"Fluctuograms" reveal the intermittent intra-protein communication in subtilisin Carlsberg and correlate mechanical coupling with co-evolution

Statistical Learning of Protein Elastic Network from Positional Covariance Matrix

Positional fluctuation and covariance during protein dynamics are key observables for understanding the molecular origin of biological functions. A frequently employed potential energy function for describing protein structural variation at the coarse-gained level is elastic network model (ENM). A long-standing issue in biomolecular simulation is thus the parametrization of ENM spring constants from the components of positional covariance matrix (PCM). Based on sensitivity analysis of PCM, the direct-coupling statistics of each spring, which is a specific combination of position fluctuation and covariance, is found to exhibit prominent signal of parameter dependence. This finding provides the basis for devising the objective function and the scheme of running through the effective one-dimensional optimization of every spring by self-consistent iteration. Formal derivation of the positional covariance statistical learning (PCSL) method also motivates the necessary data regularization for stable calculations. Robust convergence of PCSL is achieved in taking an all-atom molecular dynamics trajectory or an ensemble of homologous structures as input data. The PCSL framework can also be generalized with mixed objective functions to capture specific property such as the residue flexibility profile. Such physical chemistry-based statistical learning thus provides a useful platform for integrating the mechanical information encoded in various experimental or computational data.

Edge weights in a protein elastic network reorganize collective motions and render long-range sensitivity responses

The effects of inter-residue interactions on protein collective motions are analyzed by comparing two elastic network models (ENM)—structural contact ENM (SC-ENM) and molecular dynamics (MD)-ENM—with the edge weights computed from an all-atom MD trajectory by structure-mechanics statistical learning. A theoretical framework is devised to decompose the eigenvalues of ENM Hessian into contributions from individual springs and to compute the sensitivities of positional fluctuations and covariances to spring constant variation. Our linear perturbation approach quantifies the response mechanisms as softness modulation and orientation shift. All contacts of C α positions in SC-ENM have an identical spring constant by fitting the profile of root-of-mean-squared-fluctuation calculated from an all-atom MD simulation, and the same trajectory data are also used to compute the specific spring constant of each contact as an MD-ENM edge weight. We illustrate that the soft-mode reorganization can be understood in terms of gaining weights along the structural contacts of low elastic strengths and loosing magnitude along those of high rigidities. With the diverse mechanical strengths encoded in protein dynamics, MD-ENM is found to have more pronounced long-range couplings and sensitivity responses with orientation shift identified as a key player in driving the specific residues to have high sensitivities. Furthermore, the responses of perturbing the springs of different residues are found to have asymmetry in the action–reaction relationship. In understanding the mutation effects on protein functional properties, such as long-range communications, our results point in the directions of collective motions as a major effector.

Structure-mechanics statistical learning unravels the linkage between local rigidity and global flexibility in nucleic acids

The mechanical properties of nucleic acids underlie biological processes ranging from genome packaging to gene expression, but tracing their molecular origin has been difficult due to the structural and chemical complexity. We posit that concepts from machine learning can help to tackle this long-standing challenge. Here, we demonstrate the feasibility and advantage of this strategy through developing a structure-mechanics statistical learning scheme to elucidate how local rigidity in double-stranded (ds)DNA and dsRNA may lead to their global flexibility in bend, stretch, and twist. Specifically, the mechanical parameters in a heavy-atom elastic network model are computed from the trajectory data of all-atom molecular dynamics simulation. The results show that the inter-atomic springs for backbone and ribose puckering in dsRNA are stronger than those in dsDNA, but are similar in strengths for base-stacking and base-pairing. Our analysis shows that the experimental observation of dsDNA being easier to bend but harder to stretch than dsRNA comes mostly from the respective B- and A-form topologies. The computationally resolved composition of local rigidity indicates that the flexibility of both nucleic acids is mostly due to base-stacking. But for properties like twist-stretch coupling, backbone springs are shown to play a major role instead. The quantitative connection between local rigidity and global flexibility sets foundation for understanding how local binding and chemical modification of genetic materials effectuate longer-ranged regulatory signals.

The mechanical properties of nucleic acids underlie biological processes ranging from genome packaging to gene expression. We devise structural mechanics statistical learning method to reveal their molecular origin in terms of chemical interactions.

Molecular motions and free-energy landscape of serine proteinase K in relation to its cold-adaptation: a comparative molecular dynamics simulation study and the underlying mechanisms

The physicochemical bases for enzyme cold-adaptation remain elusive.

