A method of incorporating rate constants as kinetic constraints in molecular dynamics simulations

Experiment-Guided Refinement of Milestoning Network

Milestoning is an efficient method for calculating rare event kinetics by constructing a continuous-time kinetic network that connects the reactant and product states. Its accuracy depends on both the quality of the underlying force fields and the trajectory sampling. The sampling error can be effectively controlled through various methods. However, the force fields are often not accurate enough, leading to quantitative discrepancies between simulations and experimental data. To address this challenge, we present a refinement approach for Milestoning network based on the maximum caliber (MaxCal), a general variational principle for dynamical systems, to combine simulations and experimental data. The Kullback-Leibler divergence rate between two Milestoning networks is analytically evaluated and minimized as the loss function. Meanwhile, experimental thermodynamic (equilibrium constants) and kinetic (rate constants) data are incorporated as constraints. The use of MaxCal implies that the refined kinetic network is minimally perturbed from the original one while satisfying the experimental constraints. The refined network is expected to align better with available experimental data. The refinement approach is demonstrated using the binding and unbinding dynamics of a series of six small molecule ligands for the model host system, β-cyclodextrin.

Boosting Ensemble Refinement with Transferable Force-Field Corrections: Synergistic Optimization for Molecular Simulations

A novel method combining the force-field fitting approach and ensemble refinement by the maximum entropy principle is presented. Its formulation allows us to continuously interpolate between these two methods, which can thus be interpreted as two limiting cases. A cross-validation procedure enables us to correctly assess the relative weight of both of them, distinguishing scenarios in which the combined approach is meaningful from those in which either ensemble refinement or force-field fitting separately prevails. The efficacy of their combination is examined for a realistic case study of RNA oligomers. Within the new scheme, molecular dynamics simulations are integrated with experimental data provided by nuclear magnetic resonance measures. We show that force-field corrections are in general superior when applied to the appropriate force-field terms but are automatically discarded by the method when applied to inappropriate force-field terms.

Cryo-electron Microscopy and Molecular Modeling Methods to Characterize the Dynamics of Tau Bound to Microtubules

The electron microscopy metainference integrative structural biology method enables the combination of cryo-electron microscopy electron density maps with molecular modeling techniques such as molecular dynamics to unveil the atomistic biomolecular structural ensemble and the error in the map data in an efficient manner. Here we illustrate the electron microscopy metainference protocol and analysis used to elucidate the atomistic structural ensemble of the microtubule-associated protein tau bound to microtubules by using state-of-the-art molecular mechanic force field and the electron density map.

Advances in automated and reactive flow cytometry for synthetic biotechnology

Automated flow cytometry (FC) has been initially considered for bioprocess monitoring and optimization. More recently, new physical and software interfaces have been made available, facilitating the access to this technology for labs and industries. It also comes with new capabilities, such as being able to act on the cultivation conditions based on population data. This approach, known as reactive FC, extended the range of applications of automated FC to bioprocess control and the stabilization of cocultures, but also to the broad field of synthetic and systems biology for the characterization of gene circuits. However, several issues must be addressed before automated and reactive FC can be considered standard and modular technologies.

Optimizing molecular potential models by imposing kinetic constraints with path reweighting

Empirical force fields employed in molecular dynamics simulations of complex systems are often optimized to reproduce experimentally determined structural and thermodynamic properties. In contrast, experimental knowledge about the interconversion rates between metastable states in such systems is hardly ever incorporated in a force field due to a lack of an efficient approach. Here, we introduce such a framework based on the relationship between dynamical observables, such as rate constants, and the underlying molecular model parameters using the statistical mechanics of trajectories. Given a prior ensemble of molecular dynamics trajectories produced with imperfect force field parameters, the approach allows for the optimal adaption of these parameters such that the imposed constraint of equally predicted and experimental rate constant is obeyed. To do so, the method combines the continuum path ensemble maximum caliber approach with path reweighting methods for stochastic dynamics. When multiple solutions are found, the method selects automatically the combination that corresponds to the smallest perturbation of the entire path ensemble, as required by the maximum entropy principle. To show the validity of the approach, we illustrate the method on simple test systems undergoing rare event dynamics. Next to simple 2D potentials, we explore particle models representing molecular isomerization reactions and protein-ligand unbinding. Besides optimal interaction parameters, the methodology gives physical insights into what parts of the model are most sensitive to the kinetics. We discuss the generality and broad implications of the methodology.

