Volume and compressibility differences between protein conformations revealed by high-pressure NMR

Proteins often interconvert between different conformations in ways critical to their function. Although manipulating such equilibria for biophysical study is often challenging, the application of pressure is a potential route to achieve such control by favoring the population of lower volume states. Here, we use this feature to study the interconversion of ARNT PAS-B Y456T, which undergoes a dramatic +3 slip in the β-strand register as it switches between two stably folded conformations. Using high-pressure biomolecular NMR approaches, we obtained the first, to our knowledge, quantitative data testing two key hypotheses of this process: the slipped conformation is both smaller and less compressible than the wild-type equivalent, and the interconversion proceeds through a chiefly unfolded intermediate state. Data collected in steady-state pressure and time-resolved pressure-jump modes, including observed pressure-dependent changes in the populations of the two conformers and increased rate of interconversion between conformers, support both hypotheses. Our work exemplifies how these approaches, which can be generally applied to protein conformational switches, can provide unique information that is not easily accessible through other techniques.     

Exploring rare conformational species and ionic effects in DNA Holliday junctions using single-molecule spectroscopy

The four-way DNA (Holliday) junction is an essential intermediate in DNA recombination, and its dynamic characteristics are likely to be important in its cellular processing. In our previous study we observed transitions between two antiparallel stacked conformations using a single-molecule fluorescence approach. The magnesium concentration-dependent rates of transitions between stacking conformers suggested that an unstacked open structure, which is stable in the absence of metal ions, is an intermediate. Here, we sought to detect possible rare species such as open and parallel conformations and further characterized ionic effects. The hypothesized open intermediate cannot be resolved directly due to the limited time resolution and sensitivity, but our study suggests that the open form is achieved very frequently, hundreds of times per second under physiologically relevant conditions. Therefore despite being a minority species, its frequent formation raises the probability that it could become stabilized by protein binding. By contrast, we cannot detect even a transient existence of the junctions in a parallel form, and the probability of such forms with a lifetime greater than 5 ms is less than 0.01%. Stacking conformer transitions are observable in the presence of sodium or hexammine cobalt (III) ions as well as magnesium ions, but the transition rates are higher for lower valence ions at the same concentrations. This further supports the notion that electrostatic stabilization of the stacked structures dictates the interconversion rates between different structural forms.     

First passage time problem for a drifted Ornstein-Uhlenbeck process

We consider a continuous stochastic process defined as a drifted Ornstein-Uhlenbeck, for which the first passage time is of interest. The process being non-homogeneous, the first passage time probability density function cannot be found analytically, but numerical methods enable to find its estimate. Estimating the first passage time implies solving an unsteady convection-diffusion equation, with variable coefficients, and we use an implicit Euler scheme to solve it. This work is applied to simulated data, and the continuous process is inspired from recent work on biological marker modelling for HIV-positive patients. The first passage time probability density function can be useful to compare the marker progression in different groups. Numerical results show that the first passage time is highly dependent from the process perturbation, and is then more relevant than methods not considering the stochastic process directly to compare the progression.     

The influence of internal fluctuations and external noise on the gene frequency in a haploid population

We consider a Markov chain modeling competition between two alleles in a haploid population of constant size and undergoing mutation, selection and Fisher-Wright mating. The Markov chain is rescaled to a diffusion process. We study the interaction of external noise (due to a random selection coefficient) and internal fluctuations (due to mating); the interaction is found to be additive. The stationary probability density displays a critical point. We draw an analogy between the behavior of the probability density at the critical point and the theory of phase transitions; critical exponents are introduced and calculated. We also analyze the effect of external noise on the genetic diversity of the population and on mean first passage times of the gene frequency.     

Conformational analysis of d-tubocurarine: Implications for minimal dimensions of its binding site within ion channels

All the minimum-energy conformations of d-tubocurarine were calculated by the method of molecular mechanics. The energy was minimized from 413 closed forms of the 18-member ring. The set of minimum-energy conformations includes 10 forms with energies less than 6 kcal/mol from the most stable one. Among the four lowest minimum-energy conformations, two forms correspond to those known from X-ray studies, whereas two conformations were not detected experimentally earlier. The flexibility of d-tubocurarine was estimated by calculating six paths of interconversion between the four lowest minimum-energy conformations. Using a molecular graphics technique, it was found that the most extended minimum-energy conformation of d-tubocurarine may fit in an ion channel of a rectangular profile of 8.7 × 11.2 Å, while one tetrahydroisoquinoline head may fit a profile as small as 6.9 × 11.0 Å. A possible model of d-tubocurarine location within the ion channel of the neuronal nicotinic acetylcholine receptor is suggested.     

