An Information Bottleneck Approach for Markov Model Construction.

Markov state models (MSMs) have proven valuable in 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 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 multi-resolution 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 multi-resolution 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 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 MSMs 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.

Tutorial on how to build non-Markovian dynamic models from molecular dynamics simulations for studying protein conformational changes.

Protein conformational changes play crucial roles in their biological functions. In recent years, the Markov State Model (MSM) constructed from extensive Molecular Dynamics (MD) simulations has emerged as a powerful tool for modeling complex protein conformational changes. In MSMs, dynamics are modeled as a sequence of Markovian transitions among metastable conformational states at discrete time intervals (called lag time). A major challenge for MSMs is that the lag time must be long enough to allow transitions among states to become memoryless (or Markovian). However, this lag time is constrained by the length of individual MD simulations available to track these transitions. To address this challenge, we have recently developed Generalized Master Equation (GME)-based approaches, encoding non-Markovian dynamics using a time-dependent memory kernel. In this Tutorial, we introduce the theory behind two recently developed GME-based non-Markovian dynamic models: the quasi-Markov State Model (qMSM) and the Integrative Generalized Master Equation (IGME). We subsequently outline the procedures for constructing these models and provide a step-by-step tutorial on applying qMSM and IGME to study two peptide systems: alanine dipeptide and villin headpiece. This Tutorial is available at https://github.com/xuhuihuang/GME_tutorials. The protocols detailed in this Tutorial aim to be accessible for non-experts interested in studying the biomolecular dynamics using these non-Markovian dynamic models.

Building insightful, memory-enriched models to capture long-time biochemical processes from short-time simulations.

The ability to predict and understand complex molecular motions occurring over diverse timescales ranging from picoseconds to seconds and even hours in biological systems remains one of the largest challenges to chemical theory. Markov state models (MSMs), which provide a memoryless description of the transitions between different states of a biochemical system, have provided numerous important physically transparent insights into biological function. However, constructing these models often necessitates performing extremely long molecular simulations to converge the rates. Here, we show that by incorporating memory via the time-convolutionless generalized master equation (TCL-GME) one can build a theoretically transparent and physically intuitive memory-enriched model of biochemical processes with up to a three order of magnitude reduction in the simulation data required while also providing a higher temporal resolution. We derive the conditions under which the TCL-GME provides a more efficient means to capture slow dynamics than MSMs and rigorously prove when the two provide equally valid and efficient descriptions of the slow configurational dynamics. We further introduce a simple averaging procedure that enables our TCL-GME approach to quickly converge and accurately predict long-time dynamics even when parameterized with noisy reference data arising from short trajectories. We illustrate the advantages of the TCL-GME using alanine dipeptide, the human argonaute complex, and FiP35 WW domain.

RPnet: a reverse-projection-based neural network for coarse-graining metastable conformational states for protein dynamics.

The Markov State Model (MSM) is a powerful tool for modeling long timescale dynamics based on numerous short molecular dynamics (MD) simulation trajectories, which makes it a useful tool for elucidating the conformational changes of biological macromolecules. By partitioning the phase space into discretized states and estimating the probabilities of inter-state transitions based on short MD trajectories, one can construct a kinetic network model that could be used to extrapolate long-timescale kinetics if the Markovian condition is met. However, meeting the Markovian condition often requires hundreds or even thousands of states (microstates), which greatly hinders the comprehension of the conformational dynamics of complex biomolecules. Kinetic lumping algorithms can coarse grain numerous microstates into a handful of metastable states (macrostates), which would greatly facilitate the elucidation of biological mechanisms. In this work, we have developed a reverse-projection-based neural network (RPnet) to lump microstates into macrostates, by making use of a physics-based loss function that is based on the projection operator framework of conformational dynamics. By recognizing that microstate and macrostate transition modes can be related through a projection process, we have developed a reverse-projection scheme to directly compare the microstate and macrostate dynamics. Based on this reverse-projection scheme, we designed a loss function that allows the effective assessment of the quality of a given kinetic lumping. We then make use of a neural network to efficiently minimize this loss function to obtain an optimized set of macrostates. We have demonstrated the power of our RPnet in analyzing the dynamics of a numerical 2D potential, alanine dipeptide, and the clamp opening of an RNA polymerase. In all these systems, we have illustrated that our method could yield comparable or better results than competing methods in terms of state partitioning and reproduction of slow dynamics. We expect that our RPnet holds promise in analyzing the conformational dynamics of biological macromolecules.

