, numerous efforts have been made to design foldamers with desirable structures and functions. Computational tools are a helpful proxy for revealing the dynamic structures at atomic resolution and understanding foldamer's complex structure-function relationships. However, the performance of conventional force fields in predicting the structures of artificial peptides has not been systematically evaluated. In this study, we critically assessed three popular force fields, AMBER ff14SB, CHARMM36m, and OPLS-AA/L, in predicting conformational propensities of a β-peptide foldamer at monomer and hexamer levels. Simulation results were compared to those obtained from quantum chemistry calculations and experimental data. We also utilised replica exchange molecular dynamics simulations to investigate the energy landscape of each force field and assess the similarities and differences between force fields. We compared different solvent systems in the AMBER ff14SB and CHARMM36m frameworks and confirmed the unanimous role of hydrogen bonds in shaping energy landscapes. We anticipate that our data will pave the way for further improvements to force fields and for understanding the role of solvents in peptide folding, crystallisation, and engineering.

Benchmarking Molecular Dynamics Force Fields for All-Atom Simulations of Biological Condensates

Proteins containing intrinsically disordered regions are integral components of the cellular signaling pathways and common components of biological condensates. Point mutations in the protein sequence, genetic at birth or acquired through aging, can alter the properties of the condensates, marking the onset of neurodegenerative diseases such as ALS and dementia. While all-atom molecular dynamics method can, in principle, elucidate the conformational changes responsible for the aging of the condensate, the applications of this method to protein condensate systems is conditioned by the availability of molecular force fields that can accurately describe both structured and disordered regions of such proteins. Using the special-purpose Anton 2 supercomputer, we benchmarked the efficacy of nine presently available molecular force fields in describing the structure and dynamics of a Fused in sarcoma (FUS) protein. Five-microsecond simulations of the full-length FUS protein characterized the effect of the force field on the global conformation of the protein, self-interactions among its side chains, solvent accessible surface area and the diffusion constant. Using the results of dynamic light scattering as a benchmark for the FUS radius of gyration, we identified several force field that produced FUS conformations within the experimental range. Next, we used these force fields to perform ten-microsecond simulations of two structured RNA binding domains of FUS bound to their respective RNA targets, finding the choice of the force field to affect stability of the RNA-FUS complex. Taken together, our data suggest that a combination of protein and RNA force fields sharing a common four-point water model provides an optimal description of proteins containing both disordered and structured regions and RNA-protein interactions. To make simulations of such systems available beyond the Anton 2 machines, we describe and validate implementation of the best performing force fields in a publicly available molecular dynamics program NAMD. Our NAMD implementation enables simulations of large (tens of millions of atoms) biological condensate systems and makes such simulations accessible to a broader scientific community.

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Slicing and Dicing: Optimal Coarse-Grained Representation to Preserve Molecular Kinetics

The aim of molecular coarse-graining approaches is to recover relevant physical properties of the molecular system via a lower-resolution model that can be more efficiently simulated. Ideally, the lower resolution still accounts for the degrees of freedom necessary to recover the correct physical behavior. The selection of these degrees of freedom has often relied on the scientist's chemical and physical intuition. In this article, we make the argument that in soft matter contexts desirable coarse-grained models accurately reproduce the long-time dynamics of a system by correctly capturing the rare-event transitions. We propose a bottom-up coarse-graining scheme that correctly preserves the relevant slow degrees of freedom, and we test this idea for three systems of increasing complexity. We show that in contrast to this method existing coarse-graining schemes such as those from information theory or structure-based approaches are not able to recapitulate the slow time scales of the system.

