Why are large conformational changes well described by harmonic normal modes?

Low-frequency normal modes generated by elastic network models tend to correlate strongly with large conformational changes of proteins, despite their reliance on the harmonic approximation, which is only valid in close proximity of the native structure. We consider 12 variants of the torsional network model (TNM), an elastic network model in torsion angle space, that adopt different sets of torsion angles as degrees of freedom and reproduce with similar quality the thermal fluctuations of proteins but present drastic differences in their agreement with conformational changes. We show that these differences are related to the extent of the deviations from the harmonic approximation, assessed through an anharmonic energy function whose harmonic approximation coincides with the TNM. Our results indicate that mode anharmonicity is more strongly related to its collectivity, i.e., the number of atoms displaced by the mode, than to its amplitude; low-frequency modes can remain harmonic even at large amplitudes, provided they are sufficiently collective. Finally, we assess the potential benefits of different strategies to minimize the impact of anharmonicity. The reduction of the number of degrees of freedom or their regularization by a torsional harmonic potential significantly improves the collectivity and harmonicity of normal modes and the agreement with conformational changes. In contrast, the correction of normal mode frequencies to partially account for anharmonicity does not yield substantial benefits. The TNM program is freely available at https://github.com/ugobas/tnm.     

A theorem on amplitudes of thermal atomic fluctuations in large molecules assuming specific conformations calculated by normal mode analysis

An exact theorem is proved and its implication is discussed. The theorem states that, if a large molecule, typically biological macromolecules such as proteins, undergoes small-amplitude conformational fluctuations around its native conformation in such a way that within the range of conformational fluctuations at thermal equilibrium the conformational energy surface can be approximated by a multidimensional parabola, then the mass-weighted mean-square displacement of constituent atoms is given by the sum of the contributions from each normal mode of conformational vibration, which in turn is proportional to the inverse of the square of its frequency. This theorem provides a firm theoretical basis for the fact hitherto empirically recognized in the conformational dynamics of, for instance, native proteins that very-low-frequency normal modes make dominant contributions to the conformational fluctuations at thermal equilibrium. Discussion is given on the implication of this theorem, especially on the importance of the concept of the low-frequency normal modes, even in the case where the basic assumption of the harmonicity of the energy surface does not hold.     

Three-dimensional lipophilicity characterization of molecular pores and channel-like cavities

Molecular lipophilicity is a useful property for assessing molecular similarity or complementarity within the context of computer-aided drug design. As well, local contributions to solvent affinity help us to understand both dynamics and conformational stability in biomolecules. In this work, we discuss an approach to characterize the local contributions to hydrophobicity by using one- and two-dimensional representations of molecular channel-like cavities. The method monitors how a phenomenological lipophilicity potential (based on fragmental atom contributions) changes over a continuum of “molecular tubes” used for modeling channels and pores. Our results convey a relatively detailed picture of the spatial distribution of water affinity. The procedure can then be used as a complement to the hydrophobicity scales based on averaging contributions from single amino acids. In addition, we can study how the water affinity changes for inner and outer regious of the pores. As an application, we compute the 3D distribution of lipophilicity in the “pore conformation” of gramicidin A. The qualitative trends indicated by our results are broadly consistent with computer simulations of the gramicidin channel in the presence of hydrated ions. The behavior revealed by the simulations can then be incorporated to produce an improved, simple 2D model for water-channel interactions.     

Enhancing backbone sampling in Monte Carlo simulations using internal coordinates normal mode analysis

Normal mode methods are becoming a popular alternative to sample the conformational landscape of proteins. In this study, we describe the implementation of an internal coordinate normal mode analysis method and its application in exploring protein flexibility by using the Monte Carlo method PELE. This new method alternates two different stages, a perturbation of the backbone through the application of torsional normal modes, and a resampling of the side chains. We have evaluated the new approach using two test systems, ubiquitin and c-Src kinase, and the differences to the original ANM method are assessed by comparing both results to reference molecular dynamics simulations. The results suggest that the sampled phase space in the internal coordinate approach is closer to the molecular dynamics phase space than the one coming from a Cartesian coordinate anisotropic network model. In addition, the new method shows a great speedup (∼5–7×), making it a good candidate for future normal mode implementations in Monte Carlo methods.     

