Application of linear free energy relations to protein conformational changes: the quaternary structural change of hemoglobin

Addressing the Binding Mechanism of the Meprin and TRAF-C Homology Domain of the Speckle-Type POZ Protein Using Protein Engineering

Protein-protein interactions play crucial roles in a wide range of biological processes, including metabolic pathways, cell cycle progression, signal transduction, and the proteasomal system. For PPIs to fulfill their biological functions, they require the specific recognition of a multitude of interacting partners. In many cases, however, protein-protein interaction domains are capable of binding different partners in the intracellular environment, but they require precise regulation of the binding events in order to exert their function properly and avoid misregulation of important molecular pathways. In this work, we focused on the MATH domain of the E3 Ligase adaptor protein SPOP in order to decipher the molecular features underlying its interaction with two different peptides that mimic its physiological partners: Puc and MacroH2A. By employing stopped-flow kinetic binding experiments, together with extensive site-directed mutagenesis, we addressed the roles of specific residues, some of which, although far from the binding site, govern these transient interactions. Our findings are compatible with a scenario in which the binding of the MATH domain with its substrate is characterized by a fine energetic network that regulates its interactions with different ligands. Results are briefly discussed in the context of previously existing work regarding the MATH domain.

Distinguishing between concerted, sequential and barrierless conformational changes: Folding versus allostery

Characterization of transition and intermediate states of reactions provides insights into their mechanisms and is often achieved through analysis of linear free energy relationships. Such an approach has been used extensively in protein folding studies but less so for analyzing allosteric transitions. Here, we point out analogies in ways to characterize pathways and intermediates in folding and allosteric transitions. Achieving an understanding of the mechanisms by which proteins undergo allosteric switching is important in many cases for obtaining insights into how they function.

Thermodynamics and kinetics of DNA and RNA dinucleotide hybridization to gaps and overhangs

Hybridization of short nucleic acid segments (<4 nt) to single-strand templates occurs as a critical intermediate in processes such as nonenzymatic nucleic acid replication and toehold-mediated strand displacement. These templates often contain adjacent duplex segments that stabilize base pairing with single-strand gaps or overhangs, but the thermodynamics and kinetics of hybridization in such contexts are poorly understood because of the experimental challenges of probing weak binding and rapid structural dynamics. Here we develop an approach to directly measure the thermodynamics and kinetics of DNA and RNA dinucleotide dehybridization using steady-state and temperature-jump infrared spectroscopy. Our results suggest that dinucleotide binding is stabilized through coaxial stacking interactions with the adjacent duplex segments as well as from potential noncanonical base-pairing configurations and structural dynamics of gap and overhang templates revealed using molecular dynamics simulations. We measure timescales for dissociation ranging from 0.2-40 μs depending on the template and temperature. Dinucleotide hybridization and dehybridization involve a significant free energy barrier with characteristics resembling that of canonical oligonucleotides. Together, our work provides an initial step for predicting the stability and kinetics of hybridization between short nucleic acid segments and various templates.

Direct monitoring of the thermodynamics and kinetics of DNA and RNA dinucleotide dehybridization from gaps and overhangs

Hybridization of short nucleic acid segments (<4 nucleotides) to single-strand templates occurs as a critical intermediate in processes such as non-enzymatic nucleic acid replication and toehold-mediated strand displacement. These templates often contain adjacent duplex segments that stabilize base pairing with single-strand gaps or overhangs, but the thermodynamics and kinetics of hybridization in such contexts are poorly understood due to experimental challenges of probing weak binding and rapid structural dynamics. Here we develop an approach to directly measure the thermodynamics and kinetics of DNA and RNA dinucleotide dehybridization using steady-state and temperature-jump infrared spectroscopy. Our results suggest that dinucleotide binding is stabilized through coaxial stacking interactions with the adjacent duplex segments as well as from potential non-canonical base pairing configurations and structural dynamics of gap and overhang templates revealed using molecular dynamics simulations. We measure timescales for dissociation ranging from 0.2 to 40 µs depending on the template and temperature. Dinucleotide hybridization and dehybridization involves a significant free energy barrier with characteristics resembling that of canonical oligonucleotides. Together, our work provides an initial step for predicting the stability and kinetics of hybridization between short nucleic acid segments and various templates.

Impact of Conformational Substates and Energy Landscapes on Understanding Hemoglobin Kinetics and Function

Hans Frauenfelder's discovery of conformational substates in studies of myoglobin carbon monoxide geminate rebinding kinetics at cryogenic temperatures (Austin RH, Beeson KW, Eisenstein L, Frauenfelder H, & Gunsalus IC (1975) Dynamics of Ligand Binding to Myoglobin. Biochemistry 14(24):5355-5373) followed by his introduction of energy landscape theory with Peter Wolynes (Frauenfelder H, Sligar SG, & Wolynes PG (1991) The Energy Landscapes and Motions of Proteins. Science 254(5038):1598-1603) marked the beginning of a new era in the physics and physical chemistry of proteins. Their work played a major role in demonstrating the power and importance of dynamics and of Kramers reaction rate theory for understanding protein function. The biggest impact of energy landscape theory has been in the protein folding field, which is well-known and has been documented in numerous articles and reviews, including a recent one of my own (Eaton WA (2021) Modern Kinetics and Mechanism of Protein Folding: a Retrospective. J. Phys. Chem. B. 125(14):3452-3467). Here I will describe the much less well-known impact of their modern view of proteins on both experimental and theoretical studies of hemoglobin kinetics and function. I will first describe how Frauenfelder's experiments motivated and influenced my own research on myoglobin, which were key ingredients to my work on understanding hemoglobin.

Role of hemoglobin structural-functional relationships in oxygen transport

The molecular mechanism of O₂ binding to hemoglobin (Hb) has been critically reviewed on the basis of the information built up in the last decades. It allows to describe in detail from the kinetic and thermodynamic viewpoint the process of O₂ uptake in the lungs and release to the tissues, casting some light on the physiological and pathological aspects of this process. The relevance of structural-functional relationships for O₂ binding is particularly outlined in the case of poorly vascularized tissues, such as retina, briefly discussing of strategies employed for optimization of oxygen supply to this type of tissues.

Impact of hemoglobin biophysical studies on molecular pathogenesis and drug therapy for sickle cell disease

Basic research on hemoglobin has been essential for understanding the origin and treatment of many hematological disorders due to abnormal hemoglobins. The most important of the hemoglobinopathies is sickle cell disease - Linus Pauling's "molecular disease" that gave birth to molecular medicine. In this review, I will describe the contributions of basic biophysical research on normal and sickle cell hemoglobin (HbS) to understanding the molecular pathogenesis of the disease and providing the conceptual basis for the various approaches to drug therapy that target HbS polymerization. Most prominent among these are the experimental results on the solubility of HbS as a function of oxygen saturation explained by the allosteric model of Monod, Wyman, and Changeux and the Gill-Wyman thermodynamic linkage relation between solubility and oxygen binding, the solubility of mixtures of HbS with normal or fetal hemoglobin explained by Minton's thermodynamic model, and the highly unusual kinetics of HbS polymerization explained by a novel double nucleation mechanism that also accounts for the aggregation kinetics of the Alzheimer's peptide. The HbS polymerization kinetics are of great importance to understanding the pathophysiology and clinical course, as well as guiding drug development for treating this common and severe disease. The article focuses primarily on experimental and theoretical results from my lab, so it is not a comprehensive review of the subject.

