Prediction of protein-protein association rates from a transition-state theory

Bioorthogonal Engineered Virus-Like Nanoparticles for Efficient Gene Therapy

Gene therapy offers potentially transformative strategies for major human diseases. However, one of the key challenges in gene therapy is developing an effective strategy that could deliver genes into the specific tissue. Here, we report a novel virus-like nanoparticle, the bioorthgonal engineered virus-like recombinant biosome (reBiosome), for efficient gene therapies of cancer and inflammatory diseases. The mutant virus-like biosome (mBiosome) is first prepared by site-specific codon mutation for displaying 4-azido-L-phenylalanine on vesicular stomatitis virus glycoprotein of eBiosome at a rational site, and the reBiosome is then prepared by clicking weak acid-responsive hydrophilic polymer onto the mBiosome via bioorthogonal chemistry. The results show that the reBiosome exhibits reduced virus-like immunogenicity, prolonged blood circulation time and enhanced gene delivery efficiency to weakly acidic foci (like tumor and arthritic tissue). Furthermore, reBiosome demonstrates robust therapeutic efficacy in breast cancer and arthritis by delivering gene editing and silencing systems, respectively. In conclusion, this study develops a universal, safe and efficient platform for gene therapies for cancer and inflammatory diseases.

Multi-Level High-Throughput Screening for Discovery of Ligands That Inhibit Insulin Aggregation

We have developed a multi-level virtual screening protocol to identify lead molecules from the FDA inactives database that can inhibit insulin aggregation. The method is based on the presence of structural and interaction specificity in non-native aggregation pathway protein-protein interactions. Some key challenges specific to the present problem, when compared with native protein association, include structural heterogeneity of the protein species involved, multiple association pathways, and relatively higher probability of conformational rearrangement of the association complex. In this multi-step method, the inactives database was first screened using the dominant pharmacophore features of previously identified molecules shown to significantly inhibit insulin aggregation nucleation by binding to its aggregation-prone conformers. We then performed ensemble docking of several low-energy ligand conformations on these aggregation-prone conformers followed by molecular dynamics simulations and binding affinity calculations on a subset of docked complexes to identify a final set of five potential lead molecules to inhibit insulin aggregation nucleation. Their effect on aggregation inhibition was extensively investigated by incubating insulin under aggregation-prone aqueous buffer conditions (low pH, high temperature). Aggregation kinetics were characterized using size exclusion chromatography and Thioflavin T fluorescence assay, and the secondary structure was determined using circular dichroism spectroscopy. Riboflavin provided the best aggregation inhibition, with 85% native monomer retention after 48 h incubation under aggregation-prone conditions, whereas the no-ligand formulation showed complete monomer loss after 36 h. Further, insulin incubated with two of the screened inactives (aspartame, riboflavin) had the characteristic α-helical dip in CD spectra, while the no-ligand formulation showed a change to β-sheet rich conformations.

Multiscale Model for Quantitative Prediction of Insulin Aggregation Nucleation Kinetics

We combined kinetic, thermodynamic, and structural information from single-molecule (protein folding) and two-molecule (association) explicit-solvent simulations for determination of kinetic parameters in protein aggregation nucleation with insulin as the model protein. A structural bioinformatics approach was developed to account for heterogeneity of aggregation-prone species, with the transition complex theory found applicable in modeling association kinetics involving non-native species. Specifically, the kinetic pathway for formation of aggregation-prone oligomeric species was found to contain a structurally specific dominant binding mode, making the kinetic process similar to native protein association. The kinetic parameters thus obtained were used in a population balance model, and accurate predictions for aggregation nucleation time varying over 2 orders of magnitude with changes in either insulin concentration or an aggregation-inhibitor ligand concentration were obtained, while an empirical parameter set was not found to be transferable for prediction of ligand effects. Further, this physically determined kinetic parameter set provided several mechanistic insights, such as identification of the rate-limiting step in aggregation nucleation and a quantitative explanation for the switch from Arrhenius to non-Arrhenius aggregation kinetics around the melting temperature of insulin.

Influence of molecular rebinding on the reaction rate of complex formation

We simulated Brownian diffusion and reaction-diffusion processes to study the influence of molecular rebinding on the reaction rates of bimolecular reactions. We found that the number of rebinding events, N_reb, is proportional to the target's size and inversely proportional to the diffusion coefficient D and simulation time-step Δt. We found the proportionality constant close to π^-1/2. We confirmed that N_reb is defined as a ratio of the activation-limited rate constant k_a to the diffusion-limited rate constant, k_D. We provide the formula describing the reactivity coefficient κ, modelling the transient-native complex transition for the activation-controlled reaction rates. We show that κ is proportional to (D/Δt)^1/2. Finally, we apply our rebinding-including reaction rate model to the real reactions of photoacid dissociation and protein association. Based on literature data for both types of reactions, we found the Δt time-scale. We show that for the photodissociation of a proton, the Δt is equal to 171 ± 18 fs and the average number of rebinding events is approximately equal to 40. For proteins, Δt is of the order of 100 ps with around 20 rebinding events. In both cases the timescale is similar to the timescale of fluctuation of the solvent molecules surrounding the reactants; vibrations and bending in the case of photoacid dissociation and diffusional motion for proteins.

Using Coarse-Grained Simulations to Characterize the Mechanisms of Protein-Protein Association

The formation of functionally versatile protein complexes underlies almost every biological process. The estimation of how fast these complexes can be formed has broad implications for unravelling the mechanism of biomolecular recognition. This kinetic property is traditionally quantified by association rates, which can be measured through various experimental techniques. To complement these time-consuming and labor-intensive approaches, we developed a coarse-grained simulation approach to study the physical processes of protein–protein association. We systematically calibrated our simulation method against a large-scale benchmark set. By combining a physics-based force field with a statistically-derived potential in the simulation, we found that the association rates of more than 80% of protein complexes can be correctly predicted within one order of magnitude relative to their experimental measurements. We further showed that a mixture of force fields derived from complementary sources was able to describe the process of protein–protein association with mechanistic details. For instance, we show that association of a protein complex contains multiple steps in which proteins continuously search their local binding orientations and form non-native-like intermediates through repeated dissociation and re-association. Moreover, with an ensemble of loosely bound encounter complexes observed around their native conformation, we suggest that the transition states of protein–protein association could be highly diverse on the structural level. Our study also supports the idea in which the association of a protein complex is driven by a “funnel-like” energy landscape. In summary, these results shed light on our understanding of how protein–protein recognition is kinetically modulated, and our coarse-grained simulation approach can serve as a useful addition to the existing experimental approaches that measure protein–protein association rates.