Determination of the Structure and Dynamics of the Fuzzy Coat of an Amyloid Fibril of IAPP Using Cryo-Electron Microscopy

In recent years, major advances in cryo-electron microscopy (cryo-EM) have enabled the routine determination of complex biomolecular structures at atomistic resolution. An open challenge for this approach, however, concerns large systems that exhibit continuous dynamics. To address this problem, we developed the metadynamic electron microscopy metainference (MEMMI) method, which incorporates metadynamics, an enhanced conformational sampling approach, into the metainference method of integrative structural biology. MEMMI enables the simultaneous determination of the structure and dynamics of large heterogeneous systems by combining cryo-EM density maps with prior information through molecular dynamics, while at the same time modeling the different sources of error. To illustrate the method, we apply it to elucidate the dynamics of an amyloid fibril of the islet amyloid polypeptide (IAPP). The resulting conformational ensemble provides an accurate description of the structural variability of the disordered region of the amyloid fibril, known as fuzzy coat. The conformational ensemble also reveals that in nearly half of the structural core of this amyloid fibril, the side chains exhibit liquid-like dynamics despite the presence of the highly ordered network backbone of hydrogen bonds characteristic of the cross-β structure of amyloid fibrils.

Machine learning and protein allostery

The fundamental biological importance and complexity of allosterically regulated proteins stem from their central role in signal transduction and cellular processes. Recently, machine-learning approaches have been developed and actively deployed to facilitate theoretical and experimental studies of protein dynamics and allosteric mechanisms. In this review, we survey recent developments in applications of machine-learning methods for studies of allosteric mechanisms, prediction of allosteric effects and allostery-related physicochemical properties, and allosteric protein engineering. We also review the applications of machine-learning strategies for characterization of allosteric mechanisms and drug design targeting SARS-CoV-2. Continuous development and task-specific adaptation of machine-learning methods for protein allosteric mechanisms will have an increasingly important role in bridging a wide spectrum of data-intensive experimental and theoretical technologies.

Exploring and Learning the Universe of Protein Allostery Using Artificial Intelligence Augmented Biophysical and Computational Approaches

Allosteric mechanisms are commonly employed regulatory tools used by proteins to orchestrate complex biochemical processes and control communications in cells. The quantitative understanding and characterization of allosteric molecular events are among major challenges in modern biology and require integration of innovative computational experimental approaches to obtain atomistic-level knowledge of the allosteric states, interactions, and dynamic conformational landscapes. The growing body of computational and experimental studies empowered by emerging artificial intelligence (AI) technologies has opened up new paradigms for exploring and learning the universe of protein allostery from first principles. In this review we analyze recent developments in high-throughput deep mutational scanning of allosteric protein functions; applications and latest adaptations of Alpha-fold structural prediction methods for studies of protein dynamics and allostery; new frontiers in integrating machine learning and enhanced sampling techniques for characterization of allostery; and recent advances in structural biology approaches for studies of allosteric systems. We also highlight recent computational and experimental studies of the SARS-CoV-2 spike (S) proteins revealing an important and often hidden role of allosteric regulation driving functional conformational changes, binding interactions with the host receptor, and mutational escape mechanisms of S proteins which are critical for viral infection. We conclude with a summary and outlook of future directions suggesting that AI-augmented biophysical and computer simulation approaches are beginning to transform studies of protein allostery toward systematic characterization of allosteric landscapes, hidden allosteric states, and mechanisms which may bring about a new revolution in molecular biology and drug discovery.

