Exploring the origins of topological frustration: Design of a minimally frustrated model of fragment B of protein A

Topological frustration in an energetically unfrustrated off-lattice model of the helical protein fragment B of protein A from Staphylococcus aureus was investigated. This Gō-type model exhibited thermodynamic and kinetic signatures of a well-designed two-state folder with concurrent collapse and folding transitions and single exponential kinetics at the transition temperature. Topological frustration is determined in the absence of energetic frustration by the distribution of Fersht φ values. Topologically unfrustrated systems present a unimodal distribution sharply peaked at intermediate φ, whereas highly frustrated systems display a bimodal distribution peaked at low and high φ values. The distribution of φ values in protein A was determined both thermodynamically and kinetically. Both methods yielded a unimodal distribution centered at φ = 0.3 with tails extending to low and high φ values, indicating the presence of a small amount of topological frustration. The contacts with high φ values were located in the turn regions between helices I and II and II and III, intimating that these hairpins are in large part required in the transition state. Our results are in good agreement with all-atom simulations of protein A, as well as lattice simulations of a three- letter code 27-mer (which can be compared with a 60-residue helical protein). The relatively broad unimodal distribution of φ values obtained from the all-atom simulations and that from the minimalist model for the same native fold suggest that the structure of the transition state ensemble is determined mostly by the protein topology and not energetic frustration.

From residue matching patterns to protein folding topographies: General model and bovine pancreatic trypsin inhibitor

A coarse-grained model for protein-folding dynamics is introduced based on a discretized representation of torsional modes. The model, based on the Ramachandran map of the local torsional potential surface and the class (hydrophobic/polar/neutral) of each residue, recognizes patterns of both torsional conformations and hydrophobic-polar contacts, with tolerance for imperfect patterns. It incorporates empirical rates for formation of secondary and tertiary structure. The method yields a topological representation of the evolving local torsional configuration of the folding protein, modulo the basins of the Ramachandran map. The folding process is modeled as a sequence of transitions from one contact pattern to another, as the torsional patterns evolve. We test the model by applying it to the folding process of bovine pancreatic trypsin inhibitor, obtaining a kinetic description of the transitions between the contact patterns visited by the protein along the dominant folding pathway. The kinetics and detailed balance make it possible to invert the result to obtain a coarse topographic description of the potential energy surface along the dominant folding pathway, in effect to go backward or forward between a topological representation of the chain conformation and a topographical description of the potential energy surface governing the folding process. As a result, the strong structure-seeking character of bovine pancreatic trypsin inhibitor and the principal features of its folding pathway are reproduced in a reasonably quantitative way.

Large kinetic isotope effects in enzymatic proton transfer and the role of substrate oscillations

We propose an interpretation of the experimental findings of Klinman and coworkers [Cha, Y., Murray, C. J. & Klinman, J. P. (1989) Science 243, 1325–1330; Grant, K. L. & Klinman, J. P. (1989) Biochemistry 28, 6597–6605; and Bahnson, B. J. & Klinman, J. P. (1995) Methods Enzymol. 249, 373–397], who showed that proton transfer reactions that are catalyzed by bovine serum amine oxidase proceed through tunneling. We show that two different tunneling models are consistent with the experiments. In the first model, the proton tunnels from the ground state. The temperature dependence of the kinetic isotope effect is caused by a thermally excited substrate mode that modulates the barrier, as has been suggested by Borgis and Hynes [Borgis, D. & Hynes, J. T. (1991) J. Chem. Phys. 94, 3619–3628]. In the second model, there is both over-the-barrier transfer and tunneling from excited states. Finally, we propose two experiments that can distinguish between the possible mechanisms.

Kinetic equilibrium of forces and molecular events in muscle contraction

In biomolecular systems, the mechanical transfer of free energy occurs with both high efficiency and high speed. It is shown here that such a transfer can be achieved only if the participating free-energy-storing elements exhibit opposing relationships between their content of free energy and the force they exert in the transfer direction. A kinetic equilibrium of forces (KEF) results, in which the transfer of free energy is mediated essentially by thermal molecular motion. On the basis of present evidence, KEF is used as a guiding principle in developing a mechanical model of the crossbridge cycle in muscle contraction. The model allows the basic features of molecular events to be visualized in terms of plausible structures. Real understanding of the process will require identification of the elements that perform the functions described here. Besides chemomechanical energy transduction, KEF may have a role in other biomolecular processes in which free energy is transferred mechanically over large distances.

