Multibody correlations in the hydrophobic solvation of glycine peptides

Quantitative description of a contractile macromolecular machine

Contractile injection systems (CISs) [type VI secretion system (T6SS), phage tails, and tailocins] use a contractile sheath-rigid tube machinery to breach cell walls and lipid membranes. The structures of the pre- and postcontraction states of several CISs are known, but the mechanism of contraction remains poorly understood. Combining structural information of the end states of the 12-megadalton R-type pyocin sheath-tube complex with thermodynamic and force spectroscopy analyses and an original modeling procedure, we describe the mechanism of pyocin contraction. We show that this nanomachine has an activation energy of 160 kilocalories/mole (kcal/mol), and it releases 2160 kcal/mol of heat and develops a force greater than 500 piconewtons. Our combined approach provides a quantitative and experimental description of the membrane penetration process by a CIS.

Affinity of small-molecule solutes to hydrophobic, hydrophilic, and chemically patterned interfaces in aqueous solution

Performance of membranes for water purification is highly influenced by the interactions of solvated species with membrane surfaces, including surface adsorption of solutes upon fouling. Current efforts toward fouling-resistant membranes often pursue surface hydrophilization, frequently motivated by macroscopic measures of hydrophilicity, because hydrophobicity is thought to increase solute-surface affinity. While this heuristic has driven diverse membrane functionalization strategies, here we build on advances in the theory of hydrophobicity to critically examine the relevance of macroscopic characterizations of solute-surface affinity. Specifically, we use molecular simulations to quantify the affinities to model hydroxyl- and methyl-functionalized surfaces of small, chemically diverse, charge-neutral solutes represented in produced water. We show that surface affinities correlate poorly with two conventional measures of solute hydrophobicity, gas-phase water solubility and oil-water partitioning. Moreover, we find that all solutes show attraction to the hydrophobic surface and most to the hydrophilic one, in contrast to macroscopically based hydrophobicity heuristics. We explain these results by decomposing affinities into direct solute interaction energies (which dominate on hydroxyl surfaces) and water restructuring penalties (which dominate on methyl surfaces). Finally, we use an inverse design algorithm to show how heterogeneous surfaces, with multiple functional groups, can be patterned to manipulate solute affinity and selectivity. These findings, importantly based on a range of solute and surface chemistries, illustrate that conventional macroscopic hydrophobicity metrics can fail to predict solute-surface affinity, and that molecular-scale surface chemical patterning significantly influences affinity-suggesting design opportunities for water purification membranes and other engineered interfaces involving aqueous solute-surface interactions.

Physical Chemistry of the Protein Backbone: Enabling the Mechanisms of Intrinsic Protein Disorder

Over the last two decades it has become clear that well-defined structure is not a requisite for proteins to properly function. Rather, spectra of functionally competent, structurally disordered states have been uncovered requiring canonical paradigms in molecular biology to be revisited or reimagined. It is enticing and oftentimes practical to divide the proteome into structured and unstructured, or disordered, proteins. While function, composition, and structural properties largely differ, these two classes of protein are built upon the same scaffold, namely, the protein backbone. The versatile physicochemical properties of the protein backbone must accommodate structural disorder, order, and transitions between these states. In this review, we survey these properties through the conceptual lenses of solubility and conformational populations and in the context of protein-disorder mediated phenomena (e.g., phase separation, order-disorder transitions, allostery). Particular attention is paid to the results of computational studies, which, through thermodynamic decomposition and dissection of molecular interactions, can provide valuable mechanistic insight and testable hypotheses to guide further solution experiments. Lastly, we discuss changes in the dynamics of side chains and order-disorder transitions of the protein backbone as two modes or realizations of "entropic reservoirs" capable of tuning coupled thermodynamic processes.