Integrating experimental data with molecular simulations to investigate RNA structural dynamics

Conformational dynamics is crucial for ribonucleic acid (RNA) function. Techniques such as nuclear magnetic resonance, cryo-electron microscopy, small- and wide-angle X-ray scattering, chemical probing, single-molecule Förster resonance energy transfer, or even thermal or mechanical denaturation experiments probe RNA dynamics at different time and space resolutions. Their combination with accurate atomistic molecular dynamics (MD) simulations paves the way for quantitative and detailed studies of RNA dynamics. First, experiments provide a quantitative validation tool for MD simulations. Second, available data can be used to refine simulated structural ensembles to match experiments. Finally, comparison with experiments allows for improving MD force fields that are transferable to new systems for which data is not available. Here we review the recent literature and provide our perspective on this field.

NMR Studies of Aromatic Ring Flips to Probe Conformational Fluctuations in Proteins

Aromatic residues form a significant part of the protein core, where they make tight interactions with multiple surrounding side chains. Despite the dense packing of internal side chains, the aromatic rings of phenylalanine and tyrosine residues undergo 180° rotations, or flips, which are mediated by transient and large-scale "breathing" motions that generate sufficient void volume around the aromatic ring. Forty years after the seminal work by Wagner and Wüthrich, NMR studies of aromatic ring flips are now undergoing a renaissance as a powerful means of probing fundamental dynamic properties of proteins. Recent developments of improved NMR methods and isotope labeling schemes have enabled a number of advances in addressing the mechanisms and energetics of aromatic ring flips. The nature of the transition states associated with ring flips can be described by thermodynamic activation parameters, including the activation enthalpy, activation entropy, activation volume, and also the isothermal volume compressibility of activation. Consequently, it is of great interest to study how ring flip rate constants and activation parameters might vary with protein structure and external conditions like temperature and pressure. The field is beginning to gather such data for aromatic residues in a variety of environments, ranging from surface exposed to buried. In the future, the combination of solution and solid-state NMR spectroscopy together with molecular dynamics simulations and other computational approaches is likely to provide detailed information about the coupled dynamics of aromatic rings and neighboring residues. In this Perspective, we highlight recent developments and provide an outlook toward the future.

Sample Preparation for Time-Resolved Serial Crystallography: Practical Considerations

Time-resolved serial crystallography is an emerging method to elucidate the structure-function relationship of biomolecular systems at up to atomic resolution. However, to make this demanding method a success, a number of experimental requirements have to be met. In this chapter, we summarize general guidelines and protocols towards performing time-resolved crystallography experiments, with a particular emphasis on sample requirements and preparation but also a brief excursion into reaction initiation.

Path sampling of recurrent neural networks by incorporating known physics

Recurrent neural networks have seen widespread use in modeling dynamical systems in varied domains such as weather prediction, text prediction and several others. Often one wishes to supplement the experimentally observed dynamics with prior knowledge or intuition about the system. While the recurrent nature of these networks allows them to model arbitrarily long memories in the time series used in training, it makes it harder to impose prior knowledge or intuition through generic constraints. In this work, we present a path sampling approach based on principle of Maximum Caliber that allows us to include generic thermodynamic or kinetic constraints into recurrent neural networks. We show the method here for a widely used type of recurrent neural network known as long short-term memory network in the context of supplementing time series collected from different application domains. These include classical Molecular Dynamics of a protein and Monte Carlo simulations of an open quantum system continuously losing photons to the environment and displaying Rabi oscillations. Our method can be easily generalized to other generative artificial intelligence models and to generic time series in different areas of physical and social sciences, where one wishes to supplement limited data with intuition or theory based corrections.

How do surfactants unfold and refold proteins?