Improved Assessment of Globularity of Protein Structures and the Ellipsoid Profile of the Biological Assemblies from the PDB

In this paper, we present an update to the ellipsoid profile algorithm (EP), a simple technique for the measurement of the globularity of protein structures without the calculation of molecular surfaces. The globularity property is understood in this context as the ability of the molecule to fill a minimum volume enclosing ellipsoid (MVEE) that approximates its assumed globular shape. The more of the interior of this ellipsoid is occupied by the atoms of the protein, the better are its globularity metrics. These metrics are derived from the comparison of the volume of the voxelized representation of the atoms and the volume of all voxels that can fit inside that ellipsoid (a uniform unit Å cube lattice). The so-called ellipsoid profile shows how the globularity changes with the distance from the center. Two of its values, the so-called ellipsoid indexes, are used to classify the structure as globular, semi-globular or non-globular. Here, we enhance the workflow of the EP algorithm via an improved outlier detection subroutine based on principal component analysis. It is capable of robust distinguishing between the dense parts of the molecules and, for example, disordered chain fragments fully exposed to the solvent. The PCA-based method replaces the current approach based on kernel density estimation. The improved EP algorithm was tested on 2124 representatives of domain superfamilies from SCOP 2.08. The second part of this work is dedicated to the survey of globularity of 3594 representatives of biological assemblies from molecules currently deposited in the PDB and analyzed by the 3DComplex database (monomers and complexes up to 60 chains).

Possibilities of Using De Novo Design for Generating Diverse Functional Food Enzymes

Food enzymes have an important role in the improvement of certain food characteristics, such as texture improvement, elimination of toxins and allergens, production of carbohydrates, enhancing flavor/appearance characteristics. Recently, along with the development of artificial meats, food enzymes have been employed to achieve more diverse functions, especially in converting non-edible biomass to delicious foods. Reported food enzyme modifications for specific applications have highlighted the significance of enzyme engineering. However, using direct evolution or rational design showed inherent limitations due to the mutation rates, which made it difficult to satisfy the stability or specific activity needs for certain applications. Generating functional enzymes using de novo design, which highly assembles naturally existing enzymes, provides potential solutions for screening desired enzymes. Here, we describe the functions and applications of food enzymes to introduce the need for food enzymes engineering. To illustrate the possibilities of using de novo design for generating diverse functional proteins, we reviewed protein modelling and de novo design methods and their implementations. The future directions for adding structural data for de novo design model training, acquiring diversified training data, and investigating the relationship between enzyme-substrate binding and activity were highlighted as challenges to overcome for the de novo design of food enzymes.

Functional, pathogenic, and pharmacological roles of protein folding intermediates

Protein expression and function in eukaryotic cells are tightly harmonized processes modulated by the combination of different layers of regulation, including transcription, processing, stability, and translation of messenger RNA, as well as assembly, maturation, sorting, recycling, and degradation of polypeptides. Integrating all these pathways and the protein quality control machinery, deputed to avoid the production and accumulation of aberrantly folded proteins, determines protein homeostasis. Over the last decade, the combined development of accurate time-resolved experimental techniques and efficient computer simulations has opened the possibility of investigating biological mechanisms at atomic resolution with physics-based models. A meaningful example is the reconstruction of protein folding pathways at atomic resolution, which has enabled the characterization of the folding kinetics of biologically relevant globular proteins consisting of a few hundred amino acids. Combining these innovative computational technologies with rigorous experimental approaches reveals the existence of non-native metastable states transiently appearing along the folding process of such proteins. Here, we review the primary evidence indicating that these protein folding intermediates could play roles in disparate biological processes, from the posttranslational regulation of protein expression to disease-relevant protein misfolding mechanisms. Finally, we discuss how the information encoded into protein folding pathways could be exploited to design an entirely new generation of pharmacological agents capable of promoting the selective degradation of protein targets.

Engineering the kinetic stability of a β-trefoil protein by tuning its topological complexity

Kinetic stability, defined as the rate of protein unfolding, is central to determining the functional lifetime of proteins, both in nature and in wide-ranging medical and biotechnological applications. Further, high kinetic stability is generally correlated with high resistance against chemical and thermal denaturation, as well as proteolytic degradation. Despite its significance, specific mechanisms governing kinetic stability remain largely unknown, and few studies address the rational design of kinetic stability. Here, we describe a method for designing protein kinetic stability that uses protein long-range order, absolute contact order, and simulated free energy barriers of unfolding to quantitatively analyze and predict unfolding kinetics. We analyze two β-trefoil proteins: hisactophilin, a quasi-three-fold symmetric natural protein with moderate stability, and ThreeFoil, a designed three-fold symmetric protein with extremely high kinetic stability. The quantitative analysis identifies marked differences in long-range interactions across the protein hydrophobic cores that partially account for the differences in kinetic stability. Swapping the core interactions of ThreeFoil into hisactophilin increases kinetic stability with close agreement between predicted and experimentally measured unfolding rates. These results demonstrate the predictive power of readily applied measures of protein topology for altering kinetic stability and recommend core engineering as a tractable target for rationally designing kinetic stability that may be widely applicable.