Kinetic properties of F0F1-ATPases. Theoretical predictions from alternating-site models.

We present an analysis of models based on current structural concepts of the F0F1 synthases, accounting for coupling between proton transport and ATP synthesis. It is assumed that each of the three alpha beta-subunits of the synthase can exist in three different conformational states E, Eo and E*. Proton translocation is coupled to cyclic interconversion of the conformations of the alpha beta-subunits. The conformational changes of these subunits are assumed to be coordinated so that all three interconvert simultaneously, in a rate-limiting transition. Binding and release of the ligands ATP, ADP, Pi, and protons are assumed to be equilibrium steps. In one family of models, interconversion of the alpha beta-subunits of F1 is coupled to the translocation event in F0 acting as a proton carrier. In a second family of models, protons combine with F0F1 and are translocated during the interconversion step in a chemiport. Kinetic tests involving the mutual effects of [ATP], [ADP], H+', and H+" are described, allowing us to make a distinction between the different models and submodels.     

The Ornstein-Uhlenbeck process as a model for neuronal activity

Mean and variance of the first passage time through a constant boundary for the Ornstein-Uhlenbeck process are determined by a straight-forward differentiation of the Laplace transform of the first passage time probability density function. The results of some numerical computations are discussed to shed some light on the input-output behavior of a formal neuron whose dynamics is modeled by a diffusion process of Ornstein-Uhlenbeck type.Work supported in part by the Group for Mathematical Information Science (GNIM) of the National Council for Research     

Native-state interconversion of a metamorphic protein requires global unfolding

Lymphotactin (Ltn) is a unique chemokine that under physiological solution conditions displays large-scale structural heterogeneity, defining a new category of "metamorphic proteins". Previous Ltn studies have indicated that each form is required for proper function, but the mechanism of interconversion remains unknown. Here we have investigated the temperature dependence of kinetic rates associated with interconversion and unfolding by stopped-flow fluorescence to determine transition-state free energies. Comparisons of derived thermodynamic parameters revealed striking similarities between interconversion and protein unfolding. We conclude that Ltn native-state rearrangement proceeds by way of a large-scale unfolding process rather than a unique intermediate structure.     

The interaction of ryanoids with individual ryanodine receptor channels

Ryanodine binds with high affinity and specificity to a class of Ca(2+)-release channels known as ryanodine receptors (RyR). The interaction with RyR results in a dramatic alteration in function with open probability (Po) increasing markedly and rates of ion translocation modified. We have investigated the features of ryanodine that govern the interaction of the ligand with RyR and the mechanisms underlying the subsequent alterations in function by monitoring the effects of congeners and derivatives of ryanodine (ryanoids) on individual RyR2 channels. While the interaction of all tested ryanoids results in an increased Po, the amplitude of the modified conductance state depends upon the structure of the ryanoid. We propose that different rates of cation translocation observed in the various RyR-ryanoid complexes represent different conformations of the channel stabilized by specific conformers of the ligand. On the time scale of a single channel experiment ryanodine binds irreversibly to the channel. However, alterations in structure yield some ryanoids with dissociation rate constants orders of magnitude greater than ryanodine. The probability of occurrence of the RyR-ryanoid complex is sensitive to trans-membrane voltage, with the vast majority of the influence of potential arising from a voltage-driven alteration in the affinity of the ryanoid-binding site.     