Although the anionic surfactant sodium dodecyl sulfate, SDS, has been used for more than half a century as a versatile and efficient protein denaturant for protein separation and size estimation, there is still controversy about its mode of interaction with proteins. The term "rod-like" structures for the complexes that form between SDS and protein, originally introduced by Tanford, is not sufficiently descriptive and does not distinguish between the two current vying models, namely protein-decorated micelles a.k.a. the core-shell model (in which denatured protein covers the surface of micelles) versus beads-on-a-string model (where unfolded proteins are surrounded by surfactant micelles). Thanks to a combination of structural, kinetic and computational work particularly within the last 5-10 years, it is now possible to rule decisively in favor of the core-shell model. This is supported unambiguously by a combination of calorimetric and small-angle X-ray scattering (SAXS) techniques and confirmed by increasingly sophisticated molecular dynamics simulations. Depending on the SDS:protein ratio and the protein molecular mass, the formed structures can range from multiple partly unfolded protein molecules surrounding a single shared micelle to a single polypeptide chain decorating multiple micelles. We also have much new insight into how this species forms. It is preceded by the binding of small numbers of SDS molecules which subsequently grow by accretion. Time-resolved SAXS analysis reveals an asymmetric attack by SDS micelles followed by distribution of the increasingly unfolded protein around the micelle. The compactness of the protein chain continues to evolve at higher SDS concentrations according to single-molecule studies, though the protein remains completely denatured on the tertiary structural level. SDS denaturation can be reversed by addition of nonionic surfactants that absorb SDS forming mixed micelles, leaving the protein free to refold. Refolding can occur in parallel tracks if only a fraction of the protein is initially stripped of SDS. SDS unfolding is nearly always reversible unless carried out at low pH, where charge neutralization can lead to superclusters of protein-surfactant complexes. With the general mechanism of SDS denaturation now firmly established, it largely remains to explore how other ionic surfactants (including biosurfactants) may diverge from this path.

Information theory: A foundation for complexity science

Modeling and inference are central to most areas of science and especially to evolving and complex systems. Critically, the information we have is often uncertain and insufficient, resulting in an underdetermined inference problem; multiple inferences, models, and theories are consistent with available information. Information theory (in particular, the maximum information entropy formalism) provides a way to deal with such complexity. It has been applied to numerous problems, within and across many disciplines, over the last few decades. In this perspective, we review the historical development of this procedure, provide an overview of the many applications of maximum entropy and its extensions to complex systems, and discuss in more detail some recent advances in constructing comprehensive theory based on this inference procedure. We also discuss efforts at the frontier of information-theoretic inference: application to complex dynamic systems with time-varying constraints, such as highly disturbed ecosystems or rapidly changing economies.

Correlation between the binding affinity and the conformational entropy of nanobody SARS-CoV-2 spike protein complexes

Understanding the structural principles that determine the binding affinity of nanobodies to the spike protein of severe acute respiratory syndrome coronavirus 2 has been difficult. We analyzed electron microscopy maps of nanobody-spike complexes and quantified the conformational entropy of binding. This informed the design of an engineered nanobody with improved binding to the spike protein. This result offers a guiding principle for the rational maturation of nanobodies directed against the spike. High-binding potency nanobodies have been shown to be effective in animal models; thus, this technology could have application in future pandemics.

Camelid single-domain antibodies, also known as nanobodies, can be readily isolated from naïve libraries for specific targets but often bind too weakly to their targets to be immediately useful. Laboratory-based genetic engineering methods to enhance their affinity, termed maturation, can deliver useful reagents for different areas of biology and potentially medicine. Using the receptor binding domain (RBD) of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) spike protein and a naïve library, we generated closely related nanobodies with micromolar to nanomolar binding affinities. By analyzing the structure–activity relationship using X-ray crystallography, cryoelectron microscopy, and biophysical methods, we observed that higher conformational entropy losses in the formation of the spike protein–nanobody complex are associated with tighter binding. To investigate this, we generated structural ensembles of the different complexes from electron microscopy maps and correlated the conformational fluctuations with binding affinity. This insight guided the engineering of a nanobody with improved affinity for the spike protein.

Recent Developments in Data-Assisted Modeling of Flexible Proteins

Many proteins can fold into well-defined conformations. However, intrinsically-disordered proteins (IDPs) do not possess a defined structure. Moreover, folded multi-domain proteins often digress into alternative conformations. Collectively, the conformational dynamics enables these proteins to fulfill specific functions. Thus, most experimental observables are averaged over the conformations that constitute an ensemble. In this article, we review the recent developments in the concept and methods for the determination of the dynamic structures of flexible peptides and proteins. In particular, we describe ways to extract information from nuclear magnetic resonance small-angle X-ray scattering (SAXS), and chemical cross-linking coupled with mass spectroscopy (XL-MS) measurements. All these techniques can be used to obtain ensemble-averaged restraints or to re-weight the simulated conformational ensembles.

