Theory of cooperative transitions in protein molecules. I. Why denaturation of globular protein is a first-order phase transition

A theory of equilibrium denaturation of proteins is suggested. According to this theory, a cornerstone of protein denaturation is disruption of tight packing of side chains in protein core. Investigation of this disruption is the object of this paper. It is shown that this disruption is an "all-or-none" transition (independent of how compact is the denatured state of a protein and independent of the protein-solvent interactions) because expansion of a globule must exceed some threshold to release rotational isomerization of side chains. Smaller expansion cannot produce entropy compensation of nonbonded energy loss; this is the origin of a free-energy barrier (transition state) between the native and denatured states. The density of the transition state is so high that the solvent cannot penetrate into protein in this state. The results obtained in this paper make it possible to present in the following paper a general phase diagram of protein molecule in solution.     

Direct access to the cooperative substructure of proteins and the protein ensemble via cold denaturation

The modern view of protein thermodynamics predicts that proteins undergo cold-induced unfolding. Unfortunately, the properties of proteins and water conspire to prevent the detailed observation of this fundamental process. Here we use protein encapsulation to allow cold denaturation of the protein ubiquitin to be monitored by high-resolution NMR at temperatures approaching -35 degrees C. The cold-induced unfolding of ubiquitin is found to be highly noncooperative, in distinct contrast to the thermal melting of this and other proteins. These results demonstrate the potential of cold denaturation as a means to dissect the cooperative substructures of proteins and to provide a rigorous framework for testing statistical thermodynamic treatments of protein stability, dynamics and function.     

An increase in the rate of proteolysis in vitro after treatment with oxidized glutathione

The effect of the formation of mixed disulphides--protein-glutathione--on the proteolysis rate was studied using soluble fractions of proteins from different rat tissues as substrates. It was shown that the binding of oxidized glutathione to proteins increases the proteolysis rate under the effect of trypsin and chymotrypsin. When the concentration of oxidized glutathione is 5.10(-4) M a 1.2-1.4-fold increase in the proteolysis rate is registered and when the concentration is 5.10(-3) M a 1.4-1.8 fold increase is observed.     

Automated prediction of protein association rate constants

The association rate constants (k(a)) of proteins with other proteins or other macromolecular targets are a fundamental biophysical property. Observed rate constants span over ten orders of magnitude, from 1 to 10(10) M(-1)s(-1). Protein association can be rate limited either by the diffusional approach of the subunits to form a transient complex, with near-native separation and orientation but without short-range native interactions, or by the subsequent conformational rearrangement to form the native complex. Our transient-complex theory showed promise in predicting k(a) in the diffusion-limited regime. Here, we develop it into a web server called TransComp (http://pipe.sc.fsu.edu/transcomp/) and report on the server's accuracy and robustness based on applications to over 100 protein complexes. We expect this server to be a valuable tool for systems biology applications and for kinetic characterization of protein-protein and protein-nucleic acid association in general.     

Integrated steady state rate equations and the determination of individual rate constants.

Integrated steady state rate equations have been used to determine the kinetic constants (Vs, Ks, Vp, and Kp) and rate constants (k1, k2, k3, and k4) of the reversible enzyme mechanism: (see article). The fumarase reaction has been used as a model to illustrate the procedures for determining these constants. In contrast to initial velocity studies, the values of the constants have been obtained by examining the enzyme reaction in only one direction rather than in both forward and reverse directions. To accomplish this, a new procedure is described for fitting data to integrated rate equations which eliminates problems encountered when data are analyzed graphically. The advantages of examining on enzyme reaction in one direction with these new procedures allow this method to be extended to the examination of enzymes with simple mechanisms where initial velocities are difficult to measure because either the substrate or product is not readily available, or because the reaction is not readily reversible.     

Dynamic transition associated with the thermal denaturation of a small Beta protein

We studied the temperature dependence of the picosecond internal dynamics of an all-beta protein, neocarzinostatin, by incoherent quasielastic neutron scattering. Measurements were made between 20 degrees C and 71 degrees C in heavy water solution. At 20 degrees C, only 33% of the nonexchanged hydrogen atoms show detectable dynamics, a number very close to the fraction of protons involved in the side chains of random coil structures, therefore suggesting a rigid structure in which the only detectable diffusive movements are those involving the side chains of random coil structures. At 61.8 degrees C, although the protein structure is still native, slight dynamic changes are detected that could reflect enhanced backbone and beta-sheet side-chain motions at this higher temperature. Conversely, all internal dynamics parameters (amplitude of diffusive motions, fraction of immobile scatterers, mean-squared vibration amplitude) rapidly change during heat-induced unfolding, indicating a major loss of rigidity of the beta-sandwich structure. The number of protons with diffusive motion increases markedly, whereas the volume occupied by the diffusive motion of protons is reduced. At the half-transition temperature (T = 71 degrees C) most of backbone and beta-sheet side-chain hydrogen atoms are involved in picosecond dynamics.     