Temporal separation of protein toxin translocation from processing events

Intoxication of Vero cells by ricin, modeccin, diphtheria toxin (DT), and Pseudomonas exotoxin A requires: 1) binding to cell surface receptors; 2) transport to the cytoplasm; and 3) enzymatic inactivation of a component of the protein synthetic machinery. The kinetic profiles of all four toxins consist of a lag followed by the apparent first-order decrease in protein synthesis. Autoradiographic analysis of DT-intoxicated cell populations has demonstrated that two subpopulations of cells exist during the period of decreasing protein synthesis: one population synthesizing at control levels and the other synthesizing little or no protein (Hudson, T. H., and Neville, D. M., Jr. (1985) J. Biol. Chem. 260, 2675-2680). The present study correlates the autoradiographic data with the rates of protein synthesis decline in cells intoxicated with modeccin, ricin, Pseudomonas exotoxin A, as well DT. In all cases, the first time point which exhibits a decrease in protein synthetic activity also exhibits two subpopulations of cells, one synthesizing protein at control rates and the other synthesizing little or no protein. As the intoxication progresses, cells leave the control population by the rapid cessation of all protein synthesis. These experiments demonstrate that transport of all four toxins to the cytosol is the rate-limiting step during the pseudo first-order decline in protein synthesis. Furthermore, the final step in the transport process (translocation) must result in the release to the cytoplasm of a quantity of toxin sufficient to rapidly inactivate all protein synthesis in that cell. The probability of a translocation event occurring in any cell of the population is established during the lag and remains constant throughout the first-order decrease in protein synthesis. The requirement for acidification during the intoxication by DT, Pseudomonas exotoxin A, or modeccin is restricted to the lag period. Acidification is therefore necessary to establish the probability of translocation, but it is not directly involved in the actual translocation of these toxins. The pseudo first-order passage of DT intoxications through antitoxin and NH4Cl- or monensin-sensitive stages are shown to have the same cellular basis as the pseudo first-order decrease in protein synthesis. A kinetic model is presented which defines the DT intoxication process from one of its earliest events (endocytosis) to its penultimate event (translocation of toxin to the cytosol).(ABSTRACT TRUNCATED AT 400 WORDS)     

Fluorescence lifetime distributions in proteins.

The fluorescence lifetime value of tryptophan residues varies by more than a factor of 100 in different proteins and is determined by several factors, which include solvent exposure and interactions with other elements of the protein matrix. Because of the variety of different elements that can alter the lifetime value and the sensitivity to the particular environment of the tryptophan residue, it is likely that non-unique lifetime values result in protein systems. The emission decay of most proteins can be satisfactorily described only using several exponential components. Here it is proposed that continuous lifetime distributions can better represent the observed decay. An approach based on protein dynamics is presented, which provides fluorescence lifetime distribution functions for single tryptophan residue proteins. First, lifetime distributions for proteins interconverting between two conformations, each characterized by a different lifetime value, are derived. The evolution of the lifetime values as a function of the interconversion rate is studied. In this case lifetime distributions can be obtained from a distribution of rates of interconversion between the two conformations. Second, the existence of a continuum of energy substates within a given conformation was considered. The occupation of a particular energy substate at a given temperature is proportional to the Boltzmann factor. The density of energy states of the potential well depends upon the width of the well, which determines the degree of freedom the residue can move in the conformational space. Lifetime distributions can be obtained by association of each energy substate with a different lifetime value and assuming that the average conformation can change as the energy of the substate is increased.(ABSTRACT TRUNCATED AT 250 WORDS)     

Substrate-induced interconversion of protein quaternary structure isoforms

Human porphobilinogen synthase (PBGS) can exist in two dramatically different quaternary structure isoforms, which have been proposed to be in dynamic equilibrium. The quaternary structure isoforms of PBGS result from two alternative conformations of the monomer; one monomer structure assembles into a high activity octamer, whereas the other monomer structure assembles into a low activity hexamer. The kinetic behavior of these oligomers led to the hypothesis that turnover facilitates the interconversion of the oligomeric structures. The current work demonstrates that the interactions of ligands at the enzyme active site promote the structural interconversion between human PBGS quaternary structure isoforms, favoring formation of the octamer. This observation illustrates that the assembly and disassembly of oligomeric proteins can be facilitated by the protein motions that accompany enzymatic catalysis.     

Distributions of activation energy barriers that produce stretched exponential probability distributions for the time spent in each state of the two state reaction A⇌B

Many biochemical reactions consist of the spontaneous fluctuation between two states: A⇌B. For example these two states could be a ligand bound to an enzyme and the ligand and the enzyme separated from each other. A typical case would be the unbinding of CO from myoglobin (Mb), namely, MbCO⇌Mb+CO. Another example is the fluctuation in the ion channel protein in the cell membrane between conformations that are closed to the passage of ions and those that are open to the passage of ions, namely, closed⇌open. Such chemical reactions can be described as two energy levels corresponding to the two states, separated by a distribution of activation energy barriers. Since a kinetic rate can be associated with each energy barrier, this is also equivalent to a distribution of kinetic rate constants. We derive the distribution of the kinetic rates that produces the stretched exponential probability distribution, exp(−at ^b ) where 0<b≤1, which has been observed for such reactions. We also derive the form of the cumulative probability distribution when the pathways connecting the states have minimum or maximum rate constants.     