Best practices for time-resolved serial synchrotron crystallography

With recent developments in X-ray sources, instrumentation and data-analysis tools, time-resolved crystallographic experiments, which were originally the preserve of a few expert groups, are becoming simpler and can be carried out at more radiation sources, and are thus increasingly accessible to a growing user base. However, these experiments are just that: discrete experiments, not just `data collections'. As such, careful planning and consideration of potential pitfalls is required to enable a successful experiment. Here, some of the key factors that should be considered during the planning and execution of a time-resolved structural study are outlined, with a particular focus on synchrotron-based experiments.

Resolving Dynamics in the Ensemble: Finding Paths through Intermediate States and Disordered Protein Structures

Proteins have been found to inhabit a diverse set of three-dimensional structures. The dynamics that govern protein interconversion between structures happen over a wide range of time scales─picoseconds to seconds. Our understanding of protein functions and dynamics is largely reliant upon our ability to elucidate physically populated structures. From an experimental structural characterization perspective, we are often limited to measuring the ensemble-averaged structure both in the steady-state and time-resolved regimes. Generating kinetic models and understanding protein structure-function relationships require atomistic knowledge of the populated states in the ensemble. In this Perspective, we present ensemble refinement methodologies that integrate time-resolved experimental signals with molecular dynamics models. We first discuss integration of experimental structural restraints to molecular models in disordered protein systems that adhere to the principle of maximum entropy for creating a complete set of ensemble structures. We then propose strategies to find kinetic pathways between the refined structures, using time-resolved inputs to guide molecular dynamics trajectories and the use of inference to generate tailored stimuli to prepare a desired ensemble of protein states.

Determination of intermediate state structures in the opening pathway of SARS-CoV-2 spike using cryo-electron microscopy

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the cause of COVID-19, a highly infectious disease that is severely affecting our society and welfare systems. In order to develop therapeutic interventions against this condition, one promising strategy is to target spike, the trimeric transmembrane glycoprotein that the virus uses to recognise and bind its host cells. Here we use a metainference cryo-electron microscopy approach to determine the opening pathway that brings spike from its inactive (closed) conformation to its active (open) one. The knowledge of the structures of the intermediate states of spike along this opening pathway enables us to identify a cryptic pocket that is not exposed in the open and closed states. These results underline the opportunities offered by the determination of the structures of the transient intermediate states populated during the dynamics of proteins to allow the therapeutic targeting of otherwise invisible cryptic binding sites.

A structural ensemble derived from cryo-electron microscopy reveals a cryptic pocket site in intermediate states along the opening pathway of the SARS-CoV-2 spike protein.

Reweighting non-equilibrium steady-state dynamics along collective variables

Computer simulations generate microscopic trajectories of complex systems at a single thermodynamic state point. We recently introduced a Maximum Caliber (MaxCal) approach for dynamical reweighting. Our approach mapped these trajectories to a Markovian description on the configurational coordinates and reweighted path probabilities as a function of external forces. Trajectory probabilities can be dynamically reweighted both from and to equilibrium or non-equilibrium steady states. As the system's dimensionality increases, an exhaustive description of the microtrajectories becomes prohibitive-even with a Markovian assumption. Instead, we reduce the dimensionality of the configurational space to collective variables (CVs). Going from configurational to CV space, we define local entropy productions derived from configurationally averaged mean forces. The entropy production is shown to be a suitable constraint on MaxCal for non-equilibrium steady states expressed as a function of CVs. We test the reweighting procedure on two systems: a particle subject to a two-dimensional potential and a coarse-grained peptide. Our CV-based MaxCal approach expands dynamical reweighting to larger systems, for both static and dynamical properties, and across a large range of driving forces.