Kinetic stability as a mechanism for protease longevity

The folding of the extracellular serine protease, α-lytic protease (αLP; EC 3.4.21.12) reveals a novel mechanism for stability that appears to lead to a longer functional lifetime for the protease. For αLP, stability is based not on thermodynamics, but on kinetics. Whereas this has required the coevolution of a pro region to facilitate folding, the result has been the optimization of native-state properties independent of their consequences on thermodynamic stability. Structural and mutational data lead to a model for catalysis of folding in which the pro region binds to a conserved β-hairpin in the αLP C-terminal domain, stabilizing the folding transition state and the native state. The pro region is then proteolytically degraded, leaving the active αLP trapped in a metastable conformation. This metastability appears to be a consequence of pressure to evolve properties of the native state, including a large, highly cooperative barrier to unfolding, and extreme rigidity, that reduce susceptibility to proteolytic degradation. In a test of survival under highly proteolytic conditions, homologous mammalian proteases that have not evolved kinetic stability are much more rapidly degraded than αLP. Kinetic stability as a means to longevity is likely to be a mechanism conserved among the majority of extracellular bacterial pro-proteases and may emerge as a general strategy for intracellular eukaryotic proteases subject to harsh conditions as well.

A statistical mechanical model for β-hairpin kinetics

Understanding the mechanism of protein secondary structure formation is an essential part of the protein-folding puzzle. Here, we describe a simple statistical mechanical model for the formation of a β-hairpin, the minimal structural element of the antiparallel β-pleated sheet. The model accurately describes the thermodynamic and kinetic behavior of a 16-residue, β-hairpin-forming peptide, successfully explaining its two-state behavior and apparent negative activation energy for folding. The model classifies structures according to their backbone conformation, defined by 15 pairs of dihedral angles, and is further simplified by considering only the 120 structures with contiguous stretches of native pairs of backbone dihedral angles. This single sequence approximation is tested by comparison with a more complete model that includes the 215 possible conformations and 15 × 215 possible kinetic transitions. Finally, we use the model to predict the equilibrium unfolding curves and kinetics for several variants of the β-hairpin peptide.

Direct conversion of an oligopeptide from a β-sheet to an α-helix: A model for amyloid formation

A 16-amino acid oligopeptide forms a stable β-sheet structure in water. In physiological solutions it is able to self-assemble to form a macroscopic matrix that stains with Congo red. On raising the temperature of the aqueous solution above 70°C, an abrupt structural transition occurs in the CD spectra from a β-sheet to a stable α-helix without a detectable random-coil intermediate. With cooling, it retained the α-helical form and took several weeks at room temperature to partially return to the β-sheet form. Slow formation of the stable β-sheet structure thus shows kinetic irreversibility. Such a formation of very stable β-sheet structures is found in the amyloid of a number of neurological diseases. This oligopeptide could be a model system for studying the protein conformational changes that occurs in scrapie or Alzheimer disease. The abrupt and direct conversion from a β-sheet to an α-helix may also be found in other processes, such as protein folding and protein–protein interaction. Furthermore, such drastic structure changes may also be exploited in biomaterials designed as sensors to detect environmental changes.

Kinetic proofreading models for cell signaling predict ways to escape kinetic proofreading

In the context of cell signaling, kinetic proofreading was introduced to explain how cells can discriminate among ligands based on a kinetic parameter, the ligand-receptor dissociation rate constant. In the kinetic proofreading model of cell signaling, responses occur only when a bound receptor undergoes a complete series of modifications. If the ligand dissociates prematurely, the receptor returns to its basal state and signaling is frustrated. We extend the model to deal with systems where aggregation of receptors is essential to signal transduction, and present a version of the model for systems where signaling depends on an extrinsic kinase. We also investigate the kinetics of signaling molecules, “messengers,” that are generated by aggregated receptors but do not remain associated with the receptor complex. We show that the extended model predicts modes of signaling that exhibit kinetic discrimination for some range of parameters but for other parameter values show little or no discrimination and thus escape kinetic proofreading. We compare model predictions with experimental data.

