Miguel A. Soler

Instantaneous normal modes, resonances, and decay channels in the vibrational relaxation of the amide I mode of N-methylacetamide-D in liquid deuterated water

A nonequilibrium molecular dynamics (MD) study of the vibrational relaxation of the amide I mode of deuterated N-methylacetamide (NMAD) in aqueous (D(2)O) solution is carried out using instantaneous normal modes (INMs). The identification of the INMs as they evolve over time, which is necessary to analyze the energy fluxes, is made by using a novel algorithm which allows us to assign unequivocally each INM to an individual equilibrium normal mode (ENM) or to a group of ENMs during the MD simulations. The time evolution of the energy stored in each INM is monitored and the occurrence of resonances during the relaxation process is then investigated. The decay of the amide I mode, initially excited with one vibrational quantum, is confirmed to fit well to a biexponential function, implying that the relaxation process involves at least two mechanisms with different rate constants. By freezing the internal motions of the solvent, it is shown that the intermolecular vibration-vibration channel to the bending modes of the solvent is closed. The INM analysis reveals then the existence of a major and faster decay channel, which corresponds to an intramolecular vibrational redistribution process and a minor, and slower, decay channel which involves the participation of the librational motions of the solvent. The faster relaxation pathway can be rationalized in turn using a sequential kinetic mechanism of the type P-->M+L-->L, where P (parent) is the initially excited amide I mode, and M (medium) and L (low) are specific midrange and lower-frequency NMAD vibrational modes, respectively.

Analysis of state-specific vibrations coupled to the unidirectional energy transfer in conjugated dendrimers.

The nonadiabatic excited-state molecular dynamics (NA-ESMD) method and excited-state instantaneous normal modes (ES-INMs) analyses have been applied to describe the state-specific vibrations that participate in the unidirectional energy transfer between the coupled chromophores in a branched dendrimeric molecule. Our molecule is composed of two-, three-, and four-ring linear poly(phenyleneethynylene) (PPE) units linked through meta-substitutions. After an initial laser excitation, an ultrafast sequential S(3) → S(2) → S(1) electronic energy transfer from the shortest to longest segment takes place. During each S(n) → S(n-1) (n = 3, 2) transition, ES-INM(S(n)) and ES-INM(S(n-1)) analyses have been performed on S(n) and S(n-1) states, respectively. Our results reveal a unique vibrational mode localized on the S(n) state that significantly matches with the corresponding nonadiabatic coupling vector d(n,(n-1)). This mode also corresponds to the highest frequency ES-INM(S(n)) and it is seen mainly during the electronic transitions. Furthermore, its absence as a unique ES-INM(S(n-1)) reveals that state-specific vibrations play the main role in the efficiency of the unidirectional S(n) → S(n-1) electronic and vibrational energy funneling in light-harvesting dendrimers.

Effects of Knots on Protein Folding Properties

This work explores the impact of knots, knot depth and motif of the threading terminus in protein folding properties (kinetics, thermodynamics and mechanism) via extensive Monte Carlo simulations of lattice models. A knotted backbone has no effect on protein thermodynamic stability but it may affect key aspects of folding kinetics. In this regard, we found clear evidence for a functional advantage of knots: knots enhance kinetic stability because a knotted protein unfolds at a distinctively slower rate than its unknotted counterpart. However, an increase in knot deepness does not necessarily lead to more effective changes in folding properties. In this regard, a terminus with a non-trivial conformation (e.g. hairpin) can have a more dramatic effect in enhancing kinetic stability than knot depth. Nevertheless, our results suggest that the probability of the denatured ensemble to keep knotted is higher for proteins with deeper knots, indicating that knot depth plays a role in determining the topology of the denatured state. Refolding simulations starting from denatured knotted conformations show that not every knot is able to nucleate folding and further indicate that the formation of the knotting loop is a key event in the folding of knotted trefoils. They also show that there are specific native contacts within the knotted core that are crucial to keep a native knotting loop in denatured conformations which otherwise have no detectable structure. The study of the knotting mechanism reveals that the threading of the knotting loop generally occurs towards late folding in conformations that exhibit a significant degree of structural consolidation.

Hybrid quantum/classical simulations of the vibrational relaxation of the amide I mode of N-methylacetamide in D2O solution.