NUDT15 genetic testing-guided 6-mercaptopurine dosing in children with ALL likely to be cost-saving in China.

OBJECTIVE: The cost-effectiveness of NUDT15 genetic testing-guided initial 6-mercaptopurine (6-MP) dosing in children with acute lymphoblastic leukemia (ALL) was evaluated. METHODS: A decision tree model was used to evaluate the cost to China's medical system per quality-adjusted life-year (QALY) gained and cost per case of severe leukopenia avoided of NUDT15 genetic testing using public clinical data. RESULTS: Genetic testing-guided initial 6-MP dosing reduced overall costs by $518.61, and prevented 0.221 cases of Grade III-IV leukopenia and increased QALY by 0.00136 per patient. Results were robust in one-way analyses and probabilistic sensitivity analyses. CONCLUSION: NUDT15 genetic testing prior to the initial administration of 6-MP in pediatric ALL patients in China is less expensive than standard dosing without genetic testing.

Critical role of backbone coordination in the mRNA recognition by RNA induced silencing complex.

Despite its functional importance, the molecular mechanism underlying target mRNA recognition by Argonaute (Ago) remains largely elusive. Based on extensive all-atom molecular dynamics simulations, we constructed quasi-Markov State Model (qMSM) to reveal the dynamics during recognition at position 6-7 in the seed region of human Argonaute 2 (hAgo2). Interestingly, we found that the slowest mode of motion therein is not the gRNA-target base-pairing, but the coordination of the target phosphate groups with a set of positively charged residues of hAgo2. Moreover, the ability of Helix-7 to approach the PIWI and MID domains was found to reduce the effective volume accessible to the target mRNA and therefore facilitate both the backbone coordination and base-pair formation. Further mutant simulations revealed that alanine mutation of the D358 residue on Helix-7 enhanced a trap state to slow down the loading of target mRNA. Similar trap state was also observed when wobble pairs were introduced in g6 and g7, indicating the role of Helix-7 in suppressing non-canonical base-paring. Our study pointed to a general mechanism for mRNA recognition by eukaryotic Agos and demonstrated the promise of qMSM in investigating complex conformational changes of biomolecular systems.

Markov State Models to Study the Functional Dynamics of Proteins in the Wake of Machine Learning.

Markov state models (MSMs) based on molecular dynamics (MD) simulations are routinely employed to study protein folding, however, their application to functional conformational changes of biomolecules is still limited. In the past few years, the field of computational chemistry has experienced a surge of advancements stemming from machine learning algorithms, and MSMs have not been left out. Unlike global processes, such as protein folding, the application of MSMs to functional conformational changes is challenging because they mostly consist of localized structural transitions. Therefore, it is critical to properly select a subset of structural features that can describe the slowest dynamics of these functional conformational changes. To address this challenge, we recommend several automatic feature selection methods such as Spectral-OASIS. To identify states in MSMs, the chosen features can be subject to dimensionality reduction methods such as TICA or deep learning based VAMPNets to project MD conformations onto a few collective variables for subsequent clustering. Another challenge for the application of MSMs to the study of functional conformational changes is the ability to comprehend their biophysical mechanisms, as MSMs built for these processes often require a large number of states. We recommend the recently developed quasi-MSMs (qMSMs) to address this issue. Compared to MSMs, qMSMs encode the non-Markovian dynamics via the generalized master equation and can significantly reduce the number of states. As a result, qMSMs can be built with a handful of states to facilitate the interpretation of functional conformational changes. In the wake of machine learning, we believe that the rapid advancement in the MSM methodology will lead to their wider application in studying functional conformational changes of biomolecules.

A comprehensive mechanism for 5-carboxylcytosine-induced transcriptional pausing revealed by Markov state models.

