Driving and characterizing nucleation of urea and glycine polymorphs in water.

Crystal nucleation is relevant across the domains of fundamental and applied sciences. However, in many cases, its mechanism remains unclear due to a lack of temporal or spatial resolution. To gain insights into the molecular details of nucleation, some form of molecular dynamics simulations is typically performed; these simulations, in turn, are limited by their ability to run long enough to sample the nucleation event thoroughly. To overcome the timescale limits in typical molecular dynamics simulations in a manner free of prior human bias, here, we employ the machine learning-augmented molecular dynamics framework "reweighted autoencoded variational Bayes for enhanced sampling (RAVE)." We study two molecular systems-urea and glycine-in explicit all-atom water, due to their enrichment in polymorphic structures and common utility in commercial applications. From our simulations, we observe multiple back-and-forth nucleation events of different polymorphs from homogeneous solution; from these trajectories, we calculate the relative ranking of finite-sized polymorph crystals embedded in solution, in terms of the free-energy difference between the finite-sized crystal polymorph and the original solution state. We further observe that the obtained reaction coordinates and transitions are highly nonclassical.

Dinucleotides as simple models of the base stacking-unstacking component of DNA 'breathing' mechanisms.

Regulatory protein access to the DNA duplex 'interior' depends on local DNA 'breathing' fluctuations, and the most fundamental of these are thermally-driven base stacking-unstacking interactions. The smallest DNA unit that can undergo such transitions is the dinucleotide, whose structural and dynamic properties are dominated by stacking, while the ion condensation, cooperative stacking and inter-base hydrogen-bonding present in duplex DNA are not involved. We use dApdA to study stacking-unstacking at the dinucleotide level because the fluctuations observed are likely to resemble those of larger DNA molecules, but in the absence of constraints introduced by cooperativity are likely to be more pronounced, and thus more accessible to measurement. We study these fluctuations with a combination of Molecular Dynamics simulations on the microsecond timescale and Markov State Model analyses, and validate our results by calculations of circular dichroism (CD) spectra, with results that agree well with the experimental spectra. Our analyses show that the CD spectrum of dApdA is defined by two distinct chiral conformations that correspond, respectively, to a Watson-Crick form and a hybrid form with one base in a Hoogsteen configuration. We find also that ionic structure and water orientation around dApdA play important roles in controlling its breathing fluctuations.

Kinetics analysis of ubiquitin local fluctuations with Markov state modeling of the LE4PD normal modes.

Local fluctuations are important for protein binding and molecular recognition because they provide conformational states that can be trapped through a selection mechanism of binding. Thus, an accurate characterization of local fluctuations may be important for modeling the kinetic mechanism that leads to the biological activity of a protein. In this paper, we study the fluctuation dynamics of the regulatory protein ubiquitin and propose a novel theoretical approach to model its fluctuations. A coarse-grained, diffusive, mode-dependent description of fluctuations is accomplished using the Langevin Equation for Protein Dynamics (LE4PD). This equation decomposes the dynamics of a protein, simulated by molecular dynamics, into dynamical pathways that explore mode-dependent free energy surfaces. We calculate the time scales of the slow, high-amplitude fluctuations by modeling the kinetics of barrier crossing in the two-dimensional free energy surfaces using Markov state modeling. We find that the LE4PD predicts slow fluctuations in three important binding regions in ubiquitin: the C-terminal tail, the Lys11 loop, and the 50 s loop. These results suggest that the LE4PD can provide useful information on the role of fluctuations in the process of molecular recognition regulating the biological activity of ubiquitin.

Thermodynamically Optimized Machine-Learned Reaction Coordinates for Hydrophobic Ligand Dissociation.

Ligand unbinding is mediated by its free energy change, which has intertwined contributions from both energy and entropy. It is important, but not easy, to quantify their individual contributions to the free energy profile. We model hydrophobic ligand unbinding for two systems, a methane particle and a C60 fullerene, both unbinding from hydrophobic pockets in all-atom water. Using a modified deep learning framework, we learn a thermodynamically optimized reaction coordinate to describe the hydrophobic ligand dissociation for both systems. Interpretation of these reaction coordinates reveals the roles of entropic and enthalpic forces as the ligand and pocket sizes change. In both cases, we observe that the free-energy barrier to unbinding is dominated by entropy considerations. Furthermore, the process of methane unbinding is driven by methane solvation, while fullerene unbinding is driven first by pocket wetting and then fullerene wetting. For both solutes, the direct importance of the distance from the binding pocket to the learned reaction coordinate is present, but low. Our framework and subsequent feature important analysis thus give useful thermodynamic insight into hydrophobic ligand dissociation problems that are otherwise difficult to glean.