Force and kinetic barriers to unzipping of the DNA double helix

A theory of the unzipping of double-stranded DNA is presented and is compared to recent micromanipulation experiments. It is shown that the interactions that stabilize the double helix and the elastic rigidity of single strands simply determine the sequence-dependent ≈12-pN force threshold for DNA strand separation. Using a semimicroscopic model of the binding between nucleotide strands, we show that the greater rigidity of the strands when formed into double-stranded DNA, relative to that of isolated strands, gives rise to a potential barrier to unzipping. The effects of this barrier are derived analytically. The force to keep the extremities of the molecule at a fixed distance, the kinetic rates for strand unpairing at fixed applied force, and the rupture force as a function of loading rate are calculated. The dependence of the kinetics and of the rupture force on molecule length is also analyzed.

Kinetic coupling between electron and proton transfer in cytochrome c oxidase: simultaneous measurements of conductance and absorbance changes.

Bovine heart cytochrome c oxidase is an electron-current driven proton pump. To investigate the mechanism by which this pump operates it is important to study individual electron- and proton-transfer reactions in the enzyme, and key reactions in which they are kinetically and thermodynamically coupled. In this work, we have simultaneously measured absorbance changes associated with electron-transfer reactions and conductance changes associated with protonation reactions following pulsed illumination of the photolabile complex of partly reduced bovine cytochrome c oxidase and carbon monoxide. Following CO dissociation, several kinetic phases in the absorbance changes were observed with time constants ranging from approximately 3 microseconds to several milliseconds, reflecting internal electron-transfer reactions within the enzyme. The data show that the rate of one of these electron-transfer reactions, from cytochrome a3 to a on a millisecond time scale, is controlled by a proton-transfer reaction. These results are discussed in terms of a model in which cytochrome a3 interacts electrostatically with a protonatable group, L, in the vicinity of the binuclear center, in equilibrium with the bulk through a proton-conducting pathway, which determines the rate of proton transfer (and indirectly also of electron transfer). The interaction energy of cytochrome a3 with L was determined independently from the pH dependence of the extent of the millisecond-electron transfer and the number of protons released, as determined from the conductance measurements. The magnitude of the interaction energy, 70 meV (1 eV = 1.602 x 10(-19) J), is consistent with a distance of 5-10 A between cytochrome a3 and L. Based on the recently determined high-resolution x-ray structures of bovine and a bacterial cytochrome c oxidase, possible candidates for L and a physiological role for L are discussed.

Ras-catalyzed hydrolysis of GTP: a new perspective from model studies.

Despite the biological and medical importance of signal transduction via Ras proteins and despite considerable kinetic and structural studies of wild-type and mutant Ras proteins, the mechanism of Ras-catalyzed GTP hydrolysis remains controversial. We take a different approach to this problem: the uncatalyzed hydrolysis of GTP is analyzed, and the understanding derived is applied to the Ras-catalyzed reaction. Evaluation of previous mechanistic proposals from this chemical perspective suggests that proton abstraction from the attacking water by a general base and stabilization of charge development on the gamma-phosphoryl oxygen atoms would not be catalytic. Rather, this analysis focuses attention on the GDP leaving group, including the beta-gamma bridge oxygen of GTP, the atom that undergoes the largest change in charge in going from the ground state to the transition state. This leads to a new catalytic proposal in which a hydrogen bond from the backbone amide of Gly-13 to this bridge oxygen is strengthened in the transition state relative to the ground state, within an active site that provides a template complementary to the transition state. Strengthened transition state interactions of the active site lysine, Lys-16, with the beta-nonbridging phosphoryl oxygens and a network of interactions that positions the nucleophilic water molecule and gamma-phosphoryl group with respect to one another may also contribute to catalysis. It is speculated that a significant fraction of the GAP-activated GTPase activity of Ras arises from an additional interaction of the beta-gamma bridge oxygen with an Arg side chain that is provided in trans by GAP. The conclusions for Ras and related G proteins are expected to apply more widely to other enzymes that catalyze phosphoryl (-PO(3)2-) transfer, including kinases and phosphatases.

A general two-process model describes the hydrogen exchange behavior of RNase A in unfolding conditions.

