Interesting structural and dynamical behaviors exhibited by the AF-6 PDZ domain upon Bcr peptide binding

PDZ (postsynaptic density-95, disks large, zonula occludens-1) domains are small, protein-protein interaction modules that have multiple binding surfaces for the docking of diverse molecules. These domains can propagate signals from ligand-binding site to distal regions of the structure through allosteric communication. Recent works have revealed that picosecond to nanosecond time scale dynamics play a potential role in propagating long-range signals within a protein. Comparison of AF-6 PDZ domain structures in free and complex forms shows a conformation rearrangement of distal surface 2, which is far from the peptide binding groove. The relaxation dispersion experiments detected that the free AF-6 PDZ domain was sampling multiple conformations; millisecond dynamics mapped a network for allostery signal transmission throughout the AF-6 PDZ domain in the weak saturation state, and intramolecular motions were observed in distal surface 1 when the protein was saturated. These results provide evidence that the allosteric process in the AF-6 PDZ domain is not two-state; instead, the millisecond dynamic network provides a mechanism for the transmission of allosteric signals throughout a protein. Interestingly, the two distal surfaces of the AF-6 PDZ domain respond differently to peptide binding; distal surface 1 changes in millisecond dynamics, whereas distal surface 2 undergoes structural rearrangement. The significance of the different response patterns in the signaling pathway and its relevance to the function of the AF-6 PDZ domain should be studied further.     

Evaluation of energetic and dynamic coupling networks in a PDZ domain protein

A number of computational and experimental studies have identified intramolecular communication "pathways" or "networks" important for transmitting allostery. Here, we have used mutagenesis and NMR relaxation methods to investigate the scope and nature of the communication networks found in the second post-synaptic density-95/discs large/zonula occludens-1 (PDZ) domain of the human protein tyrosine phosphatase 1E protein (hPTP1E) (PDZ2). It was found that most mutations do not have a significant energetic contribution to peptide ligand binding. Three mutants that showed significant changes in binding also displayed context-dependent dynamic effects. Both a mutation at a partially exposed site (H71Y) and a buried core position (I35V) had a limited response in side-chain (2)H-based dynamics when compared to wild-type PDZ2. In contrast, a change at a second core position (I20F) that had previously been shown to be part of an energetic and dynamic network, resulted in extensive changes in side-chain dynamics. This response is reminiscent to that seen previously upon peptide ligand binding. These results shed light on the nature of the PDZ2 dynamic network and suggest that position 20 in PDZ2 acts as a "hub" that is energetically and dynamically critical for transmitting changes in dynamics throughout the PDZ domain.     

Change in allosteric network affects binding affinities of PDZ domains: analysis through perturbation response scanning

The allosteric mechanism plays a key role in cellular functions of several PDZ domain proteins (PDZs) and is directly linked to pharmaceutical applications; however, it is a challenge to elaborate the nature and extent of these allosteric interactions. One solution to this problem is to explore the dynamics of PDZs, which may provide insights about how intramolecular communication occurs within a single domain. Here, we develop an advancement of perturbation response scanning (PRS) that couples elastic network models with linear response theory (LRT) to predict key residues in allosteric transitions of the two most studied PDZs (PSD-95 PDZ3 domain and hPTP1E PDZ2 domain). With PRS, we first identify the residues that give the highest mean square fluctuation response upon perturbing the binding sites. Strikingly, we observe that the residues with the highest mean square fluctuation response agree with experimentally determined residues involved in allosteric transitions. Second, we construct the allosteric pathways by linking the residues giving the same directional response upon perturbation of the binding sites. The predicted intramolecular communication pathways reveal that PSD-95 and hPTP1E have different pathways through the dynamic coupling of different residue pairs. Moreover, our analysis provides a molecular understanding of experimentally observed hidden allostery of PSD-95. We show that removing the distal third alpha helix from the binding site alters the allosteric pathway and decreases the binding affinity. Overall, these results indicate that (i) dynamics plays a key role in allosteric regulations of PDZs, (ii) the local changes in the residue interactions can lead to significant changes in the dynamics of allosteric regulations, and (iii) this might be the mechanism that each PDZ uses to tailor their binding specificities regulation.     

