Equilibrium transitions between side-chain conformations in leucine and isoleucine.

Despite recent improvements in computational methods for protein design, we still lack a quantitative, predictive understanding of the intrinsic probabilities for amino acids to adopt particular side-chain conformations. Surprisingly, this question has remained unsettled for many years, in part because of inconsistent results from different experimental approaches. To explicitly determine the relative populations of different side-chain dihedral angles, we performed all-atom hard-sphere Langevin Dynamics simulations of leucine (Leu) and isoleucine (Ile) dipeptide mimetics with stereo-chemical constraints and repulsive-only steric interactions between non-bonded atoms. We determine the relative populations of the different χ(1) and χ(2) dihedral angle combinations as a function of the backbone dihedral angles ϕ and ψ. We also propose, and test, a mechanism for inter-conversion between the different side-chain conformations. Specifically, we discover that some of the transitions between side-chain dihedral angle combinations are very frequent, whereas others are orders of magnitude less frequent, because they require rare coordinated motions to avoid steric clashes. For example, to transition between different values of χ(2), the Leu side-chain bond angles κ(1) and κ(2) must increase, whereas to transition in χ(1), the Ile bond angles λ(1) and λ(2) must increase. These results emphasize the importance of computational approaches in stimulating further experimental studies of the conformations of side-chains in proteins. Moreover, our studies emphasize the power of simple steric models to inform our understanding of protein structure, dynamics, and design.

Random close packing in protein cores.

Shortly after the determination of the first protein x-ray crystal structures, researchers analyzed their cores and reported packing fractions ϕ ≈ 0.75, a value that is similar to close packing of equal-sized spheres. A limitation of these analyses was the use of extended atom models, rather than the more physically accurate explicit hydrogen model. The validity of the explicit hydrogen model was proved in our previous studies by its ability to predict the side chain dihedral angle distributions observed in proteins. In contrast, the extended atom model is not able to recapitulate the side chain dihedral angle distributions, and gives rise to large atomic clashes at side chain dihedral angle combinations that are highly probable in protein crystal structures. Here, we employ the explicit hydrogen model to calculate the packing fraction of the cores of over 200 high-resolution protein structures. We find that these protein cores have ϕ ≈ 0.56, which is similar to results obtained from simulations of random packings of individual amino acids. This result provides a deeper understanding of the physical basis of protein structure that will enable predictions of the effects of amino acid mutations to protein cores and interfaces of known structure.

Calibrated Langevin-dynamics simulations of intrinsically disordered proteins.

We perform extensive coarse-grained (CG) Langevin dynamics simulations of intrinsically disordered proteins (IDPs), which possess fluctuating conformational statistics between that for excluded volume random walks and collapsed globules. Our CG model includes repulsive steric, attractive hydrophobic, and electrostatic interactions between residues and is calibrated to a large collection of single-molecule fluorescence resonance energy transfer data on the interresidue separations for 36 pairs of residues in five IDPs: α-, ß-, and γ-synuclein, the microtubule-associated protein τ, and prothymosin α. We find that our CG model is able to recapitulate the average interresidue separations regardless of the choice of the hydrophobicity scale, which shows that our calibrated model can robustly capture the conformational dynamics of IDPs. We then employ our model to study the scaling of the radius of gyration with chemical distance in 11 known IDPs. We identify a strong correlation between the distance to the dividing line between folded proteins and IDPs in the mean charge and hydrophobicity space and the scaling exponent of the radius of gyration with chemical distance along the protein.

Connection between the packing efficiency of binary hard spheres and the glass-forming ability of bulk metallic glasses.

We perform molecular dynamics simulations to compress binary hard spheres into jammed packings as a function of the compression rate R, size ratio α, and number fraction x(S) of small particles to determine the connection between the glass-forming ability (GFA) and packing efficiency in bulk metallic glasses (BMGs). We define the GFA by measuring the critical compression rate R(c), below which jammed hard-sphere packings begin to form "random crystal" structures with defects. We find that for systems with α≳0.8 that do not demix, R(c) decreases strongly with Δϕ(J), as R(c)∼exp(-1/Δϕ(J)(2)), where Δϕ(J) is the difference between the average packing fraction of the amorphous packings and random crystal structures at R(c). Systems with α≲0.8 partially demix, which promotes crystallization, but we still find a strong correlation between R(c) and Δϕ(J). We show that known metal-metal BMGs occur in the regions of the α and x(S) parameter space with the lowest values of R(c) for binary hard spheres. Our results emphasize that maximizing GFA in binary systems involves two competing effects: minimizing α to increase packing efficiency, while maximizing α to prevent demixing.

Molecular simulations of the fluctuating conformational dynamics of intrinsically disordered proteins.

Intrinsically disordered proteins (IDPs) do not possess well-defined three-dimensional structures in solution under physiological conditions. We develop all-atom, united-atom, and coarse-grained Langevin dynamics simulations for the IDP α-synuclein that include geometric, attractive hydrophobic, and screened electrostatic interactions and are calibrated to the inter-residue separations measured in recent single-molecule fluorescence energy transfer (smFRET) experiments. We find that α-synuclein is disordered, with conformational statistics that are intermediate between random walk and collapsed globule behavior. An advantage of calibrated molecular simulations over constraint methods is that physical forces act on all residues, not only on residue pairs that are monitored experimentally, and these simulations can be used to study oligomerization and aggregation of multiple α-synuclein proteins that may precede amyloid formation.