A Systematic Test of Receptor Binding Kinetics for Ligands in Tumor Necrosis Factor Superfamily by Computational Simulations

Ligands in the tumor necrosis factor (TNF) superfamily are one major class of cytokines that bind to their corresponding receptors in the tumor necrosis factor receptor (TNFR) superfamily and initiate multiple intracellular signaling pathways during inflammation, tissue homeostasis, and cell differentiation. Mutations in the genes that encode TNF ligands or TNFR receptors result in a large variety of diseases. The development of therapeutic treatment for these diseases can be greatly benefitted from the knowledge on binding properties of these ligand–receptor interactions. In order to complement the limitations in the current experimental methods that measure the binding constants of TNF/TNFR interactions, we developed a new simulation strategy to computationally estimate the association and dissociation between a ligand and its receptor. We systematically tested this strategy to a comprehensive dataset that contained structures of diverse complexes between TNF ligands and their corresponding receptors in the TNFR superfamily. We demonstrated that the binding stabilities inferred from our simulation results were compatible with existing experimental data. We further compared the binding kinetics of different TNF/TNFR systems, and explored their potential functional implication. We suggest that the transient binding between ligands and cell surface receptors leads into a dynamic nature of cross-membrane signal transduction, whereas the slow but strong binding of these ligands to the soluble decoy receptors is naturally designed to fulfill their functions as inhibitors of signal activation. Therefore, our computational approach serves as a useful addition to current experimental techniques for the quantitatively comparison of interactions across different members in the TNF and TNFR superfamily. It also provides a mechanistic understanding to the functions of TNF-associated cell signaling pathways.

Potential Regulatory Role of Competitive Encounter Complexes in Paralogous Phosphotransferase Systems

There are two paralogous Escherichia coli phosphotransferase systems, one for sugar import (PTS^sugar) and one for nitrogen regulation (PTS^Ntr), that utilize proteins enzyme I^sugar (EI^sugar) and HPr, and enzyme I^Ntr (EI^Ntr) and NPr, respectively. The enzyme I proteins have similar folds, as do their substrates HPr and NPr, yet they show strict specificity for their cognate partner both in stereospecific protein-protein complex formation and in reversible phosphotransfer. Here, we investigate the mechanism of specific EI^Ntr:NPr complex formation by the study of transient encounter complexes. NMR paramagnetic relaxation enhancement experiments demonstrated transient encounter complexes of EI^Ntr not only with the expected partner, NPr, but also with the unexpected partner, HPr. HPr occupies transient sites on EI^Ntr but is unable to complete stereospecific complex formation. By occupying the non-productive transient sites, HPr promotes NPr transient interaction to productive sites closer to the stereospecific binding site and actually enhances specific complex formation between NPr and EI^Ntr. The cellular level of HPr is approximately 150 times higher than that of NPr. Thus, our finding suggests a potential mechanism for cross-regulation of enzyme activity through formation of competitive encounter complexes.

Computational studies of protein-protein dissociation by statistical potential and coarse-grained simulations: a case study on interactions between colicin E9 endonuclease and immunity proteins

Proteins carry out their diverse functions in cells by forming interactions with each other. The dynamics of these interactions are quantified by the measurement of association and dissociation rate constants. Relative to the efforts made to model the association of biomolecules, little has been studied to understand the principles of protein complex dissociation. Using the interaction between colicin E9 endonucleases and immunity proteins as a test system, here we develop a coarse-grained simulation method to explore the dissociation mechanisms of protein complexes. The interactions between proteins in the complex are described by the knowledge-based potential that was constructed by the statistics from available protein complexes in the structural database. Our study provides the supportive evidences to the dual recognition mechanism for the specificity of binding between E9 DNase and immunity proteins, in which the conserved residues of helix III of Im2 and Im9 proteins act as the anchor for binding, while the sequence variations in helix II make positive or negative contributions to specificity. Beyond that, we further suggest that this binding specificity is rooted in the process of complex dissociation instead of association. While we increased the flexibility of protein complexes, we further found that they are less prone to dissociation, suggesting that conformational fluctuations of protein complexes play important functional roles in regulating their binding and dissociation. Our studies therefore bring new insights to the molecule mechanisms of protein-protein interactions, while the method can serve as a new addition to a suite of existing computational tools for the simulations of protein complexes.

Integrating Structural Information to Study the Dynamics of Protein-Protein Interactions in Cells

The information of how two proteins interact is embedded in the atomic details of their binding interfaces. These interactions, spatial-temporally coordinating each other as a network in a variable cytoplasmic environment, dominate almost all biological functions. A feasible and reliable computational model is highly demanded to realistically simulate these cellular processes and unravel the complexities beneath them. We therefore present a multiscale framework that integrates simulations on two different scales. The higher-resolution model incorporates structural information of proteins and energetics of their binding, while the lower-resolution model uses a highly simplified representation of proteins to capture the long-time-scale dynamics of a system with multiple proteins. Through a systematic benchmark test and two practical applications of biomolecular systems with specific cellular functions, we demonstrated that this method could be a powerful approach to understand molecular mechanisms of dynamic interactions between biomolecules and their functional impacts with high computational efficiency.