Mapping the energy landscape of protein-ligand binding via linear free energy relationships determined by protein NMR relaxation dispersion

Biochemical signaling is mediated by complexes between macromolecular receptors and their ligands, with the duration of the signal being directly related to the lifetime of the ligand-receptor complex. In the field of drug design, the recognition that drug efficacy in vivo depends on the lifetime of the drug-protein complex has spawned the concept of designing drugs with particular binding kinetics. To advance this field it is critical to investigate how the molecular details of designed ligands might affect the binding kinetics, as well as the equilibrium binding constant. Here we use protein NMR relaxation dispersion to determine linear free energy relationships involving the on- and off-rates and the affinity for a series of congeneric ligands targeting the carbohydrate recognition domain of galectin-3. Using this approach we determine the energy landscape and the position of the transition state along the reaction coordinate of protein-ligand binding. The results show that ligands exhibiting reduced off-rates achieve this by primarily stabilizing the bound state, but do not affect the transition state to any greater extent. The transition state forms early, that is, it is located significantly closer to the free state than to the bound state, suggesting a critical role of desolvation. Furthermore, the data suggest that different subclasses of ligands show different behavior with respect to these characteristics.

Sensing the allosteric force

Allosteric regulation is an innate control in most metabolic and signalling cascades that enables living organisms to adapt to the changing environment by tuning the affinity and regulating the activity of target proteins. For a microscopic understanding of this process, a protein system has been designed in such a way that allosteric communication between the binding and allosteric site can be observed in both directions. To that end, an azobenzene-derived photoswitch has been linked to the α3-helix of the PDZ3 domain, arguably the smallest allosteric protein with a clearly identifiable binding and allosteric site. Photo-induced trans-to-cis isomerisation of the photoswitch increases the binding affinity of a small peptide ligand to the protein up to 120-fold, depending on temperature. At the same time, ligand binding speeds up the thermal cis-to-trans back-isomerisation rate of the photoswitch. Based on the energetics of the four states of the system (cis vs trans and ligand-bound vs free), the concept of an allosteric force is introduced, which can be used to drive chemical reactions.

Insight into the structural and functional analysis of the impact of missense mutation on cytochrome P450 oxidoreductase

Cytochrome P450 oxidoreductase (POR) is a steroidogenic and drug-metabolizing enzyme. It helps in the NADPH dependent transfer of electrons to cytochrome P450 (CYP) enzymes for their biological activity. In this study, we employed integrative computational approaches to decipher the impact of proline to leucine missense mutation at position 384 (P384L) in the connecting/hinge domain region which is essential for the catalytic activity of POR. Analysis of protein stability using DUET, MUpro, CUPSAT, I-Mutant2.0, iStable and SAAFEC servers predicted that mutation might alter the structural stability of POR. The significant conformational changes induced by the mutation to the POR structure were analyzed by long-range molecular dynamics simulation. The results revealed that missense mutation decreased the conformational stability of POR as compared to wild type (WT). The PCA based FEL analysis described the mutant-specific conformational alterations and dominant motions essential for the biological activity of POR. The LIGPLOT interaction analysis showed the different binding architecture of FMN, FAD, and NADPH as a result of mutation. The increased number of hydrogen bonds in the FEL conformation of WT proved the strong binding of cofactors in the binding pocket as compared to the mutant. The porcupine plot analysis associated with cross-correlation analysis depicted the high-intensity flexible motion exhibited by functionally important FAD and NADPH binding domain regions. The computational findings unravel the impact of mutation at the structural level, which could be helpful in understanding the molecular mechanism of drug metabolism.

Demonstration of Binding Induced Structural Plasticity in a SH2 Domain

SH2 domains are common protein interaction domains able to recognize short aminoacidic sequences presenting a phosphorylated tyrosine (pY). In spite of their fundamental importance for cell physiology there is a lack of information about the mechanism by which these domains recognize and bind their natural ligands. The N-terminal SH2 (N-SH2) domain of PI3K mediates the interaction with different scaffolding proteins and is known to recognize a specific pY-X-X-M consensus sequence. These interactions are at the cross roads of different molecular pathways and play a key role for cell development and division. By combining mutagenesis, chemical kinetics and NMR, here we provide a complete characterization of the interaction between N-SH2 and a peptide mimicking the scaffolding protein Gab2. Our results highlight that N-SH2 is characterized by a remarkable structural plasticity, with the binding reaction being mediated by a diffused structural region and not solely by the residues located in the binding pocket. Furthermore, the analysis of kinetic data allow us to pinpoint an allosteric network involving residues far from the binding pocket involved in specificity. Results are discussed on the light of previous works on the binding properties of SH2 domains.

Mechanistic insights into the deleterious roles of Nasu-Hakola disease associated TREM2 variants

Recently, the critical roles played by genetic variants of TREM2 (Triggering Receptor Expressed on Myeloid cells 2) in Alzheimer's disease have been aggressively highlighted. However, few studies have focused on the deleterious roles of Nasu-Hakola disease (NHD) associated TREM2 variants. In order to get insights into the contributions made by these variants to neurodegeneration, we investigated the influences of four NHD associated TREM2 mutations (Y38C, W50C, T66M, and V126G) on loss-of-function, and followed this with in silico prediction and conventional molecular dynamics simulation. NHD mutations were predicted to be highly deleterious by eight different in silico bioinformatics tools and found to induce conformational changes by molecular dynamics simulation. As compared with the wild-type, the four variants produced substantial differences in the collective motions of loop regions, which not only promoted structural remodeling in the CDR2 (complementarity-determining region 2) loop but also in the CDR1 loop, by changing inter- and intra-loop hydrogen bonding networks. In addition, structural studies in a free energy landscape analysis showed that Y38, T66, and V126 are crucial for maintaining the structural features of CDR1 and CDR2 loops, and that mutations in these positions produced steric clashes and loss of ligand binding. These results showed the presence of mutations in the TREM2 ectodomain induced flexibility and caused structural alterations. Dynamical scenarios, as provided by the present study, may be critical to our understanding of the roles of these TREM2 mutations in neurodegenerative diseases.