Potential Self-Peptide Inhibitors of the SARS-CoV-2 Main Protease

The SARS-CoV-2 main protease (Mpro) plays an essential role in viral replication, cleaving viral polyproteins into functional proteins. This makes Mpro an important drug target. Mpro consists of an N-terminal catalytic domain and a C-terminal α-helical domain (MproC). Previous studies have shown that peptides derived from a given protein sequence (self-peptides) can affect the folding and, in turn, the function of that protein. Since the SARS-CoV-1 MproC is known to stabilize its Mpro and regulate its function, we hypothesized that SARS-CoV-2 MproC-derived self-peptides may modulate the folding and the function of SARS-CoV-2 Mpro. To test this, we studied the folding of MproC in the presence of various self-peptides using coarse-grained structure-based models and molecular dynamics simulations. In these simulations of MproC and one self-peptide, we found that two self-peptides, the α1-helix and the loop between α4 and α5 (loop4), could replace the equivalent native sequences in the MproC structure. Replacement of either sequence in full-length Mpro should, in principle, be able to perturb Mpro function albeit through different mechanisms. Some general principles for the rational design of self-peptide inhibitors emerge: The simulations show that prefolded self-peptides are more likely to replace native sequences than those which do not possess structure. Additionally, the α1-helix self-peptide is kinetically stable and once inserted rarely exchanges with the native α1-helix, while the loop4 self-peptide is easily replaced by the native loop4, making it less useful for modulating function. In summary, a prefolded α1-derived peptide should be able to inhibit SARS-CoV-2 Mpro function.

Diffusion in a two-dimensional energy landscape in the presence of dynamical correlations and validity of random walk model

Diffusion in a multidimensional energy surface with minima and barriers is a problem of importance in statistical mechanics and it also has wide applications, such as protein folding. To understand it in such a system, we carry out theory and simulations of a tagged particle moving on a two-dimensional periodic potential energy surface, both in the presence and absence of noise. Langevin dynamics simulations at multiple temperatures are carried out to obtain the diffusion coefficient of a solute particle. Friction is varied from zero to large values. Diffusive motion emerges in the limit of a long time, even in the absence of noise. Noise destroys the correlations and increases diffusion at small friction. Diffusion thus exhibits a nonmonotonic friction dependence at the intermediate value of the damping, ultimately converging to our theoretically predicted value. The latter is obtained using the well-established relationship between diffusion and random walk. An excellent agreement is obtained between theory and simulations in the high-friction limit but not so in the intermediate regime. We explain the deviation in the low- to intermediate-friction regime using the modified random walk theory. The rate of escape from one cell to another is obtained from the multidimensional rate theory of Langer. We find that enhanced dimensionality plays an important role. To quantify the effects of noise on the potential-imposed coherence on the trajectories, we calculate the Lyapunov exponent. At small friction values, the Lyapunov exponent mimics the friction dependence of the rate.

N-glycosylation induced changes in tau protein dynamics reveal its role in tau misfolding and aggregation: A microsecond long molecular dynamics study

Various posttranslational modifications like hyperphosphorylation, O-GlcNAcylation, and acetylation have been attributed to induce the abnormal folding in tau protein. Recent in vitro studies revealed the possible involvement of N-glycosylation of tau protein in the abnormal folding and tau aggregation. Hence, in this study, we performed a microsecond long all atom molecular dynamics simulation to gain insights into the effects of N-glycosylation on Asn-359 residue which forms part of the microtubule binding region. Trajectory analysis of the stimulations coupled with essential dynamics and free energy landscape analysis suggested that tau, in its N-glycosylated form tends to exist in a largely folded conformation having high beta sheet propensity as compared to unmodified tau which exists in a large extended form with very less beta sheet propensity. Residue interaction network analysis of the lowest energy conformations further revealed that Phe378 and Lys353 are the functionally important residues in the peptide which helped in initiating the folding process and Phe378, Lys347, and Lys370 helped to maintain the stability of the protein in the folded state.

