Dynamics-Evolution Correspondence in Protein Structures

Developmental hourglass: Verification by numerical evolution and elucidation by dynamical-systems theory

Determining the general laws between evolution and development is a fundamental biological challenge. Developmental hourglasses have attracted increased attention as candidates for such laws, but the necessity of their emergence remains elusive. We conducted evolutionary simulations of developmental processes to confirm the emergence of the developmental hourglass and unveiled its establishment. We considered organisms consisting of cells containing identical gene networks that control morphogenesis and evolved them under selection pressure to induce more cell types. By computing the similarity between the spatial patterns of gene expression of two species that evolved from a common ancestor, a developmental hourglass was observed, that is, there was a correlation peak in the intermediate stage of development. The fraction of pleiotropic genes increased, whereas the variance in individuals decreased, consistent with previous experimental reports. Reduction of the unavoidable variance by initial or developmental noise, essential for survival, was achieved up to the hourglass bottleneck stage, followed by diversification in developmental processes, whose timing is controlled by the slow expression dynamics conserved among organisms sharing the hourglass. This study suggests why developmental hourglasses are observed within a certain phylogenetic range of species.

The Boltzmann distributions of molecular structures predict likely changes through random mutations

New folded molecular structures can only evolve after arising through mutations. This aspect is modeled using genotype-phenotype maps, which connect sequence changes through mutations to changes in molecular structures. Previous work has shown that the likelihood of appearing through mutations can differ by orders of magnitude from structure to structure and that this can affect the outcomes of evolutionary processes. Thus, we focus on the phenotypic mutation probabilities φqp, i.e., the likelihood that a random mutation changes structure p into structure q. For both RNA secondary structures and the HP protein model, we show that a simple biophysical principle can explain and predict how this likelihood depends on the new structure q: φqp is high if sequences that fold into p as the minimum-free-energy structure are likely to have q as an alternative structure with high Boltzmann frequency. This generalizes the existing concept of plastogenetic congruence from individual sequences to the entire neutral spaces of structures. Our result helps us understand why some structural changes are more likely than others, may be useful for estimating these likelihoods via sampling and makes a connection to alternative structures with high Boltzmann frequency, which could be relevant in evolutionary processes.

Canalisation and plasticity on the developmental manifold of Caenorhabditis elegans

How do the same mechanisms that faithfully regenerate complex developmental programmes in spite of environmental and genetic perturbations also allow responsiveness to environmental signals, adaptation and genetic evolution? Using the nematode Caenorhabditis elegans as a model, we explore the phenotypic space of growth and development in various genetic and environmental contexts. Our data are growth curves and developmental parameters obtained by automated microscopy. Using these, we show that among the traits that make up the developmental space, correlations within a particular context are predictive of correlations among different contexts. Furthermore, we find that the developmental variability of this animal can be captured on a relatively low-dimensional phenotypic manifold and that on this manifold, genetic and environmental contributions to plasticity can be deconvolved independently. Our perspective offers a new way of understanding the relationship between robustness and flexibility in complex systems, suggesting that projection and concentration of dimension can naturally align these forces as complementary rather than competing.

Dynamozones are the most obvious sign of the evolution of conformational dynamics in HIV-1 protease

Proteins are not static but are flexible molecules that can adopt many different conformations. The HIV-1 protease is an important target for the development of therapies to treat AIDS, due to its critical role in the viral life cycle. We investigated several dynamics studies on the HIV-1 protease families to illustrate the significance of examining the dynamic behaviors and molecular motions for an entire understanding of their dynamics-structure-function relationships. Using computer simulations and principal component analysis approaches, the dynamics data obtained revealed that: (i) The flap regions are the most obvious sign of the evolution of conformational dynamics in HIV-1 protease; (ii) There are dynamic structural regions in some proteins that contribute to the biological function and allostery of proteins via appropriate flexibility. These regions are a clear sign of the evolution of conformational dynamics of proteins, which we call dynamozones. The flap regions are one of the most important dynamozones members that are critical for HIV-1 protease function. Due to the existence of other members of dynamozones in different proteins, we propose to consider dynamozones as a footprint of the evolution of the conformational dynamics of proteins.

The quaternary question: Determining allostery in spastin through dynamics classification learning and bioinformatics

The nanomachine from the ATPases associated with various cellular activities superfamily, called spastin, severs microtubules during cellular processes. To characterize the functionally important allostery in spastin, we employed methods from evolutionary information, to graph-based networks, to machine learning applied to atomistic molecular dynamics simulations of spastin in its monomeric and the functional hexameric forms, in the presence or absence of ligands. Feature selection, using machine learning approaches, for transitions between spastin states recognizes all the regions that have been proposed as allosteric or functional in the literature. The analysis of the composition of the Markov State Model macrostates in the spastin monomer, and the analysis of the direction of change in the top machine learning features for the transitions, indicate that the monomer favors the binding of ATP, which primes the regions involved in the formation of the inter-protomer interfaces for binding to other protomer(s). Allosteric path analysis of graph networks, built based on the cross-correlations between residues in simulations, shows that perturbations to a hub specific for the pre-hydrolysis hexamer propagate throughout the structure by passing through two obligatory regions: the ATP binding pocket, and pore loop 3, which connects the substrate binding site to the ATP binding site. Our findings support a model where the changes in the terminal protomers due to the binding of ligands play an active role in the force generation in spastin. The secondary structures in spastin, which are found to be highly degenerative within the network paths, are also critical for feature transitions of the classification models, which can guide the design of allosteric effectors to enhance or block allosteric signaling.