Activation of nanoscale allosteric protein domain motion revealed by neutron spin echo spectroscopy

NHERF1 is a multidomain scaffolding protein that assembles signaling complexes, and regulates the cell surface expression and endocytic recycling of a variety of membrane proteins. The ability of the two PDZ domains in NHERF1 to assemble protein complexes is allosterically modulated by the membrane-cytoskeleton linker protein ezrin, whose binding site is located as far as 110 Ångstroms away from the PDZ domains. Here, using neutron spin echo (NSE) spectroscopy, selective deuterium labeling, and theoretical analyses, we reveal the activation of interdomain motion in NHERF1 on nanometer length-scales and on submicrosecond timescales upon forming a complex with ezrin. We show that a much-simplified coarse-grained model suffices to describe interdomain motion of a multidomain protein or protein complex. We expect that future NSE experiments will benefit by exploiting our approach of selective deuteration to resolve the specific domain motions of interest from a plethora of global translational and rotational motions. Our results demonstrate that the dynamic propagation of allosteric signals to distal sites involves changes in long-range coupled domain motions on submicrosecond timescales, and that these coupled motions can be distinguished and characterized by NSE.     

基于弹性网络模型的蛋白质变构路径与关键残基识别研究

目的 变构效应在蛋白质生物学功能执行过程中发挥着重要的调控作用，如何基于蛋白质空间结构，有效识别变构信号的传播路径和关键的残基位点是蛋白质结构-功能关系研究领域的热点科学问题。方法 本研究利用基于弹性网络模型（elastic network model，ENM）的力分布计算方法，通过分析蛋白质对外力的响应过程，来识别体系的变构路径以及变构过程中的关键残基。在该方法中，对蛋白质的关键变构位点施加外力，通过对体系形变以及内力分布情况的分析，有效识别与外力承载区域形变相耦合的关键残基，从而得到力信号在蛋白质结构内的传播路径。结果 利用该方法研究了人类磷酸甘油酸激酶（human phosphoglycerate kinase，hPGK）和蛋白质酪氨酸磷酸酶（protein tyrosine phosphatase，PTP）PDZ2结构域的变构调控路径和关键残基。对于hPGK，识别出从底物结合位点到铰链区的两条变构信号传导路径。对于PTP PDZ2，也成功识别出从配体结合位点传递到蛋白质远端的两条长程变构调控路径。计算结果与实验和分子动力学（molecular dynamics，MD）模拟得到的结果一致。结论 本研究为蛋白质体系关键残基识别及变构路径研究提供了有效的分析方法。     

Dynamic coupling and allosteric behavior in a nonallosteric protein

Long-range intraprotein interactions give rise to many important protein behaviors. Understanding how energy is transduced through protein structures to either transmit a signal or elicit conformational changes is therefore a current challenge in structural biology. In an effort to understand such linkages, multiple V --> A mutations were made in the small globular protein eglin c. The physical responses, as mapped by NMR spin relaxation, residual dipolar couplings (RDCs), and scalar couplings, illustrate that the interior of this nonallosteric protein forms a dynamic network and that local perturbations are transmitted as dynamic and structural changes to distal sites as far as 16 A away. Two basic types of propagation responses were observed: contiguous pathways of enhanced (attenuated) dynamics with no change in structure; and dispersed (noncontiguous) changes in methyl rotation rates that appear to result from subtle deformation of backbone structure. In addition, energy transmission is found to be unidirectional. In one mutant, an allosteric conformational change of a side chain is seen in the context of a pathway of propagated changes in picosecond to nanosecond dynamics. The observation of so many long-range interactions in a small, rigid system lends experimental weight to the idea that all well-folded proteins inherently possess allosteric features [Gunasekaran et al. (2004) Proteins 57, 433-443], and that dynamics are a rich source of information for mapping and gaining mechanistic insight into communication pathways in individual proteins.     