Conformational changes and allosteric communications in human serum albumin due to ligand binding

It is well recognized that knowledge of structure alone is not sufficient to understand the fundamental mechanism of biomolecular recognition. Information of dynamics is necessary to describe motions involving relevant conformational states of functional importance. We carried out principal component analysis (PCA) of structural ensemble, derived from 84 crystal structures of human serum albumin (HSA) with different ligands and/or different conditions, to identify the functionally important collective motions, and compared with the motions along the low-frequency modes obtained from normal mode analysis of the elastic network model (ENM) of unliganded HSA. Significant overlap is observed in the collective motions derived from PCA and ENM. PCA and ENM analysis revealed that ligand selects the most favored conformation from accessible equilibrium structures of unliganded HSA. Further, we analyzed dynamic network obtained from molecular dynamics simulations of unliganded HSA and fatty acids- bound HSA. Our results show that fatty acids-bound HSA has more robust community network with several routes to communicate among different parts of the protein. Critical nodes (residues) identified from dynamic network analysis are in good agreement with allosteric residues obtained from sequence-based statistical coupling analysis method. This work underscores the importance of intrinsic structural dynamics of proteins in ligand recognition and can be utilized for the development of novel drugs with optimum activity.     

Dynamics of firefly luciferase inhibition by general anesthetics: Gaussian and anisotropic network analyses

The new crystal structures of the product-bound firefly luciferase combined with the previously determined substrate-free structures allow for a detailed analysis of the dynamics basis for the luciferase enzymatic activities. Using the Gaussian network model and the anisotropic network model, we show here that the superposition of the three slowest anisotropic network model modes, consisting of the bending, rotating, and rocking motions of the C-domain, accounts for large rearrangement of domains from the substrate-free (open) to product-bound (closed) conformation and thus constitutes a critical component of the enzyme's functions. The analysis also offers a unique platform to reexamine the molecular mechanism of the anesthetic inhibition of the firefly luciferase. Through perturbing the protein backbone network by introducing additional nodes to represent anesthetics, we found that the presence of two representative anesthetics, halothane and n-decanol, in different regions of luciferase had distinctively different effects on the protein's global motion. Only at the interface of the C- and N-domains did the anesthetics cause the most profound reduction in the overall flexibility of the C-domain and the concomitant increase in the flexibility of the loop, where the substitution of a conserved lysine residue was found experimentally to lead to >2-3 orders of magnitude reduction in activity. These anesthetic-induced dynamics changes can alter the normal function of the protein, appearing as an epiphenomenon of an "inhibition". The implication of the study is that a leading element for general anesthetic action on proteins is to disrupt the modes of motion essential to protein functions.     

THE CONTRIBUTION OF SPONTANEOUS MUTATIONS TO THERMAL SENSITIVITY CURVE VARIATION IN DROSOPHILA SERRATA

Many traits studied in ecology and evolutionary biology change their expression in response to a continuously varying environmental factor. One well‐studied example are thermal performance curves (TPCs); continuous reaction norms that describe the relationship between organismal performance and temperature and are useful for understanding the trade‐offs involved in thermal adaptation. We characterized curves describing the thermal sensitivity of voluntary locomotor activity in a set of 66 spontaneous mutation accumulation lines in the fly Drosophila serrata. Factor‐analytic modeling of the mutational variance–covariance matrix, M , revealed support for three axes of mutational variation in males and two in females. These independent axes of mutational variance corresponded well to the major axes of TPC variation required for different types of thermal adaptation; “faster‐slower” representing changes in performance largely independent of temperature, and the “hotter‐colder” and “generalist‐specialist” axes, representing trade‐offs. In contrast to its near‐absence from standing variance in this species, a “faster‐slower” axis, accounted for most mutational variance (75% in males and 66% in females) suggesting selection may easily fix or remove these types of mutations in outbred populations. Axes resembling the “hotter‐colder” and “generalist‐specialist” modes of variation contributed less mutational variance but nonetheless point to an appreciable input of new mutations that may contribute to thermal adaptation.     

