Augmenting Human Expertise in Weighted Ensemble Simulations through Deep Learning based Information Bottleneck.

The weighted ensemble (WE) method stands out as a widely used segment-based sampling technique renowned for its rigorous treatment of kinetics. The WE framework typically involves initially mapping the configuration space onto a low-dimensional collective variable (CV) space and then partitioning it into bins. The efficacy of WE simulations heavily depends on the selection of CVs and binning schemes. The recently proposed State Predictive Information Bottleneck (SPIB) method has emerged as a promising tool for automatically constructing CVs from data and guiding enhanced sampling through an iterative manner. In this work, we advance this data-driven pipeline by incorporating prior expert knowledge. Our hybrid approach combines SPIB-learned CVs to enhance sampling in explored regions with expert-based CVs to guide exploration in regions of interest, synergizing the strengths of both methods. Through benchmarking on alanine dipeptide and chignoin systems, we demonstrate that our hybrid approach effectively guides WE simulations to sample states of interest, and reduces run-to-run variances. Moreover, our integration of the SPIB model also enhances the analysis and interpretation of WE simulation data by effectively identifying metastable states and pathways, and offering direct visualization of dynamics.

An Information Bottleneck Approach for Markov Model Construction.

Markov state models (MSMs) are valuable for studying dynamics of protein conformational changes via statistical analysis of molecular dynamics (MD) simulations. In MSMs, the complex configuration space is coarse-grained into conformational states, with the dynamics modeled by a series of Markovian transitions among these states at discrete lag times. Constructing the Markovian model at a specific lag time requires state defined without significant internal energy barriers, enabling internal dynamics relaxation within the lag time. This process coarse grains time and space, integrating out rapid motions within metastable states. This work introduces a continuous embedding approach for molecular conformations using the state predictive information bottleneck (SPIB), which unifies dimensionality reduction and state space partitioning via a continuous, machine learned basis set. Without explicit optimization of VAMP-based scores, SPIB demonstrates state-of-the-art performance in identifying slow dynamical processes and constructing predictive multi-resolution Markovian models. When applied to mini-proteins trajectories, SPIB showcases unique advantages compared to competing methods. It automatically 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. Furthermore, SPIB's ability to learn a low-dimensional continuous embedding of the underlying MSMs enhances the interpretation of dynamic pathways. Accordingly, we propose SPIB as an easy-to-implement methodology for end-to-end MSM construction.

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.

Calculating Protein-Ligand Residence Times Through State Predictive Information Bottleneck based Enhanced Sampling.

Understanding drug residence times in target proteins is key to improving drug efficacy and understanding target recognition in biochemistry. While drug residence time is just as important as binding affinity, atomic-level understanding of drug residence times through molecular dynamics (MD) simulations has been difficult primarily due to the extremely long timescales. Recent advances in rare event sampling have allowed us to reach these timescales, yet predicting protein-ligand residence times remains a significant challenge. Here we present a semi-automated protocol to calculate the ligand residence times across 12 orders of magnitudes of timescales. In our proposed framework, we integrate a deep learning-based method, the state predictive information bottleneck (SPIB), to learn an approximate reaction coordinate (RC) and use it to guide the enhanced sampling method metadynamics. We demonstrate the performance of our algorithm by applying it to six different protein-ligand complexes with available benchmark residence times, including the dissociation of the widely studied anti-cancer drug Imatinib (Gleevec) from both wild-type Abl kinase and drug-resistant mutants. We show how our protocol can recover quantitatively accurate residence times, potentially opening avenues for deeper insights into drug development possibilities and ligand recognition mechanisms.

From Latent Dynamics to Meaningful Representations.

While representation learning has been central to the rise of machine learning and artificial intelligence, a key problem remains in making the learned representations meaningful. For this, the typical approach is to regularize the learned representation through prior probability distributions. However, such priors are usually unavailable or are ad hoc. To deal with this, recent efforts have shifted toward leveraging the insights from physical principles to guide the learning process. In this spirit, we propose a purely dynamics-constrained representation learning framework. Instead of relying on predefined probabilities, we restrict the latent representation to follow overdamped Langevin dynamics with a learnable transition density─a prior driven by statistical mechanics. We show that this is a more natural constraint for representation learning in stochastic dynamical systems, with the crucial ability to uniquely identify the ground truth representation. We validate our framework for different systems including a real-world fluorescent DNA movie data set. We show that our algorithm can uniquely identify orthogonal, isometric, and meaningful latent representations.

AlphaFold2-RAVE: From Sequence to Boltzmann Ranking.

While AlphaFold2 is rapidly being adopted as a new standard in protein structure predictions, it is limited to single structures. This can be insufficient for the inherently dynamic world of biomolecules. In this Letter, we propose AlphaFold2-RAVE, an efficient protocol for obtaining Boltzmann-ranked ensembles from sequence. The method uses structural outputs from AlphaFold2 as initializations for artificial intelligence-augmented molecular dynamics. We release the method as an open-source code and demonstrate results on different proteins.

Accelerating All-Atom Simulations and Gaining Mechanistic Understanding of Biophysical Systems through State Predictive Information Bottleneck.