When NMR hydrogen exchange was used previously to monitor the kinetics of RNase A unfolding, some peptide NH protons were found to show EX2 exchange (detected by base catalysis) in addition to the expected EX1 exchange, whose rate is limited by the kinetic unfolding process. In earlier work, two groups showed independently that a restricted two-process model successfully fits published hydrogen exchange rates of native RNase A in the range 0-0.7 M guanidinium chloride. We find that this model predicts properties that are very different from the observed properties of the EX2 exchange reactions of RNase A in conditions where guanidine-induced unfolding takes place. The model predicts that EX2 exchange should be too fast to measure by the technique used, whereas it is readily measurable. Possible explanations for the contradiction are considered here, and we show that removing the restriction from the earlier two-process model is sufficient to resolve the contradiction; instead of specifying that exchange caused by global unfolding occurs by the EX2 mechanism, we allow it to occur by the general mechanism, which includes both the EX1 and EX2 cases. It is logical to remove this restriction because global unfolding of RNase A is known to give rise to EX1 exchange in these unfolding conditions. Resolving the contradiction makes it possible to determine whether populated unfolding intermediates contribute to the EX2 exchange, and this question is considered elsewhere. The results and simulations indicate that moderate or high denaturant concentrations readily give rise to EX1 exchange in native proteins. Earlier studies showed that hydrogen exchange in native proteins typically occurs by the EX2 mechanism but that high temperatures or pH values above 7 may give rise to EX1 exchange. High denaturant concentrations should be added to the list of variables likely to cause EX1 exchange.

Kinetic discrimination in T-cell activation.

We propose a quantitative model for T-cell activation in which the rate of dissociation of ligand from T-cell receptors determines the agonist and antagonist properties of the ligand. The ligands are molecular complexes between antigenic peptides and proteins of the major histocompatibility complex on the surfaces of antigen-presenting cells. Binding of ligand to receptor triggers a series of biochemical reactions in the T cell. If the ligand dissociates after these reactions are complete, the T cell receives a positive activation signal. However, dissociation of ligand after completion of the first reaction but prior to generation of the final products results in partial T-cell activation, which acts to suppress a positive response. Such a negative signal is brought about by T-cell ligands containing the variants of antigenic peptides referred to as T-cell receptor antagonists. Results of recent experiments with altered peptide ligands compare favorably with T-cell responses predicted by this model.

The folding of GroEL-bound barnase as a model for chaperonin-mediated protein folding.

We have analyzed the pathway of folding of barnase bound to GroEL to resolve the controversy of whether proteins can fold while bound to chaperonins (GroEL or Cpn60) or fold only after their release into solution. Four phases in the folding were detected by rapid-reaction kinetic measurements of the intrinsic fluorescence of both wild type and barnase mutants. The phases were assigned from their rate laws, sensitivity to mutations, and correspondence to regain of catalytic activity. At high ratios of denatured barnase to GroEL, 4 mol of barnase rapidly bind per 14-mer of GroEL. At high ratios of GroEL to barnase, 1 mol of barnase binds with a rate constant of 3.5 x 10(7) s-1.M-1. This molecule then refolds with a low rate constant that changes on mutation in parallel with the rate constant for the folding in solution. This rate constant corresponds to the regain of the overall catalytic activity of barnase and increases 15-fold on the addition of ATP to a physiologically relevant value of approximately 0.4 s-1. The multiply bound molecules of barnase that are present at high ratios of GroEL to barnase fold with a rate constant that is also sensitive to mutation but is 10 times higher. If the 110-residue barnase can fold when bound to GroEL and many moles can bind simultaneously, then smaller parts of large proteins should be able to fold while bound.

Kinetic proofreading in T-cell receptor signal transduction.

Like other cell-surface receptors with intrinsic or associated protein-tyrosine kinase activity, the T-cell receptor complex undergoes a number of modifications, including tyrosine phosphorylation steps, after ligand binding but before transmitting a signal. The requirement for these modifications introduces a temporal lag between ligand binding and receptor signaling. A model for the T-cell receptor is proposed in which this feature greatly enhances the receptor's ability to discriminate between a foreign antigen and self-antigens with only moderately lower affinity. The proposed scheme is a form of kinetic proofreading, known to be essential for the fidelity of protein and DNA synthesis. A variant of this scheme is also described in which a requirement for formation of large aggregates may lead to a further enhancement of the specificity of T-cell activation. Through these mechanisms, ligands of different affinity potentially may elicit qualitatively different signals.