The impact of missense mutation in PIGA associated to paroxysmal nocturnal hemoglobinuria and multiple congenital anomalies-hypotonia-seizures syndrome 2: A computational study

Paroxysmal nocturnal hemoglobinuria (PNH) is an acquired clonal blood disorder that manifests with hemolytic anemia, thrombosis, and peripheral blood cytopenias. The disease is caused by the deficiency of two glycosylphosphatidylinositols (GPI)-anchored proteins (CD55 and CD59) in the hemopoietic stem cells. The deficiency of GPI-anchored proteins has been associated with the somatic mutations in phosphatidylinositol glycan class A (PIGA). However, the mutations that do not cause PNH is associated with the multiple congenital anomalies-hypotonia-seizures syndrome 2 (MCAHS2). To best of our knowledge, no computational study has been performed to explore at an atomistic level the impact of PIGA missense mutations on the structure and dynamics of the protein. Therefore, we focused our study to provide molecular insights into the changes in protein structural dynamics upon mutation. In the initial step, screening for the most pathogenic mutations from the pool of publicly available mutations was performed. Further, to get a better understanding, pathogenic mutations were mapped to the modeled structure and the resulting protein was subjected to 100 ns molecular dynamics simulation. The residues close to C- and N-terminal regions of the protein were found to exhibit greater flexibility upon mutation. Our study suggests that four mutations are highly effective in altering the structural conformation and stability of the PIGA protein. Among them, mutant G48D was found to alter protein's structural dynamics to the greatest extent, both on a local and a global scale.

Allostery in Its Many Disguises: From Theory to Applications

Allosteric regulation plays an important role in many biological processes, such as signal transduction, transcriptional regulation, and metabolism. Allostery is rooted in the fundamental physical properties of macromolecular systems, but its underlying mechanisms are still poorly understood. A collection of contributions to a recent interdisciplinary CECAM (Center Européen de Calcul Atomique et Moléculaire) workshop is used here to provide an overview of the progress and remaining limitations in the understanding of the mechanistic foundations of allostery gained from computational and experimental analyses of real protein systems and model systems. The main conceptual frameworks instrumental in driving the field are discussed. We illustrate the role of these frameworks in illuminating molecular mechanisms and explaining cellular processes, and describe some of their promising practical applications in engineering molecular sensors and informing drug design efforts.

Molecular insights of the G2019S substitution in LRRK2 kinase domain associated with Parkinson's disease: A molecular dynamics simulation approach

The G2019S substitution in the Leucine-rich repeat kinase 2 (LRRK2) is significantly associated with Parkinson's disease (PD). This substitution was identified in both familial and sporadic forms of PD with a higher frequency. Few computational studies have reported the impact of G2019S substitution on inhibitors of the kinase domain of LRRK2. However, no computational study deeply investigated the possible impact of the G2019S substitution on the kinase domain in its Apo conformation. Therefore, in this study, we used 200 ns molecular dynamic simulation using the GROMACS 5.1.4 package software to investigate the impact of the G2019S substitution on the structure of the kinase domain of LRRK2. Our results indicate that the G2019S substitution affects the dynamics and stability of LRRK2 by decreasing the flexibility and increasing the compactness of the kinase domain and showing its tendency to be in an active conformation for long time interval because of the high energy barrier between active and inactive conformation. This study predicts the molecular pathogenicity mechanism of the G2019S on patients with PD and provides a potential platform for developing therapeutics for patients with PD that harbor this amino acid substitution.

Universality of supersaturation in protein-fiber formation

The thermodynamics and kinetics of the aggregation of sickle-cell hemoglobin into fibers have been studied in great detail under a wide range of solution conditions. The stability of the fiber is measured by the solubility; the kinetics is characterized by a delay before the appearance of fibers. A review of data in the literature shows that there is no correlation of the delay time with fiber stability and only a weak correlation with the initial protein concentration. There is, however, a striking collapse of all the data onto a single universal curve when the delay time is plotted versus the supersaturation, which is the ratio of the initial protein concentration to the solubility, expressed as activities. Collapse onto the same universal curve is also obtained when using delay times calculated from the double-nucleation theoretical model.

The time scale of the quaternary structural changes in hemoglobin revealed using the transient grating technique

The quaternary structural transition between the R and T states of human hemoglobin was investigated using the transient grating technique. The results presented herein reveal that the quaternary structural change accompanied by the R-T transition occurs within a few microseconds.

Both protein dynamics and ligand concentration can shift the binding mechanism between conformational selection and induced fit

This study aimed to shed light on the long debate over whether conformational selection (CS) or induced fit (IF) is the governing mechanism for protein-ligand binding. The main difference between the two scenarios is whether the conformational transition of the protein from the unbound form to the bound form occurs before or after encountering the ligand. Here we introduce the IF fraction (i.e., the fraction of binding events achieved via IF), to quantify the binding mechanism. Using simulations of a model protein-ligand system, we demonstrate that both the rate of the conformational transition and the concentration of ligand molecules can affect the IF fraction. CS dominates at slow conformational transition and low ligand concentration. An increase in either quantity results in a higher IF fraction. Despite the many-body nature of the system and the involvement of multiple, disparate types of dynamics (i.e., ligand diffusion, protein conformational transition, and binding reaction), the overall binding kinetics over wide ranges of parameters can be fit to a single exponential, with the apparent rate constant exhibiting a linear dependence on ligand concentration. The present study may guide future kinetics experiments and dynamics simulations in determining the IF fraction.

Structure of the transition state for the binding of c-Myb and KIX highlights an unexpected order for a disordered system

A classical dogma of molecular biology dictates that the 3D structure of a protein is necessary for its function. However, a considerable fraction of the human proteome, although functional, does not adopt a defined folded state under physiological conditions. These intrinsically disordered proteins tend to fold upon binding to their partners with a molecular mechanism that is elusive to experimental characterization. Indeed, although many hypotheses have been put forward, the functional role (if any) of disorder in these intrinsically denatured systems is still shrouded in mystery. Here, we characterize the structure of the transition state of the binding-induced folding in the reaction between the KIX domain of the CREB-binding protein and the transactivation domain of c-Myb. The analysis, based on the characterization of a series of conservative site-directed mutants, reveals a very high content of native-like structure in the transition state and indicates that the recognition between KIX and c-Myb is geometrically precise. The implications of our results in the light of previous work on intrinsically unstructured systems are discussed.

Ligand migration through hemeprotein cavities: insights from laser flash photolysis and molecular dynamics simulations

The presence of cavities and tunnels in the interior of proteins, in conjunction with the structural plasticity arising from the coupling to the thermal fluctuations of the protein scaffold, has profound consequences on the pathways followed by ligands moving through the protein matrix. In this perspective we discuss how quantitative analysis of experimental rebinding kinetics from laser flash photolysis, trapping of unstable conformational states by embedding proteins within the nanopores of silica gels, and molecular simulations can synergistically converge to gain insight into the migration mechanism of ligands. We show how the evaluation of the free energy landscape for ligand diffusion based on the outcome of computational techniques can assist the definition of sound reaction schemes, leading to a comprehensive understanding of the broad range of chemical events and time scales that encompass the transport of small ligands in hemeproteins.

