Quantification of Drive-Response Relationships Between Residues During Protein Folding

Granger Causality Analysis of Chignolin Folding

Constantly advancing computer simulations of biomolecules provide huge amounts of data that are difficult to interpret. In particular, obtaining insights into functional aspects of macromolecular dynamics, often related to cascades of transient events, calls for methodologies that depart from the well-grounded framework of equilibrium statistical physics. One of the approaches toward the analysis of complex temporal data which has found applications in the fields of neuroscience and econometrics is Granger causality analysis. It allows determining which components of multidimensional time series are most influential for the evolution of the entire system, thus providing insights into causal relations within the dynamic structure of interest. In this work, we apply Granger analysis to a long molecular dynamics trajectory depicting repetitive folding and unfolding of a mini β-hairpin protein, CLN025. We find objective, quantitative evidence indicating that rearrangements within the hairpin turn region are determinant for protein folding and unfolding. On the contrary, interactions between hairpin arms score low on the causality scale. Taken together, these findings clearly favor the concept of zipperlike folding, which is one of two postulated β-hairpin folding mechanisms. More importantly, the results demonstrate the possibility of a conclusive application of Granger causality analysis to a biomolecular system.

Coarse-Grained Molecular Dynamics Simulations of Paclitaxel-Loaded Polymeric Micelles

A continuous manufacturing technology based on coaxial turbulent jet in coflow was previously developed to produce paclitaxel-loaded polymeric micelles. Herein, coarse-grained molecular dynamics (CG-MD) simulations were implemented to better understand the effect of the material attributes (i.e., the drug-polymer ratio and the ethanol concentration) and process parameters (i.e., temperature) on the self-assembly process of polymeric micelles as well as to provide molecular details on micelle instability. An all-atom (AA) poly (ethylene glycol)-poly (lactic acid) (PEG-PLA) polymer model was developed as the reference for parameterizing a coarse-grained (CG) model, and the AA polymer model was further validated with experimental glass transition temperature (T_g). The model transferability was verified by comparing structural properties between the AA and CG models. The CG model was further validated with experimental data, including micelle particle size measurements and drug encapsulation efficiency. Furthermore, the encapsulation of paclitaxel into the polymeric micelles was included in the simulations, taking into consideration the interactions between the paclitaxel and the polymers. The results from various points of view demonstrated a strong dependence of the shape of the micelles on the drug encapsulation, with micelles transitioning from spherical to ellipsoidal structures with an increasing paclitaxel amount. Simulation data were also used to identify the critical aggregation number (i.e., the number of polymer and drug molecules required for transition from one shape to another). Improved micellar structural stability was found with a larger micellar size and less solvent accessibility. Lastly, an evaluation was performed on the micellar dissociation free energy using a steered molecular dynamics simulation over a range of temperatures and ethanol concentrations. These simulations revealed that at higher ethanol and temperature conditions, micelles become destabilized, resulting in greater paclitaxel release. The increased drug release was determined to originate from the solvation of the hydrophobic core, which promoted micellar swelling and an associated reduction in hydrophobic interactions, leading to a loosely packed micellar structure.

Long-range Regulation of Partially Folded Amyloidogenic Peptides

Neurodegeneration involves abnormal aggregation of intrinsically disordered amyloidogenic peptides (IDPs), usually mediated by hydrophobic protein-protein interactions. There is mounting evidence that formation of α-helical intermediates is an early event during self-assembly of amyloid-β42 (Aβ42) and α-synuclein (αS) IDPs in Alzheimer’s and Parkinson’s disease pathogenesis, respectively. However, the driving force behind on-pathway molecular assembly of partially folded helical monomers into helical oligomers assembly remains unknown. Here, we employ extensive molecular dynamics simulations to sample the helical conformational sub-spaces of monomeric peptides of both Aβ42 and αS. Our computed free energies, population shifts, and dynamic cross-correlation network analyses reveal a common feature of long-range intra-peptide modulation of partial helical folds of the amyloidogenic central hydrophobic domains via concerted coupling with their charged terminal tails (N-terminus of Aβ42 and C-terminus of αS). The absence of such inter-domain fluctuations in both fully helical and completely unfolded (disordered) states suggests that long-range coupling regulates the dynamicity of partially folded helices, in both Aβ42 and αS peptides. The inter-domain coupling suggests a form of intra-molecular allosteric regulation of the aggregation trigger in partially folded helical monomers. This approach could be applied to study the broad range of amyloidogenic peptides, which could provide a new path to curbing pathogenic aggregation of partially folded conformers into oligomers, by inhibition of sites far from the hydrophobic core.