Enhanced statistical sampling reveals microscopic complexity in the talin mechanosensor folding energy landscape

Statistical mechanics can describe the major conformational ensembles determining the equilibrium free-energy landscape of a folding protein. The challenge is to capture the full repertoire of low-occurrence conformations separated by high kinetic barriers that define complex landscapes. Computationally, enhanced sampling methods accelerate the exploration of molecular rare events. However, accessing the entire protein's conformational space in equilibrium experiments requires technological developments to enable extended observation times. We developed single-molecule magnetic tweezers to capture over a million individual transitions as a single talin protein unfolds and refolds under force in equilibrium. When observed at classically-probed timescales, talin folds in an apparently uncomplicated two-state manner. As the sampling time extends from minutes to days, the underlying energy landscape exhibits gradually larger signatures of complexity, involving a finite number of well-defined rare conformations. A fluctuation analysis allows us to propose plausible structures of each low-probability conformational state. The physiological relevance of each distinct conformation can be connected to the binding of the cytoskeletal protein vinculin, suggesting an extra layer of complexity in talin-mediated mechanotransduction. More generally, our experiments directly test the fundamental notion that equilibrium dynamics depend on the observation timescale.

Virus Evolution on Fitness Landscapes

The landscape paradigm is revisited in the light of evolution in simple systems. A brief overview of different classes of fitness landscapes is followed by a more detailed discussion of the RNA model, which is currently the only evolutionary model that allows for a comprehensive molecular analysis of a fitness landscape. Neutral networks of genotypes are indispensable for the success of evolution. Important insights into the evolutionary mechanism are gained by considering the topology of sequence and shape spaces. The dynamic concept of molecular quasispecies is viewed in the light of the landscape paradigm. The distribution of fitness values in state space is mirrored by the population structures of mutant distributions. Two classes of thresholds for replication error or mutations are important: (i) the-conventional-genotypic error threshold, which separates ordered replication from random drift on neutral networks, and (ii) a phenotypic error threshold above which the molecular phenotype is lost. Empirical landscapes are reviewed and finally, the implications of the landscape concept for virus evolution are discussed.

Optical tweezers for drug discovery

The time taken and the cost of producing novel therapeutic drugs presents a significant burden - a typical target-based drug discovery process involves computational screening of drug libraries, compound assays and expensive clinical trials. This review summarises the value of dynamic conformational information obtained by optical tweezers and how this information can target 'undruggable' proteins. Optical tweezers provide insights into the link between biological mechanisms and structural conformations, which can be used in drug discovery. Developing workflows including software and sample preparation will improve throughput, enabling adoption of optical tweezers in biopharma. As a complementary tool, optical tweezers increase the number of drug candidates, improve the understanding of a target's complex structural dynamics and elucidate interactions between compounds and their targets.

Illuminating the "Twilight Zone": Advances in Difficult Protein Modeling

Homology modeling was long considered a method of choice in tertiary protein structure prediction. However, it used to provide models of acceptable quality only when templates with appreciable sequence identity with a target could be found. The threshold value was long assumed to be around 20-30%. Below this level, obtained sequence identity was getting dangerously close to values that can be obtained by chance, after aligning any random, unrelated sequences. In these cases, other approaches, including ab initio folding simulations or fragment assembly, were usually employed. The most recent editions of the CASP and CAMEO community-wide modeling methods assessment have brought some surprising outcomes, proving that much more clues can be inferred from protein sequence analyses than previously thought. In this chapter, we focus on recent advances in the field of difficult protein modeling, pushing the threshold deep into the "twilight zone", with particular attention devoted to improvements in applications of machine learning and model evaluation.