Functional Protein Dynamics Directly from Sequences

The sequence correlations within a protein multiple sequence alignment are routinely being used to predict contacts within its structure, but here we point out that these data can also be used to predict a protein's dynamics directly. The elastic network protein dynamics models rely directly upon the contacts, and the normal modes of motion are obtained from the decomposition of the inverse of the contact map. To make the direct connection between sequence and dynamics, it is necessary to apply coarse-graining to the structure at the level of one point per amino acid, which has often been done, and protein coarse-grained dynamics from elastic network models has been highly successful, particularly in representing the large-scale motions of proteins that usually relate closely to their functions. The interesting implication of this is that it is not necessary to know the structure itself to obtain its dynamics and instead to use the sequence information directly to obtain the dynamics.

Building Quantitative Bridges between Dynamics and Sequences of SARS-CoV-2 Main Protease and a Diverse Set of Thirty-Two Proteins

Proteases are major drug targets for many viral diseases. However, mutations can render several antiprotease drugs inefficient rapidly even though these mutations may not alter protein structures significantly. Understanding relations between quickly mutating residues, protease structures, and the dynamics of the proteases is crucial for designing potent drugs. Due to this reason, we studied relations between the evolutionary information on residues in the amino acid sequences and protein dynamics for SARS-CoV-2 main protease. More precisely, we analyzed three dynamical quantities (Schlitter entropy, root-mean-square fluctuations, and dynamical flexibility index) and their relation to the amino acid conservation extracted from multiple sequence alignments of the main protease. We showed that a quantifiable similarity can be built between a sequence-based quantity called Jensen-Shannon conservation and those three dynamical quantities. We validated this similarity for a diverse set of 32 different proteins, other than the SARS-CoV-2 main protease. We believe that establishing these kinds of quantitative bridges will have larger implications for all viral proteases as well as all proteins.

Experimental evidence for the correlation between RNA structural fluctuations and the frequency of beneficial mutations

RNA has been used as a model molecule to understand the adaptive evolution process owing to the simple relationship between the structure (i.e., phenotype) and sequence (i.e., genotype). RNA usually forms multiple substructures with similar thermodynamic stabilities, called structural fluctuations. Ancel and Fontana theoretically proposed that structural fluctuation is directly related to the ease of change in structures by mutations and thus works as a source of adaptive evolution; however, experimental verification is limited. Here, we analyzed 76 RNA genotypes that appeared in our previous in vitro evolution to examine whether (i) RNA fluctuation decreases as adaptive evolution proceeds and (ii) RNAs that have larger fluctuations tend to have higher frequencies of beneficial mutations. We first computationally estimated the structural fluctuations of all RNAs and observed that they tended to decrease as their fitness increased. We next measured the frequency of beneficial mutations for 10 RNA genotypes and observed that the total number of beneficial mutations was correlated with the size of the structural fluctuations. These results consistently support the idea that the structural fluctuation of RNA, at least those evaluated in our study, works as a source of adaptive evolution.

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.

Optimising Elastic Network Models for Protein Dynamics and Allostery: Spatial and Modal Cut-offs and Backbone Stiffness

The family of coarse-grained models for protein dynamics known as Elastic Network Models (ENMs) require careful choice of parameters to represent well experimental measurements or fully-atomistic simulations. The most basic ENM that represents each protein residue by a node at the position of its C-alpha atom, all connected by springs of equal stiffness, up to a cut-off in distance. Even at this level a choice is required of the optimum cut-off distance and the upper limit of elastic normal modes taken in any sum for physical properties, such as dynamic correlation or allosteric effects on binding. Additionally, backbone-enhanced ENM (BENM) may improve the model by allocating a higher stiffness to springs that connect along the protein backbone. This work reports on the effect of varying these three parameters (distance and mode cutoffs, backbone stiffness) on the dynamical structure of three proteins, Catabolite Activator Protein (CAP), Glutathione S-transferase (GST), and the SARS-CoV-2 Main Protease (M pro ). Our main results are: (1) balancing B-factor and dispersion-relation predictions, a near-universal optimal value of 8.5 Å is advisable for ENMs; (2) inhomogeneity in elasticity brings the first mode containing spatial structure not well-resolved by the ENM typically within the first 20; (3) the BENM only affects modes in the upper third of the distribution, and, additionally to the ENM, is only able to model the dispersion curve better in this vicinity; (4) BENM does not typically affect fluctuation-allostery, which also requires careful treatment of the effector binding to the host protein to capture.

Insights of conformational dynamics on catalytic activity in the computational stability design of Bacillus subtilis LipA

In protein engineering, the contributions of individual mutations to designed combinatorial mutants are unpredictable. Screening designed mutations that affect enzyme catalytic activity enables evolutions towards efficient activities. Here, Bacillus subtilis LipA (BSLA) was selected as a model protein for thermostabilization designs, and the circular dichroism measurements showed six combinatorial designs with improved stability (from 5.81 °C to 13.61 °C). Based on molecular dynamic simulations, the conformational dynamics of the mutants revealed that mutations alter the populations of conformational states and the increased ensembles of inactive conformations might lead to a reduction in activity. We further demonstrated that the mutations responsible for the reduced enzyme catalytic activity involved a short dynamic correlation path to disturbing the equilibrium conformation of active sites. By removing N82V, which had a close dynamic correlation to the active sites in mutant D3, the redesigned mutant RD3 had an increased activity of 57.6%. By combining computational simulation with experimental verification, this work established that essential sites to counteract the activity-stability trade-off in multipoint combinatorial mutants could be computationally predicted and thus provide a possible strategy by which to indirectly or directly guide protein design.