Orientational and Folding Thermodynamics via Electric Dipole Moment Restraining

The projection of molecular processes onto a small set of relevant descriptors, the so-called reaction coordinates or collective variables (CVs), is a technique nowadays routinely employed by the biomolecular simulation community. In this work, we implemented two CVs to manipulate the orientation (i.e., angle) (μ⃗_a) and magnitude (|μ⃗|) of the electric dipole moment. In doing so, we studied the thermodynamics of water orientation under the application of external voltages and the folding of two polypeptides at zero-field conditions. The projection of the free-energy [potential of mean force (PMF)] along water orientation defined an upper limit of around 0.3 V for irrelevant thermodynamic effects. On the other hand, sufficiently strong μ⃗_a restraints applied on 12-alanine (Ala₁₂) triggered structural effects because of the alignment of local dipoles; for lower restraints, a full-body rotation is achieved. The manipulation of |μ⃗| produced strong perturbations on the secondary structure of Ala₁₂, promoting an enhanced sampling to its configurational space. Rigorous free-energy calculations in the form of 2-D PMFs for deca-alanine showed the utility of |μ⃗| as a reaction coordinate to study folding in small α helices. As a whole, we propose that the manipulation of both components of the dipole moment, μ⃗_a and |μ⃗|, provides thermodynamics insights into the structural conformation and stability of biomolecules. These new CVs are implemented in the Colvars module, available for NAMD and LAMMPS.

Intramolecular Interactions Overcome Hydration to Drive the Collapse Transition of Gly15

Simulations and experiments show oligo-glycines, polypeptides lacking any side chains, can collapse in water. We assess the hydration thermodynamics of this collapse by calculating the hydration free energy at each of the end points of the reaction coordinate, here taken as the end-to-end distance (r) in the chain. To examine the role of the various conformations for a given r, we study the conditional distribution, P(R_g|r), of the radius of gyration for a given value of r. The free energy change versus R_g, -k_BT ln P(R_g|r), is found to vary more gently compared to the corresponding variation in the excess hydration free energy. Using this observation within a multistate generalization of the potential distribution theorem, we calculate a tight upper bound for the hydration free energy of the peptide for a given r. On this basis, we find that peptide hydration greatly favors the expanded state of the chain, despite primitive hydrophobic effects favoring chain collapse. The net free energy of collapse is seen to be a delicate balance between opposing intrapeptide and hydration effects, with intrapeptide contributions favoring collapse.

Solvation Thermodynamics of Oligoglycine with Respect to Chain Length and Flexibility

Oligoglycine is a backbone mimic for all proteins and is prevalent in the sequences of intrinsically disordered proteins. We have computed the absolute chemical potential of glycine oligomers at infinite dilution by simulation with the CHARMM36 and Amber ff12SB force fields. We performed a thermodynamic decomposition of the solvation free energy (ΔG(sol)) of Gly2-5 into enthalpic (ΔH(sol)) and entropic (ΔS(sol)) components as well as their van der Waals and electrostatic contributions. Gly2-5 was either constrained to a rigid/extended conformation or allowed to be completely flexible during simulations to assess the effects of flexibility on these thermodynamic quantities. For both rigid and flexible oligoglycine models, the decrease in ΔG(sol) with chain length is enthalpically driven with only weak entropic compensation. However, the apparent rates of decrease of ΔG(sol), ΔH(sol), ΔS(sol), and their elec and vdw components differ for the rigid and flexible models. Thus, we find solvation entropy does not drive aggregation for this system and may not explain the collapse of long oligoglycines. Additionally, both force fields yield very similar thermodynamic scaling relationships with respect to chain length despite both force fields generating different conformational ensembles of various oligoglycine chains.

Reconciling the understanding of 'hydrophobicity' with physics-based models of proteins

The idea that a 'hydrophobic energy' drives protein folding, aggregation, and binding by favoring the sequestration of bulky residues from water into the protein interior is widespread. The solvation free energies (ΔGsolv) of small nonpolar solutes increase with surface area (A), and the free energies of creating macroscopic cavities in water increase linearly with A. These observations seem to imply that there is a hydrophobic component (ΔGhyd) of ΔGsolv that increases linearly with A, and this assumption is widely used in implicit solvent models. However, some explicit-solvent molecular dynamics studies appear to contradict these ideas. For example, one definition (ΔG(LJ)) of ΔGhyd is that it is the free energy of turning on the Lennard-Jones (LJ) interactions between the solute and solvent. However, ΔG(LJ) decreases with A for alanine and glycine peptides. Here we argue that these apparent contradictions can be reconciled by defining ΔGhyd to be a near hard core insertion energy (ΔGrep), as in the partitioning proposed by Weeks, Chandler, and Andersen. However, recent results have shown that ΔGrep is not a simple function of geometric properties of the molecule, such as A and the molecular volume, and that the free energy of turning on the attractive part of the LJ potential cannot be computed from first-order perturbation theory for proteins. The theories that have been developed from these assumptions to predict ΔGhyd are therefore inadequate for proteins.