Harnessing Pressure-Axis Experiments to Explore Volume Fluctuations, Conformational Substates, and Solvation of Biomolecular Systems

Intrinsic thermodynamic fluctuations within biomolecules are crucial for their function, and flexibility is one of the strategies that evolution has developed to adapt to extreme environments. In this regard, pressure perturbation is an important tool for mechanistically exploring the causes and effects of volume fluctuations in biomolecules and biomolecular assemblies, their role in biomolecular interactions and reactions, and how they are affected by the solvent properties. High hydrostatic pressure is also a key parameter in the context of deep-sea and subsurface biology and the study of the origin and physical limits of life. We discuss the role of pressure-axis experiments in revealing intrinsic structural fluctuations as well as high-energy conformational substates of proteins and other biomolecular systems that are important for their function and provide some illustrative examples. We show that the structural and dynamic information obtained from such pressure-axis studies improves our understanding of biomolecular function, disease, biological evolution, and adaptation.

Ensemble Generation for Linear and Cyclic Peptides Using a Reservoir Replica Exchange Molecular Dynamics Implementation in GROMACS

The profile of shapes presented by a cyclic peptide modulates its therapeutic efficacy and is represented by the ensemble of its sampled conformations. Although some algorithms excel at creating a diverse ensemble of cyclic peptide conformations, they seldom address the entropic contribution of flexible conformations and often have significant practical difficulty producing an ensemble with converged and reliable thermodynamic properties. In this study, an accelerated molecular dynamics (MD) method, namely, reservoir replica exchange MD (R-REMD or Res-REMD), was implemented in GROMACS ver. 4.6.7 and benchmarked on two small cyclic peptide model systems: a cyclized furin cleavage site of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) spike (cyclo-(CGPRRARSG)) and oxytocin (disulfide-bonded CYIQNCPLG). Additionally, we also benchmarked Res-REMD on alanine dipeptide and Trpzip2 to demonstrate its validity and efficiency over REMD. For Trpzip2, Res-REMD coupled with an umbrella-sampling-derived reservoir generated similar folded fractions as regular REMD but on a much faster time scale. For cyclic peptides, Res-REMD appeared to be marginally faster than REMD in ensemble generation. Finally, Res-REMD was more effective in sampling rare events such as trans to cis peptide bond isomerization. We provide a GitHub page with the modified GROMACS source code for running Res-REMD at https://github.com/PlotkinLab/Reservoir-REMD.

Chemical tools for study and modulation of biomolecular phase transitions

Biomolecular phase transitions play an important role in organizing cellular processes in space and time. Methods and tools for studying these transitions, and the intrinsically disordered proteins (IDPs) that often drive them, are typically less developed than tools for studying their folded protein counterparts. In this perspective, we assess the current landscape of chemical tools for studying IDPs, with a specific focus on protein liquid-liquid phase separation (LLPS). We highlight methodologies that enable imaging and spectroscopic studies of these systems, including site-specific labeling with small molecules and the diverse range of capabilities offered by inteins and protein semisynthesis. We discuss strategies for introducing post-translational modifications that are central to IDP and LLPS function and regulation. We also investigate the nascent field of noncovalent small-molecule modulators of LLPS. We hope that this review of the state-of-the-art in chemical tools for interrogating IDPs and LLPS, along with an associated perspective on areas of unmet need, can serve as a valuable and timely resource for these rapidly expanding fields of study.

Effects of External Perturbations on Protein Systems: A Microscopic View

Protein folding can be viewed as the origami engineering of biology resulting from the long process of evolution. Even decades after its recognition, research efforts worldwide focus on demystifying molecular factors that underlie protein structure-function relationships; this is particularly relevant in the era of proteopathic disease. A complex co-occurrence of different physicochemical factors such as temperature, pressure, solvent, cosolvent, macromolecular crowding, confinement, and mutations that represent realistic biological environments are known to modulate the folding process and protein stability in unique ways. In the current review, we have contextually summarized the substantial efforts in unveiling individual effects of these perturbative factors, with major attention toward bottom-up approaches. Moreover, we briefly present some of the biotechnological applications of the insights derived from these studies over various applications including pharmaceuticals, biofuels, cryopreservation, and novel materials. Finally, we conclude by summarizing the challenges in studying the combined effects of multifactorial perturbations in protein folding and refer to complementary advances in experiment and computational techniques that lend insights to the emergent challenges.