Side-chain interactions form late and cooperatively in the binding reaction between disordered peptides and PDZ domains

Intrinsically disordered proteins are very common and mediate numerous protein-protein and protein-DNA interactions. While it is clear that these interactions are instrumental for the life of the mammalian cell, there is a paucity of data regarding their molecular binding mechanisms. Here we have used short peptides as a model system for intrinsically disordered proteins. Linear free energy relationships based on rate and equilibrium constants for the binding of these peptides to ordered target proteins, PDZ domains, demonstrate that native side-chain interactions form mainly after the rate-limiting barrier for binding and in a cooperative fashion. This finding suggests that these disordered peptides first form a weak encounter complex with non-native interactions. The data do not support the recent notion that the affinities of intrinsically disordered proteins toward their targets are generally governed by their association rate constants. Instead, we observed the opposite for peptide-PDZ interactions, namely, that changes in K(d) correlate with changes in k(off).

Changes in dynamics upon oligomerization regulate substrate binding and allostery in amino acid kinase family members

Oligomerization is a functional requirement for many proteins. The interfacial interactions and the overall packing geometry of the individual monomers are viewed as important determinants of the thermodynamic stability and allosteric regulation of oligomers. The present study focuses on the role of the interfacial interactions and overall contact topology in the dynamic features acquired in the oligomeric state. To this aim, the collective dynamics of enzymes belonging to the amino acid kinase family both in dimeric and hexameric forms are examined by means of an elastic network model, and the softest collective motions (i.e., lowest frequency or global modes of motions) favored by the overall architecture are analyzed. Notably, the lowest-frequency modes accessible to the individual subunits in the absence of multimerization are conserved to a large extent in the oligomer, suggesting that the oligomer takes advantage of the intrinsic dynamics of the individual monomers. At the same time, oligomerization stiffens the interfacial regions of the monomers and confers new cooperative modes that exploit the rigid-body translational and rotational degrees of freedom of the intact monomers. The present study sheds light on the mechanism of cooperative inhibition of hexameric N-acetyl-L-glutamate kinase by arginine and on the allosteric regulation of UMP kinases. It also highlights the significance of the particular quaternary design in selectively determining the oligomer dynamics congruent with required ligand-binding and allosteric activities.

Protein function requires a three-dimensional structure with specific dynamic features for catalytic and binding events, and, in many cases, the structure results from the assembly of more than one polypeptide chain (also called monomer or subunit) to form an oligomer or multimer. Proteins such as hemoglobin or chaperonin GroEL are oligomers formed by 2 and 14 subunits, respectively, whereas virus capsids are multimers composed of hundreds of monomers. In these cases, the architecture of the interface between the subunits and the overall assembly geometry are essential in determining the functional motions that these sophisticated structures are able to perform under physiological conditions. Here we present results from our computational study of the large-amplitude motions of dimeric and hexameric proteins that belong to the Amino Acid Kinase family. Our study reveals that the monomers in these oligomeric proteins are arranged in such a way that the oligomer inherits the intrinsic dynamic features of its components. The packing geometry additionally confers the ability to perform highly cooperative conformational changes that involve all monomers and enable the biological activity of the multimer. The study highlights the significance of the quaternary design in favoring the oligomer dynamics that enables ligand-binding and allosteric regulation functions.

Scalable rule-based modelling of allosteric proteins and biochemical networks

Much of the complexity of biochemical networks comes from the information-processing abilities of allosteric proteins, be they receptors, ion-channels, signalling molecules or transcription factors. An allosteric protein can be uniquely regulated by each combination of input molecules that it binds. This “regulatory complexity” causes a combinatorial increase in the number of parameters required to fit experimental data as the number of protein interactions increases. It therefore challenges the creation, updating, and re-use of biochemical models. Here, we propose a rule-based modelling framework that exploits the intrinsic modularity of protein structure to address regulatory complexity. Rather than treating proteins as “black boxes”, we model their hierarchical structure and, as conformational changes, internal dynamics. By modelling the regulation of allosteric proteins through these conformational changes, we often decrease the number of parameters required to fit data, and so reduce over-fitting and improve the predictive power of a model. Our method is thermodynamically grounded, imposes detailed balance, and also includes molecular cross-talk and the background activity of enzymes. We use our Allosteric Network Compiler to examine how allostery can facilitate macromolecular assembly and how competitive ligands can change the observed cooperativity of an allosteric protein. We also develop a parsimonious model of G protein-coupled receptors that explains functional selectivity and can predict the rank order of potency of agonists acting through a receptor. Our methodology should provide a basis for scalable, modular and executable modelling of biochemical networks in systems and synthetic biology.

The complexity of biochemical networks challenges our ability to create quantitative and predictive models of cellular responses to extracellular changes. In these networks, the regulation of allosteric receptors and proteins by multiple drugs or endogenous ligands introduces “regulatory complexity” because a large number of parameters is required to describe such interactions. Protein interactions also give rise to “combinatorial complexity” by generating large numbers of protein complexes and covalent modification states. To address these twin problems, we propose a modelling framework that combines a modular description of protein structure and function with a rule-based description of protein interactions. We define the input-output function of an allosteric protein through its thermodynamic properties and structural components. We show that our “biomolecule-centric” methodology, in contrast to ad hoc approaches that emphasize the regulatory logic of interactions, can reduce the number of parameters required to model experimental observations. We also demonstrate how the application of our framework gives insights into the assembly of macromolecular complexes and increases the predictive power of a standard model of G protein-coupled receptors. These benefits are possible in many systems, given the ubiquity of allostery in biochemical networks. Our research delineates a fundamental relationship between allostery, modularity, and complexity in biochemical networks.

Relationships between structural dynamics and functional kinetics in oligomeric membrane receptors

Recent efforts to broaden understanding of the molecular mechanisms of membrane receptors in signal transduction make use of rate-equilibrium free-energy relationships (REFERs), previously applied to chemical reactions, enzyme kinetics, and protein folding. For oligomeric membrane receptors, we distinguish between a), the Leffler parameter α_L, to characterize the global transition state for the interconversion between conformations; and b), the Fersht parameter, ϕ_F, to assign the degree of progression of individual residue positions at the transition state. For both α_L and ϕ_F, insights are achieved by using harmonic energy profiles to reflect the dynamic nature of proteins, as illustrated with single-channel results reported for normal and mutant nicotinic receptors. We also describe new applications of α_L based on published results. For large-conductance calcium-activated potassium channels, data are satisfactorily fit with an α_L value of 0.65, in accord with REFERs. In contrast, results reported for the flip conformational state of glycine and nicotinic receptors are in disaccord with REFERs, since they yield α_L values outside the usual limits of 0–1. Concerning published ϕ_F values underlying the conformational wave hypothesis for nicotinic receptors, we note that interpretations may be complicated by variations in the width of harmonic energy profiles.

