Darwinian evolution as a dynamical principle.

Darwinian evolution (DE)-biology's powerful process of adaptation-is remarkably different from other known dynamical processes. It is antithermodynamic, driving away from equilibrium; it has persisted for 3.5 billion years; and its target, fitness, can seem like "Just So" stories. For insights, we make a computational model. In the Darwinian Evolution Machine (DEM) model, resource-driven duplication and competition operate inside a cycle of search/compete/choose. We find the following: 1) DE requires multiorganism coexistence for its long-term persistence and ability to cross fitness valleys. 2) DE is driven by resource dynamics, like booms and busts, not just by mutational change. And, 3) fitness ratcheting requires a mechanistic separation between variation and selection steps, perhaps explaining biology's use of separate polymers, DNA and proteins.

Early path dominance as a principle for neurodevelopment.

We perform targeted attack, a systematic computational unlinking of the network, to analyze its effects on global communication across the brain network through its giant cluster. Across diffusion magnetic resonance images from individuals in the UK Biobank, Adolescent Brain Cognitive Development Study and Developing Human Connectome Project, we find that targeted attack procedures on increasing white matter tract lengths and densities are remarkably invariant to aging and disease. Time-reversing the attack computation suggests a mechanism for how brains develop, for which we derive an analytical equation using percolation theory. Based on a close match between theory and experiment, our results demonstrate that tracts are limited to emanate from regions already in the giant cluster and tracts that appear earliest in neurodevelopment are those that become the longest and densest.

MHC-Fine: Fine-tuned AlphaFold for precise MHC-peptide complex prediction.

The precise prediction of major histocompatibility complex (MHC)-peptide complex structures is pivotal for understanding cellular immune responses and advancing vaccine design. In this study, we enhanced AlphaFold's capabilities by fine-tuning it with a specialized dataset consisting of exclusively high-resolution class I MHC-peptide crystal structures. This tailored approach aimed to address the generalist nature of AlphaFold's original training, which, while broad-ranging, lacked the granularity necessary for the high-precision demands of class I MHC-peptide interaction prediction. A comparative analysis was conducted against the homology-modeling-based method Pandora as well as the AlphaFold multimer model. Our results demonstrate that our fine-tuned model outperforms others in terms of root-mean-square deviation (median value for Cα atoms for peptides is 0.66 Å) and also provides enhanced predicted local distance difference test scores, offering a more reliable assessment of the predicted structures. These advances have substantial implications for computational immunology, potentially accelerating the development of novel therapeutics and vaccines by providing a more precise computational lens through which to view MHC-peptide interactions.

Cryo-EM model validation recommendations based on outcomes of the 2019 EMDataResource challenge.

This paper describes outcomes of the 2019 Cryo-EM Model Challenge. The goals were to (1) assess the quality of models that can be produced from cryogenic electron microscopy (cryo-EM) maps using current modeling software, (2) evaluate reproducibility of modeling results from different software developers and users and (3) compare performance of current metrics used for model evaluation, particularly Fit-to-Map metrics, with focus on near-atomic resolution. Our findings demonstrate the relatively high accuracy and reproducibility of cryo-EM models derived by 13 participating teams from four benchmark maps, including three forming a resolution series (1.8 to 3.1 Å). The results permit specific recommendations to be made about validating near-atomic cryo-EM structures both in the context of individual experiments and structure data archives such as the Protein Data Bank. We recommend the adoption of multiple scoring parameters to provide full and objective annotation and assessment of the model, reflective of the observed cryo-EM map density.

Evolution of mechanical cooperativity among myosin II motors.

Myosin II is a biomolecular machine that is responsible for muscle contraction. Myosin II motors act cooperatively: during muscle contraction, multiple motors bind to a single actin filament and pull it against an external load, like people pulling on a rope in a tug-of-war. We model the dynamics of actomyosin filaments in order to study the evolution of motor-motor cooperativity. We find that filament backsliding-the distance an actin slides backward when a motor at the end of its cycle releases-is central to the speed and efficiency of muscle contraction. Our model predicts that this backsliding has been reduced through evolutionary adaptations to the motor's binding propensity, the strength of the motor's power stroke, and the force dependence of the motor's release from actin. These properties optimize the collective action of myosin II motors, which is not a simple sum of individual motor actions. The model also shows that these evolutionary variables can explain the speed-efficiency trade-off observed across different muscle tissues. This is an example of how evolution can tune the microscopic properties of individual proteins in order to optimize complex biological functions.