Knotting Optimization and Folding Pathways of a Go-Model with a Deep Knot

Formation of protein knots is an intriguing offshoot of the protein folding problem. Since experimental resolution on knot formation is limited, theoretical methods currently provide the most detailed insights into the knotting process. While suitable for shallow knots, molecular dynamics simulations have faced challenges capturing the formation of deep knots in proteins such as the minimally tied trefoil α/β methyltransferase from Thermotoga maritima (MTTTM). To improve the efficiency of MTTTM knotting in Cα Go-model simulations, mutant variants of the MTTTM Go-model were investigated. Through a structure-based analysis of knotted and unknotted states, four residues (K71, R72, E75, V76) were identified to increase the knotting efficiency from 2% to 83% when their contact energies were doubled and dihedral strength around the knot loop increased. The key features of this model are (i) a C-terminal slipknot intermediate that threads the knot in a highly unstructured intermediate, (ii) the inability to knot in native-like intermediate states, and (iii) a minor population in a long-lived trap that cannot knot. Examination of residue 71-76 contacts provides a small set of potential mutants that can directly test the model's validity. In addition, the knotting optimization process developed here has broad applicability in generating knotting-efficient models of other knotted proteins.

Evolutionary adaptation of the protein folding pathway for secretability

Secretory preproteins of the Sec pathway are targeted post-translationally and cross cellular membranes through translocases. During cytoplasmic transit, mature domains remain non-folded for translocase recognition/translocation. After translocation and signal peptide cleavage, mature domains fold to native states in the bacterial periplasm or traffic further. We sought the structural basis for delayed mature domain folding and how signal peptides regulate it. We compared how evolution diversified a periplasmic peptidyl-prolyl isomerase PpiA mature domain from its structural cytoplasmic PpiB twin. Global and local hydrogen-deuterium exchange mass spectrometry showed that PpiA is a slower folder. We defined at near-residue resolution hierarchical folding initiated by similar foldons in the twins, at different order and rates. PpiA folding is delayed by less hydrophobic native contacts, frustrated residues and a β-turn in the earliest foldon and by signal peptide-mediated disruption of foldon hierarchy. When selected PpiA residues and/or its signal peptide were grafted onto PpiB, they converted it into a slow folder with enhanced in vivo secretion. These structural adaptations in a secretory protein facilitate trafficking.

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.

Molecular Information Theory Meets Protein Folding

We propose an application of molecular information theory to analyze the folding of single domain proteins. We analyze results from various areas of protein science, such as sequence-based potentials, reduced amino acid alphabets, backbone configurational entropy, secondary structure content, residue burial layers, and mutational studies of protein stability changes. We found that the average information contained in the sequences of evolved proteins is very close to the average information needed to specify a fold ∼2.2 ± 0.3 bits/(site·operation). The effective alphabet size in evolved proteins equals the effective number of conformations of a residue in the compact unfolded state at around 5. We calculated an energy-to-information conversion efficiency upon folding of around 50%, lower than the theoretical limit of 70%, but much higher than human-built macroscopic machines. We propose a simple mapping between molecular information theory and energy landscape theory and explore the connections between sequence evolution, configurational entropy, and the energetics of protein folding.

Semantic parsing of the life process by quantum biology

A fact that an ever-increasingly number of research attention has focused on quantum biology demonstrates that it is, by no means, new to works in physic and mathematics, but to molecular biologists, geneticists, and biochemists. This is owing to that quantum biology serves as a distinctive discipline, by using quantum theory to study life sciences in combination with physics, mechanics, mathematics, statistics, and modern biology. Notably, quantum mechanics and its fundamental principles have been employed to clarify complex biological processes and molecular homeostasis within the organic life. Consequently, using the principles of quantum mechanics to study dynamic changes and energy transfer of molecules at the quantum level in biology has been accepted as an unusually distinguishable way to a better explanation of many phenomena in life. It is plausible that a clear conceptual quantum theoretical event is also considered to generally occur for short-term picoseconds or femtoseconds on microscopic nano- and subnanometer scales in biology and biosciences. For instance, photosynthesis, enzyme -catalyzed reactions, magnetic perception, the capture of smell and vision, DNA fragmentation, cellular breathing, mitochondrial processing, as well as brain thinking and consciousness, are all manifested within quantum superposition, quantum coherence, quantum entanglement, quantum tunneling, and other effects. In this mini-review, we describe the recent progress in quantum biology, with a promising direction for further insights into this field.

