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.

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.

Avoidance of protein unfolding constrains protein stability in long-term evolution.

Every amino acid residue can influence a protein's overall stability, making stability highly susceptible to change throughout evolution. We consider the distribution of protein stabilities evolutionarily permittable under two previously reported protein fitness functions: flux dynamics and misfolding avoidance. We develop an evolutionary dynamics theory and find that it agrees better with an extensive protein stability data set for dihydrofolate reductase orthologs under the misfolding avoidance fitness function rather than the flux dynamics fitness function. Further investigation with ribonuclease H data demonstrates that not any misfolded state is avoided; rather, it is only the unfolded state. At the end, we discuss how our work pertains to the universal protein abundance-evolutionary rate correlation seen across organisms' proteomes. We derive a closed-form expression relating protein abundance to evolutionary rate that captures Escherichia coli, Saccharomyces cerevisiae, and Homo sapiens experimental trends without fitted parameters.

Effects of Single Mutations on Protein Stability Are Gaussian Distributed.

The distribution of protein stability effects is known to be well approximated by a Gaussian distribution from previous empirical fits. Starting from first-principles statistical mechanics, we more rigorously motivate this empirical observation by deriving per-residue-position protein stability effects to be Gaussian. Our derivation requires the number of amino acids to be large, which is satisfied by the standard set of 20 amino acids found in nature. No assumption is needed on the number of residues in close proximity in space, in contrast to previous applications of the central limit theorem to protein energetics. We support our derivation results with computational and experimental data on mutant protein stabilities across all types of protein residues.

Protein Melting Temperature Cannot Fully Assess Whether Protein Folding Free Energy Underlies the Universal Abundance-Evolutionary Rate Correlation Seen in Proteins.

The protein misfolding avoidance hypothesis explains the universal negative correlation between protein abundance and sequence evolutionary rate across the proteome by identifying protein folding free energy (ΔG) as the confounding variable. Abundant proteins resist toxic misfolding events by being more stable, and more stable proteins evolve slower because their mutations are more destabilizing. Direct supporting evidence consists only of computer simulations. A study taking advantage of a recent experimental breakthrough in measuring protein stability proteome-wide through melting temperature (Tm) (Leuenberger et al. 2017), found weak misfolding avoidance hypothesis support for the Escherichia coli proteome, and no support for the Saccharomyces cerevisiae, Homo sapiens, and Thermus thermophilus proteomes (Plata and Vitkup 2018). I find that the nontrivial relationship between Tm and ΔG and inaccuracy in Tm measurements by Leuenberger et al. 2017 can be responsible for not observing strong positive abundance-Tm and strong negative Tm-evolutionary rate correlations.

ProteomeVis: a web app for exploration of protein properties from structure to sequence evolution across organisms' proteomes.

Motivation: Protein evolution spans time scales and its effects span the length of an organism. A web app named ProteomeVis is developed to provide a comprehensive view of protein evolution in the Saccharomyces cerevisiae and Escherichia coli proteomes. ProteomeVis interactively creates protein chain graphs, where edges between nodes represent structure and sequence similarities within user-defined ranges, to study the long time scale effects of protein structure evolution. The short time scale effects of protein sequence evolution are studied by sequence evolutionary rate (ER) correlation analyses with protein properties that span from the molecular to the organismal level. Results: We demonstrate the utility and versatility of ProteomeVis by investigating the distribution of edges per node in organismal protein chain universe graphs (oPCUGs) and putative ER determinants. S.cerevisiae and E.coli oPCUGs are scale-free with scaling constants of 1.79 and 1.56, respectively. Both scaling constants can be explained by a previously reported theoretical model describing protein structure evolution. Protein abundance most strongly correlates with ER among properties in ProteomeVis, with Spearman correlations of -0.49 (P-value < 10-10) and -0.46 (P-value < 10-10) for S.cerevisiae and E.coli, respectively. This result is consistent with previous reports that found protein expression to be the most important ER determinant. Availability and implementation: ProteomeVis is freely accessible at http://proteomevis.chem.harvard.edu. Supplementary information: Supplementary data are available at Bioinformatics online.

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.

The Protein Folding Problem: The Role of Theory.

The protein folding problem was first articulated as question of how order arose from disorder in proteins: How did the various native structures of proteins arise from interatomic driving forces encoded within their amino acid sequences, and how did they fold so fast? These matters have now been largely resolved by theory and statistical mechanics combined with experiments. There are general principles. Chain randomness is overcome by solvation-based codes. And in the needle-in-a-haystack metaphor, native states are found efficiently because protein haystacks (conformational ensembles) are funnel-shaped. Order-disorder theory has now grown to encompass a large swath of protein physical science across biology.