Metabolism modulates network synchrony in the aging brain.

Brain aging is associated with hypometabolism and global changes in functional connectivity. Using functional MRI (fMRI), we show that network synchrony, a collective property of brain activity, decreases with age. Applying quantitative methods from statistical physics, we provide a generative (Ising) model for these changes as a function of the average communication strength between brain regions. We find that older brains are closer to a critical point of this communication strength, in which even small changes in metabolism lead to abrupt changes in network synchrony. Finally, by experimentally modulating metabolic activity in younger adults, we show how metabolism alone-independent of other changes associated with aging-can provide a plausible candidate mechanism for marked reorganization of brain network topology.

MELD-Bracket Ranks Binding Affinities of Diverse Sets of Ligands.

Affinity ranking of structurally diverse small-molecule ligands is a challenging problem with important applications in structure-based drug discovery. Absolute binding free energy methods can model diverse ligands, but the high computational cost of the current methods limits application to data sets with few ligands. We recently developed MELD-Bracket, a Molecular Dynamics method for efficient affinity ranking of ligands [ JCTC 2022, 18 (1), 374-379]. It utilizes a Bayesian framework to guide sampling to relevant regions of phase space, and it couples this with a bracket-like competition on a pool of ligands. Here we find that 6-competitor MELD-Bracket can rank dozens of diverse ligands that have low structural similarity and different net charges. We benchmark it on four protein systems─PTB1B, Tyk2, BACE, and JAK3─having varied modes of interactions. We also validated 8-competitor and 12-competitor protocols. The MELD-Bracket protocols presented here may have the appropriate balance of accuracy and computational efficiency to be suitable for ranking diverse ligands from typical drug discovery campaigns.

Diet modulates brain network stability, a biomarker for brain aging, in young adults.

Epidemiological studies suggest that insulin resistance accelerates progression of age-based cognitive impairment, which neuroimaging has linked to brain glucose hypometabolism. As cellular inputs, ketones increase Gibbs free energy change for ATP by 27% compared to glucose. Here we test whether dietary changes are capable of modulating sustained functional communication between brain regions (network stability) by changing their predominant dietary fuel from glucose to ketones. We first established network stability as a biomarker for brain aging using two large-scale (n = 292, ages 20 to 85 y; n = 636, ages 18 to 88 y) 3 T functional MRI (fMRI) datasets. To determine whether diet can influence brain network stability, we additionally scanned 42 adults, age < 50 y, using ultrahigh-field (7 T) ultrafast (802 ms) fMRI optimized for single-participant-level detection sensitivity. One cohort was scanned under standard diet, overnight fasting, and ketogenic diet conditions. To isolate the impact of fuel type, an independent overnight fasted cohort was scanned before and after administration of a calorie-matched glucose and exogenous ketone ester (d-ß-hydroxybutyrate) bolus. Across the life span, brain network destabilization correlated with decreased brain activity and cognitive acuity. Effects emerged at 47 y, with the most rapid degeneration occurring at 60 y. Networks were destabilized by glucose and stabilized by ketones, irrespective of whether ketosis was achieved with a ketogenic diet or exogenous ketone ester. Together, our results suggest that brain network destabilization may reflect early signs of hypometabolism, associated with dementia. Dietary interventions resulting in ketone utilization increase available energy and thus may show potential in protecting the aging brain.

Mechanisms for achieving high speed and efficiency in biomolecular machines.

How does a biomolecular machine achieve high speed at high efficiency? We explore optimization principles using a simple two-state dynamical model. With this model, we establish physical principles-such as the optimal way to distribute free-energy changes and barriers across the machine cycle-and connect them to biological mechanisms. We find that a machine can achieve high speed without sacrificing efficiency by varying its conformational free energy to directly link the downhill, chemical energy to the uphill, mechanical work and by splitting a large work step into more numerous, smaller substeps. Experimental evidence suggests that these mechanisms are commonly used by biomolecular machines. This model is useful for exploring questions of evolution and optimization in molecular machines.

Proteostasis collapse is a driver of cell aging and death.