Precise Steric Features Control Aminoacyl-tRNA Accommodation on the Ribosome

Protein synthesis involves a complex series of large-scale conformational changes in the ribosome. While long-lived intermediate states of these processes can be characterized by experiments, computational methods can be used to identify the interactions that contribute to the rate-limiting free-energy barriers. To this end, we use a simplified energetic model to perform molecular dynamics (MD) simulations of aminoacyl-tRNA (aa-tRNA) accommodation on the ribosome. While numerous studies have probed the energetics of the early stages of accommodation, we focus on the final stage of accommodation, where the 3'-CCA tail of aa-tRNA enters the peptidyl transferase center (PTC). These simulations show how a distinct intermediate is induced by steric confinement of the tail, immediately before it completes accommodation. Multiple pathways for 3'-CCA tail accommodation can be quantitatively distinguished, where the tail enters the PTC by moving past a pocket enclosed by Helix 89, 90, and 92, or through an alternate route formed by Helix 93 and the P-site tRNA. C2573, located within Helix 90, is shown to provide the largest contribution to this late-accommodation steric barrier, such that sub-Å perturbations to this residue can alter the time scale of tail accommodation by nearly an order of magnitude. In terms of biological function, these calculations suggest how this late-stage sterically induced barrier may contribute to tRNA proofreading by the ribosome.

Role of Repeated Conformational Transitions in Substrate Binding of Adenylate Kinase

The catalytic cycle of the enzyme adenylate kinase involves large conformational motions between open and closed states. A previous single-molecule experiment showed that substrate binding tends to accelerate both the opening and the closing rates and that a single turnover event often involves multiple rounds of conformational switching. In this work, we showed that the repeated conformational transitions of adenylate kinase are essential for the relaxation of incorrectly bound substrates into the catalytically competent conformation by combining all-atom and coarse-grained molecular simulations. In addition, free energy calculations based on all-atom and coarse-grained models demonstrated that the enzyme with incorrectly bound substrates has much a lower free energy barrier for domain opening compared to that with the correct substrate conformation, which may explain the the acceleration of the domain opening rate by substrate binding. The results of this work provide mechanistic understanding to previous experimental observations and shed light onto the interplay between conformational dynamics and enzyme catalysis.

Dynamic effects of the spine of hydrated magnesium on viral RNA pseudoknot structure

In the cellular environment, a viral RNA Pseudoknot (PK) structure is responsive to its prevailing ion atmosphere created by a mixture of monovalent and divalent cations. We investigate the influence of such a mixed-salt environment on RNA-PK structure at an atomic resolution through three sets of 1.5 μs explicit solvent molecular dynamics (MD) simulations and also by building a dynamic counterion-condensation (DCC) model at varying divalent Mg²⁺ concentrations. The DCC model includes explicit interaction of the ligand and adjacent chelated Mg²⁺ by extending the recently developed generalized Manning condensation model. Its implementation within an all-atom structure-based molecular dynamics framework bolsters its opportunity to explore large-length scale and long-timescale phenomena associated with complex RNA systems immersed in its dynamic ion environment. In the present case of RNA-PK, both explicit MD and DCC simulations reveal a spine of hydrated-Mg²⁺ to induce stem-I and stem-II closure where the minor groove between these stems is akin to breathing. Mg²⁺ mediated minor-groove narrowing is coupled with local base-flipping dynamics of a base triple and quadruple, changing the stem structure of such RNA. Contrary to the conversational view of the indispensable need for Mg²⁺ for the tertiary structure of RNA, the study warns about the plausible detrimental effect of specific Mg²⁺-phosphate interactions on the RNA-PK structure beyond a certain concentration of Mg²⁺.