Cross-Sectoral Information Transfer in the Chinese Stock Market around Its Crash in 2015

This paper applies effective transfer entropy to research the information transfer in the Chinese stock market around its crash in 2015. According to the market states, the entire period is divided into four sub-phases: the tranquil, bull, crash, and post-crash periods. Kernel density estimation is used to calculate the effective transfer entropy. Then, the information transfer network is constructed. Nodes’ centralities and the directed maximum spanning trees of the networks are analyzed. The results show that, in the tranquil period, the information transfer is weak in the market. In the bull period, the strength and scope of the information transfer increases. The utility sector outputs a great deal of information and is the hub node for the information flow. In the crash period, the information transfer grows further. The market efficiency in this period is worse than that in the other three sub-periods. The information technology sector is the biggest information source, while the consumer staples sector receives the most information. The interactions of the sectors become more direct. In the post-crash period, information transfer declines but is still stronger than the tranquil time. The financial sector receives the largest amount of information and is the pivot node.

Entropy Transfer between Residue Pairs and Allostery in Proteins: Quantifying Allosteric Communication in Ubiquitin

It has recently been proposed by Gunasakaran et al. that allostery may be an intrinsic property of all proteins. Here, we develop a computational method that can determine and quantify allosteric activity in any given protein. Based on Schreiber's transfer entropy formulation, our approach leads to an information transfer landscape for the protein that shows the presence of entropy sinks and sources and explains how pairs of residues communicate with each other using entropy transfer. The model can identify the residues that drive the fluctuations of others. We apply the model to Ubiquitin, whose allosteric activity has not been emphasized until recently, and show that there are indeed systematic pathways of entropy and information transfer between residues that correlate well with the activities of the protein. We use 600 nanosecond molecular dynamics trajectories for Ubiquitin and its complex with human polymerase iota and evaluate entropy transfer between all pairs of residues of Ubiquitin and quantify the binding susceptibility changes upon complex formation. We explain the complex formation propensities of Ubiquitin in terms of entropy transfer. Important residues taking part in allosteric communication in Ubiquitin predicted by our approach are in agreement with results of NMR relaxation dispersion experiments. Finally, we show that time delayed correlation of fluctuations of two interacting residues possesses an intrinsic causality that tells which residue controls the interaction and which one is controlled. Our work shows that time delayed correlations, entropy transfer and causality are the required new concepts for explaining allosteric communication in proteins.

Roles of glycans in interactions between gp120 and HIV broadly neutralizing antibodies

Many novel broadly neutralizing antibodies against human immunodeficiency virus (HIV) have been identified during the past decade, providing promising templates for the development of an effective HIV-1 vaccine. Structural studies reveal that the epitopes of some of these antibodies involve one or more crucial glycans, without which the binding is completely abolished. In this study, we have investigated the critical roles of glycans in interactions between HIV-1 gp120 and two broadly neutralizing antibodies PG9 (targeting V1/V2) and PGT128 (targeting V3) that are able to neutralize more than 70% of HIV-1 isolates. We have performed molecular dynamics simulations of a number of systems including antibody-gp120 complex with and without glycans, antibody, gp120 with and without glycans, and glycan-only systems. The simulation results show that the complex structures are stabilized by the glycans, and the multivalent interactions between the antibody and gp120 promote cooperativities to further enhance the binding. In the free gp120, the glycans increase the flexibility of the V1/V2 and V3 loops, which likely increases the entropy cost of the antibody recognition. However, the antibodies are able to bind the flexible interface by recognizing the preexisting glycan conformation, and penetrating the glycan shield with flexible complementarity determining region loops that sample the bound conformations occasionally.