Probing the transition state of the allosteric pathway of the Shaker Kv channel pore by linear free-energy relations

Long-range coupling between distant functional elements of proteins may rely on allosteric communication trajectories lying along the protein structure, as described in the case of the Shaker voltage-activated potassium (Kv) channel model allosteric system. Communication between the distant Kv channel activation and slow inactivation pore gates was suggested to be mediated by a network of local pairwise and higher-order interactions among the functionally unique residues that constitute the allosteric trajectory. The mechanism by which conformational changes propagate along the Kv channel allosteric trajectory to achieve pore opening, however, remains unclear. Such conformational changes may propagate in either a concerted or a sequential manner during the reaction coordinate of channel opening. Residue-level structural information on the transition state of channel gating is required to discriminate between these possibilities. Here, we combine patch-clamp electrophysiology recordings of Kv channel gating and analysis using linear free-energy relations, focusing on a select set of residues spanning the allosteric trajectory of the Kv channel pore. We show that all allosteric trajectory residues tested exhibit an open-like conformation in the transition state of channel opening, implying that coupling interactions occur along the trajectory break in a concerted manner upon moving from the closed to the open state. Energetic coupling between the Kv channel gates thus occurs in a concerted fashion in both the spatial and the temporal dimensions, strengthening the notion that such trajectories correspond to pathways of mechanical deformation along which conformational changes propagate.

Raman dispersion spectroscopy probes heme distortions in deoxyHb-trout IV involved in its T-state Bohr effect

The depolarization ratios of heme protein Raman lines arising from vibrations of the heme group exhibit significant dependence on the excitation wavelength. From the analysis of this depolarization ratio dispersion, one obtains information about symmetry-lowering distortions deltaQ(Gamma) of the heme group that can be classified in terms of the symmetry races Gamma = A(1g), B(1g), B(2g), and A(2g) in D(4h) symmetry. The heme-protein interaction can be changed by the protonation of distinct amino acid side chains (i.e., for instance the Bohr groups in hemoglobin derivates), which gives rise to specific static heme distortions for each protonation state. From the Raman dispersion data, it is possible to obtain parameters by fitting to a theoretical expression of the Raman tensor, which provide information on these static distortions and also about the pK values of the involved titrable side chains. We have applied this method to the nu(4) (1,355 cm(-1)) and nu(10) (1,620 cm(-1)) lines of deoxygenated hemoglobin of the fourth component of trout and have measured their depolarization ratio dispersion as a function of pH between 6 and 9. From the pH dependence of the thus derived parameters, we obtain pK values identical to those of the Bohr groups, which were earlier derived from the corresponding O(2)-binding isotherms. These are pK(alpha1) = pK(alpha2) = 8.5 for the alpha and pK(beta1) = 7.5, pK(beta2) = 7.4 for the beta chains. We also obtain the specific distortion parameters for each protonation state. As shown in earlier studies, the nu(4) mode mainly probes distortions from interactions between the proximal histidine and atoms of the heme core (i.e., the nitrogens and the C(alpha) atoms of the pyrroles). Group theoretical argumentation allows us to relate specific changes of the imidazole geometry as determined by its tilt and azimuthal angle and the iron-out-of-plane displacement to distinct variations of the normal distortions deltaQ(Gamma) derived from the Raman dispersion data. Thus, we found that the pH dependence of the heme distortions deltaQ(A1g) (totally symmetric) and deltaQ(B1g) (asymmetric) is caused by variations of the azimuthal rather than the tilt angle of the Fe-His (F8) bond. In contrast to this, the nu(10) line mainly monitors changes resulting from the interaction between peripheral substituents of the porphyrin macrocycle (vinyl). From the pH dependence of the parameters, it is possible to separately identify distortions deltaQ(Gamma) affecting the hemes in the alpha and beta chains, respectively. From this, we find that in the alpha subunit structural changes induced on protonation of the corresponding Bohr groups are mainly transferred via the Fe-N(epsilon) bond and give rise to changes in the azimuthal angle. In the beta subunit, however, in addition, structural changes of the heme pocket arise, which most probably result from protonation of the imidazole of the COOH-terminal His (HC3 beta). This rearranges the net of H bonds between His HC3 beta, Ser (F9 beta), and Glu (F7 beta).

Tracking the structural dynamics of proteins in solution using time-resolved wide-angle X-ray scattering

We demonstrate tracking of protein structural changes with time-resolved wide-angle X-ray scattering (TR-WAXS) with nanosecond time resolution. We investigated the tertiary and quaternary conformational changes of human hemoglobin under nearly physiological conditions triggered by laser-induced ligand photolysis. We also report data on optically induced tertiary relaxations of myoglobin and refolding of cytochrome c to illustrate the wide applicability of the technique. By providing insights into the structural dynamics of proteins functioning in their natural environment, TR-WAXS complements and extends results obtained with time-resolved optical spectroscopy and X-ray crystallography.

Time evolution of the quaternary structure of Escherichia coli aspartate transcarbamoylase upon reaction with the natural substrates and a slow, tight-binding inhibitor

Here, we present a study of the conformational changes of the quaternary structure of Escherichia coli aspartate transcarbamoylase, as monitored by time-resolved small-angle X-ray scattering, upon combining with substrates, substrate analogs, and nucleotide effectors at temperatures between 5 and 22 degrees C, obviating the need for ethylene glycol. Time-resolved small-angle X-ray scattering time courses tracking the T-->R structural change after mixing with substrates or substrate analogs appeared to be a single phase under some conditions and biphasic under other conditions, which we ascribe to multiple ligation states producing a time course composed of multiple rates. Increasing the concentration of substrates up to a certain point increased the T-->R transition rate, with no further increase in rate beyond that point. Most strikingly, after addition of N-phosphonacetyl-l-aspartate to the enzyme, the transition rate was more than 1 order of magnitude slower than with the natural substrates. These results on the homotropic mechanism are consistent with a concerted transition between structural and functional states of either low affinity, low activity or high affinity, high activity for aspartate. Addition of ATP along with the substrates increased the rate of the transition from the T to the R state and also decreased the duration of the R-state steady-state phase. Addition of CTP or the combination of CTP/UTP to the substrates significantly decreased the rate of the T-->R transition and caused a shift in the enzyme population towards the T state even at saturating substrate concentrations. These results on the heterotropic mechanism suggest a destabilization of the T state by ATP and a destabilization of the R state by CTP and CTP/UTP, consistent with the T and R state crystallographic structures of aspartate transcarbamoylase in the presence of the heterotropic effectors.

Plasticity of acetylcholine receptor gating motions via rate-energy relationships

Like other protein conformational changes, ion channel gating requires the protein to achieve a high-energy transition-state structure. It is not known whether ion channel gating takes place on a broad energy landscape on which many alternative transition state structures are accessible, or on a narrow energy landscape where only a few transition-state structures are possible. To address this question, we measured how rate-equilibrium free energy relationships (REFERs) for di-liganded and unliganded acetylcholine receptor gating vary as a function of the gating equilibrium constant. A large slope for the REFER plot indicates an openlike transition state, whereas a small slope indicates a closedlike transition state. Due to this relationship between REFERs and transition-state structure, the sensitivity of the REFER slope to mutation-induced energetic perturbations allows estimation of the breadth of the energy landscape underlying gating. The relatively large sensitivity of di-liganded REFER slopes to energetic perturbations suggests that the motions underlying di-liganded gating take place on a broad, shallow energy landscape where many alternative transition-state structures are accessible.