Some (dis)assembly required: partial unfolding in the Par-6 allosteric switch

Allostery is commonly described as a functional connection between two distant sites in a protein, where a binding event at one site alters affinity at the other. Here, we review the conformational dynamics that encode an allosteric switch in the PDZ domain of Par-6, which is a scaffold protein that organizes other proteins into a complex required to initiate and maintain cell polarity. NMR measurements revealed that the PDZ domain samples an evolutionarily conserved unfolding intermediate allowing rearrangement of two adjacent loop residues that control ligand binding affinity. Cdc42 binding to Par-6 creates a novel interface between the PDZ domain and the adjoining CRIB motif that stabilizes the high-affinity PDZ conformation. Thermodynamic and kinetic studies suggest that partial PDZ unfolding is an integral part of the Par-6 switching mechanism. The Par-6 CRIB-PDZ module illustrates two important structural aspects of protein evolution: the interface between adjacent domains in the same protein can give rise to allosteric regulation, and thermodynamic stability may be sacrificed to increase the sampling frequency of an unfolding intermediate required for conformational switching.     

The structural and dynamic response of MAGI-1 PDZ1 with noncanonical domain boundaries to the binding of human papillomavirus E6

PDZ domains are protein interaction domains that are found in cytoplasmic proteins involved in signaling pathways and subcellular transport. Their roles in the control of cell growth, cell polarity, and cell adhesion in response to cell contact render this family of proteins targets during the development of cancer. Targeting of these network hubs by the oncoprotein E6 of “high-risk” human papillomaviruses (HPVs) serves to effect the efficient disruption of cellular processes. Using NMR, we have solved the three-dimensional solution structure of an extended construct of the second PDZ domain of MAGI-1 (MAGI-1 PDZ1) alone and bound to a peptide derived from the C-terminus of HPV16 E6, and we have characterized the changes in backbone dynamics and hydrogen bonding that occur upon binding. The binding event induces quenching of high-frequency motions in the C-terminal tail of the PDZ domain, which contacts the peptide upstream of the canonical X-[T/S]-X-[L/V] binding motif. Mutations designed in the C-terminal flanking region of the PDZ domain resulted in a significant decrease in binding affinity for E6 peptides. This detailed analysis supports the notion of a global response of the PDZ domain to the binding event, with effects propagated to distal sites, and reveals unexpected roles for the sequences flanking the canonical PDZ domain boundaries.     

The order of PDZ3 and TrpCage in fusion chimeras determines their properties—a biophysical characterization

Most of the structural proteins known today are composed of domains that carry their own functions while keeping their structural properties. It is supposed that such domains, when taken out of the context of the whole protein, can retain their original structure and function to a certain extent. Information on the specific functional and structural characteristics of individual domains in a new context of artificial fusion proteins may help to reveal the rules of internal and external domain communication. Moreover, this could also help explain the mechanism of such communication and address how the mutual allosteric effect plays a role in a such multi‐domain protein system. The simple model system of the two‐domain fusion protein investigated in this work consisted of a well‐folded PDZ3 domain and an artificially designed small protein domain called Tryptophan Cage (TrpCage). Two fusion proteins with swapped domain order were designed to study their structural and functional features as well as their biophysical properties. The proteins composed of PDZ3 and TrpCage, both identical in amino acid sequence but different in composition (PDZ3‐TrpCage, TrpCage‐PDZ3), were studied using circualr dichroism (CD) spectrometry, analytical ultracentrifugation, and molecular dynamic simulations. The biophysical analysis uncovered different structural and denaturation properties of both studied proteins, revealing their different unfolding pathways and dynamics.     

A Highlights from MBoC Selection: The tails of apical scaffolding proteins EBP50 and E3KARP regulate their localization and dynamics