Calculation of Enzyme Fluctuograms from All-Atom Molecular Dynamics Simulation

In this work, a computational framework is presented to compute the time evolution of force constants for a coarse grained (CG) elastic network model along an all-atom molecular dynamics trajectory of a protein system. Obtained via matching distance fluctuations, these force constants represent strengths of mechanical coupling between CG beads. Variation of coupling strengths with time is hence termed the fluctuogram of protein dynamics. In addition to the schematic procedure and implementation considerations, several ways of combining force constants and data analysis are presented to illustrate the potential application of protein fluctuograms. The unique angle provided by the fluctuogram expands the scope of atomistic simulations and is expected to impact upon fundamental understanding of protein dynamics as well as protein engineering technologies.

Discovery of Novel Allosteric Eg5 Inhibitors Through Structure-Based Virtual Screening

Mitotic kinesin Eg5 is an attractive anticancer drug target. Discovery of Eg5 inhibitors has been focused on targeting the 'monastrol-binding site'. However, acquired drug resistance has been reported for such inhibitors. Therefore, identifying new Eg5 inhibitors which function through a different mechanism(s) could complement current drug candidates and improve drug efficacy. In this study, we explored a novel allosteric site of Eg5 and identified new Eg5 inhibitors through structure-based virtual screening. Experiments with the saturation-transfer difference NMR demonstrated that the identified Eg5 inhibitor SRI35566 binds directly to Eg5 without involving microtubules. Moreover, SRI35566 and its two analogs significantly induced monopolar spindle formation in colorectal cancer HCT116 cells and suppressed cancer cell viability and colony formation. Together, our findings reveal a new allosteric regulation mechanism of Eg5 and a novel drug targeting site for cancer therapy.

(Dis)similarity Index To Compare Correlated Motions in Molecular Simulations

Molecular dynamics (MD) simulations are widely used to complement or guide experimental studies in the characterization of protein dynamics, thanks to improvements in force-field accuracy, along with in the software and hardware to sample the conformational landscape of proteins. Among the different applications of MD simulations, the study of correlated motions is largely employed for different purposes. Several metrics have been developed to describe correlated motions in the MD ensemble, such as methods based on Pearson Correlation or Mutual Information. Cross-correlation analysis of MD trajectories is indeed appealing not only to identify residues characterized by coupled fluctuations in protein structures but also since it can be used to extrapolate motions along directions in which major conformational changes should occur, for example on longer time scales than the ones that are actually simulated. Nevertheless, most of the MD studies employ average correlation maps and mostly in a qualitative way, even when different systems or different replicates of the same system are compared. The broad application of correlation metrics in the analysis of MD simulations, especially for comparative purposes, requires a step forward toward more quantitative and accurate comparisons. We thus here employed a simple but effective index, which is based on a normalized Frobenius norm of the differences between protein correlation maps, to compare correlated motions. We applied this index for a quantitative comparison of correlated motions from MD simulations of seven proteins of different size and fold. We also employed the index to assess the robustness of correlation description when multi-replicate MD simulations of a same system are used, and we compared our index to metrics for comparison of structural ensembles such as Root Mean Square Inner Product and the Bhattacharyya Coefficient.

Loop 7 of E2 enzymes: an ancestral conserved functional motif involved in the E2-mediated steps of the ubiquitination cascade

The ubiquitin (Ub) system controls almost every aspect of eukaryotic cell biology. Protein ubiquitination depends on the sequential action of three classes of enzymes (E1, E2 and E3). E2 Ub-conjugating enzymes have a central role in the ubiquitination pathway, interacting with both E1 and E3, and influencing the ultimate fate of the substrates. Several E2s are characterized by an extended acidic insertion in loop 7 (L7), which if mutated is known to impair the proper E2-related functions. In the present contribution, we show that acidic loop is a conserved ancestral motif in E2s, relying on the presence of alternate hydrophobic and acidic residues. Moreover, the dynamic properties of a subset of family 3 E2s, as well as their binary and ternary complexes with Ub and the cognate E3, have been investigated. Here we provide a model of L7 role in the different steps of the ubiquitination cascade of family 3 E2s. The L7 hydrophobic residues turned out to be the main determinant for the stabilization of the E2 inactive conformations by a tight network of interactions in the catalytic cleft. Moreover, phosphorylation is known from previous studies to promote E2 competent conformations for Ub charging, inducing electrostatic repulsion and acting on the L7 acidic residues. Here we show that these active conformations are stabilized by a network of hydrophobic interactions between L7 and L4, the latter being a conserved interface for E3-recruitment in several E2s. In the successive steps, L7 conserved acidic residues also provide an interaction interface for both Ub and the Rbx1 RING subdomain of the cognate E3. Our data therefore suggest a crucial role for L7 of family 3 E2s in all the E2-mediated steps of the ubiquitination cascade. Its different functions are exploited thank to its conserved hydrophobic and acidic residues in a finely orchestrate mechanism.