New insights into allosteric mechanisms from trapping unstable protein conformations in silica gels

To understand why the classical two-state allosteric model of Monod, Wyman, and Changeux explains cooperative oxygen binding by hemoglobin but does not explain changes in oxygen affinity by allosteric inhibitors, we have investigated the kinetic properties of unstable conformations transiently trapped by encapsulation in silica gels. Conformational trapping reveals that after nanosecond photodissociation of carbon monoxide a large fraction of the subunits of the T quaternary structure has kinetic properties almost identical to those of subunits of the R quaternary structure. Addition of allosteric inhibitors reduces both the fraction of R-like subunits and the oxygen affinity of the T quaternary structure. These kinetic and equilibrium results are readily explained by a recently proposed generalization of the Monod-Wyman-Changeux model in which a pre-equilibrium between two functionally different tertiary, rather than quaternary, conformations plays the central role.

Time-resolved Absorption and UV Resonance Raman Spectra Reveal Stepwise Formation of T Quaternary Contacts in the Allosteric Pathway of Hemoglobin

Hemoglobin undergoes a series of molecular changes on the nanosecond and microsecond time-scale following photodissociation of CO ligands. We have monitored these processes with a combination of transient absorption and resonance Raman (RR) spectroscopy. The latter have been acquired at higher data rates than previously available, thanks to kilohertz Ti:sapphire laser technology, with frequency-quadrupling into the ultraviolet. As a result of improved resolution of the UVRR time-course, a new intermediate has been identified in the pathway from the R (HbCO) to the T (deoxyHb) state. This intermediate is not detected via absorption transients, since the change in heme absorption is insignificant, but its lifetime agrees with a reported magnetic circular dichroism transient, which has been attributed to a quaternary tryptophan interaction. The new UVRR data allow elaboration of the allosteric pathway by establishing that the T-state quaternary contacts are formed in two well-separated steps, with time constants of 2.9 micros and 21 micros, instead of a single 20 micros process. The first step involves the "hinge" region contacts, as monitored by the Trp beta 37...Asp alpha 94 H-bond, while the second involves the "switch" region, as monitored by the Tyr alpha 42...Asp beta 99 H-bond. A working model for the allosteric pathway is presented.

Free-energy landscapes of ion-channel gating are malleable: changes in the number of bound ligands are accompanied by changes in the location of the transition state in acetylcholine-receptor channels

Acetylcholine-receptor channels (AChRs) are allosteric membrane proteins that mediate synaptic transmission by alternatively opening and closing ("gating") a cation-selective transmembrane pore. Although ligand binding is not required for the channel to open, the binding of agonists (for example, acetylcholine) increases the closed right harpoon over left harpoon open equilibrium constant because the ion-impermeable --> ion-permeable transition of the ion pathway is accompanied by a low-affinity --> high-affinity change at the agonist-binding sites. The fact that the gating conformational change of muscle AChRs can be kinetically modeled as a two-state reaction has paved the way to the experimental characterization of the corresponding transition state, which represents a snapshot of the continuous sequence of molecular events separating the closed and open states. Previous studies of fully (di) liganded AChRs, combining single-channel kinetic measurements, site-directed mutagenesis, and data analysis in the framework of the linear free-energy relationships of physical organic chemistry, have suggested a transition-state structure that is consistent with channel opening being an asynchronous conformational change that starts at the extracellular agonist-binding sites and propagates toward the intracellular end of the pore. In this paper, I characterize the gating transition state of unliganded AChRs, and report a remarkable difference: unlike that of diliganded gating, the unliganded transition state is not a hybrid of the closed- and open-state structures but, rather, is almost indistinguishable from the open state itself. This displacement of the transition state along the reaction coordinate obscures the mechanism underlying the unliganded closed right harpoon over left harpoon open reaction but brings to light the malleable nature of free-energy landscapes of ion-channel gating.

Nonlinear elasticity, proteinquakes, and the energy landscapes of functional transitions in proteins

Large-scale motions of biomolecules involve linear elastic deformations along low-frequency normal modes, but for function nonlinearity is essential. In addition, unlike macroscopic machines, biological machines can locally break and then reassemble during function. We present a model for global structural transformations, such as allostery, that involve large-scale motion and possible partial unfolding, illustrating the method with the conformational transition of adenylate kinase. Structural deformation between open and closed states occurs via low-frequency modes on separate reactant and product surfaces, switching from one state to the other when energetically favorable. The switching model is the most straightforward anharmonic interpolation, which allows the barrier for a process to be estimated from a linear normal mode calculation, which by itself cannot be used for activated events. Local unfolding, or cracking, occurs in regions where the elastic stress becomes too high during the transition. Cracking leads to a counterintuitive catalytic effect of added denaturant on allosteric enzyme function. It also leads to unusual relationships between equilibrium constant and rate like those seen recently in single-molecule experiments of motor proteins.

Allosteric Changes in Protein Structure Computed by a Simple Mechanical Model: Hemoglobin T↔R2 Transition

Information on protein dynamics has been usually inferred from spectroscopic studies of parts of the proteins, or indirectly from the comparison of the conformations assumed in the presence of different substrates or ligands. While molecular simulations also provide information on protein dynamics, they usually suffer from incomplete sampling of conformational space, and become prohibitively expensive when exploring the collective dynamics of large macromolecular structures. Here, we explore the dynamics of a well-studied allosteric protein, hemoglobin (Hb), to show that a simple mechanical model based on Gaussian fluctuations of residues can efficiently predict the transition between the tense (T, unliganded) and relaxed (R or R2, O(2) or CO-bound) forms of Hb. The passage from T into R2 is shown to be favored by the global mode of motion, which, in turn is driven by entropic effects. The major difference between the dynamics of the T and R2 forms is the loss of the hinge-bending role of alpha(1)-beta(2) (or alpha(2)-beta(1)) interfacial residues at alpha Phe36-His45 and beta Thr87-Asn102 in the R2 form, which implies a decreased cooperativity in the higher affinity (R2) form of Hb, consistent with many experimental studies. The involvement of the proximal histidine beta His92 in this hinge region suggests that the allosteric propagation of the local structural changes (induced upon O(2) binding) into global ones occur via hinge regions. This is the first demonstration that there is an intrinsic tendency of Hb to undergo T-->R2 transition, induced by purely elastic forces of entropic origin that are uniquely defined for the particular contact topology of the T form.

Phi value analysis of heterogeneity in pathways of allosteric transitions: Evidence for parallel pathways of ATP-induced conformational changes in a GroEL ring

What are the mechanisms of ligand-induced allosteric transitions in proteins? A powerful method to characterize pathways and transition states of reactions is phi value analysis. A phi value is the ratio between the changes on a perturbation (e.g., mutation) in the activation and equilibrium free energies of a reaction. Here, phi value analysis is used to characterize the ATP-induced allosteric transitions of GroEL by using changes in ATP concentration as perturbations. GroEL consists of two stacked back-to-back heptameric rings that bind ATP with positive cooperativity within rings and negative cooperativity between rings. Evidence is presented for the existence of parallel pathways for the allosteric transition of each ring. In both allosteric transitions, there is an abrupt ATP-dependent switch from a pathway with ATP-binding sites in the transition state that are very similar to those of the initial T state (phi = 0) to a pathway with a phi value of approximately 0.3. The phi value procedure outlined here should be useful in mapping the energy landscape of allosteric transitions of other proteins.