Analysis of a procedure for the determination of kinetic rate constants

This paper is concerned with a mathematical analysis of the modified Guggenheim procedure. Theorems concerning the solutions of the differential equations which describe the general reaction

$$E + SB\xrightarrow{{k_2 }}C + X, C\xrightarrow{{k_3 }}E + D$$     

A new method for the determination of stability parameters of proteins from their heat-induced denaturation curves

A new method has been developed for determining the stability parameters of proteins from their heat-induced transition curves followed by observation of changes in the far-UV circular dichroism (CD). This method of analysis of the thermal denaturation curve of a protein gave values of stability parameters that not only are identical to those measured by the differential scanning calorimetry (DSC), but also are measured with the same error as that observed with a calorimeter. This conclusion has been reached from our studies of the reversible heat-induced denaturation of lysozyme and ribonuclease A at various pH values. For each protein, the conventional method of analysis of the conformational transition curve, which assumes a linear temperature dependence of the pre- and posttransition baselines, gave the estimate of DeltaH(van)(m) (enthalpy change on denaturation at T(m), the midpoint of denaturation) which is significantly lower than DeltaH(cal)(m), the value obtained from DSC measurements. However, if the analysis of the same denaturation curve assumes that a parabolic function describes the temperature dependence of the pre- and posttransition baselines, there exists an excellent agreement between DeltaH(van)(m) and DeltaH(cal)(m) of the protein. The latter analysis is supported by the far-UV CD measurements of the oxidized ribonuclease A as a function of temperature, for the temperature dependence of this optical property of the protein is indeed nonlinear. Furthermore, it has been observed that, for each protein, the constant-pressure heat capacity change (DeltaC(p)) determined from the plots of DeltaH(van)(m) versus T(m) is independent of the method of analysis of the transition curve.     

On-chip non-equilibrium dissociation curves and dissociation rate constants as methods to assess specificity of oligonucleotide probes

Nucleic acid hybridization serves as backbone for many high-throughput systems for detection, expression analysis, comparative genomics and re-sequencing. Specificity of hybridization between probes and intended targets is always critical. Approaches to ensure and evaluate specificity include use of mismatch probes, obtaining dissociation curves rather than single temperature hybridizations, and comparative hybridizations. In this study, we quantify effects of mismatch type and position on intensity of hybridization signals and provide a new approach based on dissociation rate constants to evaluate specificity of hybridized signals in complex target mixtures. Using an extensive set of 18mer oligonucleotide probes on an in situ synthesized biochip platform, we demonstrate that mismatches in the center of the probe are more discriminating than mismatches toward the extremities of the probe and mismatches toward the attached end are less discriminating than those toward the loose end. The observed destabilizing effect of a mismatch type agreed in general with predictions using the nearest neighbor model. Use of a new parameter, specific dissociation temperature (T_d-w, temperature of maximum specific dissociation rate constant), obtained from probe–target duplex dissociation profiles considerably improved the evaluation of specificity. These results have broad implications for hybridization data obtained from complex mixtures of nucleic acids.     

Estimating the degree of expansion in the transition state for protein unfolding: analysis of the pH dependence of the rate constant for caricain denaturation

The thermal denaturation of caricain (the most alkaline of papain-related proteinases) was studied in acid media. Under all conditions tested, caricain denatured irreversibly following a single first-order reaction that involves simultaneous loss of secondary and tertiary structures. Besides, variation of the rate constant with temperature gave linear Eyring's plots. Thus, despite its irreversibility, this process resembles the kinetics of reversible protein unfolding. Due to the basicity of caricain, all of the carboxylates in the native protein interact with nearby positively charged groups. Then, it may be thought that pK values of titratable sites are mainly influenced by interactions of this type. Accordingly, we set up a simple electrostatic perturbation model, based on charge-charge interactions at distances not larger than 10 A, which reproduces reasonably well the titration curve of native caricain. Because the pH dependence of the activation free energy for unfolding (DeltaG()) can be related to differences in the protonation behavior of the native (N) state with respect to the transition (TS) state, the model was further used to analyze the experimental DeltaG() vs pH curve. Results from this analysis suggest that there is an increase of about 3 A in the average ion-pair distance when N globally expands to form TS. Alternatively, if the expansion were restricted to only one molecular domain, the structure of this domain in TS would be highly disordered. In either case, it is probable that the solvent-accessible area augments significantly during the expansion.     

Insight into the denaturation transition of DNA

DNA undergoes a helix-to-coil transition (also called denaturation transition) upon heating. This transition can also be facilitated by using solvent mixtures (for example water–alcohol). An increase in the hydrophobic tail of the second solvent molecule first decreases then increases the melting temperature appreciably. Measurement on 4% DNA in a series of water–alcohol mixtures shows that the helix-to-coil melting transition is driven by the solvent ability to cross the hydrophobic sugar-rich region. DNA is behaving like a cylindrical micelle.     

A numerical experiment on the determination of kinetic rate constants in the presence of diffusion

Two chemicals,A andB, are allowed to diffuse together and a reaction described by $$A + B\mathop \rightleftharpoons \limits_{K_{ - 1} }^{K_1 } C$$ is allowed to proceed. This system is described mathematically by a system of partial differential equations. A numerical procedure is presented to find the rate constants ofK ₁ andK _?1. A systematic analysis of the effects of errors is also presented.     

