Markov methods for hierarchical coarse-graining of large protein dynamics

Protein dynamics developments for the large scale and cryoEM: case study of ProDy 2.0

Cryo-electron microscopy (cryoEM) has become a well established technique with the potential to produce structures of large and dynamic supramolecular complexes that are not amenable to traditional approaches for studying structure and dynamics. The size and low resolution of such molecular systems often make structural modelling and molecular dynamics simulations challenging and computationally expensive. This, together with the growing wealth of structural data arising from cryoEM and other structural biology methods, has driven a trend in the computational biophysics community towards the development of new pipelines for analysing global dynamics using coarse-grained models and methods. At the centre of this trend has been a return to elastic network models, normal mode analysis (NMA) and ensemble analyses such as principal component analysis, and the growth of hybrid simulation methodologies that make use of them. Here, this field is reviewed with a focus on ProDy, the Python application programming interface for protein dynamics, which has been developed over the last decade. Two key developments in this area are highlighted: (i) ensemble NMA towards extracting and comparing the signature dynamics of homologous structures, aided by the recent SignDy pipeline, and (ii) pseudoatom fitting for more efficient global dynamics analyses of large and low-resolution supramolecular assemblies from cryoEM, revisited in the CryoDy pipeline. It is believed that such a renewal and extension of old models and methods in new pipelines will be critical for driving the field forward into the next cryoEM revolution.

Inferring functional units in ion channel pores via relative entropy

Coarse-grained protein models approximate the first-principle physical potentials. Among those modeling approaches, the relative entropy framework yields promising and physically sound results, in which a mapping from the target protein structure and dynamics to a model is defined and subsequently adjusted by an entropy minimization of the model parameters. Minimization of the relative entropy is equivalent to maximization of the likelihood of reproduction of (configurational ensemble) observations by the model. In this study, we extend the relative entropy minimization procedure beyond parameter fitting by a second optimization level, which identifies the optimal mapping to a (dimension-reduced) topology. We consider anisotropic network models of a diverse set of ion channels and assess our findings by comparison to experimental results.

Transient Unfolding and Long-Range Interactions in Viral BCL2 M11 Enable Binding to the BECN1 BH3 Domain

Viral BCL2 proteins (vBCL2s) help to sustain chronic infection of host proteins to inhibit apoptosis and autophagy. However, details of conformational changes in vBCL2s that enable binding to BH3Ds remain unknown. Using all-atom, multiple microsecond-long molecular dynamic simulations (totaling 17 μs) of the murine γ-herpesvirus 68 vBCL2 (M11), and statistical inference techniques, we show that regions of M11 transiently unfold and refold upon binding of the BH3D. Further, we show that this partial unfolding/refolding within M11 is mediated by a network of hydrophobic interactions, which includes residues that are 10 Å away from the BH3D binding cleft. We experimentally validate the role of these hydrophobic interactions by quantifying the impact of mutating these residues on binding to the Beclin1/BECN1 BH3D, demonstrating that these mutations adversely affect both protein stability and binding. To our knowledge, this is the first study detailing the binding-associated conformational changes and presence of long-range interactions within vBCL2s.

Conformational Sub-states and Populations in Enzyme Catalysis

Enzyme function involves substrate and cofactor binding, precise positioning of reactants in the active site, chemical turnover, and release of products. In addition to formation of crucial structural interactions between enzyme and substrate(s), coordinated motions within the enzyme-substrate complex allow reaction to proceed at a much faster rate, compared to the reaction in solution and in the absence of enzyme. An increasing number of enzyme systems show the presence of conserved protein motions that are important for function. A wide variety of motions are naturally sampled (over femtosecond to millisecond time-scales) as the enzyme complex moves along the energetic landscape, driven by temperature and dynamical events from the surrounding environment. Areas of low energy along the landscape form conformational sub-states, which show higher conformational populations than surrounding areas. A small number of these protein conformational sub-states contain functionally important structural and dynamical features, which assist the enzyme mechanism along the catalytic cycle. Identification and characterization of these higher-energy (also called excited) sub-states and the associated populations are challenging, as these sub-states are very short-lived and therefore rarely populated. Specialized techniques based on computer simulations, theoretical modeling, and nuclear magnetic resonance have been developed for quantitative characterization of these sub-states and populations. This chapter discusses these techniques and provides examples of their applications to enzyme systems.

Approaching Elastic Network Models to Molecular Dynamics Flexibility

Elastic network models (ENMs) are coarse-grained descriptions of proteins as networks of coupled harmonic oscillators. However, despite their widespread application to study collective movements, there is still no consensus parametrization for the ENMs. When compared to molecular dynamics (MD) flexibility in solution, the ENMs tend to disperse the important motions into multiple modes. We present here a new ENM, trained against a database of atomistic MD trajectories. The role of residue connectivity, the analytical form of the force constants, and the threshold for interactions were systematically explored. We found that contacts between the three nearest sequence neighbors are crucial determinants of the fundamental motions. We developed a new general potential function including both the sequential and spatial relationships between interacting residue pairs which is robust against size and fold variations. The proposed model provides a systematic improvement compared to standard ENMs: Not only do its results match the MD results-even for long time scales-but also the model is able to capture large X-ray conformational transitions as well as NMR ensemble diversity.