Bottom-up Coarse-Graining: Principles and Perspectives

Large-scale computational molecular models provide scientists a means to investigate the effect of microscopic details on emergent mesoscopic behavior. Elucidating the relationship between variations on the molecular scale and macroscopic observable properties facilitates an understanding of the molecular interactions driving the properties of real world materials and complex systems (e.g., those found in biology, chemistry, and materials science). As a result, discovering an explicit, systematic connection between microscopic nature and emergent mesoscopic behavior is a fundamental goal for this type of investigation. The molecular forces critical to driving the behavior of complex heterogeneous systems are often unclear. More problematically, simulations of representative model systems are often prohibitively expensive from both spatial and temporal perspectives, impeding straightforward investigations over possible hypotheses characterizing molecular behavior. While the reduction in resolution of a study, such as moving from an atomistic simulation to that of the resolution of large coarse-grained (CG) groups of atoms, can partially ameliorate the cost of individual simulations, the relationship between the proposed microscopic details and this intermediate resolution is nontrivial and presents new obstacles to study. Small portions of these complex systems can be realistically simulated. Alone, these smaller simulations likely do not provide insight into collectively emergent behavior. However, by proposing that the driving forces in both smaller and larger systems (containing many related copies of the smaller system) have an explicit connection, systematic bottom-up CG techniques can be used to transfer CG hypotheses discovered using a smaller scale system to a larger system of primary interest. The proposed connection between different CG systems is prescribed by (i) the CG representation (mapping) and (ii) the functional form and parameters used to represent the CG energetics, which approximate potentials of mean force (PMFs). As a result, the design of CG methods that facilitate a variety of physically relevant representations, approximations, and force fields is critical to moving the frontier of systematic CG forward. Crucially, the proposed connection between the system used for parametrization and the system of interest is orthogonal to the optimization used to approximate the potential of mean force present in all systematic CG methods. The empirical efficacy of machine learning techniques on a variety of tasks provides strong motivation to consider these approaches for approximating the PMF and analyzing these approximations.

The Statistical Trends of Protein Evolution: A Lesson from AlphaFold Database

The recent development of artificial intelligence provides us with new and powerful tools for studying the mysterious relationship between organism evolution and protein evolution. In this work, based on the AlphaFold Protein Structure Database (AlphaFold DB), we perform comparative analyses of the proteins of different organisms. The statistics of AlphaFold-predicted structures show that, for organisms with higher complexity, their constituent proteins will have larger radii of gyration, higher coil fractions, and slower vibrations, statistically. By conducting normal mode analysis and scaling analyses, we demonstrate that higher organismal complexity correlates with lower fractal dimensions in both the structure and dynamics of the constituent proteins, suggesting that higher functional specialization is associated with higher organismal complexity. We also uncover the topology and sequence bases of these correlations. As the organismal complexity increases, the residue contact networks of the constituent proteins will be more assortative, and these proteins will have a higher degree of hydrophilic-hydrophobic segregation in the sequences. Furthermore, by comparing the statistical structural proximity across the proteomes with the phylogenetic tree of homologous proteins, we show that, statistical structural proximity across the proteomes may indirectly reflect the phylogenetic proximity, indicating a statistical trend of protein evolution in parallel with organism evolution. This study provides new insights into how the diversity in the functionality of proteins increases and how the dimensionality of the manifold of protein dynamics reduces during evolution, contributing to the understanding of the origin and evolution of lives.

Self-Effected Allosteric Coupling and Cooperativity in Hypoxic Response Regulation with Disordered Proteins

Hypersensitive regulation of cellular hypoxic response relies on cooperative displacement of one disordered protein (HIF-1α) by another disordered protein (CITED2) from the target in a negative feedback loop. Considering the weak intramolecule coupling in disordered proteins, the molecular mechanism of high cooperativity in the molecular displacement event remains elusive. Herein, we show that disordered proteins utilize a "self-effected allostery" mechanism to achieve high binding cooperativity. Different from the conventional allostery mechanisms shown by many structured or disordered proteins, this mechanism utilizes one part of the disordered protein as the effector to trigger the allosteric coupling and enhance the binding of the remaining part of the same disordered protein, contributing to high cooperativity of the displacement event. The conserved charge motif of CITED2 is the key determinant of the molecular displacement event by serving as the effector of allosteric coupling. Such self-effected allostery provides an efficient strategy to achieve high cooperativity in the molecular events involving disordered proteins.