xPyder: a PyMOL plugin to analyze coupled residues and their networks in protein structures

A versatile method to directly identify and analyze short- or long-range coupled or communicating residues in a protein conformational ensemble is of extreme relevance to achieve a complete understanding of protein dynamics and structural communication routes. Here, we present xPyder, an interface between one of the most employed molecular graphics systems, PyMOL, and the analysis of dynamical cross-correlation matrices (DCCM). The approach can also be extended, in principle, to matrices including other indexes of communication propensity or intensity between protein residues, as well as the persistence of intra- or intermolecular interactions, such as those underlying protein dynamics. The xPyder plugin for PyMOL 1.4 and 1.5 is offered as Open Source software via the GPL v2 license, and it can be found, along with the installation package, the user guide, and examples, at http://linux.btbs.unimib.it/xpyder/.

Dynamic prestress in a globular protein

A protein at equilibrium is commonly thought of as a fully relaxed structure, with the intra-molecular interactions showing fluctuations around their energy minimum. In contrast, here we find direct evidence for a protein as a molecular tensegrity structure, comprising a balance of tensed and compressed interactions, a concept that has been put forward for macroscopic structures. We quantified the distribution of inter-residue prestress in ubiquitin and immunoglobulin from all-atom molecular dynamics simulations. The network of highly fluctuating yet significant inter-residue forces in proteins is a consequence of the intrinsic frustration of a protein when sampling its rugged energy landscape. In beta sheets, this balance of forces is found to compress the intra-strand hydrogen bonds. We estimate that the observed magnitude of this pre-compression is enough to induce significant changes in the hydrogen bond lifetimes; thus, prestress, which can be as high as a few 100 pN, can be considered a key factor in determining the unfolding kinetics and pathway of proteins under force. Strong pre-tension in certain salt bridges on the other hand is connected to the thermodynamic stability of ubiquitin. Effective force profiles between some side-chains reveal the signature of multiple, distinct conformational states, and such static disorder could be one factor explaining the growing body of experiments revealing non-exponential unfolding kinetics of proteins. The design of prestress distributions in engineering proteins promises to be a new tool for tailoring the mechanical properties of made-to-order nanomaterials.

A tensegrity structure is one composed of members that are permanently under either tension or compression, and the balance of these tensile and compressive forces provides the structure with its mechanical stability. Macroscale tensegrity structures, which include Buckminster Fuller's geodesic domes, achieve exceptional structural integrity with a minimal use of resources. The question we address in this work is whether nature makes use of molecular-scale tensegrity in the design of proteins. Using Molecular Dynamics simulations of the protein ubiquitin, we measure the network of pairwise forces connecting the amino acid residues and show that this network does indeed have the character of a tensegrity structure. Furthermore, we find that the arrangement of tensile and compressive forces is such that hydrogen bonds in the protein's beta sheet, which are crucial for bearing mechanical loads, are compressed. This pre-compression is enough to significantly lengthen the lifetime of a bond under a given force, and thus should be an important factor in determining the protein's mechanical strength. The rational design of molecular prestress networks promises to be a new avenue for the engineering of proteins with made-to-order mechanical properties, for applications in medicine, materials and nanotechnology.

Mechanisms of intramolecular communication in a hyperthermophilic acylaminoacyl peptidase: a molecular dynamics investigation

Protein dynamics and the underlying networks of intramolecular interactions and communicating residues within the three-dimensional (3D) structure are known to influence protein function and stability, as well as to modulate conformational changes and allostery. Acylaminoacyl peptidase (AAP) subfamily of enzymes belongs to a unique class of serine proteases, the prolyl oligopeptidase (POP) family, which has not been thoroughly investigated yet. POPs have a characteristic multidomain three-dimensional architecture with the active site at the interface of the C-terminal catalytic domain and a β-propeller domain, whose N-terminal region acts as a bridge to the hydrolase domain. In the present contribution, protein dynamics signatures of a hyperthermophilic acylaminoacyl peptidase (AAP) of the prolyl oligopeptidase (POP) family, as well as of a deletion variant and alanine mutants (I12A, V13A, V16A, L19A, I20A) are reported. In particular, we aimed at identifying crucial residues for long range communications to the catalytic site or promoting the conformational changes to switch from closed to open ApAAP conformations. Our investigation shows that the N-terminal α1-helix mediates structural intramolecular communication to the catalytic site, concurring to the maintenance of a proper functional architecture of the catalytic triad. Main determinants of the effects induced by α1-helix are a subset of hydrophobic residues (V16, L19 and I20). Moreover, a subset of residues characterized by relevant interaction networks or coupled motions have been identified, which are likely to modulate the conformational properties at the interdomain interface.