The closely related apical scaffolding proteins ERM-binding phosphoprotein of 50 kDa (EBP50) and NHE3 kinase A regulatory protein (E3KARP) both consist of two postsynaptic density 95/disks large/zona occludens-1 (PDZ) domains and a tail ending in an ezrin-binding domain. Scaffolding proteins are thought to provide stable linkages between components of multiprotein complexes, yet in several types of epithelial cells, EBP50, but not E3KARP, shows rapid exchange from microvilli compared with its binding partners. The difference in dynamics is determined by the proteins’ tail regions. Exchange rates of EBP50 and E3KARP correlated strongly with their abilities to precipitate ezrin in vivo. The EBP50 tail alone is highly dynamic, but in the context of the full-length protein, the dynamics is lost when the PDZ domains are unable to bind ligand. Proteomic analysis of the effects of EBP50 dynamics on binding-partner preferences identified a novel PDZ1 binding partner, the I-BAR protein insulin receptor substrate p53 (IRSp53). Additionally, the tails promote different microvillar localizations for EBP50 and E3KARP, which localized along the full length and to the base of microvilli, respectively. Thus the tails define the localization and dynamics of these scaffolding proteins, and the high dynamics of EBP50 is regulated by the occupancy of its PDZ domains.     

Allosteric communication in cysteinyl tRNA synthetase: a network of direct and indirect readout

Protein structure networks are constructed for the identification of long-range signaling pathways in cysteinyl tRNA synthetase (CysRS). Molecular dynamics simulation trajectory of CysRS-ligand complexes were used to determine conformational ensembles in order to gain insight into the allosteric signaling paths. Communication paths between the anticodon binding region and the aminoacylation region have been identified. Extensive interaction between the helix bundle domain and the anticodon binding domain, resulting in structural rigidity in the presence of tRNA, has been detected. Based on the predicted model, six residues along the communication paths have been examined by mutations (single and double) and shown to mediate a coordinated coupling between anticodon recognition and activation of amino acid at the active site. This study on CysRS clearly shows that specific key residues, which are involved in communication between distal sites in allosteric proteins but may be elusive in direct structure analysis, can be identified from dynamics of protein structure networks.     

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

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

Distinct ligand specificity of the Tiam1 and Tiam2 PDZ domains

Guanine nucleotide exchange factor proteins of the Tiam family are activators of the Rho GTPase Rac1 and critical for cell morphology, adhesion, migration, and polarity. These proteins are modular and contain a variety of interaction domains, including a single post-synaptic density-95/discs large/zonula occludens-1 (PDZ) domain. Previous studies suggest that the specificities of the Tiam1 and Tiam2 PDZ domains are distinct. Here, we sought to conclusively define these specificities and determine their molecular origin. Using a combinatorial peptide library, we identified a consensus binding sequence for each PDZ domain. Analysis of these consensus sequences and binding assays with peptides derived from native proteins indicated that these two PDZ domains have overlapping but distinct specificities. We also identified residues in two regions (S(0) and S(-2) pockets) of the Tiam1 PDZ domain that are important determinants of ligand specificity. Site-directed mutagenesis of four nonconserved residues in these two regions along with peptide binding analyses confirmed that these residues are crucial for ligand affinity and specificity. Furthermore, double mutant cycle analysis of each region revealed energetic couplings that were dependent on the ligand being investigated. Remarkably, a Tiam1 PDZ domain quadruple mutant had the same specificity as the Tiam2 PDZ domain. Finally, analysis of Tiam family PDZ domain sequences indicated that the PDZ domains segregate into four distinct families based on the residues studied here. Collectively, our data suggest that Tiam family proteins have highly evolved PDZ domain-ligand interfaces with distinct specificities and that they have disparate PDZ domain-dependent biological functions.     

Conserved tertiary couplings stabilize elements in the PDZ fold,leading to characteristic patterns of domain conformational flexibility

Single‐domain allostery has been postulated to occur through intramolecular pathways of signaling within a protein structure. We had previously investigated these pathways by introducing a local thermal perturbation and analyzed the anisotropic propagation of structural changes throughout the protein. Here, we develop an improved approach, the Rotamerically Induced Perturbation (RIP), that identifies strong couplings between residues by analyzing the pathways of heat‐flow resulting from thermal excitation of rotameric rotations at individual residues. To explore the nature of these couplings, we calculate the complete coupling maps of 5 different PDZ domains. Although the PDZ domain is a well conserved structural fold that serves as a scaffold in many protein–protein complexes, different PDZ domains display unique patterns of conformational flexibility in response to ligand binding: some show a significant shift in a set of α‐helices, while others do not. Analysis of the coupling maps suggests a simple relationship between the computed couplings and observed conformational flexibility. In domains where the α‐helices are rigid, we find couplings of the α‐helices to the body of the protein, whereas in domains having ligand‐responsive α‐helices, no couplings are found. This leads to a model where the α‐helices are intrinsically dynamic but can be damped if sidechains interact at key tertiary contacts. These tertiary contacts correlate to high covariation contacts as identified by the statistical coupling analysis method. As these dynamic modules are exploited by various allosteric mechanisms, these tertiary contacts have been conserved by evolution.     