The Tiam1 guanine nucleotide exchange factor is auto-inhibited by its pleckstrin homology coiled-coil extension domain

T-cell lymphoma invasion and metastasis 1 (Tiam1) is a Dbl-family guanine nucleotide exchange factor (GEF) that specifically activates the Rho-family GTPase Rac1 in response to upstream signals, thereby regulating cellular processes including cell adhesion and migration. Tiam1 contains multiple domains, including an N-terminal pleckstrin homology coiled-coiled extension (PHn-CC-Ex) and catalytic Dbl homology and C-terminal pleckstrin homology (DH-PHc) domain. Previous studies indicate that larger fragments of Tiam1, such as the region encompassing the N-terminal to C-terminal pleckstrin homology domains (PHn-PHc), are auto-inhibited. However, the domains in this region responsible for inhibition remain unknown. Here, we show that the PHn-CC-Ex domain inhibits Tiam1 GEF activity by directly interacting with the catalytic DH-PHc domain, preventing Rac1 binding and activation. Enzyme kinetics experiments suggested that Tiam1 is auto-inhibited through occlusion of the catalytic site rather than by allostery. Small angle X-ray scattering and ensemble modeling yielded models of the PHn-PHc fragment that indicate it is in equilibrium between "open" and "closed" conformational states. Finally, single-molecule experiments support a model in which conformational sampling between the open and closed states of Tiam1 contributes to Rac1 dissociation. Our results highlight the role of the PHn-CC-Ex domain in Tiam1 GEF regulation and suggest a combinatorial model for GEF inhibition and activation of the Rac1 signaling pathway.

A Computational Model for Kinetic Studies of Cadherin Binding and Clustering

Cadherin is a cell-surface transmembrane receptor that mediates calcium-dependent cell-cell adhesion and is a major component of adhesive junctions. The formation of intercellular adhesive junctions is initiated by trans binding between cadherins on adjacent cells, which is followed by the clustering of cadherins via the formation of cis interactions between cadherins on the same cell membranes. Moreover, classical cadherins have multiple glycosylation sites along their extracellular regions. It was found that aberrant glycosylation affects the adhesive function of cadherins and correlates with metastatic phenotypes of several cancers. However, a mechanistic understanding of cadherin clustering during cell adhesion and the role of glycosylation in this process is still lacking. Here, we designed a kinetic model that includes multistep reaction pathways for cadherin clustering. We further applied a diffusion-reaction algorithm to numerically simulate the clustering process using a recently developed coarse-grained model. Using experimentally measured rates of trans binding between soluble E-cadherin extracellular domains, we conducted simulations of cadherin-mediated cell-cell binding kinetics, and the results are quantitatively comparable to experimental data from micropipette experiments. In addition, we show that incorporating cadherin clustering via cis interactions further increases intercellular binding. Interestingly, a two-phase kinetic profile was derived under the assumption that glycosylation regulates the kinetic rates of cis interactions. This two-phase profile is qualitatively consistent with experimental results from micropipette measurements. Therefore, our computational studies provide new, to our knowledge, insights into the molecular mechanism of cadherin-based cell adhesion.

Electrostatic forces govern the binding mechanism of intrinsically disordered histone chaperones

A unified picture to understand the protein recognition and function must include the native binding complex structure ensembles and the underlying binding mechanisms involved in specific biological processes. However, quantifications of both binding complex structures and dynamical mechanisms are still challenging for IDP. In this study, we have investigated the underlying molecular mechanism of the chaperone Chz1 and histone H2A.Z-H2B association by equilibrium and kinetic stopped-flow fluorescence spectroscopy. The dependence of free energy and kinetic rate constant on electrolyte mean activity coefficient and urea concentration are uncovered. Our results indicate a previous unseen binding kinetic intermediate. An initial conformation selection step of Chz1 is also revealed before the formation of this intermediate state. Based on these observations, a mixed mechanism of three steps including both conformation selection and induced fit is proposed. By combination of the ion- and denaturant-induced experiments, we demonstrate that electrostatic forces play a dominant role in the recognition of bipolar charged intrinsically disordered protein Chz1 to its preferred partner H2A.Z-H2B. Both the intra-chain and inter-chain electrostatic interactions have direct impacts on the native collapsed structure and binding mechanism.

Predicting Protein-protein Association Rates using Coarse-grained Simulation and Machine Learning

Protein–protein interactions dominate all major biological processes in living cells. We have developed a new Monte Carlo-based simulation algorithm to study the kinetic process of protein association. We tested our method on a previously used large benchmark set of 49 protein complexes. The predicted rate was overestimated in the benchmark test compared to the experimental results for a group of protein complexes. We hypothesized that this resulted from molecular flexibility at the interface regions of the interacting proteins. After applying a machine learning algorithm with input variables that accounted for both the conformational flexibility and the energetic factor of binding, we successfully identified most of the protein complexes with overestimated association rates and improved our final prediction by using a cross-validation test. This method was then applied to a new independent test set and resulted in a similar prediction accuracy to that obtained using the training set. It has been thought that diffusion-limited protein association is dominated by long-range interactions. Our results provide strong evidence that the conformational flexibility also plays an important role in regulating protein association. Our studies provide new insights into the mechanism of protein association and offer a computationally efficient tool for predicting its rate.

The RNF168 paralog RNF169 defines a new class of ubiquitylated histone reader involved in the response to DNA damage

Site-specific histone ubiquitylation plays a central role in orchestrating the response to DNA double-strand breaks (DSBs). DSBs elicit a cascade of events controlled by the ubiquitin ligase RNF168, which promotes the accumulation of repair factors such as 53BP1 and BRCA1 on the chromatin flanking the break site. RNF168 also promotes its own accumulation, and that of its paralog RNF169, but how they recognize ubiquitylated chromatin is unknown. Using methyl-TROSY solution NMR spectroscopy and molecular dynamics simulations, we present an atomic resolution model of human RNF169 binding to a ubiquitylated nucleosome, and validate it by electron cryomicroscopy. We establish that RNF169 binds to ubiquitylated H2A-Lys13/Lys15 in a manner that involves its canonical ubiquitin-binding helix and a pair of arginine-rich motifs that interact with the nucleosome acidic patch. This three-pronged interaction mechanism is distinct from that by which 53BP1 binds to ubiquitylated H2A-Lys15 highlighting the diversity in site-specific recognition of ubiquitylated nucleosomes.

Elucidating the general principles of cell adhesion with a coarse-grained simulation model

Coarse-grained simulation of interplay between cell adhesion and cell signaling.