Coupling between voltage sensor activation, Ca2+ binding and channel opening in large conductance (BK) potassium channels

To determine how intracellular Ca(2+) and membrane voltage regulate the gating of large conductance Ca(2+)-activated K(+) (BK) channels, we examined the steady-state and kinetic properties of mSlo1 ionic and gating currents in the presence and absence of Ca(2+) over a wide range of voltage. The activation of unliganded mSlo1 channels can be accounted for by allosteric coupling between voltage sensor activation and the closed (C) to open (O) conformational change (Horrigan, F.T., and R.W. Aldrich. 1999. J. Gen. Physiol. 114:305-336; Horrigan, F.T., J. Cui, and R.W. Aldrich. 1999. J. Gen. Physiol. 114:277-304). In 0 Ca(2+), the steady-state gating charge-voltage (Q(SS)-V) relationship is shallower and shifted to more negative voltages than the conductance-voltage (G(K)-V) relationship. Calcium alters the relationship between Q-V and G-V, shifting both to more negative voltages such that they almost superimpose in 70 microM Ca(2+). This change reflects a differential effect of Ca(2+) on voltage sensor activation and channel opening. Ca(2+) has only a small effect on the fast component of ON gating current, indicating that Ca(2+) binding has little effect on voltage sensor activation when channels are closed. In contrast, open probability measured at very negative voltages (less than -80 mV) increases more than 1,000-fold in 70 microM Ca(2+), demonstrating that Ca(2+) increases the C-O equilibrium constant under conditions where voltage sensors are not activated. Thus, Ca(2+) binding and voltage sensor activation act almost independently, to enhance channel opening. This dual-allosteric mechanism can reproduce the steady-state behavior of mSlo1 over a wide range of conditions, with the assumption that activation of individual Ca(2+) sensors or voltage sensors additively affect the energy of the C-O transition and that a weak interaction between Ca(2+) sensors and voltage sensors occurs independent of channel opening. By contrast, macroscopic I(K) kinetics indicate that Ca(2+) and voltage dependencies of C-O transition rates are complex, leading us to propose that the C-O conformational change may be described by a complex energy landscape.

The crystal structure of a tetrameric hemoglobin in a partial hemichrome state

Tetrameric hemoglobins are the most widely used systems in studying protein cooperativity. Allosteric effects in hemoglobins arise from the switch between a relaxed (R) state and a tense (T) state occurring upon oxygen release. Here we report the 2.0-A crystal structure of the main hemoglobin component of the Antarctic fish Trematomus newnesi, in a partial hemichrome form. The two alpha-subunit iron atoms are bound to a CO molecule, whereas in the beta subunits the distal histidine residue is the sixth ligand of the heme iron. This structure, a tetrameric hemoglobin in the hemichrome state, demonstrates that the iron coordination by the distal histidine, usually associated with denaturing states, may be tolerated in a native-like hemoglobin structure. In addition, several features of the tertiary and quaternary organization of this structure are intermediate between the R and T states and agree well with the R --> T transition state properties obtained by spectroscopic and kinetic techniques. The analysis of this structure provides a detailed pathway of heme-heme communication and it indicates that the plasticity of the beta heme pocket plays a role in the R --> T transition of tetrameric hemoglobins.

A tertiary two-state allosteric model for hemoglobin

The two-state allosteric model of Monod, Wyman, and Changeux (MWC) provides an excellent description of homotropic effects in a vast array of equilibrium and kinetic measurements on cooperative ligand binding by hemoglobin. However, in contrast to experimental observations, the model does not allow for alteration of the ligand affinity of the T quaternary structure by allosteric effectors. This failure to explain heterotropic effects has been appreciated for over 30 years, and it has been generally assumed to result from tertiary conformational changes in the absence of a quaternary change. Here we explore a model that preserves the essential MWC idea that binding without a quaternary conformational change is non-cooperative, but where tertiary conformations of individual subunits play the primary role instead of the quaternary conformations. In this model, which we call the 'tertiary two-state (TTS) model', the two affinity states correspond to two tertiary conformations of individual subunits rather than the two quaternary conformations of the MWC two-state allosteric model. Ligation and the R quaternary structure bias the subunit population toward the high affinity tertiary conformation, while deligation and the T quaternary structure favor the low affinity tertiary conformation. We show that the model is successful in quantitatively explaining a demanding set of kinetic data from nanosecond carbon monoxide photodissociation experiments at times longer than approximately 1 micros. Better agreement between the model and the submicrosecond kinetic data may result from detailed considerations of the distribution and dynamics of conformational substates of the two tertiary conformations. The model is consistent with the results of solution, gel, and single crystal oxygen binding studies, but underestimates the population of doubly-liganded molecules determined in low-temperature electrophoresis experiments.

New insights into the allosteric mechanism of human hemoglobin from molecular dynamics simulations

It is still difficult to obtain a precise structural description of the transition between the deoxy T-state and oxy R-state conformations of human hemoglobin, despite a large number of experimental studies. We used molecular dynamics with the Path Exploration with Distance Constraints (PEDC) method to provide new insights into the allosteric mechanism at the atomic level, by simulating the T-to-R transition. The T-state molecule in the absence of ligands was seen to have a natural propensity for dimer rotation, which nevertheless would be hampered by steric hindrance in the "joint" region. The binding of a ligand to the alpha subunit would prevent such hindrance due to the coupling between this region and the alpha proximal histidine, and thus facilitate completion of the dimer rotation. Near the end of this quaternary transition, the "switch" region adopts the R conformation, resulting in a shift of the beta proximal histidine. This leads to a sliding of the beta-heme, the effect of which is to open the beta-heme's distal side, increasing the accessibility of the Fe atom and thereby the affinity of the protein. Our simulations are globally consistent with the Perutz strereochemical mechanism.

The effect of water on the rate of conformational change in protein allostery

The influence of solvation on the rate of quaternary structural change is investigated in human hemoglobin, an allosteric protein in which reduced water activity destabilizes the R state relative to T. Nanosecond absorption spectroscopy of the heme Soret band was used to monitor protein relaxation after photodissociation of aqueous HbCO complex under osmotic stress induced by the nonbinding cosolute poly(ethylene glycol) (PEG). Photolysis data were analyzed globally for six exponential time constants and amplitudes as a function of osmotic stress and viscosity. Increases in time constants associated with geminate rebinding, tertiary relaxation, and quaternary relaxation were observed in the presence of PEG, along with a decrease in the fraction of hemes rebinding CO with the slow rate constant characteristic of the T state. An analysis of these results along with those obtained by others for small cosolutes showed that both osmotic stress and solvent viscosity are important determinants of the microscopic R --> T rate constant. The size and direction of the osmotic stress effect suggests that at least nine additional water molecules are required to solvate the allosteric transition state relative to the R-state hydration, implying that the transition state has a greater solvent-exposed area than either end state.