Hybrid quantum/classical molecular dynamics (MD) is applied to simulate the vibrational relaxation (VR) of the amide I mode of deuterated N-methylacetamide (NMAD) in aqueous (D(2)O) solution. A novel version of the vibrational molecular dynamics with quantum transitions (MDQT) treatment is developed in which the amide I mode is treated quantum mechanically while the remaining degrees of freedom are treated classically. The instantaneous normal modes of the initially excited NMAD molecule (INM(0)) are used as internal coordinates since they provide a proper initial partition of the system in quantum and classical subsystems. The evolution in time of the energy stored in each individual normal mode is subsequently quantified using the hybrid quantum-classical instantaneous normal modes (INM(t)). The identities of both the INM(0)s and the INM(t)s are tracked using the equilibrium normal modes (ENMs) as templates. The results extracted from the hybrid MDQT simulations show that the quantum treatment of the amide I mode accelerates the whole VR process versus pure classical simulations and gives better agreement with experiments. The relaxation of the amide I mode is found to be essentially an intramolecular vibrational redistribution (IVR) process with little contribution from the solvent, in agreement with previous theoretical and experimental studies. Two well-defined relaxation mechanisms are identified. The faster one accounts for ≈40% of the total vibrational energy that flows through the NMAD molecule and involves the participation of the lowest frequency vibrations as short-life intermediate modes. The second and slower mechanism accounts for the remaining ≈60% of the energy released and is associated to the energy flow through specific mid-range and high-frequency modes.

Molecular Dynamics Simulations and Instantaneous Normal-Mode Analysis of the Vibrational Relaxation of the C-H Stretching Modes of N-methylacetamide-d in Liquid Deuterated Water

Nonequilibrium molecular dynamics (MD) simulations and instantaneous normal mode (INMs) analyses are used to study the vibrational relaxation of the C-H stretching modes (ν(s)(CH₃)) of deuterated N-methylacetamide (NMAD) in aqueous (D2O) solution. The INMs are identified unequivocally in terms of the equilibrium normal modes (ENMs), or groups of them, using a restricted version of the recently proposed Min-Cost assignment method. After excitation of the parent ν(s)(CH₃) modes with one vibrational quantum, the vibrational energy is shown to dissipate through both intramolecular vibrational redistribution (IVR) and intermolecular vibrational energy transfer (VET). The decay of the vibrational energy of the ν(s)(CH₃) modes is well fitted to a triple exponential function, with each characterizing a well-defined stage of the entire relaxation process. The first, and major, relaxation stage corresponds to a coherent ultrashort (τ(rel) = 0.07 ps) energy transfer from the parent ν(s)(CH₃) modes to the methyl bending modes δ(CH₃), so that the initially excited state rapidly evolves into a mixed stretch-bend state. In the second stage, characterized by a time of 0.92 ps, the vibrational energy flows through IVR to a number of mid-range-energy vibrations of the solute. In the third stage, the vibrational energy accumulated in the excited modes dissipates into the bath through an indirect VET process mediated by lower-energy modes, on a time scale of 10.6 ps. All the specific relaxation channels participating in the whole relaxation process are properly identified. The results from the simulations are finally compared with the recent experimental measurements of the ν(s)(CH₃) vibrational energy relaxation in NMAD/D₂O(l) reported by Dlott et al. (J. Phys. Chem. A 2009, 113, 75.) using ultrafast infrared-Raman spectroscopy.

How Difficult Is It to Fold a Knotted Protein? In Silico Insights from Surface-Tethered Folding Experiments

We explore the effect of surface tethering on the folding process of a lattice protein that contains a trefoil knot in its native structure via Monte Carlo simulations. We show that the outcome of the tethering experiment depends critically on which terminus is used to link the protein to a chemically inert plane. In particular, if surface tethering occurs at the bead that is closer to the knotted core the folding rate becomes exceedingly slow and the protein is not able to find the native structure in all the attempted folding trajectories. Such low folding efficiency is also apparent from the analysis of the probability of knot formation, pknot, as a function of nativeness. Indeed, pknot increases abruptly from ∼0 to ∼1 only when the protein has more than 80% of its native contacts formed, showing that a highly compact conformation must undergo substantial structural re-arrangement in order to get effectively knotted. When the protein is surface tethered by the bead that is placed more far away from the knotted core pknot is higher than in the other folding setups (including folding in the bulk), especially if conformations are highly native-like. These results show that the mobility of the terminus closest to the knotted core is critical for successful folding of trefoil proteins, which, in turn, highlights the importance of a knotting mechanism that is based on a threading movement of this terminus through a knotting loop. The results reported here predict that if this movement is blocked, knotting occurs via an alternative mechanism, the so-called spindle mechanism, which is prone to misfolding. Our simulations show that in the three considered folding setups the formation of the knot is typically a late event in the folding process. We discuss the implications of our findings for co-translational folding of knotted trefoils.

