Origins of Life: The Protein Folding Problem all over again?

How did specific useful protein sequences arise from simpler molecules at the origin of life? This seemingly needle-in-a-haystack problem has remarkably close resemblance to the old Protein Folding Problem, for which the solution is now known from statistical physics. Based on the logic that Origins must have come only after there was an operative evolution mechanism-which selects on phenotype, not genotype-we give a perspective that proteins and their folding processes are likely to have been the primary driver of the early stages of the origin of life.

The prebiotic emergence of biological evolution.

The origin of life must have been preceded by Darwin-like evolutionary dynamics that could propagate it. How did that adaptive dynamics arise? And from what prebiotic molecules? Using evolutionary invasion analysis, we develop a universal framework for describing any origin story for evolutionary dynamics. We find that cooperative autocatalysts, i.e. autocatalysts whose per-unit reproductive rate grows as their population increases, have the special property of being able to cross a barrier that separates their initial degradation-dominated state from a growth-dominated state with evolutionary dynamics. For some model parameters, this leap to persistent propagation is likely, not rare. We apply this analysis to the Foldcat Mechanism, wherein peptides fold and help catalyse the elongation of each other. Foldcats are found to have cooperative autocatalysis and be capable of emergent evolutionary dynamics.

Transcriptional drift in aging cells: A global decontroller.

As cells age, they undergo a remarkable global change: In transcriptional drift, hundreds of genes become overexpressed while hundreds of others become underexpressed. Using archetype modeling and Gene Ontology analysis on data from aging Caenorhabditis elegans worms, we find that the up-regulated genes code for sensory proteins upstream of stress responses and down-regulated genes are growth- and metabolism-related. We observe similar trends within human fibroblasts, suggesting that this process is conserved in higher organisms. We propose a simple mechanistic model for how such global coordination of multiprotein expression levels may be achieved by the binding of a single factor that concentrates with age in C. elegans. A key implication is that a cell's own responses are part of its aging process, so unlike wear-and-tear processes, intervention might be able to modulate these effects.

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.

Antibody association in solution: cluster distributions and mechanisms.

Understanding factors that affect the clustering and association of antibodies molecules in solution is critical to their development as therapeutics. For 19 different monoclonal antibody (mAb) solutions, we measured the viscosities, the second virial coefficients, the Kirkwood-Buff integrals, and the cluster distributions of the antibody molecules as functions of protein concentration. Solutions were modeled using the statistical-physics Wertheim liquid-solution theory, representing antibodies as Y-shaped molecular structures of seven beads each. We found that high-viscosity solutions result from more antibody molecules per cluster. Multi-body properties such as viscosity are well predicted experimentally by the 2-body Kirkwood-Buff quantity, G22, but not by the second virial coefficient, B22, and well-predicted theoretically from the Wertheim protein-protein sticking energy. Weakly interacting antibodies are rate-limited by nucleation; strongly interacting ones by propagation. This approach gives a way to relate micro to macro properties of solutions of associating proteins.

Computational Procedure for Predicting Excipient Effects on Protein-Protein Affinities.

Protein-protein interactions lie at the center of many biological processes and are a challenge in formulating biological drugs, such as antibodies. A key to mitigating protein association is to use small-molecule additives, i.e., excipients that can weaken protein-protein interactions. Here, we develop a computationally efficient model for predicting the viscosity-reducing effect of different excipient molecules by combining atomic-resolution MD simulations, binding polynomials, and a thermodynamic perturbation theory. In a proof of principle, this method successfully ranks the order of four types of excipients known to reduce the viscosity of solutions of a particular monoclonal antibody. This approach appears useful for predicting the effects of excipients on protein association and phase separation, as well as the effects of buffers on protein solutions.

Functional transcriptional signatures for tumor-type-agnostic phenotype prediction.

Cancer transcriptional patterns exhibit both shared and unique features across diverse cancer types, but whether these patterns are sufficient to characterize the full breadth of tumor phenotype heterogeneity remains an open question. We hypothesized that cancer transcriptional diversity mirrors patterns in normal tissues optimized for distinct functional tasks. Starting with normal tissue transcriptomic profiles, we use non-negative matrix factorization to derive six distinct transcriptomic phenotypes, called archetypes, which combine to describe both normal tissue patterns and variations across a broad spectrum of malignancies. We show that differential enrichment of these signatures correlates with key tumor characteristics, including overall patient survival and drug sensitivity, independent of clinically actionable DNA alterations. Additionally, we show that in HR+/HER2-breast cancers, metastatic tumors adopt transcriptomic signatures consistent with the invaded tissue. Broadly, our findings suggest that cancer often arrogates normal tissue transcriptomic characteristics as a component of both malignant progression and drug response. This quantitative framework provides a strategy for connecting the diversity of cancer phenotypes and could potentially help manage individual patients.

Transcriptional drift in aging cells: A global de-controller.