600 ps Molecular dynamics reveals stable substructures and flexible hinge points in cAMP dependent protein kinase

Molecular dynamics simulations of the catalytic subunit of cAMP dependent protein kinase (cAPK) have been performed in an aqueous environment. The relations among the protein hydrogen‐bonding network, secondary structural elements, and the internal motions of rigid domains were examined. The values of fluctuations of protein dihedral angles during dynamics show quite distinct maxima in the regions of loops and minima in the regions of α‐helices and β‐strands. Analyses of conformation snapshots throughout the run show stable subdomains and indicate that these rigid domains are constrained during the dynamics by a stable network of hydrogen bonds. The most stable subdomain during the dynamics was in the small lobe including part of the carboxy‐terminal tail. The most significant flexible region was the highly conserved glycine‐rich loop between β strands 1 and 2 in the small lobe. Many of the main chain dihedral angle changes measured in a comparison of the crystallographic structures of “open” and “closed” conformations of cAPK correspond to the highly flexible residues found during dynamics. © 1999 John Wiley & Sons, Inc. Biopoly 50: 513–524, 1999     

Cofilin increases the torsional flexibility and dynamics of actin filaments

We have measured the effects of cofilin on the conformation and dynamics of actin filaments labeled at Cys374 with erythrosin-iodoacetemide (ErIA), using time-resolved phosphorescence anisotropy (TPA). Cofilin quenches the phosphorescence intensity of actin-bound ErIA, indicating that binding changes the local environment of the probe. The cofilin concentration-dependence of the phosphorescence intensity is sigmoidal, consistent with cooperative actin filament binding. Model-independent analysis of the anisotropies indicates that cofilin increases the rates of the microsecond rotational motions of actin. In contrast to the reduction in phosphorescence intensity, the changes in the rates of rotational motions display non-nearest-neighbor cooperative interactions and saturate at substoichiometric cofilin binding densities. Detailed analysis of the TPA decays indicates that cofilin decreases the torsional rigidity (C) of actin, increasing the thermally driven root-mean-square torsional angle between adjacent filament subunits from approximately 4 degrees (C = 2.30 x 10(-27) Nm2 radian(-1)) to approximately 17 degrees (C = 0.13 x 10(-27) Nm2 radian(-1)) at 25 degrees C. We favor a mechanism in which cofilin binding shifts the equilibrium between thermal ErIA-actin filament conformers, and facilitates two distinct structural changes in actin. One is local in nature, which affects the structure of actin's C terminus and is likely to mediate nearest-neighbor cooperative binding and filament severing. The second is a change in the internal dynamics of actin, which displays non-nearest-neighbor cooperativity and increases the torsional flexibility of filaments. The long-range effects of cofilin on the torsional dynamics of actin may accelerate P(i) release from filaments and modulate interactions with other regulatory actin filament binding proteins.     

Coupling between global dynamics and signal transduction pathways: a mechanism of allostery for chaperonin GroEL

Despite significant efforts toward understanding the molecular basis of allosteric communication, the mechanisms by which local energetic and conformational changes cooperatively diffuse from ligand-binding sites to distal regions across the 3-dimensional structure of allosteric proteins remain to be established. Recent experimental and theoretical evidence supports the view that allosteric communication is facilitated by the intrinsic ability of the biomolecules to undergo collective changes in structure, triggered by ligand binding. Two groups of studies recently proved to provide insights into such intrinsic, structure-induced effects: elastic network models that permit us to visualize the cooperative changes in conformation that are most readily accessible near native state conditions, and information-theoretic approaches that elucidate the most efficient pathways of signal transmission favored by the overall architecture. Using a combination of these two approaches, we highlight, by way of application to the bacterial chaperonin complex GroEL-GroES, how the most cooperative modes of motion play a role in mediating the propagation of allosteric signals. A functional coupling between the global dynamics sampled under equilibrium conditions and the signal transduction pathways inherently favored by network topology appears to control allosteric effects.     

Molecular mechanisms of chaperonin GroEL-GroES function.

The dynamics of the GroEL-GroES complex is investigated with a coarse-grained model. This model is one in which single-residue points are connected to other such points, which are nearby, by identical springs, forming a network of interactions. The nature of the most important (slowest) normal modes reveals a wide variety of motions uniquely dependent upon the central cavity of the structure, including opposed torsional rotation of the two GroEL rings accompanied by the alternating compression and expansion of the GroES cap binding region, bending, shear, opposed radial breathing of the cis and trans rings, and stretching and contraction along the protein assembly's long axis. The intermediate domains of the subunits are bifunctional due to the presence of two hinges, which are alternatively activated or frozen by an ATP-dependent mechanism. ATP binding stabilizes a relatively open conformation (with respect to the central cavity) and hinders the motion of the hinge site connecting the intermediate and equatorial domains, while enhancing the flexibility of the second hinge that sets in motion the apical domains. The relative flexibilities of the hinges are reversed in the nucleotide-free form. Cooperative cross-correlations between subunits provide information about the mechanism of action of the protein. The mechanical motions driven by the different modes provide variable binding surfaces and variable sized cavities in the interior to enable accommodation of a broad range of protein substrates. These modes of motion could be used to manipulate the substrate's conformations.     