Influence of transition rates and scan rate on kinetic simulations of differential scanning calorimetry profiles of reversible and irreversible protein denaturation.

The thermodynamic parameters characterizing protein folding can be obtained directly using differential scanning calorimetry (DSC). They are meaningful only for reversible unfolding at equilibrium, which holds for small globular proteins; however, the unfolding or denaturation of most large, multidomain or multisubunit proteins is either partially or totally irreversible. The simplest kinetic model describing partially irreversible denaturation requires three states: Formula [see text] We obtain numerical solutions for N, U, and D as a function of temperature for this model and derive profiles of excess specific heat (Cp) in terms of the reduced variables v/ki and k1/k3, where v is the scan rate. The three-state model reduces to the two-state reversible or irreversible models for very large or very small values of k1/k3, respectively. The apparent transition temperature (Tapp) is always reduced by the irreversible step (U-->D). For all values of k3, Tapp is independent of v/k1 at sufficiently slow scan rates, even when denaturation is highly irreversible, but increases identically for all models at fast scan rates in which case the excess specific heat profile is determined by the rate of unfolding. Accurate values of delta H and delta S can be obtained for the reversible step only when k1 is more than 2000-50,000 times greater than k3. In principle, approximate values for the ratio k1/k3 can be obtained from plots of fraction unfolded vs fraction irreversibly denatured as a function of temperature; however, the fraction irreversibly denatured is difficult to measure accurately by DSC alone.(ABSTRACT TRUNCATED AT 250 WORDS)     

Study of the thermal denaturation of ribonuclease A by differential thermal analysis and susceptibility to proteolysis

1. The thermally induced change in conformation of ribonuclease A in solution was investigated by differential thermal analysis and the susceptibility of the enzyme to proteolytic digestion by ficin. 2. A transition with a mid-point of 60.5°C at pH4.2 was observed directly by differential thermal analysis and shown to be a property of the native structure. 3. At pH4.2 ribonuclease A is susceptible to ficin digestion at 60°C but not at 18°C. 4. Chromatographic analysis of the digestion products reveals that transient active intermediates are produced during the digestion. 5. Three of these intermediates were purified and partially characterized. 6. The nature of those sections of the ribonuclease molecule that are involved in the thermal transition is discussed.     

Use of acivicin in the determination of rate constants for turnover of rat renal gamma-glutamyltranspeptidase

The specific enzymatic activity of renal gamma-glutamyltranspeptidase is decreased from control levels (0.86 unit-1 mg-1) to minimal values within 2 h postinjection of 100-g rats with acivicin, an irreversible inhibitor of the enzyme. The recovery of transpeptidase specific activity was followed from 2 to 24 h postinjection and the data were used to calculate the absolute rate constants for degradation (kd = 0.47 +/- 0.03 day-1) and synthesis (ks = 0.41 +/- 0.04 unit-1 mg-1 day-1). This corresponds to a half-life for the renal transpeptidase of 1.46 +/- 0.09 days and 99% recovery of the specific activity by 10 days postinjection. Recovery was followed for 14 days and closely approximates this theoretical curve. The data from control experiments designed to test for secondary effects of the drug, acivicin, show that neither the relative rate of synthesis nor apparent rate of degradation for either total protein or gamma-glutamyltranspeptidase is significantly altered by acivicin treatment of rats. The results also show that the acivicin-inhibited transpeptidase is not degraded differently than enzymatically active enzyme. The individual heterodimer subunits also exhibit similar apparent half-lives in both control and treated animals. Thus, recovery of renal gamma-glutamyltranspeptidase specific activity after acivicin treatment can be used in vivo to determine absolute values of ks and kd for this enzyme. These values have not been reported for any other constituent of the renal brush-border membrane.     

Gating current kinetics in Myxicola giant axons. Order of the back transition rate constants.

Gating current, Ig, was recorded in Myxicola axons with series resistance compensation and higher time resolution than in previous studies. Ig at ON decays as two exponentials with time constants, tau ON-F and tau ON-S, very similar to squid values. No indication of an additional very fast relaxation was detected, but could be still unresolved. Ig at OFF also displays two exponentials, neither reflecting recovery from charge immobilization. Deactivation of the two I(ON) components may proceed with well-separated exponentials at -100 mV. INa tail currents at OFF also display two exponentials plus a third very slow relaxation of 5-9% of the total tail current. The very slow component is probably deactivation of a very small subpopulation of TTX sensitive channels. A -100 mV, means for INa tail component time constants (four axons) are 76 microseconds (range: 53-89 microseconds) and 344 microseconds (range: 312-387 microseconds), and for IOFF (six axons) 62 microseconds (range: 34-87 microseconds) and 291 microseconds (range: 204-456 microseconds) in reasonable agreement. INa ON activation time constant, tau A, is clearly slower than tau ON-F at all potentials. Except for the interval -30 to -15 mV, tau A is clearly faster than tau ON-S, and has a different dependency on potential. tau ON-S is several fold smaller than tau h. Computations with a closed2----closed1----open activation model indicated Na tail currents are consistent with a closed1----open rate constant greater than the closed2----closed1.