As cells age, they undergo a remarkable global change: In transcriptional drift, hundreds of genes become overexpressed while hundreds of others become underexpressed. Using archetype modeling and Gene Ontology analysis on data from aging Caenorhabditis elegans worms, we find that the upregulated genes code for sensory proteins upstream of stress responses and downregulated genes are growth- and metabolism-related. We propose a simple mechanistic model for how such global coordination of multi-protein expression levels may be achieved by the binding of a single ligand that concentrates with age. A key implication is that a cell's own responses are part of its aging process, so unlike for wear-and-tear processes, intervention might be able to modulate these effects.

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 comprised by exclusively high-resolution 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 MHC-peptide interaction prediction. A comparative analysis was conducted against the homology-modeling-based method Pandora [13], as well as the AlphaFold multimer model [8]. Our results demonstrate that our fine-tuned model outperforms both in terms of RMSD (median value is 0.65 Å) but also provides enhanced predicted lDDT 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.

Protein Association in Solution: Statistical Mechanical Modeling.

Protein molecules associate in solution, often in clusters beyond pairwise, leading to liquid phase separations and high viscosities. It is often impractical to study these multi-protein systems by atomistic computer simulations, particularly in multi-component solvents. Instead, their forces and states can be studied by liquid state statistical mechanics. However, past such approaches, such as the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, were limited to modeling proteins as spheres, and contained no microscopic structure-property relations. Recently, this limitation has been partly overcome by bringing the powerful Wertheim theory of associating molecules to bear on protein association equilibria. Here, we review these developments.

Brain signaling becomes less integrated and more segregated with age.

The integration-segregation framework is a popular first step to understand brain dynamics because it simplifies brain dynamics into two states based on global vs. local signaling patterns. However, there is no consensus for how to best define what the two states look like. Here, we map integration and segregation to order and disorder states from the Ising model in physics to calculate state probabilities, Pint and Pseg, from functional MRI data. We find that integration/segregation decreases/increases with age across three databases, and changes are consistent with weakened connection strength among regions rather than topological connectivity based on structural and diffusion MRI data.

Computing Free Energies of Fold-Switching Proteins Using MELD x MD.

Some proteins are conformational switches, able to transition between relatively different conformations. To understand what drives them requires computing the free-energy difference ΔGAB between their stable states, A and B. Molecular dynamics (MD) simulations alone are often slow because they require a reaction coordinate and must sample many transitions in between. Here, we show that modeling employing limited data (MELD) x MD on known endstates A and B is accurate and efficient because it does not require passing over barriers or knowing reaction coordinates. We validate this method on two problems: (1) it gives correct relative populations of α and ß conformers for small designed chameleon sequences of protein G; and (2) it correctly predicts the conformations of the C-terminal domain (CTD) of RfaH. Free-energy methods like MELD x MD can often resolve structures that confuse machine-learning (ML) methods.

Simple Model of Liquid Water Dynamics.

We develop an analytical statistical-mechanical model to study the dynamic properties of liquid water. In this two-dimensional model, neighboring waters can interact through a hydrogen bond, a van der Waals contact, or an ice-like cage structure or have no interaction. We calculate the diffusion coefficient, viscosity, and thermal conductivity versus temperature and pressure. The trends follow those seen in the water experiments. The model explains that in warm water, heating drives faster diffusion but less interaction, so the viscosity and conductivity decrease. Cooling cold water causes poorer energy exchange because water's ice-like cages are big and immobile and collide infrequently. The main antagonism in water dynamics is not between vdW and H bonds, but it is an interplay between both those pair interactions, multibody cages, and no interaction. The value of this simple model is that it is analytical, so calculations are immediate, and it gives interpretations based on molecular physics.

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.

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.

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.

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.

Nonequilibrium statistical physics beyond the ideal heat bath approximation.

Important models of nonequilibrium statistical physics (NESP) are limited by a commonly used, but often unrecognized, near-equilibrium approximation. Fokker-Planck and Langevin equations, the Einstein and random-flight diffusion models, and the Schnakenberg model of biochemical networks suppose that fluctuations are due to an ideal equilibrium bath. But far from equilibrium, this perfect bath concept does not hold. A more principled approach should derive the rate fluctuations from an underlying dynamical model, rather than assuming a particular form. Here, using maximum caliber as the underlying principle, we derive corrections for NESP processes in an imperfect-but more realistic-environment, corrections which become particularly important for a system driven strongly away from equilibrium. Beyond characterizing a heat bath by the single equilibrium property of its temperature, the bath's speed and size must also be used to characterize the bath's ability to handle fast or large fluctuations.

A computational procedure for predicting excipient effects on protein-protein affinities.

Protein-protein interactions lie at the center of much biology and are a challenge in formulating biological drugs such as antibodies. A key to mitigating protein association is to use small molecule additives, i.e. excipients that can weaken protein-protein interactions. Here, we develop a computationally efficient model for predicting the viscosity-reducing effect of different excipient molecules by combining atomic-resolution MD simulations, binding polynomials and a thermodynamic perturbation theory. In a proof of principle, this method successfully rank orders four types of excipients known to reduce the viscosity of solutions of a particular monoclonal antibody. This approach appears useful for predicting effects of excipients on protein association and phase separation, as well as the effects of buffers on protein solutions.