Highly Efficient Computation of the Basal kon using Direct Simulation of Protein-Protein Association with Flexible Molecular Models

An essential baseline for determining the extent to which electrostatic interactions enhance the kinetics of protein–protein association is the “basal” k_on, which is the rate constant for association in the absence of electrostatic interactions. However, since such association events are beyond the milliseconds time scale, it has not been practical to compute the basal k_on by directly simulating the association with flexible models. Here, we computed the basal k_on for barnase and barstar, two of the most rapidly associating proteins, using highly efficient, flexible molecular simulations. These simulations involved (a) pseudoatomic protein models that reproduce the molecular shapes, electrostatic, and diffusion properties of all-atom models, and (b) application of the weighted ensemble path sampling strategy, which enhanced the efficiency of generating association events by >130-fold. We also examined the extent to which the computed basal k_on is affected by inclusion of intermolecular hydrodynamic interactions in the simulations.

Conformational frustration in calmodulin-target recognition

Calmodulin (CaM) is a primary calcium (Ca(2+) )-signaling protein that specifically recognizes and activates highly diverse target proteins. We explored the molecular basis of target recognition of CaM with peptides representing the CaM-binding domains from two Ca(2+) -CaM-dependent kinases, CaMKI and CaMKII, by employing experimentally constrained molecular simulations. Detailed binding route analysis revealed that the two CaM target peptides, although similar in length and net charge, follow distinct routes that lead to a higher binding frustration in the CaM-CaMKII complex than in the CaM-CaMKI complex. We discovered that the molecular origin of the binding frustration is caused by intermolecular contacts formed with the C-domain of CaM that need to be broken before the formation of intermolecular contacts with the N-domain of CaM. We argue that the binding frustration is important for determining the kinetics of the recognition process of proteins involving large structural fluctuations.

Linking 3D and 2D binding kinetics of membrane proteins by multiscale simulations

Membrane proteins are among the most functionally important proteins in cells. Unlike soluble proteins, they only possess two translational degrees of freedom on cell surfaces, and experience significant constraints on their rotations. As a result, it is currently challenging to characterize the in situ binding of membrane proteins. Using the membrane receptors CD2 and CD58 as a testing system, we developed a multiscale simulation framework to study the differences of protein binding kinetics between 3D and 2D environments. The association and dissociation processes were implemented by a coarse-grained Monte-Carlo algorithm, while the dynamic properties of proteins diffusing on lipid bilayer were captured from all-atom molecular dynamic simulations. Our simulations show that molecular diffusion, linker flexibility and membrane fluctuations are important factors in adjusting binding kinetics. Moreover, by calibrating simulation parameters to the measurements of 3D binding, we derived the 2D binding constant which is quantitatively consistent with the experimental data, indicating that the method is able to capture the difference between 3D and 2D binding environments. Finally, we found that the 2D dissociation between CD2 and CD58 is about 100-fold slower than the 3D dissociation. In summary, our simulation framework offered a generic approach to study binding mechanisms of membrane proteins.

Electrostatic interactions in the binding pathway of a transient protein complex studied by NMR and isothermal titration calorimetry

Much of our knowledge of protein binding pathways is derived from extremely stable complexes that interact very tightly, with lifetimes of hours to days. Much less is known about weaker interactions and transient complexes because these are challenging to characterize experimentally. Nevertheless, these types of interactions are ubiquitous in living systems. The combination of NMR relaxation dispersion Carr-Purcell-Meiboom-Gill (CPMG) experiments and isothermal titration calorimetry allows the quantification of rapid binding kinetics for complexes with submillisecond lifetimes that are difficult to study using conventional techniques. We have used this approach to investigate the binding pathway of the Src homology 3 (SH3) domain from the Fyn tyrosine kinase, which forms complexes with peptide targets whose lifetimes are on the order of about a millisecond. Long range electrostatic interactions have been shown to play a critical role in the binding pathways of tightly binding complexes. The role of electrostatics in the binding pathways of transient complexes is less well understood. Similarly to previously studied tight complexes, we find that SH3 domain association rates are enhanced by long range electrostatics, whereas short range interactions are formed late in the docking process. However, the extent of electrostatic association rate enhancement is several orders of magnitudes less, whereas the electrostatic-free basal association rate is significantly greater. Thus, the SH3 domain is far less reliant on electrostatic enhancement to achieve rapid association kinetics than are previously studied systems. This suggests that there may be overall differences in the role played by electrostatics in the binding pathways of extremely stable versus transient complexes.

Protein recognition and selection through conformational and mutually induced fit

Protein-protein interactions drive most every biological process, but in many instances the domains mediating recognition are disordered. How specificity in binding is attained in the absence of defined structure contrasts with well-established experimental and theoretical work describing ligand binding to protein. The signaling protein calmodulin presents a unique opportunity to investigate mechanisms for target recognition given that it interacts with several hundred different targets. By advancing coarse-grained computer simulations and experimental techniques, mechanistic insights were gained in defining the pathways leading to recognition and in how target selectivity can be achieved at the molecular level. A model requiring mutually induced conformational changes in both calmodulin and target proteins was necessary and broadly informs how proteins can achieve both high affinity and high specificity.

Protein flexibility, not disorder, is intrinsic to molecular recognition

An 'intrinsically disordered protein' (IDP) is assumed to be unfolded in the cell and perform its biological function in that state. We contend that most intrinsically disordered proteins are in fact proteins waiting for a partner (PWPs), parts of a multi-component complex that do not fold correctly in the absence of other components. Flexibility, not disorder, is an intrinsic property of proteins, exemplified by X-ray structures of many enzymes and protein-protein complexes. Disorder is often observed with purified proteins in vitro and sometimes also in crystals, where it is difficult to distinguish from flexibility. In the crowded environment of the cell, disorder is not compatible with the known mechanisms of protein-protein recognition, and, foremost, with its specificity. The self-assembly of multi-component complexes may, nevertheless, involve the specific recognition of nascent polypeptide chains that are incompletely folded, but then disorder is transient, and it must remain under the control of molecular chaperones and of the quality control apparatus that obviates the toxic effects it can have on the cell.