Perspective: Coarse-grained models for biomolecular systems

By focusing on essential features, while averaging over less important details, coarse-grained (CG) models provide significant computational and conceptual advantages with respect to more detailed models. Consequently, despite dramatic advances in computational methodologies and resources, CG models enjoy surging popularity and are becoming increasingly equal partners to atomically detailed models. This perspective surveys the rapidly developing landscape of CG models for biomolecular systems. In particular, this review seeks to provide a balanced, coherent, and unified presentation of several distinct approaches for developing CG models, including top-down, network-based, native-centric, knowledge-based, and bottom-up modeling strategies. The review summarizes their basic philosophies, theoretical foundations, typical applications, and recent developments. Additionally, the review identifies fundamental inter-relationships among the diverse approaches and discusses outstanding challenges in the field. When carefully applied and assessed, current CG models provide highly efficient means for investigating the biological consequences of basic physicochemical principles. Moreover, rigorous bottom-up approaches hold great promise for further improving the accuracy and scope of CG models for biomolecular systems.

Structure and dynamics of molecular networks: a novel paradigm of drug discovery: a comprehensive review

Despite considerable progress in genome- and proteome-based high-throughput screening methods and in rational drug design, the increase in approved drugs in the past decade did not match the increase of drug development costs. Network description and analysis not only give a systems-level understanding of drug action and disease complexity, but can also help to improve the efficiency of drug design. We give a comprehensive assessment of the analytical tools of network topology and dynamics. The state-of-the-art use of chemical similarity, protein structure, protein-protein interaction, signaling, genetic interaction and metabolic networks in the discovery of drug targets is summarized. We propose that network targeting follows two basic strategies. The "central hit strategy" selectively targets central nodes/edges of the flexible networks of infectious agents or cancer cells to kill them. The "network influence strategy" works against other diseases, where an efficient reconfiguration of rigid networks needs to be achieved by targeting the neighbors of central nodes/edges. It is shown how network techniques can help in the identification of single-target, edgetic, multi-target and allo-network drug target candidates. We review the recent boom in network methods helping hit identification, lead selection optimizing drug efficacy, as well as minimizing side-effects and drug toxicity. Successful network-based drug development strategies are shown through the examples of infections, cancer, metabolic diseases, neurodegenerative diseases and aging. Summarizing >1200 references we suggest an optimized protocol of network-aided drug development, and provide a list of systems-level hallmarks of drug quality. Finally, we highlight network-related drug development trends helping to achieve these hallmarks by a cohesive, global approach.

The Theory of Ultra-Coarse-Graining. 1. General Principles

Coarse-grained (CG) models provide a computationally efficient means to study biomolecular and other soft matter processes involving large numbers of atoms correlated over distance scales of many covalent bond lengths and long time scales. Variational methods based on information from simulations of finer-grained (e.g., all-atom) models, for example the multiscale coarse-graining (MS-CG) and relative entropy minimization methods, provide attractive tools for the systematic development of CG models. However, these methods have important drawbacks when used in the "ultra-coarse-grained" (UCG) regime, e.g., at a resolution level coarser or much coarser than one amino acid residue per effective CG particle in proteins. This is due to the possible existence of multiple metastable states "within" the CG sites for a given UCG model configuration. In this work, systematic variational UCG methods are presented that are specifically designed to CG entire protein domains and subdomains into single effective CG particles. This is accomplished by augmenting existing effective particle CG schemes to allow for discrete state transitions and configuration-dependent resolution. Additionally, certain conclusions of this work connect back to single-state force matching and open up new avenues for method development in that area. These results provide a formal statistical mechanical basis for UCG methods related to force matching and relative entropy CG methods and suggest practical algorithms for constructing optimal approximate UCG models from fine-grained simulation data.

A rigid network of long-range contacts increases thermostability in a mutant endoglucanase

Thermodynamic stability of a protein at elevated temperatures is a key factor for thermostable enzymes to catalyze their specific reactions. Yet our understanding of biological determinants of thermostability is far from complete. Many different atomistic factors have been suggested as possible means for such proteins to preserve their activity at high temperatures. Among these factors are specific local interatomic interactions or enrichment of specific amino acid types. The case of glycosyl hydrolase family endoglucanase of Trichoderma reesei defies current hypotheses for thermostability because a single mutation far from the active site (A35 V) converts this mesostable protein into a thermostable protein without significant change in the protein structure. This substantial change in enzymatic activity cannot be explained on the basis of local intramolecular interactions alone. Here we present a more global view of the induced thermostability and show that the A35 V mutation affects the underlying structural rigidity of the whole protein via a number of long-range, non-local interactions. Our analysis of this structure reveals a precisely tuned, rigid network of atomic interactions. This cooperative, allosteric effect promotes the transformation of this mesostable protein into a thermostable one.