An effective implementation of enhanced sampling algorithms for molecular dynamics simulations requires a priori knowledge of the approximate reaction coordinate describing the relevant mechanisms in the system. In this work, we focus on the recently developed artificial intelligence-based State Predictive Information Bottleneck (SPIB) approach and demonstrate how SPIB can learn such a reaction coordinate as a deep neural network even from undersampled trajectories. We exemplify its usefulness by achieving more than 40 times acceleration in simulating two model biophysical systems through well-tempered metadynamics performed by biasing along the SPIB-learned reaction coordinate. These include left- to right-handed chirality transitions in a synthetic helical peptide (Aib)9 and permeation of a small benzoic acid molecule through a synthetic, symmetric phospholipid bilayer. In addition to significantly accelerating the dynamics and achieving back and forth movement between different metastable states, the SPIB-based reaction coordinate gives mechanistic insights into the processes driving these two important problems.

Influence of Long-Range Forces on the Transition States and Dynamics of NaCl Ion-Pair Dissociation in Water.

We study NaCl ion-pair dissociation in a dilute aqueous solution using computer simulations both for the full system with long-range Coulomb interactions and for a well-chosen reference system with short-range intermolecular interactions. Analyzing results using concepts from Local Molecular Field (LMF) theory and the recently proposed AI-based analysis tool "State predictive information bottleneck" (SPIB), we show that the system with short-range interactions can accurately reproduce the transition rate for the dissociation process, the dynamics for moving between the underlying metastable states, and the transition state ensemble. Contributions from long-range interactions can be largely neglected for these processes because long-range forces from the direct interionic Coulomb interactions are almost completely canceled (>90%) by those from solvent interactions over the length scale where the transition takes place. Thus, for this important monovalent ion-pair system, short-range forces alone are able to capture detailed consequences of the collective solvent motion, allowing the use of physically suggestive and computationally efficient short-range models for the dissociation event. We believe that the framework here should be applicable to disentangling mechanisms for more complex processes such as multivalent ion disassociation, where previous work has suggested that long-range contributions may be more important.

State predictive information bottleneck.

The ability to make sense of the massive amounts of high-dimensional data generated from molecular dynamics simulations is heavily dependent on the knowledge of a low-dimensional manifold (parameterized by a reaction coordinate or RC) that typically distinguishes between relevant metastable states, and which captures the relevant slow dynamics of interest. Methods based on machine learning and artificial intelligence have been proposed over the years to deal with learning such low-dimensional manifolds, but they are often criticized for a disconnect from more traditional and physically interpretable approaches. To deal with such concerns, in this work we propose a deep learning based state predictive information bottleneck approach to learn the RC from high-dimensional molecular simulation trajectories. We demonstrate analytically and numerically how the RC learnt in this approach is connected to the committor in chemical physics and can be used to accurately identify transition states. A crucial hyperparameter in this approach is the time delay or how far into the future the algorithm should make predictions about. Through careful comparisons for benchmark systems, we demonstrate that this hyperparameter choice gives useful control over how coarse-grained we want the metastable state classification of the system to be. We thus believe that this work represents a step forward in systematic application of deep learning based ideas to molecular simulations.

Critical slowing down and attractive manifold: A mechanism for dynamic robustness in the yeast cell-cycle process.

Biological processes that execute complex multiple functions, such as the cell cycle, must ensure the order of sequential events and maintain dynamic robustness against various fluctuations. Here, we examine the mechanisms and fundamental structure that achieve these properties in the cell cycle of the budding yeast Saccharomyces cerevisiae. We show that this process behaves like an excitable system containing three well-decoupled saddle-node bifurcations to execute DNA replication and mitosis events. The yeast cell-cycle regulatory network can be divided into three modules-the G1/S phase, early M phase, and late M phase-wherein both positive feedback loops in each module and interactions among modules play important roles. Specifically, when the cell-cycle process operates near the critical points of the saddle-node bifurcations, a critical slowing down effect takes place. Such interregnum then allows for an attractive manifold and sufficient duration for cell-cycle events, within which to assess the completion of DNA replication and mitosis, e.g., spindle assembly. Moreover, such arrangement ensures that any fluctuation in an early module or event will not transmit to a later module or event. Thus, our results suggest a possible dynamical mechanism of the cell-cycle process to ensure event order and dynamic robustness and give insight into the evolution of eukaryotic cell-cycle processes.

A polymorphism in the transcriptional regulatory region strongly influences ovine FSHR mRNA decay.

Follicle-stimulating hormone receptor (FSHR) is an important G protein-coupled receptor, which is required for steroidogenesis, follicular development and female infertility. Here, we report a novel polymorphism in the 3'-UTR that strongly influences ovine FSHR mRNA decay. The partial 3'-UTR sequence of Hu sheep FSHR gene was isolated and characterized, and a polymorphism (c.2327A>G) was identified. Luciferase assay and qRT-PCR showed that c.2327A>G polymorphism in the 3'-UTR exerts a strong regulatory role in FSHR transcription. This regulatory role is achieved by affecting FSHR mRNA decay. Furthermore, the c.2327A>G mutation in the 3'-UTR influences ARE (AU-rich element, a cis-acting element promoting mRNA decay)-mediated mRNA decay of Hu sheep FSHR gene. Together, our study identified a novel polymorphism and elucidated a new mechanism underlying transcriptional regulation of FSHR in mammals.