The 3D reference interaction site model (3DRISM) provides an efficient grid-based solvation model to compute the structural and thermodynamic properties of biomolecules in aqueous solutions. However, it remains challenging for existing 3DRISM methods to correctly predict water distributions around negatively charged solute molecules. In this paper, we first show that this challenge is mainly due to the orientation of water molecules in the first solvation shell of the negatively charged solute molecules. To properly consider this orientational preference, position-dependent two-body intramolecular correlations of solvent need to be included in the 3DRISM theory, but direct evaluations of these position-dependent two-body intramolecular correlations remain numerically intractable. To address this challenge, we introduce the Ion-Dipole Correction (IDC) to the 3DRISM theory, in which we incorporate the orientation preference of water molecules via an additional solute–solvent interaction term (i.e., the ion-dipole interaction) while keeping the formulism of the 3DRISM equation unchanged. We prove that this newly introduced IDC term is equivalent to an effective direct correlation function which can effectively consider the orientation effect that arises from position dependent two-body correlations. We first quantitatively validate our 3DRISM-IDC theory combined with the PSE3 closure on Cl–, [ClO]− (a two-site anion), and [NO2]− (a three-site anion). For all three anions, we show that our 3DRISM-IDC theory significantly outperforms the 3DRISM theory in accurately predicting the solvation structures in comparison to MD simulations, including RDFs and 3D water distributions. Furthermore, we have also demonstrated that the 3DRISM-IDC can improve the accuracy of hydration free-energy calculation for Cl–. We further demonstrate that our 3DRISM-IDC theory yields significant improvements over the 3DRISM theory when applied to compute the solvation structures for various negatively charged solute molecules, including adenosine triphosphate (ATP), a short peptide containing 19 residues, a DNA hairpin containing 24 nucleotides, and a riboswitch RNA molecule with 77 nucleotides. We expect that our 3DRISM-IDC-PSE3 solvation model holds great promise to be widely applied to study solvation properties for nucleic acids and other biomolecules containing negatively charged functional groups.

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The generalized master equation (GME) provides a powerful approach to study biomolecular dynamics via non-Markovian dynamic models built from molecular dynamics (MD) simulations. Previously, we have implemented the GME for biomolecular dynamics, namely the quasi Markov State Model (qMSM), where we explicitly calculate the memory kernel and propagate protein dynamics using a discretized GME. qMSM can be constructed with much shorter MD simulation trajectories than the Markov State Model (MSM). However, since qMSM needs to explicitly compute the time-dependent memory kernels, it is heavily affected by the numerical fluctuations of simulation data when applied to study complicated conformational changes of biomolecules. This can lead to numerical instability of predicted long-time dynamics, greatly limiting the applicability of the qMSM in complicated molecules. In this paper, we propose a new theory, the Integrative GME (IGME), to overcome the challenges of the qMSM by using the time integrations of memory kernels. The IGME avoids the numerical instability induced by explicit computation of time-dependent memory kernel functions, giving more robust predictions of long-time dynamics. Using our analytical solution of the IGME, we propose a new approach to compute memory kernels and long-time dynamics in a numerically stable, accurate and efficient way. To demonstrate its effectiveness, we have applied the IGME in three biomolecules: the alanine dipeptide, the FIP35 WW domain, and Taq RNAP. In each system, the IGME achieves significantly smaller fluctuations for both memory kernels and long-time dynamics compared to the qMSM. We anticipate that the IGME can be widely applied to investigate complex conformational changes of biomolecules.

The generalized master equation (GME) provides a powerful approach to study biomolecular dynamics via non-Markovian dynamic models built from molecular dynamics (MD) simulations. Previously, we have implemented the GME for biomolecular dynamics, namely the quasi Markov State Model (qMSM), where we explicitly calculate the memory kernel and propagate protein dynamics using a discretized GME. qMSM can be constructed with much shorter MD simulation trajectories than the Markov State Model (MSM). However, since qMSM needs to explicitly compute the time-dependent memory kernels, it is heavily affected by the numerical fluctuations of simulation data when applied to study complicated conformational changes of biomolecules. This can lead to numerical instability of predicted long-time dynamics, greatly limiting the applicability of the qMSM in complicated molecules. In this paper, we propose a new theory, the Integrative GME (IGME), to overcome the challenges of the qMSM by using the time integrations of memory kernels. The IGME avoids the numerical instability induced by explicit computation of time-dependent memory kernel functions, giving more robust predictions of long-time dynamics. Using our analytical solution of the IGME, we propose a new approach to compute memory kernels and long-time dynamics in a numerically stable, accurate and efficient way. To demonstrate its effectiveness, we have applied the IGME in three biomolecules: the alanine dipeptide, the FIP35 WW domain, and Taq RNAP. In each system, the IGME achieves significantly smaller fluctuations for both memory kernels and long-time dynamics compared to the qMSM. We anticipate that the IGME can be widely applied to investigate complex conformational changes of biomolecules.

Conformational changes (i.e., dynamic transitions between pairs of conformational states) play important roles in many chemical and biological processes. Constructing the Markov state model (MSM) from extensive molecular dynamics (MD) simulations is an effective approach to dissect the mechanism of conformational changes. When combined with transition path theory (TPT), MSM can be applied to elucidate the ensemble of kinetic pathways connecting pairs of conformational states. However, the application of TPT to analyze complex conformational changes often results in a vast number of kinetic pathways with comparable fluxes. This obstacle is particularly pronounced in heterogeneous self-assembly and aggregation processes. The large number of kinetic pathways makes it challenging to comprehend the molecular mechanisms underlying conformational changes of interest. To address this challenge, we have developed a path classification algorithm named latent-space path clustering (LPC) that efficiently lumps parallel kinetic pathways into distinct metastable path channels, making them easier to comprehend. In our algorithm, MD conformations are first projected onto a low-dimensional space containing a small set of collective variables (CVs) by time-structure-based independent component analysis (tICA) with kinetic mapping. Then, MSM and TPT are constructed to obtain the ensemble of pathways, and a deep learning architecture named the variational autoencoder (VAE) is used to learn the spatial distributions of kinetic pathways in the continuous CV space. Based on the trained VAE model, the TPT-generated ensemble of kinetic pathways can be embedded into a latent space, where the classification becomes clear. We show that LPC can efficiently and accurately identify the metastable path channels in three systems: a 2D potential, the aggregation of two hydrophobic particles in water, and the folding of the Fip35 WW domain. Using the 2D potential, we further demonstrate that our LPC algorithm outperforms the previous path-lumping algorithms by making substantially fewer incorrect assignments of individual pathways to four path channels. We expect that LPC can be widely applied to identify the dominant kinetic pathways underlying complex conformational changes.