Information Bottleneck Approach for Markov Model Construction.

Markov state models (MSMs) have proven valuable in studying the dynamics of protein conformational changes via statistical analysis of molecular dynamics simulations. In MSMs, the complex configuration space is coarse-grained into conformational states, with dynamics modeled by a series of Markovian transitions among these states at discrete lag times. Constructing the Markovian model at a specific lag time necessitates defining states that circumvent significant internal energy barriers, enabling internal dynamics relaxation within the lag time. This process effectively coarse-grains time and space, integrating out rapid motions within metastable states. Thus, MSMs possess a multiresolution nature, where the granularity of states can be adjusted according to the time-resolution, offering flexibility in capturing system dynamics. This work introduces a continuous embedding approach for molecular conformations using the state predictive information bottleneck (SPIB), a framework that unifies dimensionality reduction and state space partitioning via a continuous, machine learned basis set. Without explicit optimization of the VAMP-based scores, SPIB demonstrates state-of-the-art performance in identifying slow dynamical processes and constructing predictive multiresolution Markovian models. Through applications to well-validated mini-proteins, SPIB showcases unique advantages compared to competing methods. It autonomously and self-consistently adjusts the number of metastable states based on a specified minimal time resolution, eliminating the need for manual tuning. While maintaining efficacy in dynamical properties, SPIB excels in accurately distinguishing metastable states and capturing numerous well-populated macrostates. This contrasts with existing VAMP-based methods, which often emphasize slow dynamics at the expense of incorporating numerous sparsely populated states. Furthermore, SPIB's ability to learn a low-dimensional continuous embedding of the underlying MSMs enhances the interpretation of dynamic pathways. With these benefits, we propose SPIB as an easy-to-implement methodology for end-to-end MSM construction.

Quantifying Energetic and Entropic Pathways in Molecular Systems.

When examining dynamics occurring at nonzero temperatures, both energy and entropy must be taken into account to describe activated barrier crossing events. Furthermore, good reaction coordinates need to be constructed to describe different metastable states and the transition mechanisms between them. Here we use a physics-based machine learning method called state predictive information bottleneck (SPIB) to find nonlinear reaction coordinates for three systems of varying complexity. SPIB is able to correctly predict an entropic bottleneck for an analytical flat-energy double-well system and identify the entropy- and energy-dominated pathways for an analytical four-well system. Finally, for a simulation of benzoic acid permeation through a lipid bilayer, SPIB is able to discover the entropic and energetic barriers to the permeation process. Given these results, we thus establish that SPIB is a reasonable and robust method for finding the important entropy, energy, and enthalpy barriers in physical systems, which can then be used to enhance the understanding and sampling of different activated mechanisms.

Tyrosine hydroxylase-producing neurons in the human cerebral cortex do not colocalize with calcium-binding proteins or the serotonin 3A receptor.

Interneurons of the cerebral cortex play a significant role in cortical information processing and are of clinical interest due to their involvement in neurological disorders. In the human neocortex, three subsets of interneurons can be identified based on the production of the calcium-binding proteins parvalbumin, calretinin or calbindin. A subset of interneurons in the mouse cortex expresses the serotonin 3A receptor (5-HT3AR). Previous work in humans has also demonstrated the presence of a subgroup of cortical neurons that produces the catecholaminergic enzyme tyrosine hydroxylase (TH). Many TH-producing cells in the rat cortex coexpress calretinin and are adjacent to blood vessels. However, little is known about the phenotype of these TH interneurons in humans. Here we immunohistochemically examined the coexpression of TH with parvalbumin, calretinin, calbindin or 5-HT3AR in human Brodmann's areas 10 and 24, cortical regions with high densities of TH-containing neurons. Colocalization of TH with these calcium-binding proteins and with 5-HT3AR was not detected in either area. Cortical TH cells were rarely apposed to blood vessels, denoted by immunolabeling for the gliovascular marker aquaporin-4. Our results suggest that the TH-immunoreactive cells in the human cortex do not overlap with any known neurochemically-defined subsets of interneurons and provide further evidence of differences in the phenotype of these cells across species.