What molecular processes drive cell aging and death? Here, we model how proteostasis-i.e., the folding, chaperoning, and maintenance of protein function-collapses with age from slowed translation and cumulative oxidative damage. Irreparably damaged proteins accumulate with age, increasingly distracting the chaperones from folding the healthy proteins the cell needs. The tipping point to death occurs when replenishing good proteins no longer keeps up with depletion from misfolding, aggregation, and damage. The model agrees with experiments in the worm Caenorhabditis elegans that show the following: Life span shortens nonlinearly with increased temperature or added oxidant concentration, and life span increases in mutants having more chaperones or proteasomes. It predicts observed increases in cellular oxidative damage with age and provides a mechanism for the Gompertz-like rise in mortality observed in humans and other organisms. Overall, the model shows how the instability of proteins sets the rate at which damage accumulates with age and upends a cell's normal proteostasis balance.

BioMThermDB 1.0: Thermophysical Database of Proteins in Solutions.

We present here a freely available web-based database, called BioMThermDB 1.0, of thermophysical and dynamic properties of various proteins and their aqueous solutions. It contains the hydrodynamic radius, electrophoretic mobility, zeta potential, self-diffusion coefficient, solution viscosity, and cloud-point temperature, as well as the conditions for those determinations and details of the experimental method. It can facilitate the meta-analysis and visualization of data, can enable comparisons, and may be useful for comparing theoretical model predictions with experiments.

The Maximum Caliber Variational Principle for Nonequilibria.

Ever since Clausius in 1865 and Boltzmann in 1877, the concepts of entropy and of its maximization have been the foundations for predicting how material equilibria derive from microscopic properties. But, despite much work, there has been no equally satisfactory general variational principle for nonequilibrium situations. However, in 1980, a new avenue was opened by E.T. Jaynes and by Shore and Johnson. We review here maximum caliber, which is a maximum-entropy-like principle that can infer distributions of flows over pathways, given dynamical constraints. This approach is providing new insights, particularly into few-particle complex systems, such as gene circuits, protein conformational reaction coordinates, network traffic, bird flocking, cell motility, and neuronal firing.

Inferring a network from dynamical signals at its nodes.

We give an approximate solution to the difficult inverse problem of inferring the topology of an unknown network from given time-dependent signals at the nodes. For example, we measure signals from individual neurons in the brain, and infer how they are inter-connected. We use Maximum Caliber as an inference principle. The combinatorial challenge of high-dimensional data is handled using two different approximations to the pairwise couplings. We show two proofs of principle: in a nonlinear genetic toggle switch circuit, and in a toy neural network.

Proteostasis is adaptive: Balancing chaperone holdases against foldases.

Because a cell must adapt to different stresses and growth rates, its proteostasis system must too. How do cells detect and adjust proteome folding to different conditions? Here, we explore a biophysical cost-benefit principle, namely that the cell should keep its proteome as folded as possible at the minimum possible energy cost. This can be achieved by differential expression of chaperones-balancing foldases (which accelerate folding) against holdases (which act as parking spots). The model captures changes in the foldase-holdase ratio observed both within organisms during aging and across organisms of varying metabolic rates. This work describes a simple biophysical mechanism by which cellular proteostasis adapts to meet the needs of a changing growth environment.

Protein evolution speed depends on its stability and abundance and on chaperone concentrations.

Proteins evolve at different rates. What drives the speed of protein sequence changes? Two main factors are a protein's folding stability and aggregation propensity. By combining the hydrophobic-polar (HP) model with the Zwanzig-Szabo-Bagchi rate theory, we find that: (i) Adaptation is strongly accelerated by selection pressure, explaining the broad variation from days to thousands of years over which organisms adapt to new environments. (ii) The proteins that adapt fastest are those that are not very stably folded, because their fitness landscapes are steepest. And because heating destabilizes folded proteins, we predict that cells should adapt faster when put into warmer rather than cooler environments. (iii) Increasing protein abundance slows down evolution (the substitution rate of the sequence) because a typical protein is not perfectly fit, so increasing its number of copies reduces the cell's fitness. (iv) However, chaperones can mitigate this abundance effect and accelerate evolution (also called evolutionary capacitance) by effectively enhancing protein stability. This model explains key observations about protein evolution rates.

Modeling beta-sheet peptide-protein interactions: Rosetta FlexPepDock in CAPRI rounds 38-45.