Biophysical simulations and structure-based modeling of residue interaction networks in the tumor suppressor proteins reveal functional role of cancer mutation hotspots in molecular communication

In the current study, we have combined molecular simulations and energetic analysis with dynamics-based network modeling and perturbation response scanning to determine molecular signatures of mutational hotspot residues in the p53, PTEN, and SMAD4 tumor suppressor proteins. By examining structure, energetics and dynamics of these proteins, we have shown that inactivating mutations preferentially target a group of structurally stable residues that play a fundamental role in global propagation of dynamic fluctuations and mediating allosteric interaction networks. Through integration of long-range perturbation dynamics and network-based approaches, we have quantified allosteric potential of residues in the studied proteins. The results have revealed that mutational hotspot sites often correspond to high centrality mediating centers of the residue interaction networks that are responsible for coordination of global dynamic changes and allosteric signaling. Our findings have also suggested that structurally stable mutational hotpots can act as major effectors of allosteric interactions and mutations in these positions are typically associated with severe phenotype. Modeling of shortest inter-residue pathways has shown that mutational hotspot sites can also serve as key mediating bridges of allosteric communication in the p53 and PTEN protein structures. Multiple regression models have indicated that functional significance of mutational hotspots can be strongly associated with the network signatures serving as robust predictors of critical regulatory positions responsible for loss-of-function phenotype. The results of this computational investigation are compared with the experimental studies and reveal molecular signatures of mutational hotspots, providing a plausible rationale for explaining and localizing disease-causing mutations in tumor suppressor genes.     

Mechanistic Insights into the Long-range Allosteric Regulation of KRAS Via Neurofibromatosis Type 1 (NF1) Scaffold Upon SPRED1 Loading

Allosteric regulation is the most direct and efficient way of regulating protein function, wherein proteins transmit the perturbations at one site to another distinct functional site. Deciphering the mechanism of allosteric regulation is of vital importance for the comprehension of both physiological and pathological events in vivo as well as the rational allosteric drug design. However, it remains challenging to elucidate dominant allosteric signal transduction pathways, especially for large and multi-component protein machineries where long-range allosteric regulation exits. One of the quintessential examples having long-range allosteric regulation is the ternary complex, SPRED1–RAS–neurofibromin type 1 (NF1, a RAS GTPase–activating protein), in which SPRED1 facilitates RAS–GTP hydrolysis by interacting with NF1 at a distal, allosteric site from the RAS binding site. To address the underlying mechanism, we performed extensive Gaussian accelerated molecular dynamics simulations and Markov state model analysis of KRAS–NF1 complex in the presence and absence of SPRED1. Our findings suggested that SPRED1 loading allosterically enhanced KRAS–NF1 binding, but hindered conformational transformation of the NF1 catalytic center for RAS hydrolysis. Moreover, we unveiled the possible allosteric pathways upon SPRED1 binding through difference contact network analysis. This study not only provided an in-depth mechanistic insight into the allosteric regulation of KRAS by SPRED1, but also shed light on the investigation of long-range allosteric regulation among complex macromolecular systems.     