Directed self-assembly of proteins into discrete radial patterns

Unlike physical patterning of materials at nanometer scale, manipulating soft matter such as biomolecules into patterns is still in its infancy. Self-assembled monolayer (SAM) with surface density gradient has the capability to drive biomolecules in specific directions to create hierarchical and discrete structures. Here, we report on a two-step process of self-assembly of the human serum albumin (HSA) protein into discrete ring structures based on density gradient of SAM. The methodology involves first creating a 2-dimensional (2D) polyethylene glycol (PEG) islands with responsive carboxyl functionalities. Incubation of proteins on such pre-patterned surfaces results in direct self-assembly of protein molecules around PEG islands. Immobilization and adsorption of protein on such structures over time evolve into the self-assembled patterns.

Rationalizing 5000-fold differences in receptor-binding rate constants of four cytokines

The four cytokines erythropoietin (EPO), interleukin-4 (IL4), human growth hormone (hGH), and prolactin (PRL) all form four-helix bundles and bind to type I cytokine receptors. However, their receptor-binding rate constants span a 5000-fold range. Here, we quantitatively rationalize these vast differences in rate constants by our transient-complex theory for protein-protein association. In the transient complex, the two proteins have near-native separation and relative orientation, but have yet to form the short-range specific interactions of the native complex. The theory predicts the association rate constant as k(a)=k(a0)exp(-ΔG(el)(∗)/k(B)T) where k(a0) is the basal rate constant for reaching the transient complex by random diffusion, and the Boltzmann factor captures the rate enhancement due to electrostatic attraction. We found that the vast differences in receptor-binding rate constants of the four cytokines arise mostly from the differences in charge complementarity among the four cytokine-receptor complexes. The basal rate constants (k(a0)) of EPO, IL4, hGH, and PRL were similar (5.2 × 10(5) M(-1)s(-1), 2.4 × 10(5) M(-1)s(-1), 1.7 × 10(5) M(-1)s(-1), and 1.7 × 10(5) M(-1)s(-1), respectively). However, the average electrostatic free energies (ΔG(e1)(∗)) were very different (-4.2 kcal/mol, -2.4 kcal/mol, -0.1 kcal/mol, and -0.5 kcal/mol, respectively, at ionic strength=160 mM). The receptor-binding rate constants predicted without adjusting any parameters, 6.2 × 10(8) M(-1)s(-1), 1.3 × 10(7) M(-1)s(-1), 2.0 × 10(5) M(-1)s(-1), and 7.6 × 10(4) M(-1)s(-1), respectively, for EPO, IL4, hGH, and PRL agree well with experimental results. We uncover that these diverse rate constants are anticorrelated with the circulation concentrations of the cytokines, with the resulting cytokine-receptor binding rates very close to the limits set by the half-lives of the receptors, suggesting that these binding rates are functionally relevant and perhaps evolutionarily tuned. Our calculations also reproduced well-observed effects of mutations and ionic strength on the rate constants and produced a set of mutations on the complex of hGH with its receptor that putatively enhances the rate constant by nearly 100-fold through increasing charge complementarity. To quantify charge complementarity, we propose a simple index based on the charge distribution within the binding interface, which shows good correlation with ΔG(e1)(∗). Together these results suggest that protein charges can be manipulated to tune k(a) and control biological function.

Predicting kinetic constants of protein-protein interactions based on structural properties

Elucidating kinetic processes of protein-protein interactions (PPI) helps to understand how basic building blocks affect overall behavior of living systems. In this study, we used structure-based properties to build predictive models for kinetic constants of PPI. A highly diverse PPI dataset, protein-protein kinetic interaction data and structures (PPKIDS), was built. PPKIDS contains 62 PPI with complex structures and kinetic constants measured experimentally. The influence of structural properties on kinetics of PPI was studied using 35 structure-based features, describing different aspects of complex structures. Linear models for the prediction of kinetic constants were built by fitting with selected subsets of structure-based features. The models gave correlation coefficients of 0.801, 0.732, and 0.770 for k(off), k(on), and K(d), respectively, in leave-one-out cross validations. The predictive models reported here use only protein complex structures as input and can be generally applied in PPI studies as well as systems biology modeling. Our study confirmed that different properties play different roles in the kinetic process of PPI. For example, k(on) was affected by overall structural features of complexes, such as the composition of secondary structures, the change of translational and rotational entropy, and the electrostatic interaction; while k(off) was determined by interfacial properties, such as number of contacted atom pairs per 100 Ų. This information provides useful hints for PPI design.

Assembly dynamics and stability of the pneumococcal epsilon zeta antitoxin toxin (PezAT) system from Streptococcus pneumoniae

The pneumococcal epsilon zeta antitoxin toxin (PezAT) system is a chromosomally encoded, class II toxin antitoxin system from the human pathogen Streptococcus pneumnoniae. Neutralization of the bacteriotoxic protein PezT is carried out by complex formation with its cognate antitoxin PezA. Here we study the stability of the inhibitory complex in vivo and in vitro. We found that toxin release is impeded in Escherichia coli and Bacillus subtilis due to the proteolytic resistance of PezA once bound to PezT. These findings are supported by in vitro experiments demonstrating a strong thermodynamic stabilization of both proteins upon binding. A detailed kinetic analysis of PezAT assembly revealed that these particular features of PezAT are based on a strong, electrostatically guided binding mechanism leading to a stable toxin antitoxin complex with femtomolar affinity. Our data show that PezAT complex formation is distinct to all other conventional toxin antitoxin modules and a controlled mode of toxin release is required for activation.

Rate theories for biologists

Some of the rate theories that are most useful for modeling biological processes are reviewed. By delving into some of the details and subtleties in the development of the theories, the review will hopefully help the reader gain a more than superficial perspective. Examples are presented to illustrate how rate theories can be used to generate insight at the microscopic level into biomolecular behaviors. An attempt is made to clear up a number of misconceptions in the literature regarding popular rate theories, including the appearance of Planck's constant in the transition-state theory and the Smoluchowski result as an upper limit for protein-protein and protein-DNA association rate constants. Future work in combining the implementation of rate theories through computer simulations with experimental probes of rate processes, and in modeling effects of intracellular environments so that theories can be used for generating rate constants for systems biology studies is particularly exciting.