Importance of Hydrophilic Hydration and Intramolecular Interactions in the Thermodynamics of Helix-Coil Transition and Helix-Helix Assembly in a Deca-Alanine Peptide

For a model deca-alanine peptide the cavity (ideal hydrophobic) contribution to hydration favors the helix state over extended states and the paired helix bundle in the assembly of two helices. The energetic contributions of attractive protein-solvent interactions are separated into quasi-chemical components consisting of a short-range part arising from interactions with solvent in the first hydration shell and the remaining long-range part that is well described by a Gaussian. In the helix-coil transition, short-range attractive protein-solvent interactions outweigh hydrophobic hydration and favor the extended coil states. Analysis of enthalpic effects shows that it is the favorable hydration of the peptide backbone that favors the unfolded state. Protein intramolecular interactions favor the helix state and are decisive in favoring folding. In the pairing of two helices, the cavity contribution outweighs the short-range attractive protein-water interactions. However, long-range, protein-solvent attractive interactions can either enhance or reverse this trend depending on the mutual orientation of the helices. In helix-helix assembly, change in enthalpy arising from change in attractive protein-solvent interactions favors disassembly. In helix pairing as well, favorable protein intramolecular interactions are found to be as important as hydration effects. Overall, hydrophilic protein-solvent interactions and protein intramolecular interactions are found to play a significant role in the thermodynamics of folding and assembly in the system studied.

Examining the assumptions underlying continuum-solvent models

Continuum-solvent models (CSMs) have successfully predicted many quantities, including the solvation-free energies (ΔG) of small molecules, but they have not consistently succeeded at reproducing experimental binding free energies (ΔΔG), especially for protein-protein complexes. Several CSMs break ΔG into the free energy (ΔGvdw) of inserting an uncharged molecule into solution and the free energy (ΔGel) gained from charging. Some further divide ΔGvdw into the free energy (ΔGrep) of inserting a nearly hard cavity into solution and the free energy (ΔGatt) gained from turning on dispersive interactions between the solute and solvent. We show that for 9 protein-protein complexes neither ΔGrep nor ΔGvdw was linear in the solvent-accessible area A, as assumed in many CSMs, and the corresponding components of ΔΔG were not linear in changes in A. We show that linear response theory (LRT) yielded good estimates of ΔGatt and ΔΔGatt, but estimates of ΔΔGatt obtained from either the initial or final configurations of the solvent were not consistent with those from LRT. The LRT estimates of ΔGel differed by more than 100 kcal/mol from the explicit solvent model's (ESM's) predictions, and its estimates of the corresponding component (ΔΔGel) of ΔΔG differed by more than 10 kcal/mol. Finally, the Poisson-Boltzmann equation produced estimates of ΔGel that were correlated with those from the ESM, but its estimates of ΔΔGel were much less so. These findings may help explain why many CSMs have not been consistently successful at predicting ΔΔG for many complexes, including protein-protein complexes.

Force field-dependent solution properties of glycine oligomers

Molecular simulations can be used to study disordered polypeptide systems and to generate hypotheses on the underlying structural and thermodynamic mechanisms that govern their function. As the number of disordered protein systems investigated with simulations increase, it is important to understand how particular force fields affect the structural properties of disordered polypeptides in solution. To this end, we performed a comparative structural analysis of Gly(3) and Gly(10) in aqueous solution from all atom, microsecond molecular dynamics (MD) simulations using the CHARMM 27 (C27), CHARMM 36 (C36), and Amber ff12SB force fields. For each force field, Gly(3) and Gly(10) were simulated for at least 300 ns and 1 μs, respectively. Simulating oligoglycines of two different lengths allows us to evaluate how force field effects depend on polypeptide length. Using a variety of structural metrics (e.g., end-to-end distance, radius of gyration, dihedral angle distributions), we characterize the distribution of oligoglycine conformers for each force field and show that each sample conformation space differently, yielding considerably different structural tendencies of the same oligoglycine model in solution. Notably, we find that C36 samples more extended oligoglycine structures than both C27 and ff12SB.