RNA polymerase II (Pol II) surveils the genome, pausing as it encounters DNA lesions and base modifications and initiating signals for DNA repair among other important regulatory events. Recent work suggests that Pol II pauses at 5-carboxycytosine (5caC), an epigenetic modification of cytosine, because of a specific hydrogen bond between the carboxyl group of 5caC and a specific residue in fork loop 3 of Pol II. This hydrogen bond compromises productive NTP binding and slows down elongation. Apart from this specific interaction, the carboxyl group of 5caC can potentially interact with numerous charged residues in the cleft of Pol II. However, it is not clear how other interactions between Pol II and 5caC contribute to pausing. In this study, we use Markov state models (a type of kinetic network models) built from extensive molecular dynamics simulations to comprehensively study the impact of 5caC on Pol II translocation. We describe two translocation intermediates with specific interactions that prevent the template base from loading into the Pol II active site. In addition to the previously observed state with 5caC constrained by fork loop 3, we discovered a new intermediate state with a hydrogen bond between 5caC and fork loop 2. Surprisingly, we find that 5caC may curb translocation by suppressing kinking of the helix bordering the active site (the bridge helix) because its high flexibility is critical to translocation. Our work provides new insights into how epigenetic modifications of genomic DNA can modulate Pol II translocation, inducing pauses in transcription.

Role of bacterial RNA polymerase gate opening dynamics in DNA loading and antibiotics inhibition elucidated by quasi-Markov State Model.

To initiate transcription, the holoenzyme (RNA polymerase [RNAP] in complex with σ factor) loads the promoter DNA via the flexible loading gate created by the clamp and ß-lobe, yet their roles in DNA loading have not been characterized. We used a quasi-Markov State Model (qMSM) built from extensive molecular dynamics simulations to elucidate the dynamics of Thermus aquaticus holoenzyme's gate opening. We showed that during gate opening, ß-lobe oscillates four orders of magnitude faster than the clamp, whose opening depends on the Switch 2's structure. Myxopyronin, an antibiotic that binds to Switch 2, was shown to undergo a conformational selection mechanism to inhibit clamp opening. Importantly, we reveal a critical but undiscovered role of ß-lobe, whose opening is sufficient for DNA loading even when the clamp is partially closed. These findings open the opportunity for the development of antibiotics targeting ß-lobe of RNAP. Finally, we have shown that our qMSMs, which encode non-Markovian dynamics based on the generalized master equation formalism, hold great potential to be widely applied to study biomolecular dynamics.

Elucidating molecular mechanisms of functional conformational changes of proteins via Markov state models.

Functional conformational changes of proteins can facilitate numerous biological events in cells. The Markov state model (MSM) built from molecular dynamics simulations provide a powerful approach to study them. We here introduce a protocol that is tailor-made for constructing MSMs to study the functional conformational changes of proteins. In this protocol, one of the important steps is to select proper molecular features that can collectively describe the slowest timescales of conformational changes of interest. We recommend spectral oASIS, the modified version of oASIS, as a promising approach for automatic feature selection. Recently developed deep learning methods could also serve efficient approaches for selecting features and finding collective variables. Using DNA repair enzymes and RNA polymerases as examples, we review recent applications of MSMs to elucidate molecular mechanisms of functional conformational changes. Finally, we discuss remaining challenges and future perspectives for constructing MSMs to study functional conformational changes of proteins.

Target search and recognition mechanisms of glycosylase AlkD revealed by scanning FRET-FCS and Markov state models.

DNA glycosylase is responsible for repairing DNA damage to maintain the genome stability and integrity. However, how glycosylase can efficiently and accurately recognize DNA lesions across the enormous DNA genome remains elusive. It has been hypothesized that glycosylase translocates along the DNA by alternating between a fast but low-accuracy diffusion mode and a slow but high-accuracy mode when searching for DNA lesions. However, the slow mode has not been successfully characterized due to the limitation in the spatial and temporal resolutions of current experimental techniques. Using a newly developed scanning fluorescence resonance energy transfer (FRET)-fluorescence correlation spectroscopy (FCS) platform, we were able to observe both slow and fast modes of glycosylase AlkD translocating on double-stranded DNA (dsDNA), reaching the temporal resolution of microsecond and spatial resolution of subnanometer. The underlying molecular mechanism of the slow mode was further elucidated by Markov state model built from extensive all-atom molecular dynamics simulations. We found that in the slow mode, AlkD follows an asymmetric diffusion pathway, i.e., rotation followed by translation. Furthermore, the essential role of Y27 in AlkD diffusion dynamics was identified both experimentally and computationally. Our results provided mechanistic insights on how conformational dynamics of AlkD-dsDNA complex coordinate different diffusion modes to accomplish the search for DNA lesions with high efficiency and accuracy. We anticipate that the mechanism adopted by AlkD to search for DNA lesions could be a general one utilized by other glycosylases and DNA binding proteins.