Electrostatic contacts in the activator protein-1 coiled coil enhance stability predominantly by decreasing the unfolding rate

The hypothesis is tested that Jun-Fos activator protein-1 coiled coil interactions are dominated during late folding events by the formation of intricate intermolecular electrostatic contacts. A previously derived cJun-FosW was used as a template as it is a highly stable relative of the wild-type cJun-cFos coiled coil protein (thermal melting temperature = 63 degrees C versus 16 degrees C), allowing kinetic folding data to be readily extracted. An electrostatic mutant, cJun(R)-FosW(E), was created to generate six Arg-Glu interactions at e-g'+1 positions between cJun(R) and FosW(E), and investigations into how their contribution to stability is manifested in the folding pathway were undertaken. The evidence now strongly indicates that the formation of interhelical electrostatic contacts exert their effect predominantly on the coiled coil unfolding/dissociation rate. This has major implications for future antagonist design whereby kinetic rules could be applied to increase the residency time of the antagonist-peptide complex, and therefore significantly increase the efficacy of the antagonist.

Electron transfer from cytochrome c(2) to the reaction center: a transition state model for ionic strength effects due to neutral mutations

Interprotein electron transfer plays an important role in biological energy conversion. In this work, the electron transfer reaction between cytochrome c(2) (cyt) and the reaction center (RC) was studied to determine the mechanisms coupling association and electron transfer. Previous studies have shown that mutation of hydrophobic residues in the reaction interface, particularly Tyr L162, changes the binding affinity and rates of electron transfer at low ionic strengths. In this study, the effect of ionic strength on the second-order electron transfer rate constant, k(2), between cyt c(2) and native or mutant RCs was examined. Mutations of hydrophobic and hydrogen bonding residues caused k(2) to decrease more rapidly with an increase in ionic strength. This change is explained with a transition state model by a switch from a diffusion-limited reaction in native RCs, where electron transfer occurs upon each binding event, to a fast exchange reaction in the Tyr L162 mutant, where dissociation occurs before electron transfer and k(2) depends upon the equilibrium between bound and free protein complexes. The difference in ionic strength dependence is attributed to a smaller effect of ionic strength on the energy of the transition state compared to the bound state due to larger distances between charged residues in the transition state. This model explains the faster dissociation rate at higher ionic strengths that may assist rapid turnover that is important for biological function. These results provide a quantitative model for coupling protein association with electron transfer and elucidate the role of short-range interactions in determining the rate of electron transfer.

Fruitful and futile encounters along the association reaction between proteins

The association reaction between pairs of proteins proceeds through an encounter complex that develops into the final complex. Here, we combined Brownian dynamics simulations with experimental studies to analyze the structures of the encounter complexes along the association reaction between TEM1-beta-lactamase and its inhibitor, beta-lactamase-inhibitor protein. The encounter complex can be considered as an ensemble of short-lived low free-energy states that are stabilized primarily by electrostatic forces and desolvation. For the wild-type, the simulation showed two main encounter regions located outside the physical binding site. One of these regions was located near the experimentally determined transition state. To validate whether these encounters are fruitful or futile, we examined three groups of mutations that altered the encounter. The first group consisted of mutations that increased the experimental rate of association through electrostatic optimization. This resulted in an increase in the size of the encounter region located near the experimentally determined transition state, as well as a decrease in the energy of this region and an increase in the number of successful trajectories (i.e., encounters that develop into complex). A second group of mutations was specifically designed to either increase or decrease the size and energy of the second encounter complex, but either way it did not affect k(on). A third group of mutations consisted of residues that increased k(on) without significantly affecting the encounter complexes. These results indicate that the size and energy of the encounter regions are only two of several parameters that lead to fruitful association, and that electrostatic optimization is a major driving force in fast association.

Kinetic and thermodynamic properties of the folding and assembly of formate dehydrogenase

The folding mechanism and stability of dimeric formate dehydrogenase from Candida methylica was analysed by exposure to denaturing agents and to heat. Equilibrium denaturation data yielded a dissociation constant of about 10(-13)M for assembly of the protein from unfolded chains and the kinetics of refolding and unfolding revealed that the overall process comprises two steps. In the first step a marginally stable folded monomeric state is formed at a rate (k(1)) of about 2x10(-3)s(-1) (by deduction k(-1) is about 10(-4)s(-1)) and assembles into the active dimeric state with a bimolecular rate constant (k(2)) of about 2x10(4)M(-1)s(-1). The rate of dissociation of the dimeric state in physiological conditions is extremely slow (k(-2) approximately 3x10(-7)s(-1)).

Dissection of the high rate constant for the binding of a ribotoxin to the ribosome

Restrictocin belongs to a family of site-specific ribonucleases that kill cells by inactivating the ribosome. The restrictocin-ribosome binding rate constant was observed to exceed 10(10) M(-1) s(-1). We have developed a transient-complex theory to model the binding rates of protein-protein and protein-RNA complexes. The theory predicts the rate constant as k(a) = k(a0) exp(-DeltaG(el)*/k(B)T), where k(a0) is the basal rate constant for reaching the transient complex, located at the outer boundary of the bound state, by random diffusion, and DeltaG(el)* is the average electrostatic interaction free energy of the transient complex. Here, we applied the transient-complex theory to dissect the high restrictocin-ribosome binding rate constant. We found that the binding rate of restrictocin to the isolated sarcin/ricin loop is electrostatically enhanced by approximately 300-fold, similar to results found in other protein-protein and protein-RNA complexes. The ribosome provides an additional 10,000-fold rate enhancement because of two synergistic mechanisms afforded by the distal regions of the ribosome. First, they provide additional electrostatic attraction with restrictocin. Second, they reposition the transient complex into a region where local electrostatic interactions of restrictocin with the sarcin/ricin loop are particularly favorable. Our calculations rationalize a host of experimental observations and identify a strategy for designing proteins that bind their targets with high speed.

