Esmael J. Haddadian

Loss of conformational entropy in protein folding calculated using realistic ensembles and its implications for NMR-based calculations

Significance Despite 40 years of study, no consensus has been achieved on the magnitude of the loss of backbone (BB) and side-chain (SC) entropies upon folding, even though these quantities are essential for characterizing the energetics of folding and conformational change. We calculate the loss using experimentally validated denatured and native state ensembles, avoiding the drastic assumptions used in many past analyses. By also accounting for correlated motions, we find that the loss of BB entropy is three- to fourfold larger than the SC contribution. Our values differ with some calculations by up to a factor of 3 and depend strongly on 2° structure. These results have implications upon other thermodynamic properties, the estimation of entropy using NMR methods, and coarse-grained simulations. The loss of conformational entropy is a major contribution in the thermodynamics of protein folding. However, accurate determination of the quantity has proven challenging. We calculate this loss using molecular dynamic simulations of both the native protein and a realistic denatured state ensemble. For ubiquitin, the total change in entropy is TΔSTotal = 1.4 kcal⋅mol−1 per residue at 300 K with only 20% from the loss of side-chain entropy. Our analysis exhibits mixed agreement with prior studies because of the use of more accurate ensembles and contributions from correlated motions. Buried side chains lose only a factor of 1.4 in the number of conformations available per rotamer upon folding (ΩU/ΩN). The entropy loss for helical and sheet residues differs due to the smaller motions of helical residues (TΔShelix−sheet = 0.5 kcal⋅mol−1), a property not fully reflected in the amide N-H and carbonyl C=O bond NMR order parameters. The results have implications for the thermodynamics of folding and binding, including estimates of solvent ordering and microscopic entropies obtained from NMR.

Automated Real-Space Refinement of Protein Structures Using a Realistic Backbone Move Set

Crystals of many important biological macromolecules diffract to limited resolution, rendering accurate model building and refinement difficult and time-consuming. We present a torsional optimization protocol that is applicable to many such situations and combines Protein Data Bank-based torsional optimization with real-space refinement against the electron density derived from crystallography or cryo-electron microscopy. Our method converts moderate- to low-resolution structures at initial (e.g., backbone trace only) or late stages of refinement to structures with increased numbers of hydrogen bonds, improved crystallographic R-factors, and superior backbone geometry. This automated method is applicable to DNA-binding and membrane proteins of any size and will aid studies of structural biology by improving model quality and saving considerable effort. The method can be extended to improve NMR and other structures. Our backbone score and its sequence profile provide an additional standard tool for evaluating structural quality.

Molecular Origins of Cofilin-Linked Changes in Actin Filament Mechanics

The actin regulatory protein cofilin plays a central role in actin assembly dynamics by severing filaments and increasing the concentration of ends from which subunits add and dissociate. Cofilin binding modifies the average structure and mechanical properties of actin filaments, thereby promoting fragmentation of partially decorated filaments at boundaries of bare and cofilin-decorated segments. Despite extensive evidence for cofilin-dependent changes in filament structure and mechanics, it is unclear how the two processes are linked at the molecular level. Here, we use molecular dynamics simulations and coarse-grained analyses to evaluate the molecular origins of the changes in filament compliance due to cofilin binding. Filament subunits with bound cofilin are less flat and maintain a significantly more open nucleotide cleft than bare filament subunits. Decorated filament segments are less twisted, thinner (considering only actin), and less connected than their bare counterparts, which lowers the filament bending persistence length and torsional stiffness. Using coarse-graining as an analysis method reveals that cofilin binding increases the average distance between the adjacent long-axis filament subunit, thereby weakening their interaction. In contrast, a fraction of lateral filament subunit contacts are closer and presumably stronger with cofilin binding. A cofilactin interface contact identified by cryo-electron microscopy is unstable during simulations carried out at 310K, suggesting that this particular interaction may be short lived at ambient temperatures. These results reveal the molecular origins of cofilin-dependent changes in actin filament mechanics that may promote filament severing.

A Novel Implicit Solvent Model for Simulating the Molecular Dynamics of RNA

Although molecular dynamics simulations can be accelerated by more than an order of magnitude by implicitly describing the influence of the solvent with a continuum model, most currently available implicit solvent simulations cannot robustly simulate the structure and dynamics of nucleic acids. The difficulties become exacerbated especially for RNAs, suggesting the presence of serious physical flaws in the prior continuum models for the influence of the solvent and counter ions on the nucleic acids. We present a novel, to our knowledge, implicit solvent model for simulating nucleic acids by combining the Langevin-Debye model and the Poisson-Boltzmann equation to provide a better estimate of the electrostatic screening of both the water and counter ions. Tests of the model involve comparisons of implicit and explicit solvent simulations for three RNA targets with 20, 29, and 75 nucleotides. The model provides reasonable agreement with explicit solvent simulations, and directions for future improvement are noted.

Comparative Study of the Collective Dynamics of Proteins and Inorganic Nanoparticles

Molecular dynamics simulations of ubiquitin in water/glycerol solutions are used to test the suggestion by Karplus and coworkers that proteins in their biologically active state should exhibit a dynamics similar to ‘surface-melted’ inorganic nanoparticles (NPs). Motivated by recent studies indicating that surface-melted inorganic NPs are in a ‘glassy’ state that is an intermediate dynamical state between a solid and liquid, we probe the validity and significance of this proposed analogy. In particular, atomistic simulations of ubiquitin in solution based on CHARMM36 force field and pre-melted Ni NPs (Voter-Chen Embedded Atom Method potential) indicate a common dynamic heterogeneity, along with other features of glass-forming (GF) liquids such as collective atomic motion in the form of string-like atomic displacements, potential energy fluctuations and particle displacements with long range correlations (‘colored’ or ‘pink’ noise), and particle displacement events having a power law scaling in magnitude, as found in earthquakes. On the other hand, we find the dynamics of ubiquitin to be even more like a polycrystalline material in which the α-helix and β-sheet regions of the protein are similar to crystal grains so that the string-like collective atomic motion is concentrated in regions between the α-helix and β-sheet domains.