On the advantages of exploiting memory in Markov state models for biomolecular dynamics.

Biomolecular dynamics play an important role in numerous biological processes. Markov State Models (MSMs) provide a powerful approach to study these dynamic processes by predicting long time scale dynamics based on many short molecular dynamics (MD) simulations. In an MSM, protein dynamics are modeled as a kinetic process consisting of a series of Markovian transitions between different conformational states at discrete time intervals (called "lag time"). To achieve this, a master equation must be constructed with a sufficiently long lag time to allow interstate transitions to become truly Markovian. This imposes a major challenge for MSM studies of proteins since the lag time is bound by the length of relatively short MD simulations available to estimate the frequency of transitions. Here, we show how one can employ the generalized master equation formalism to obtain an exact description of protein conformational dynamics both at short and long time scales without the time resolution restrictions imposed by the MSM lag time. Using a simple kinetic model, alanine dipeptide, and WW domain, we demonstrate that it is possible to construct these quasi-Markov State Models (qMSMs) using MD simulations that are 5-10 times shorter than those required by MSMs. These qMSMs only contain a handful of metastable states and, thus, can greatly facilitate the interpretation of mechanisms associated with protein dynamics. A qMSM opens the door to the study of conformational changes of complex biomolecules where a Markovian model with a few states is often difficult to construct due to the limited length of available MD simulations.

TAPS: A traveling-salesman based automated path searching method for functional conformational changes of biological macromolecules.

Locating the minimum free energy paths (MFEPs) between two conformational states is among the most important tasks of biomolecular simulations. For example, knowledge of the MFEP is critical for focusing the effort of unbiased simulations that are used for the construction of Markov state models to the biologically relevant regions of the system. Typically, existing path searching methods perform local sampling around the path nodes in a pre-selected collective variable (CV) space to allow a gradual downhill evolution of the path toward the MFEP. Despite the wide application of such a strategy, the gradual path evolution and the non-trivial a priori choice of CVs are also limiting its overall efficiency and automation. Here we demonstrate that non-local perpendicular sampling can be pursued to accelerate the search, provided that all nodes are reordered thereafter via a traveling-salesman scheme. Moreover, path-CVs can be computed on-the-fly and used as a coordinate system, minimizing the necessary prior knowledge about the system. Our traveling-salesman based automated path searching method achieves a 5-8 times speedup over the string method with swarms-of-trajectories for two peptide systems in vacuum and solution, making it a promising method for obtaining initial pathways when investigating functional conformational changes between a pair of structures.

An efficient Bayesian kinetic lumping algorithm to identify metastable conformational states via Gibbs sampling.

Markov State Model (MSM) has become a popular approach to study the conformational dynamics of complex biological systems in recent years. Built upon a large number of short molecular dynamics simulation trajectories, MSM is able to predict the long time scale dynamics of complex systems. However, to achieve Markovianity, an MSM often contains hundreds or thousands of states (microstates), hindering human interpretation of the underlying system mechanism. One way to reduce the number of states is to lump kinetically similar states together and thus coarse-grain the microstates into macrostates. In this work, we introduce a probabilistic lumping algorithm, the Gibbs lumping algorithm, to assign a probability to any given kinetic lumping using the Bayesian inference. In our algorithm, the transitions among kinetically distinct macrostates are modeled by Poisson processes, which will well reflect the separation of time scales in the underlying free energy landscape of biomolecules. Furthermore, to facilitate the search for the optimal kinetic lumping (i.e., the lumped model with the highest probability), a Gibbs sampling algorithm is introduced. To demonstrate the power of our new method, we apply it to three systems: a 2D potential, alanine dipeptide, and a WW protein domain. In comparison with six other popular lumping algorithms, we show that our method can persistently produce the lumped macrostate model with the highest probability as well as the largest metastability. We anticipate that our Gibbs lumping algorithm holds great promise to be widely applied to investigate conformational changes in biological macromolecules.

Molecular mechanisms of RNA polymerase II transcription elongation elucidated by kinetic network models.

Transcription elongation cycle (TEC) of RNA polymerase II (Pol II) is a process of adding a nucleoside triphosphate to the growing messenger RNA chain. Due to the long timescale events in Pol II TEC, an advanced computational technique, such as Markov State Model (MSM), is needed to provide atomistic mechanism and reaction rates. The combination of MSM and experimental results can be used to build a kinetic network model (KNM) of the whole TEC. This review provides a brief protocol to build MSM and KNM of the whole TEC, along with the latest findings of MSM and other computational studies of Pol II TEC. Lastly, we offer a perspective on potentially using a sequence dependent KNM to predict genome-wide transcription error.