Binding kinetics of histone chaperone Chz1 and variant histone H2A.Z-H2B by relaxation dispersion NMR spectroscopy

The genome of eukaryotic cells is packed into a compact structure called chromatin that consists of DNA as well as histone and non-histone proteins. Histone chaperones associate with histone proteins and play important roles in the assembly of chromatin structure and transport of histones in the cell. The recently discovered histone chaperone Chz1 associates with the variant histone H2A.Z of budding yeast and plays a critical role in the exchange of the canonical histone pair H2A-H2B for the variant H2A.ZH2B. Here, we present an NMR approach that provides accurate estimates for the rates of association and dissociation of Chz1 and H2A.Z-H2B. The methodology exploits the fact that in a 1:1 mixture of Chz1 and H2A.Z-H2B, the small amounts of unbound proteins that are invisible in spectra produce line broadening of signals from the complex that can be quantified in terms of the thermodynamics and kinetics of the exchange process. The dissociation rate constant measured, 22 +/- 2 s(-1), provides an upper bound for the rate of transfer of H2A.Z-H2B to the chromatin remodeling complex, and the faster-than-diffusion association rate, 10(8) +/- 10(7) M(-1) s(-1), establishes the importance of attractive electrostatic interactions that form the chaperone-histone complex.

The ruggedness of protein-protein energy landscape and the cutoff for 1/r(n) potentials

MOTIVATION

Computational studies of the energetics of protein association are important for revealing the underlying fundamental principles and for designing better tools to model protein complexes. The interaction cutoff contribution to the ruggedness of protein-protein energy landscape is studied in terms of relative energy fluctuations for 1/r(n) potentials based on a simplistic model of a protein complex. This artificial ruggedness exists for short cutoffs and gradually disappears with the cutoff increase.

RESULTS

The critical values of the cutoff were calculated for each of 11 popular power-type potentials with n=0/9, 12 and for two thresholds of 5% and 10%. The artificial ruggedness decreases to tolerable thresholds for cutoffs larger than the critical ones. The results showed that for both thresholds the critical cutoff is a non-monotonic function of the potential power n. The functions reach the maximum at n=3/4 and then decrease with the increase of the potential power. The difference between two cutoffs for 5% and 10% artificial ruggedness becomes negligible for potentials decreasing faster than 1/r(12). The analytical results obtained for the simple model of protein complexes agree with the analysis of artificial ruggedness in a dataset of 62 protein-protein complexes, with different parameterizations of soft Lennard-Jones potential and two types of protein representations: all-atom and coarse-grained. The results suggest that cutoffs larger than the critical ones can be recommended for protein-protein potentials.

Fast predictions of thermodynamics and kinetics of protein-protein recognition from structures: from molecular design to systems biology

The increasing call for an overall picture of the interactions between the components of a biological system that give rise to the observed function is often summarized by the expression systems biology. Both the interpretative and predictive capabilities of holistic models of biochemical systems, however, depend to a large extent on the level of physico-chemical knowledge of the individual molecular interactions making up the network. This review is focused on the structure-based quantitative characterization of protein-protein interactions, ubiquitous in any biochemical pathway. Recently developed, fast and effective computational methods are reviewed, which allow the assessment of kinetic and thermodynamic features of the association-dissociation processes of protein complexes, both in water soluble and membrane environments. The performance and the accuracy of fast and semi-empirical structure-based methods have reached comparable levels with respect to the classical and more elegant molecular simulations. Nevertheless, the broad accessibility and lower computational cost provide the former methods with the advantageous possibility to perform systems-level analyses including extensive in silico mutagenesis screenings and large-scale structural predictions of multiprotein complexes.

Interaction of onconase with the human ribonuclease inhibitor protein

One of the tightest known protein-protein interactions in biology is that between members of the ribonuclease A superfamily and the ribonuclease inhibitor protein (RI). Some members of this superfamily are able to kill cancer cells, and the ability to evade RI is a major determinant of whether a ribonuclease will be cytotoxic. The archetypal cytotoxic ribonuclease, onconase (ONC), is in late-stage clinical trials for the treatment of malignant mesothelioma. We present here the first measurement of the inhibition of the ribonucleolytic activity of ONC by RI. This inhibition occurs with K(i)=0.15muM in a solution of low salt concentration.

Accurate Calculations of Binding, Folding, and Transfer Free Energies by a Scaled Generalized Born Method

The Poisson-Boltzmann (PB) equation is widely used for modeling solvation effects. The computational cost of PB has restricted its applications largely to single-conformation calculations. The generalized Born (GB) model provides an approximation at substantially reduced cost. Currently the best GB methods reproduce PB results for electrostatic solvation energies with errors at ~5 kcal/mol. When two proteins form a complex, the net electrostatic contributions to the binding free energy are typically of the order of 5 to 10 kcal/mol. Similarly, the net contributions of individual residues to protein folding free energy are < 5 kcal/mol. Clearly in these applications the accuracy of current GB methods is insufficient. Here we present a simple scaling scheme that allows our GB method, GBr⁶, to reproduce PB results for binding, folding, and transfer free energies with high accuracy. From an ensemble of conformations sampled from molecular dynamics simulations, five were judiciously selected for PB calculations. These PB results were used for scaling GBr⁶. Tests on the binding free energies of the barnase-barstar, GTPase-WASp, and U1A-U1hpII complexes and on the folding free energy of FKBP show that the effects of point mutations calculated by scaled GBr⁶ are accurate to within 0.3 kcal/mol of PB results. Similar accuracy was also achieved for the free energies of transfer for ribonuclease Sa and insulin from the crystalline phase to the solution phase at various pH's. This method makes it possible to thoroughly sample the transient-complex ensemble in predicting protein binding rate constants and to incorporate conformational sampling in electrostatic modeling (such as done in the MM-GBSA approach) without loss of accuracy.

