Physics-Based Machine Learning Trains Hamiltonians and Decodes the Sequence-Conformation Relation in the Disordered Proteome.

Intrinsically disordered proteins and regions (IDPs) are involved in vital biological processes. To understand the IDP function, often controlled by conformation, we need to find the link between sequence and conformation. We decode this link by integrating theory, simulation, and machine learning (ML) where sequence-dependent electrostatics is modeled analytically while nonelectrostatic interaction is extracted from simulations for many sequences and subsequently trained using ML.

Beyond monopole electrostatics in regulating conformations of intrinsically disordered proteins.

Conformations and dynamics of an intrinsically disordered protein (IDP) depend on its composition of charged and uncharged amino acids, and their specific placement in the protein sequence. In general, the charge (positive or negative) on an amino acid residue in the protein is not a fixed quantity. Each of the ionizable groups can exist in an equilibrated distribution of fully ionized state (monopole) and an ion-pair (dipole) state formed between the ionizing group and its counterion from the background electrolyte solution.

Rules of selective condensation in cells.

Liquid droplets form in cells to concentrate specific biomolecules (while excluding others) in order to perform specific functions. The molecular mechanisms that determine whether different macromolecules undergo co-partitioning or exclusion has so far remained elusive. Now, two studies uncover key principles underlying this selectivity.

HYPK: A marginally disordered protein sensitive to charge decoration.

Intrinsically disordered proteins (IDPs) that lie close to the empirical boundary separating IDPs and folded proteins in Uversky's charge-hydropathy plot may behave as "marginal IDPs" and sensitively switch conformation upon changes in environment (temperature, crowding, and charge screening), sequence, or both. In our search for such a marginal IDP, we selected Huntingtin-interacting protein K (HYPK) near that boundary as a candidate; PKIα, also near that boundary, has lower secondary structure propensity; and Crk1, just across the boundary on the folded side, has higher secondary structure propensity. We used a qualitative Förster resonance energy transfer-based assay together with circular dichroism to simultaneously probe global and local conformation.

A cyclin-dependent kinase-mediated phosphorylation switch of disordered protein condensation.

Cell cycle transitions result from global changes in protein phosphorylation states triggered by cyclin-dependent kinases (CDKs). To understand how this complexity produces an ordered and rapid cellular reorganisation, we generated a high-resolution map of changing phosphosites throughout unperturbed early cell cycles in single Xenopus embryos, derived the emergent principles through systems biology analysis, and tested them by biophysical modelling and biochemical experiments. We found that most dynamic phosphosites share two key characteristics: they occur on highly disordered proteins that localise to membraneless organelles, and are CDK targets.

MaxCal can infer models from coupled stochastic trajectories of gene expression and cell division.

Gene expression is inherently noisy due to small numbers of proteins and nucleic acids inside a cell. Likewise, cell division is stochastic, particularly when tracking at the level of a single cell. The two can be coupled when gene expression affects the rate of cell division.

Critical Assessment of Self-Consistency Checks in the All-Atom Molecular Dynamics Simulation of Intrinsically Disordered Proteins.

All atom simulations can be used to quantify conformational properties of Intrinsically Disordered Proteins (IDP). However, simulations must satisfy convergence checks to ensure observables computed from simulation are reliable and reproducible. While absolute convergence is purely a theoretical concept requiring infinitely long simulation, a more practical, yet rigorous, approach is to impose Self Consistency Checks (SCCs) to gain confidence in the simulated data.

Intrachain interaction topology can identify functionally similar intrinsically disordered proteins.

Functionally similar IDPs (intrinsically disordered proteins) often have little sequence similarity. This is in stark contrast to folded proteins and poses a challenge for the inverse problem, functional classification of IDPs using sequence alignment. The problem is further compounded because of the lack of structure in IDPs, preventing structural alignment as an alternate tool for classification.

Critical Comparison of MaxCal and Other Stochastic Modeling Approaches in Analysis of Gene Networks.

Learning the underlying details of a gene network with feedback is critical in designing new synthetic circuits. Yet, quantitative characterization of these circuits remains limited. This is due to the fact that experiments can only measure partial information from which the details of the circuit must be inferred.

An analytical theory to describe sequence-specific inter-residue distance profiles for polyampholytes and intrinsically disordered proteins.

Intrinsically Disordered Proteins (IDPs), unlike folded proteins, lack a unique folded structure and rapidly interconvert among ensembles of disordered states. However, they have specific conformational properties when averaged over their ensembles of disordered states. It is critical to develop a theoretical formalism to predict these ensemble average conformational properties that are encoded in the IDP sequence (the specific order in which amino acids/residues are linked).

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.

A unified analytical theory of heteropolymers for sequence-specific phase behaviors of polyelectrolytes and polyampholytes.