β-Galactosidase: Immune recognition of conformation and mechanism of antibody-induced catalytic activation

Activation of mutant β-galactosidase by antibodies can be explained by a “selection” mechanism in which the antibody binds and stabilizes those mutants in a native-like conformation and by an “induction” mechanism where binding of the antibody itself induces a conformational change activating β-galactosidase. The “selection” hypothesis was tested by passing β-galactosidase through a column packed with monoclonal antibody-derivatized Sepharose. The antibody retains the active, in preference to the inactive, proteins. The “induction” mechanism was tested by mixing antibody–Sepharose with mutant β-galactosidase and measuring enzyme activity before mixing and that remaining in the supernatant. The activity of the antibody–Sepharose pellet exceeded the sum of the original activity plus supernatant activity. As a result of these experiments, both mechanisms are found to be operative.     

An analysis of the influence of protein intrinsic dynamical properties on its thermal unfolding behavior

The influence of the protein topology-encoded dynamical properties on its thermal unfolding motions was studied in the present work. The intrinsic dynamics of protein topology was obtained by the anisotropic network model (ANM). The ANM has been largely used to investigate protein collective functional motions, but it is not well elucidated if this model can also reveal the preferred large-scale motions during protein unfolding. A small protein barnase is used as a typical case study to explore the relationship between protein topology-encoded dynamics and its unfolding motions. Three thermal unfolding simulations at 500 K were performed for barnase and the entire unfolding trajectories were sampled and partitioned into several windows. For each window, the preferred unfolding motions were investigated by essential dynamics analysis, and then associated with the intrinsic dynamical properties of the starting conformation in this window, which is detected by ANM. The results show that only a few slow normal modes imposed by protein structure are sufficient to give a significant overlap with the preferred unfolding motions. Especially, the large amplitude unfolding movements, which imply that the protein jumps out of a local energy basin, can be well described by a single or several ANM slow modes. Besides the global motions, it is also found that the local residual fluctuations encoded in protein structure are highly correlated with those in the protein unfolding process. Furthermore, we also investigated the relationship between protein intrinsic flexibility and its unfolding events. The results show that the intrinsic flexible regions tend to unfold early. Several early unfolding events can be predicted by analysis of protein structural flexibility. These results imply that protein structure-encoded dynamical properties have significant influences on protein unfolding motions.     

Ubiquitin folds via a flip-twist-lock mechanism

To perform specific functional activities, the majority of proteins should fold into their distinct three-dimensional conformations. However, the biologically active conformation of a protein is generally found to be marginally stable than the other conformations that the chain can adopt. How a protein finds its native conformation from its post-synthesis unfolded structure in a complex conformational landscape is the unsolved question that still drives the protein folding community. Here, we report the folding mechanism of a globular protein, ubiquitin, from its chemically denatured state using all-atom molecular dynamics simulations. From the kinetic analysis of the simulated trajectories we show that the folding process can be described by the hydrophobic collapse mechanism, initiated by the “dewetting transition”, and subsequently assisted by the origination of an N-terminal folding nucleus, and finally supported by a native salt-bridge interaction between K11 and E34. We show that ubiquitin folds via an intermediate. Finally, we confirm the presence of “biological water” and explain its role to the folding process.     

Large‐scale comparison of protein essential dynamics from molecular dynamics simulations and coarse‐grained normal mode analyses

A large‐scale comparison of essential dynamics (ED) modes from molecular dynamic simulations and normal modes from coarse‐grained normal mode methods (CGNM) was performed on a dataset of 335 proteins. As CGNM methods, the elastic network model (ENM) and the rigid cluster normal mode analysis (RCNMA) were used. Low‐frequency normal modes from ENM correlate very well with ED modes in terms of directions of motions and relative amplitudes of motions. Notably, a similar performance was found if normal modes from RCNMA were used, despite a higher level of coarse graining. On average, the space spanned by the first quarter of ENM modes describes 84% of the space spanned by the five ED modes. Furthermore, no prominent differences for ED and CGNM modes among different protein structure classes (CATH classification) were found. This demonstrates the general potential of CGNM approaches for describing intrinsic motions of proteins with little computational cost. For selected cases, CGNM modes were found to be more robust among proteins that have the same topology or are of the same homologous superfamily than ED modes. In view of recent evidence regarding evolutionary conservation of vibrational dynamics, this suggests that ED modes, in some cases, might not be representative of the underlying dynamics that are characteristic of a whole family, probably due to insufficient sampling of some of the family members by MD. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Quantitative analysis of protein interaction network dynamics in yeast