Distance-Based Configurational Entropy of Proteins from Molecular Dynamics Simulations

Estimation of configurational entropy from molecular dynamics trajectories is a difficult task which is often performed using quasi-harmonic or histogram analysis. An entirely different approach, proposed recently, estimates local density distribution around each conformational sample by measuring the distance from its nearest neighbors. In this work we show this theoretically well grounded the method can be easily applied to estimate the entropy from conformational sampling. We consider a set of systems that are representative of important biomolecular processes. In particular: reference entropies for amino acids in unfolded proteins are obtained from a database of residues not participating in secondary structure elements; the conformational entropy of folding of β2-microglobulin is computed from molecular dynamics simulations using reference entropies for the unfolded state; backbone conformational entropy is computed from molecular dynamics simulations of four different states of the EPAC protein and compared with order parameters (often used as a measure of entropy); the conformational and rototranslational entropy of binding is computed from simulations of 20 tripeptides bound to the peptide binding protein OppA and of β2-microglobulin bound to a citrate coated gold surface. This work shows the potential of the method in the most representative biological processes involving proteins, and provides a valuable alternative, principally in the shown cases, where other approaches are problematic.

Accurate Estimation of the Entropy of Rotation–Translation Probability Distributions

The estimation of rotational and translational entropies in the context of ligand binding has been the subject of long-time investigations. The high dimensionality (six) of the problem and the limited amount of sampling often prevent the required resolution to provide accurate estimates by the histogram method. Recently, the nearest-neighbor distance method has been applied to the problem, but the solutions provided either address rotation and translation separately, therefore lacking correlations, or use a heuristic approach. Here we address rotational-translational entropy estimation in the context of nearest-neighbor-based entropy estimation, solve the problem numerically, and provide an exact and an approximate method to estimate the full rotational-translational entropy.

Molecular dynamics simulations and docking enable to explore the biophysical factors controlling the yields of engineered nanobodies

Nanobodies (VHHs) have proved to be valuable substitutes of conventional antibodies for molecular recognition. Their small size represents a precious advantage for rational mutagenesis based on modelling. Here we address the problem of predicting how Camelidae nanobody sequences can tolerate mutations by developing a simulation protocol based on all-atom molecular dynamics and whole-molecule docking. The method was tested on two sets of nanobodies characterized experimentally for their biophysical features. One set contained point mutations introduced to humanize a wild type sequence, in the second the CDRs were swapped between single-domain frameworks with Camelidae and human hallmarks. The method resulted in accurate scoring approaches to predict experimental yields and enabled to identify the structural modifications induced by mutations. This work is a promising tool for the in silico development of single-domain antibodies and opens the opportunity to customize single functional domains of larger macromolecules.

Conformational Changes of Trialanine in Water Induced by Vibrational Relaxation of the Amide I Mode

Most of the protein-based diseases are caused by anomalies in the functionality and stability of these molecules. Experimental and theoretical studies of the conformational dynamics of proteins are becoming in this respect essential to understand the origin of these anomalies. However, a description of the conformational dynamics of proteins based on mechano-energetic principles still remains elusive because of the intrinsic high flexibility of the peptide chains, the participation of weak noncovalent interactions, and the role of the ubiquitous water solvent. In this work, the conformational dynamics of trialanine dissolved in water (D2O) is investigated through Molecular Dynamics (MD) simulations combined with instantaneous normal modes (INMs) analysis both at equilibrium and after the vibrational excitation of the C-terminal amide I mode. The conformational equilibrium between α and pPII conformers is found to be altered by the intramolecular relaxation of the amide I mode as a consequence of the different relaxation pathways of each conformer which modify the amount of vibrational energy stored in the torsional motions of the tripeptide, so the α → pPII and pPII → α conversion rates are increased differently. The selectivity of the process comes from the shifts of the vibrational frequencies with the conformational changes that modify the resonance conditions driving the intramolecular energy flows.