Preferred conformations of N-glycan core pentasaccharide in solution and in glycoproteins

N-linked glycans are on protein surfaces and have direct and water/ion-mediated interactions with surrounding amino acids. Such contacts could restrict their conformational freedom compared to the same glycans free in solution. In this work, we have examined the conformational freedom of the N-glycan core pentasaccharide moiety in solution using standard molecular dynamics (MD) simulations as well as temperature replica-exchange MD simulations. Both simulations yield the comparable conformational variability of the pentasaccharide in solution, indicating the convergence of both simulations. The glycoprotein crystal structures are analyzed to compare the conformational freedom of the N-glycan on the protein surface with the simulation result. Surprisingly, the pentasaccharide free in solution shows more restricted conformational variability than the N-glycan on the protein surface. The interactions between the carbohydrate and the protein side chain appear to be responsible for the increased conformational diversity of the N-glycan on the protein surface. Finally, the transfer entropy analysis of the simulation trajectory also reveals an unexpected causality relationship between intramolecular hydrogen bonds and the conformational states in that the hydrogen bonds play a role in maintaining the conformational states rather than driving the change in glycosidic torsional states.

Structure and dynamics analysis on plexin-B1 Rho GTPase binding domain as a monomer and dimer

Plexin-B1 is a single-pass transmembrane receptor. Its Rho GTPase binding domain (RBD) can associate with small Rho GTPases and can also self-bind to form a dimer. In total, more than 400 ns of NAMD molecular dynamics simulations were performed on RBD monomer and dimer. Different analysis methods, such as root mean squared fluctuation (RMSF), order parameters (S(2)), dihedral angle correlation, transfer entropy, principal component analysis, and dynamical network analysis, were carried out to characterize the motions seen in the trajectories. RMSF results show that after binding, the L4 loop becomes more rigid, but the L2 loop and a number of residues in other regions become slightly more flexible. Calculating order parameters (S(2)) for CH, NH, and CO bonds on both backbone and side chain shows that the L4 loop becomes essentially rigid after binding, but part of the L1 loop becomes slightly more flexible. Backbone dihedral angle cross-correlation results show that loop regions such as the L1 loop including residues Q25 and G26, the L2 loop including residue R61, and the L4 loop including residues L89-R91, are highly correlated compared to other regions in the monomer form. Analysis of the correlated motions at these residues, such as Q25 and R61, indicate two signal pathways. Transfer entropy calculations on the RBD monomer and dimer forms suggest that the binding process should be driven by the L4 loop and C-terminal. However, after binding, the L4 loop functions as the motion responder. The signal pathways in RBD were predicted based on a dynamical network analysis method using the pathways predicted from the dihedral angle cross-correlation calculations as input. It is found that the shortest pathways predicted from both inputs can overlap, but signal pathway 2 (from F90 to R61) is more dominant and overlaps all of the routes of pathway 1 (from F90 to P111). This project confirms the allosteric mechanism in signal transmission inside the RBD network, which was in part proposed in the previous experimental study.

Preferred orientations of phosphoinositides in bilayers and their implications in protein recognition mechanisms

Phosphoinositides (PIPs), phosphorylated derivatives of phosphatidylinositol (PI), are essential regulatory lipids involved in various cellular processes, including signal transduction, membrane trafficking, and cytoskeletal remodeling. To gain insight into the protein-PIPs recognition process, it is necessary to study the inositol ring orientation (with respect to the membrane) of PIPs with different phosphorylation states. In this study, 8 PIPs (3 PIP, 2 PIP2, and 3 PIP3) with different phosphorylation and protonation sites have been separately simulated in two mixed bilayers (one with 20% phosphatidylserine (PS) lipids and another with PS lipids switched to phosphatidylcholine (PC) lipids), which roughly correspond to yeast membranes. Uniformity of the bilayer properties including hydrophobic thickness, acyl chain order parameters, and heavy atom density profiles is observed in both PS-contained and PC-enriched membranes due to the same hydrophobic core composition. The relationship between the inositol ring orientation (tilt and rotation angles) and its solvent-accessible surface area indicates that the orientation is mainly determined by its solvation energy. Different PIPs exhibit a clear preference in the inositol ring rotation angle. Surprisingly, a larger proportion of PIPs inositol rings stay closer to the surface of PS-contained membranes compared to PC-enriched ones. Such a difference is rationalized with the formation of more hydrogen bonds between the PS/PI headgroups and the PIPs inositol rings in PS-contained membranes. This hydrogen bond network could be functionally important; thus, the present results can potentially add important and detailed features into the existing protein-PIPs recognition mechanism.