Many cellular functions are mediated by protein–protein interaction networks, which are environment dependent. However, systematic measurement of interactions in diverse environments is required to better understand the relative importance of different mechanisms underlying network dynamics. To investigate environment‐dependent protein complex dynamics, we used a DNA‐barcode‐based multiplexed protein interaction assay in Saccharomyces cerevisiae to measure in vivo abundance of 1,379 binary protein complexes under 14 environments. Many binary complexes (55%) were environment dependent, especially those involving transmembrane transporters. We observed many concerted changes around highly connected proteins, and overall network dynamics suggested that “concerted” protein‐centered changes are prevalent. Under a diauxic shift in carbon source from glucose to ethanol, a mass‐action‐based model using relative mRNA levels explained an estimated 47% of the observed variance in binary complex abundance and predicted the direction of concerted binary complex changes with 88% accuracy. Thus, we provide a resource of yeast protein interaction measurements across diverse environments and illustrate the value of this resource in revealing mechanisms of network dynamics.     

Learning a functional grammar of protein domains using natural language word embedding techniques

In this paper, using Word2vec, a widely-used natural language processing method, we demonstrate that protein domains may have a learnable implicit semantic “meaning” in the context of their functional contributions to the multi-domain proteins in which they are found. Word2vec is a group of models which can be used to produce semantically meaningful embeddings of words or tokens in a fixed-dimension vector space. In this work, we treat multi-domain proteins as “sentences” where domain identifiers are tokens which may be considered as “words.” Using all InterPro (Finn et al. 2017) pfam domain assignments we observe that the embedding could be used to suggest putative GO assignments for Pfam (Finn et al. 2016) domains of unknown function.     

Quality control of mitochondria during aging: Is there a good and a bad side of mitochondrial dynamics?

Maintenance of functional mitochondria is essential in order to prevent degenerative processes leading to disease and aging. Mitochondrial dynamics plays a crucial role in ensuring mitochondrial quality but may also generate and spread molecular damage through a population of mitochondria. Computational simulations suggest that this dynamics is advantageous when mitochondria are not or only marginally damaged. In contrast, at a higher degree of damage, mitochondrial dynamics may be disadvantageous. Deceleration of fusion‐fission cycles could be one way to adapt to this situation and to delay a further decline in mitochondrial quality. However, this adaptive response makes the mitochondrial network more vulnerable to additional molecular damage. The “mitochondrial infectious damage adaptation” (MIDA) model explains a number of inconsistent and counterintuitive data such as the “clonal expansion” of mutant mitochondrial DNA. We propose that mitochondrial dynamics is a double‐edged sword and suggest ways to test this experimentally.     

Peptide mechanics: A force field for peptides and proteins working with entire residues as smallest units

The central ingredient of any structure modeling tool is a molecular model or force field that accounts for proper geometry and energy calculation. For protein and peptide modeling based on entire amino acids as building blocks, we describe a peptide force field in which each amino acid is represented by a single point in space, taken at the position of the α-carbon atom. Apart from the positional coordinates, these units carry the two torsional angles φ and Ψ as additional degrees of freedom to account for the orientations of the peptide links. While some of the energy terms are analogous to expressions in atomic force fields, the presence of the angular variables leads to fundamental differences with new features and additional terms with no atomic counterparts. The force field reproduces secondary structure elements with very good accuracy. Globular parts of tertiary packing stay near the experimental structures with a rms deviation in C-α positions of 0.1–0.3 nm and about 25° in φ and Ψ depending on the size of the structure. A tendency for larger discrepancies is observed in exposed loops or terminal segments the conformations of which may be strongly influenced by neighboring domains. Finally, a scope of possible applications is presented. They range from modeling activities, such as model building by homology, to coarse scanning of conformation space in conformation analysis and structure determination. An extension to a dynamics model would offer the possibility to eliminate the less interesting high-frequency modes that in all-atom force-field dynamics absorb most of the computational effort.