The physical chemistry of liquid-liquid phase separation (LLPS) of polymer solutions bears directly on the assembly of biologically functional dropletlike bodies from proteins and nucleic acids. These biomolecular condensates include certain extracellular materials and intracellular compartments that are characterized as "membraneless organelles." Analytical theories are a valuable, computationally efficient tool for addressing general principles.

The Anti-Aggregation Holdase Hsp33 Promotes the Formation of Folded Protein Structures.

Holdase chaperones are known to be central to suppressing aggregation, but how they affect substrate conformations remains poorly understood. Here, we use optical tweezers to study how the holdase Hsp33 alters folding transitions within single maltose binding proteins and aggregation transitions between maltose binding protein substrates. Surprisingly, we find that Hsp33 not only suppresses aggregation but also guides the folding process.

Kinetic versus thermodynamic control of mutational effects on protein homeostasis: A perspective from computational modeling and experiment.

The effect of mutations in individual proteins on protein homeostasis, or "proteostasis," can in principle depend on the mutations' effects on the thermodynamics or kinetics of folding, or both. Here, we explore this issue using a computational model of in vivo protein folding that we call FoldEcoSlim. Our model predicts that kinetic versus thermodynamic control of mutational effects on proteostasis hinges on the relationship between how fast a protein's folding reaction reaches equilibrium and a critical time scale that characterizes the lifetime of a protein in its environment: for rapidly dividing bacteria, this time scale is that of cell division; for proteins that are produced in heterologous expression systems, this time scale is the amount of time before the protein is harvested; for proteins that are synthesized in and then exported from the eukaryotic endoplasmic reticulum, this time scale is that of protein secretion, and so forth.

Maximum Caliber Can Build and Infer Models of Oscillation in a Three-Gene Feedback Network.

Single-cell protein expression time trajectories provide rich temporal data quantifying cellular variability and its role in dictating fitness. However, theoretical models to analyze and fully extract information from these measurements remain limited for three reasons: (i) gene expression profiles are noisy, rendering models of averages inapplicable, (ii) experiments typically measure only a few protein species while leaving other molecular actors-necessary to build traditional bottom-up models-unnoticed, and (iii) measured data are in fluorescence, not particle number. We recently addressed these challenges in an alternate top-down approach using the principle of Maximum Caliber (MaxCal) to model genetic switches with one and two protein species.

Modulating charge patterning and ionic strength as a strategy to induce conformational changes in intrinsically disordered proteins.

We present an analytical theory to describe conformational changes as a function of salt for polymers with a given sequence of charges. We apply this model to describe Intrinsically Disordered Proteins (IDPs) by explicitly accounting for charged residues and their exact placement in the primary sequence while approximating the effect of non-electrostatic interactions at a mean-field level by effective short-range (two body and three-body) interaction parameters. The effect of ions is introduced by treating electrostatic interactions within Debye-Huckle approximation.

Ancient thioredoxins evolved to modern-day stability-function requirement by altering native state ensemble.

Thioredoxins (THRXs)-small globular proteins that reduce other proteins-are ubiquitous in all forms of life, from Archaea to mammals. Although ancestral thioredoxins share sequential and structural similarity with the modern-day (extant) homologues, they exhibit significantly different functional activity and stability. We investigate this puzzle by comparative studies of their (ancient and modern-day THRXs') native state ensemble, as quantified by the dynamic flexibility index (DFI), a metric for the relative resilience of an amino acid to perturbations in the rest of the protein.

Sequence charge decoration dictates coil-globule transition in intrinsically disordered proteins.

We present an analytical theory to compute conformations of heteropolymers-applicable to describe disordered proteins-as a function of temperature and charge sequence. The theory describes coil-globule transition for a given protein sequence when temperature is varied and has been benchmarked against the all-atom Monte Carlo simulation (using CAMPARI) of intrinsically disordered proteins (IDPs). In addition, the model quantitatively shows how subtle alterations of charge placement in the primary sequence-while maintaining the same charge composition-can lead to significant changes in conformation, even as drastic as a coil (swelled above a purely random coil) to globule (collapsed below a random coil) and vice versa.

Maximum Caliber Can Characterize Genetic Switches with Multiple Hidden Species.

Gene networks with feedback often involve interactions between multiple species of biomolecules, much more than experiments can actually monitor. Coupled with this is the challenge that experiments often measure gene expression in noisy fluorescence instead of protein numbers. How do we infer biophysical information and characterize the underlying circuits from this limited and convoluted data? We address this by building stochastic models using the principle of Maximum Caliber (MaxCal).

Perspective: Maximum caliber is a general variational principle for dynamical systems.

We review here Maximum Caliber (Max Cal), a general variational principle for inferring distributions of paths in dynamical processes and networks. Max Cal is to dynamical trajectories what the principle of maximum entropy is to equilibrium states or stationary populations. In Max Cal, you maximize a path entropy over all possible pathways, subject to dynamical constraints, in order to predict relative path weights.