Peptide-protein docking is challenging due to the considerable conformational freedom of the peptide. CAPRI rounds 38-45 included two peptide-protein interactions, both characterized by a peptide forming an additional beta strand of a beta sheet in the receptor. Using the Rosetta FlexPepDock peptide docking protocol we generated top-performing, high-accuracy models for targets 134 and 135, involving an interaction between a peptide derived from L-MAG with DLC8. In addition, we were able to generate the only medium-accuracy models for a particularly challenging target, T121. In contrast to the classical peptide-mediated interaction, in which receptor side chains contact both peptide backbone and side chains, beta-sheet complementation involves a major contribution to binding by hydrogen bonds between main chain atoms. To establish how binding affinity and specificity are established in this special class of peptide-protein interactions, we extracted PeptiDBeta, a benchmark of solved structures of different protein domains that are bound by peptides via beta-sheet complementation, and tested our protocol for global peptide-docking PIPER-FlexPepDock on this dataset. We find that the beta-strand part of the peptide is sufficient to generate approximate and even high resolution models of many interactions, but inclusion of adjacent motif residues often provides additional information necessary to achieve high resolution model quality.

Opposing Pressures of Speed and Efficiency Guide the Evolution of Molecular Machines.

Many biomolecular machines need to be both fast and efficient. How has evolution optimized these machines along the tradeoff between speed and efficiency? We explore this question using optimizable dynamical models along coordinates that are plausible evolutionary degrees of freedom. Data on 11 motors and ion pumps are consistent with the hypothesis that evolution seeks an optimal balance of speed and efficiency, where any further small increase in one of these quantities would come at great expense to the other. For FoF1-ATPases in different species, we also find apparent optimization of the number of subunits in the c-ring, which determines the number of protons pumped per ATP synthesized. Interestingly, these ATPases appear to more optimized for efficiency than for speed, which can be rationalized through their key role as energy transducers in biology. The present modeling shows how the dynamical performance properties of biomolecular motors and pumps may have evolved to suit their corresponding biological actions.

Sampling and refinement protocols for template-based macrocycle docking: 2018 D3R Grand Challenge 4.

We describe a new template-based method for docking flexible ligands such as macrocycles to proteins. It combines Monte-Carlo energy minimization on the manifold, a fast manifold search method, with BRIKARD for complex flexible ligand searching, and with the MELD accelerator of Replica-Exchange Molecular Dynamics simulations for atomistic degrees of freedom. Here we test the method in the Drug Design Data Resource blind Grand Challenge competition. This method was among the best performers in the competition, giving sub-angstrom prediction quality for the majority of the targets.

Foldamer hypothesis for the growth and sequence differentiation of prebiotic polymers.

It is not known how life originated. It is thought that prebiotic processes were able to synthesize short random polymers. However, then, how do short-chain molecules spontaneously grow longer? Also, how would random chains grow more informational and become autocatalytic (i.e., increasing their own concentrations)? We study the folding and binding of random sequences of hydrophobic ([Formula: see text]) and polar ([Formula: see text]) monomers in a computational model. We find that even short hydrophobic polar (HP) chains can collapse into relatively compact structures, exposing hydrophobic surfaces. In this way, they act as primitive versions of today's protein catalysts, elongating other such HP polymers as ribosomes would now do. Such foldamer catalysts are shown to form an autocatalytic set, through which short chains grow into longer chains that have particular sequences. An attractive feature of this model is that it does not overconverge to a single solution; it gives ensembles that could further evolve under selection. This mechanism describes how specific sequences and conformations could contribute to the chemistry-to-biology (CTB) transition.

Bacterial proteostasis balances energy and chaperone utilization efficiently.

Chaperones are protein complexes that help to fold and disaggregate a cell's proteins. It is not understood how four major chaperone systems of Escherichia coli work together in proteostasis: the recognition, sorting, folding, and disaggregating of the cell's many different proteins. Here, we model this machine. We combine extensive data on chaperoning, folding, and aggregation rates with expression levels of proteins and chaperones measured at different growth rates. We find that the proteostasis machine recognizes and sorts a client protein based on two biophysical properties of the client's misfolded state (M state): its stability and its kinetic accessibility from its unfolded state (U state). The machine is energy-efficient (the sickest proteins use the most ATP-expensive chaperones), comprehensive (it can handle any type of protein), and economical (the chaperone concentrations are just high enough to keep the whole proteome folded and disaggregated but no higher). The cell needs higher chaperone levels in two situations: fast growth (when protein production rates are high) and very slow growth (to mitigate the effects of protein degradation). This type of model complements experimental knowledge by showing how the various chaperones work together to achieve the broad folding and disaggregation needs of the cell.