Conformational stability and folding mechanisms of dimeric proteins

The folding of multisubunit proteins is of tremendous biological significance since the large majority of proteins exist as protein-protein complexes. Extensive experimental and computational studies have provided fundamental insights into the principles of folding of small monomeric proteins. Recently, important advances have been made in extending folding studies to multisubunit proteins, in particular homodimeric proteins. This review summarizes the equilibrium and kinetic theory and models underlying the quantitative analysis of dimeric protein folding using chemical denaturation, as well as the experimental results that have been obtained. Although various principles identified for monomer folding also apply to the folding of dimeric proteins, the effects of subunit association can manifest in complex ways, and are frequently overlooked. Changes in molecularity typically give rise to very different overall folding behaviour than is observed for monomeric proteins. The results obtained for dimers have provided key insights pertinent to understanding biological assembly and regulation of multisubunit proteins. These advances have set the stage for future advances in folding involving protein-protein interactions for natural multisubunit proteins and unnatural assemblies involved in disease.

Electrostatic rate enhancement and transient complex of protein-protein association

The association of two proteins is bounded by the rate at which they, via diffusion, find each other while in appropriate relative orientations. Orientational constraints restrict this rate to approximately 10(5)-10(6) M(-1) s(-1). Proteins with higher association rates generally have complementary electrostatic surfaces; proteins with lower association rates generally are slowed down by conformational changes upon complex formation. Previous studies (Zhou, Biophys J 1997;73:2441-2445) have shown that electrostatic enhancement of the diffusion-limited association rate can be accurately modeled by $k_{\bf D}$ = $k_{D}0\ {exp} ( - \langle U_{el} \rangle;{\star}/k_{B} T),$ where k(D) and k(D0) are the rates in the presence and absence of electrostatic interactions, respectively, U(el) is the average electrostatic interaction energy in a "transient-complex" ensemble, and k(B)T is the thermal energy. The transient-complex ensemble separates the bound state from the unbound state. Predictions of the transient-complex theory on four protein complexes were found to agree well with the experiment when the electrostatic interaction energy was calculated with the linearized Poisson-Boltzmann (PB) equation (Alsallaq and Zhou, Structure 2007;15:215-224). Here we show that the agreement is further improved when the nonlinear PB equation is used. These predictions are obtained with the dielectric boundary defined as the protein van der Waals surface. When the dielectric boundary is instead specified as the molecular surface, electrostatic interactions in the transient complex become repulsive and are thus predicted to retard association. Together these results demonstrate that the transient-complex theory is predictive of electrostatic rate enhancement and can help parameterize PB calculations.

On the Dielectric Boundary in Poisson-Boltzmann Calculations

In applying the Poisson-Boltzmann (PB) equation for calculating the electrostatic free energies of solute molecules, an open question is how to specify the boundary between the low-dielectric solute and the high-dielectric solvent. Two common specifications of the dielectric boundary, as the molecular surface (MS) or the van der Waals (vdW) surface of the solute, give very different results for the electrostatic free energy of the solute. With the same atomic radii, the solute is more solvent-exposed in the vdW specification. One way to resolve the difference is to use different sets of atomic radii for the two surfaces. The radii for the vdW surface would be larger in order to compensate for the higher solvent exposure. Here we show that radius re-parameterization required for bringing MS-based and vdW-based PB results to agreement is solute-size dependent. The difference in atomic radii for individual amino acids as solutes is only 2-5% but increases to over 20% for proteins with ~200 residues. Therefore two sets of radii that yield identical MS-based and vdW-based PB results for small solutes will give very different PB results for large solutes. This finding raises issues about two common practices. The first is the use of atomic radii, which are parameterized against either experimental solvation data or data obtained from explicit-solvent simulations on small compounds, for PB calculations on proteins. The second is the parameterization of vdW-based generalized Born models against MS-based PB results.

Prediction of salt and mutational effects on the association rate of U1A protein and U1 small nuclear RNA stem/loop II

We have developed a computational approach for predicting protein-protein association rates (Alsallaq and Zhou, Structure 2007, 15, 215). Here we expand the range of applicability of this approach to protein-RNA binding and report the first results for protein-RNA binding rates predicted from atomistic modeling. The system studied is the U1A protein and stem/loop II of the U1 small nuclear RNA. Experimentally it was observed that the binding rate is significantly reduced by increasing salt concentration while the dissociation changes little with salt concentration, and charges distant from the binding site make marginal contribution to the binding rate. These observations are rationalized. Moreover, predicted effects of salt and charge mutations are found to be in quantitative agreement with experimental results.

Coarse-grained models for simulations of multiprotein complexes: application to ubiquitin binding

We develop coarse-grained models and effective energy functions for simulating thermodynamic and structural properties of multiprotein complexes with relatively low binding affinity (K(d) >1 microM) and apply them to binding of Vps27 to membrane-tethered ubiquitin. Folded protein domains are represented as rigid bodies. The interactions between the domains are treated at the residue level with amino-acid-dependent pair potentials and Debye-Hückel-type electrostatic interactions. Flexible linker peptides connecting rigid protein domains are represented as amino acid beads on a polymer with appropriate stretching, bending, and torsion-angle potentials. In simulations of membrane-attached protein complexes, interactions between amino acids and the membrane are described by residue-dependent short-range potentials and long-range electrostatics. We parameterize the energy functions by fitting the osmotic second virial coefficient of lysozyme and the binding affinity of the ubiquitin-CUE complex. For validation, extensive replica-exchange Monte Carlo simulations are performed of various protein complexes. Binding affinities for these complexes are in good agreement with the experimental data. The simulated structures are clustered on the basis of distance matrices between two proteins and ranked according to cluster population. In approximately 70% of the complexes, the distance root-mean-square is less than 5 A from the experimental structures. In approximately 90% of the complexes, the binding interfaces on both proteins are predicted correctly, and in all other cases at least one interface is correct. Transient and nonspecifically bound structures are also observed. With the validated model, we simulate the interaction between the Vps27 multiprotein complex and a membrane-tethered ubiquitin. Ubiquitin is found to bind preferentially to the two UIM domains of Vps27, but transient interactions between ubiquitin and the VHS and FYVE domains are observed as well. These specific and nonspecific interactions are found to be positively cooperative, resulting in a substantial enhancement of the overall binding affinity beyond the approximately 300 microM of the specific domains. We also find that the interactions between ubiquitin and Vps27 are highly dynamic, with conformational rearrangements enabling binding of Vps27 to diverse targets as part of the multivesicular-body protein-sorting pathway.