Elucidation of the conformational dynamics of multi-body systems by construction of Markov state models.

Constructing Markov State Models (MSMs) based on short molecular dynamics simulations is a powerful computational technique to complement experiments in predicting long-time kinetics of biomolecular processes at atomic resolution. Even though the MSM approach has been widely applied to study one-body processes such as protein folding and enzyme conformational changes, the majority of biological processes, e.g. protein-ligand recognition, signal transduction, and protein aggregation, essentially involve multiple entities. Here we review the attempts at constructing MSMs for multi-body systems, point out the challenges therein and discuss recent algorithmic progresses that alleviate these challenges. In particular, we describe an automatic kinetics based partitioning method that achieves optimal definition of the conformational states in a multi-body system, and discuss a novel maximum-likelihood approach that efficiently estimates the slow uphill kinetics utilizing pre-computed equilibrium populations of all states. We expect that these new algorithms and their combinations may boost investigations of important multi-body biological processes via the efficient construction of MSMs.

Automatic state partitioning for multibody systems (APM): an efficient algorithm for constructing Markov state models to elucidate conformational dynamics of multibody systems.

The conformational dynamics of multibody systems plays crucial roles in many important problems. Markov state models (MSMs) are powerful kinetic network models that can predict long-time-scale dynamics using many short molecular dynamics simulations. Although MSMs have been successfully applied to conformational changes of individual proteins, the analysis of multibody systems is still a challenge because of the complexity of the dynamics that occur on a mixture of drastically different time scales. In this work, we have developed a new algorithm, automatic state partitioning for multibody systems (APM), for constructing MSMs to elucidate the conformational dynamics of multibody systems. The APM algorithm effectively addresses different time scales in the multibody systems by directly incorporating dynamics into geometric clustering when identifying the metastable conformational states. We have applied the APM algorithm to a 2D potential that can mimic a protein-ligand binding system and the aggregation of two hydrophobic particles in water and have shown that it can yield tremendous enhancements in the computational efficiency of MSM construction and the accuracy of the models.

Markov State Models Reveal a Two-Step Mechanism of miRNA Loading into the Human Argonaute Protein: Selective Binding followed by Structural Re-arrangement.

Argonaute (Ago) proteins and microRNAs (miRNAs) are central components in RNA interference, which is a key cellular mechanism for sequence-specific gene silencing. Despite intensive studies, molecular mechanisms of how Ago recognizes miRNA remain largely elusive. In this study, we propose a two-step mechanism for this molecular recognition: selective binding followed by structural re-arrangement. Our model is based on the results of a combination of Markov State Models (MSMs), large-scale protein-RNA docking, and molecular dynamics (MD) simulations. Using MSMs, we identify an open state of apo human Ago-2 in fast equilibrium with partially open and closed states. Conformations in this open state are distinguished by their largely exposed binding grooves that can geometrically accommodate miRNA as indicated in our protein-RNA docking studies. miRNA may then selectively bind to these open conformations. Upon the initial binding, the complex may perform further structural re-arrangement as shown in our MD simulations and eventually reach the stable binary complex structure. Our results provide novel insights in Ago-miRNA recognition mechanisms and our methodology holds great potential to be widely applied in the studies of other important molecular recognition systems.

Quantitatively characterizing the ligand binding mechanisms of choline binding protein using Markov state model analysis.

Protein-ligand recognition plays key roles in many biological processes. One of the most fascinating questions about protein-ligand recognition is to understand its underlying mechanism, which often results from a combination of induced fit and conformational selection. In this study, we have developed a three-pronged approach of Markov State Models, Molecular Dynamics simulations, and flux analysis to determine the contribution of each model. Using this approach, we have quantified the recognition mechanism of the choline binding protein (ChoX) to be ∼90% conformational selection dominant under experimental conditions. This is achieved by recovering all the necessary parameters for the flux analysis in combination with available experimental data. Our results also suggest that ChoX has several metastable conformational states, of which an apo-closed state is dominant, consistent with previous experimental findings. Our methodology holds great potential to be widely applied to understand recognition mechanisms underlining many fundamental biological processes.