The extracellular linker of muscle acetylcholine receptor channels is a gating control element

We describe the functional consequences of mutations in the linker between the second and third transmembrane segments (M2-M3L) of muscle acetylcholine receptors at the single-channel level. Hydrophobic mutations (Ile, Cys, and Phe) placed near the middle of the linker of the alpha subunit (alphaS269) prolong apparent openings elicited by low concentrations of acetylcholine (ACh), whereas hydrophilic mutations (Asp, Lys, and Gln) are without effect. Because the gating kinetics of the alphaS269I receptor (a congenital myasthenic syndrome mutant) in the presence of ACh are too fast, choline was used as the agonist. This revealed an approximately 92-fold increased gating equilibrium constant, which is consistent with an approximately 10-fold decreased EC(50) in the presence of ACh. With choline, this mutation accelerates channel opening approximately 28-fold, slows channel closing approximately 3-fold, but does not affect agonist binding to the closed state. These ratios suggest that, with ACh, alphaS269I acetylcholine receptors open at a rate of approximately 1.4 x 10(6) s(-1) and close at a rate of approximately 760 s(-1). These gating rate constants, together with the measured duration of apparent openings at low ACh concentrations, further suggest that ACh dissociates from the diliganded open receptor at a rate of approximately 140 s(-1). Ile mutations at positions flanking alphaS269 impair, rather than enhance, channel gating. Inserting or deleting one residue from this linker in the alpha subunit increased and decreased, respectively, the apparent open time approximately twofold. Contrary to the alphaS269I mutation, Ile mutations at equivalent positions of the beta, straightepsilon, and delta subunits do not affect apparent open-channel lifetimes. However, in beta and straightepsilon, shifting the mutation one residue to the NH(2)-terminal end enhances channel gating. The overall results indicate that this linker is a control element whose hydrophobicity determines channel gating in a position- and subunit-dependent manner. Characterization of the transition state of the gating reaction suggests that during channel opening the M2-M3L of the alpha subunit moves before the corresponding linkers of the beta and straightepsilon subunits.

Application of linear free energy relationships to the serpin-proteinase inhibition mechanism

Linear free energy relationships can be used to link the changes in rate constant for a reaction to changes in the equilibrium caused by alterations in structure. While they have most often been used in the analysis of chemical reactions, they have also been employed to resolve questions in enzymology and protein folding. Here we analyze the reaction of a serpin with a panel of six serine proteinases, and observe that a linear free energy relationship exists between the true second-order rate constant for reaction, k(inh), and the inhibition constant, K(I), indicating that formation of the covalent serpin-enzyme complex may be reversible.

Mapping the conformational wave of acetylcholine receptor channel gating

Allosteric transitions allow fast regulation of protein function in living systems. Even though the end points of such conformational changes are known for many proteins, the characteristics of the paths connecting these states remain largely unexplored. Rate-equilibrium linear free-energy relationships (LFERs) provide information about such pathways by relating changes in the free energy of the transition state to those of the ground states upon systematic perturbation of the system. Here we present an LFER analysis of the gating reaction pathway of the muscle acetylcholine receptor. We studied the closed <==> open conformational change at the single-molecule level following perturbation by series of single-site mutations, agonists and membrane voltages. This method provided a snapshot of several regions of the receptor at the transition state in terms of their approximate positions along the reaction coordinate, on a scale from 0 (closed-like) to 1 (open-like). The resulting map reveals a spatial gradient of positional values, which suggests that the conformational change proceeds in a wave-like manner, with the low-to-high affinity change at the transmitter-binding sites preceding the complete opening of the pore.

A kinetic analysis of the nucleotide-induced allosteric transitions of GroEL

Single-point mutants of GroEL were constructed with tryptophan replacing a tyrosine residue in order to examine nucleotide-induced structural transitions spectrofluorometrically. The tyrosine residues at positions 203, 360, 476 and 485 were mutated. Of these, the probe at residue 485 gave the clearest fluorescence signals upon nucleotide binding. The probe at 360 reported similar signals. In response to the binding of ATP, the indole fluorescence reports four distinct structural transitions occurring on well-separated timescales, all of which precede hydrolysis of the nucleotide. All four of these rearrangements were analysed, two in detail. The fastest is an order of magnitude more rapid than previously identified rearrangements and is proposed to be a T-to-R transition. The next kinetic phase is a rearrangement to the open state identified by electron cryo-microscopy and this we designate an R to R* transition. Both of these rearrangements can occur when only a single ring of GroEL is loaded with ATP, and the results are consistent with the occupied ring behaving in a concerted, cooperative manner. At higher ATP concentrations both rings can be loaded with the nucleotide and the R to R* transition is accelerated. The resultant GroEL:ATP14 species can then undergo two final rearrangements, RR*-->[RR](+)-->[RR](#). These final slow steps are completely blocked when ADP occupies the second ring, i.e. it does not occur in the GroEL:ATP7:ADP7 or the GroEL:ATP7 species. All equilibrium and kinetic data conform to a minimal model in which the GroEL ring can exist in five distinct states which then give rise to seven types of oligomeric conformer: TT, TR, TR*, RR, RR*, [RR](+) and [RR](#), with concerted transitions between each. The other eight possible conformers are presumably disallowed by constraints imposed by inter-ring contacts. This kinetic behaviour is consistent with the GroEL ring passing through distinct functional states in a binding-encapsulation-folding process, with the T-form having high substrate affinity (binding), the R-form being able to bind GroES but retaining substrate affinity (encapsulation), and the R*-form retaining high GroES affinity but allowing the substrate to dissociate into the enclosed cavity (folding). ADP induces only one detectable rearrangement (designated T to T*) which has no properties in common with those elicited by ATP. However, asymmetric ADP binding prevents ATP occupying both rings and, hence, restricts the system to the T*T, T*R and T*R* complexes.

Coupling of the oxygen-linked interaction energy for inositol hexakisphosphate and bezafibrate binding to human HbA0

The energetics of signal propagation between different functional domains (i.e. the binding sites for O2, inositol hexakisphospate (IHP), and bezafibrate (BZF)) of human HbA0 was analyzed at different heme ligation states and through the use of a stable, partially heme ligated intermediate. Present data allow three main conclusions to be drawn, and namely: (i) IHP and BZF enhance each others binding as the oxygenation proceeds, the coupling free energy going from close to zero in the deoxy state to -3.4 kJ/mol in the oxygenated form; (ii) the simultaneous presence of IHP and BZF stabilizes the hemoglobin T quaternary structure at very low O2 pressures, but as oxygenation proceeds it does not impair the transition toward the R structure, which indeed occurs also under these conditions; (iii) under room air pressure (i.e. pO2 = 150 torr), IHP and BZF together induce the formation of an asymmetric dioxygenated hemoglobin tetramer, whose features appear reminiscent of those suggested for transition state species (i.e. T- and R-like tertiary conformation(s) within a quaternary R-like structure).