Exploring Mechanisms of Allosteric Regulation and Communication Switching in the Multiprotein Regulatory Complexes of the Hsp90 Chaperone with Cochaperones and Client Proteins: Atomistic Insights from Integrative Biophysical Modeling and Network Analysis of Conformational Landscapes

Understanding molecular principles underlying Hsp90 chaperone functions and modulation of client activity is fundamental to dissect activation mechanisms of many proteins. In this work, we performed a computational investigation of the Hsp90-Hsp70-Hop-CR client complex to examine allosteric regulatory mechanisms underlying dynamic chaperone interactions and principles of chaperone-dependent client recognition and remodeling. Conformational dynamics analysis using high-resolution coarse-grained simulations and ensemble-based local frustration analysis suggest that the Hsp90 chaperone could recognize and recruit the GR client by invoking reciprocal dynamic exchanges near the intermolecular interfaces with the client. Using mutational scanning of the intermolecular residues in the Hsp90-Hsp70-Hop-GR complex, we identified binding energy hotspots in the regulatory complex. Perturbation-based network analysis and dynamic fluctuations-based modeling of allosteric residue potentials are employed for a detailed analysis of allosteric interaction networks and identification of conformational communication switches. We found that allosteric interactions between the Hsp90, the client-bound Hsp70 and Hop cochaperone can define two allosteric residue clusters that control client recruitment in which the intrinsic Hsp70 allostery is exploited to mediate integration of the Hsp70-bound client into the Hsp90 chaperone system. The results suggest a model of dynamics-driven allostery that enables efficient client recruitment and loading through allosteric couplings between intermolecular interfaces and communication switch centers. This study showed that the Hsp90 interactions with client proteins may operate under dynamic-based allostery in which ensembles of preexisting conformational states and intrinsic allosteric pathways present in the Hsp90 and Hsp70 chaperones can be exploited for recognition and integration of substrate proteins.     

Ezrin Induces Long-Range Interdomain Allostery in the Scaffolding Protein NHERF1

Scaffolding proteins are molecular switches that control diverse signaling events. The scaffolding protein Na⁺/H⁺ exchanger regulatory factor 1 (NHERF1) assembles macromolecular signaling complexes and regulates the macromolecular assembly, localization, and intracellular trafficking of a number of membrane ion transport proteins, receptors, and adhesion/antiadhesion proteins. NHERF1 begins with two modular protein-protein interaction domains—PDZ1 and PDZ2—and ends with a C-terminal (CT) domain. This CT domain binds to ezrin, which, in turn, interacts with cytosekeletal actin. Remarkably, ezrin binding to NHERF1 increases the binding capabilities of both PDZ domains. Here, we use deuterium labeling and contrast variation neutron-scattering experiments to determine the conformational changes in NHERF1 when it forms a complex with ezrin. Upon binding to ezrin, NHERF1 undergoes significant conformational changes in the region linking PDZ2 and its CT ezrin-binding domain, as well as in the region linking PDZ1 and PDZ2, involving very long range interactions over 120 Å. The results provide a structural explanation, at mesoscopic scales, of the allosteric control of NHERF1 by ezrin as it assembles protein complexes. Because of the essential roles of NHERF1 and ezrin in intracellular trafficking in epithelial cells, we hypothesize that this long-range allosteric regulation of NHERF1 by ezrin enables the membrane-cytoskeleton to assemble protein complexes that control cross-talk and regulate the strength and duration of signaling.     

Signaling pathways of PDZ2 domain: a molecular dynamics interaction correlation analysis

PDZ domains are found in many signaling proteins. One of their functions is to provide scaffolds for forming membrane-associated protein complexes by binding to the carboxyl termini of their partners. PDZ domains are thought also to play a signal transduction role by propagating the information that binding has occurred to remote sites. In this study, a molecular dynamics (MD) simulation-based approach, referred to as an interaction correlation analysis, is applied to the PDZ2 domain to identify the possible signal transduction pathways. A residue correlation matrix is constructed from the interaction energy correlations between all residue pairs obtained from the MD simulations. Two continuous interaction pathways, starting at the ligand binding pocket, are identified by a hierarchical clustering analysis of the residue correlation matrix. One pathway is mainly localized at the N-terminal side of helix alpha1 and the adjacent C-terminus of loop beta1-beta2. The other pathway is perpendicular to the central beta-sheet and extends toward the side of PDZ2 domain opposite to the ligand binding pocket. The results complement previous studies based on multiple sequence analysis, NMR, and MD simulations. Importantly, they reveal the energetic origin of the long-range coupling. The PDZ2 results, as well as the earlier rhodopsin analysis, show that the interaction correlation analysis is a robust approach for determining pathways of intramolecular signal transduction.