Coarse-graining of multiprotein assemblies

Multiscale models are important tools to elucidate how small changes in local subunit conformations may propagate to affect the properties of macromolecular complexes. We review recent advances in coarse-graining methods for poly-protein assemblies, systems that are composed of many copies of relatively few components, with a particular focus on viral capsids and cytoskeletal filaments. These methods are grouped into two broad categories-mapping methods, which use information from one scale of representation to parameterize a lower resolution model, and bridging methods, which repeatedly connect different scales during simulation-and we provide examples of both classes at different levels of complexity. Collectively, these models illustrate the numerous approaches to information transfer between scales and demonstrate that the complexity required of the model depends in general on the nature of the information sought.

QAARM: quasi-anharmonic autoregressive model reveals molecular recognition pathways in ubiquitin

MOTIVATION

Molecular dynamics (MD) simulations have dramatically improved the atomistic understanding of protein motions, energetics and function. These growing datasets have necessitated a corresponding emphasis on trajectory analysis methods for characterizing simulation data, particularly since functional protein motions and transitions are often rare and/or intricate events. Observing that such events give rise to long-tailed spatial distributions, we recently developed a higher-order statistics based dimensionality reduction method, called quasi-anharmonic analysis (QAA), for identifying biophysically-relevant reaction coordinates and substates within MD simulations. Further characterization of conformation space should consider the temporal dynamics specific to each identified substate.

RESULTS

Our model uses hierarchical clustering to learn energetically coherent substates and dynamic modes of motion from a 0.5 μs ubiqutin simulation. Autoregressive (AR) modeling within and between states enables a compact and generative description of the conformational landscape as it relates to functional transitions between binding poses. Lacking a predictive component, QAA is extended here within a general AR model appreciative of the trajectory's temporal dependencies and the specific, local dynamics accessible to a protein within identified energy wells. These metastable states and their transition rates are extracted within a QAA-derived subspace using hierarchical Markov clustering to provide parameter sets for the second-order AR model. We show the learned model can be extrapolated to synthesize trajectories of arbitrary length.

CONTACT

ramanathana@ornl.gov; chakracs@pitt.edu.

Mechanism of cohesin loading onto chromosomes: a conformational dynamics study

The structure-function relationship of cohesin, an essential chromosome maintenance protein, is investigated by analyzing its collective dynamics and conformational flexibility, enhancing our understanding of the sister chromatid cohesion process. A three-dimensional model of cohesin has been constructed by homology modeling using both crystallographic and electron microscopy image data. The harmonic dynamics of the cohesin structure are calculated with a coarse-grained elastic network model. The model shows that the bending motion of the cohesin ring is able to adopt a head-to-tail conformation, in agreement with experimental data. Low-frequency conformational changes are observed to deform the highly conserved glycine residues at the interface of the cohesin heterodimer. Normal mode analysis further reveals that, near large globular structures such as nucleosome and accessory proteins docked to cohesin, the mobility of the coiled-coil regions is notably affected. Moreover, fully solvated molecular dynamics calculations, performed specifically on the hinge region, indicate that hinge opening starts from one side of the dimerization interface, and is coordinated by highly conserved glycine residues.

The ribosome structure controls and directs mRNA entry, translocation and exit dynamics

The protein-synthesizing ribosome undergoes large motions to effect the translocation of tRNAs and mRNA; here, the domain motions of this system are explored with a coarse-grained elastic network model using normal mode analysis. Crystal structures are used to construct various model systems of the 70S complex with/without tRNA, elongation factor Tu and the ribosomal proteins. Computed motions reveal the well-known ratchet-like rotational motion of the large subunits, as well as the head rotation of the small subunit and the high flexibility of the L1 and L7/L12 stalks, even in the absence of ribosomal proteins. This result indicates that these experimentally observed motions during translocation are inherently controlled by the ribosomal shape and only partially dependent upon GTP hydrolysis. Normal mode analysis further reveals the mobility of A- and P-tRNAs to increase in the absence of the E-tRNA. In addition, the dynamics of the E-tRNA is affected by the absence of the ribosomal protein L1. The mRNA in the entrance tunnel interacts directly with helicase proteins S3 and S4, which constrain the mRNA in a clamp-like fashion, as well as with protein S5, which likely orients the mRNA to ensure correct translation. The ribosomal proteins S7, S11 and S18 may also be involved in assuring translation fidelity by constraining the mRNA at the exit site of the channel. The mRNA also interacts with the 16S 3' end forming the Shine-Dalgarno complex at the initiation step; the 3' end may act as a 'hook' to reel in the mRNA to facilitate its exit.