A photophysical model for diphenylhexatriene fluorescence decay in solvents and in phospholipid vesicles.

The fluorescence decay of 1,6-diphenyl-1,3,5-hexatriene (DPH) in pure solvents and in phospholipid vesicles has been measured using frequency domain fluorometry. Data analysis uses a model with two energetically close excited states. The model explains the high quantum yield and the double exponential decay of DPH observed in some pure solvents and in phospholipid vesicles. This model assumes that after excitation to a first excited state, there is a rapid interconversion to a lower excited state and that most of the emission occurs from this state. The interconversion rates between the two excited states determine the average lifetime. For DPH in solvents, we find that the interconversion rates are solvent and temperature dependent. For DPH in phospholipid vesicles, we find that the back reaction rate from excited state 2 to excited state 1 (R12) is what determines the fluorescence properties. The phospholipid phase transition affects only this back reaction rate. The model was analyzed globally for a range of solvents, temperatures and vesicle composition. Of the six parameters of the model, only two, the interconversion rates between the two excited states, varied in all different samples examined. For DPH in phospholipid vesicles, there is an additional feature of the model, which is related to the apparent distribution of the rate R12. Significantly better fits were obtained using a continuous lorentzian distribution of interconversion rates. The resulting lifetime distribution was asymmetric and showed a definite narrowing above the phase transition.     

A biological interpretation of transient anomalous subdiffusion. II. Reaction kinetics

Reaction kinetics in a cell or cell membrane is modeled in terms of the first passage time for a random walker at a random initial position to reach an immobile target site in the presence of a hierarchy of nonreactive binding sites. Monte Carlo calculations are carried out for the triangular, square, and cubic lattices. The mean capture time is expressed as the product of three factors: the analytical expression of Montroll for the capture time in a system with a single target and no binding sites; an exact expression for the mean escape time from the set of lattice points; and a correction factor for the number of targets present. The correction factor, obtained from Monte Carlo calculations, is between one and two. Trapping may contribute significantly to noise in reaction rates. The statistical distribution of capture times is obtained from Monte Carlo calculations and shows a crossover from power-law to exponential behavior. The distribution is analyzed using probability generating functions; this analysis resolves the contributions of the different sources of randomness to the distribution of capture times. This analysis predicts the distribution function for a lattice with perfect mixing; deviations reflect imperfect mixing in an ordinary random walk.     

Conformational flexibility of four-way junctions in RNA

Helical junctions are common architectural features in RNA. They are particularly important in autonomously folding molecules, as exemplified by the hairpin ribozyme. We have used single-molecule fluorescence spectroscopy to study the dynamic properties of the perfect (4H) four-way helical junction derived from the hairpin ribozyme. In the presence of Mg(2+), the junction samples parallel and antiparallel conformations and both stacking conformers, with a bias towards one antiparallel stacking conformer. There is continual interconversion between the forms, such that there are several transitions per second under physiological conditions. Our data suggest that interconversion proceeds via an open intermediate with reduced cation binding in which coaxial stacking between helices is disrupted. The rate of interconversion becomes slower at higher Mg(2+) concentrations, yet the activation barrier decreases under these conditions, indicating that entropic effects are important. Transitions also occur in the presence of Na(+) only; however, the coaxial stacking appears incomplete under these conditions. The polymorphic and dynamic character of the four-way RNA junction provides a source of structural diversity, from which particular conformations required for biological function might be stabilised by additional RNA interactions or protein binding.     

Parameter estimation for a leaky integrate-and-fire neuronal model from ISI data

The Ornstein-Uhlenbeck process has been proposed as a model for the spontaneous activity of a neuron. In this model, the firing of the neuron corresponds to the first passage of the process to a constant boundary, or threshold. While the Laplace transform of the first-passage time distribution is available, the probability distribution function has not been obtained in any tractable form. We address the problem of estimating the parameters of the process when the only available data from a neuron are the interspike intervals, or the times between firings. In particular, we give an algorithm for computing maximum likelihood estimates and their corresponding confidence regions for the three identifiable (of the five model) parameters by numerically inverting the Laplace transform. A comparison of the two-parameter algorithm (where the time constant tau is known a priori) to the three-parameter algorithm shows that significantly more data is required in the latter case to achieve comparable parameter resolution as measured by 95% confidence intervals widths. The computational methods described here are a efficient alternative to other well known estimation techniques for leaky integrate-and-fire models. Moreover, it could serve as a template for performing parameter inference on more complex integrate-and-fire neuronal models.