Structural models and surface equation of state for pulmonary surfactant monolayers

A simple surface equation of state is proposed to describe pi-A isotherms of pulmonary surfactant monolayers. The monolayer is considered as undergoing three characteristic states during the compression: the disordered liquid-expanded (LE) state, the ordered liquid-condensed (LC) state and the collapse state. Structural models of pure protein (SP-B and SP-C) monolayer are proposed to interpret the behavior characteristics of monolayer in the states. The area, ALC, is defined as an instantaneous LC-state area when the monolayer is under the complete LC state. The area, At, is defined as a transition area from the ordered LC state to the collapse state. And the collapse pressure, pi(max), is defined as the maximum surface pressure that the monolayer can bear before collapse. The ideal equation of state is revised by ALC, At and pi(max), and a new equation of state is obtained, which is applicable for pure components of pulmonary surfactant. The theoretical pi-A isotherms described by the equation of state are compared with the experimental ones for SP-B, SP-C, DPPC and DPPG, and good agreements are obtained. The equation of state is generalized to protein-lipid binary mixtures by introducing mixing rules. The predicted pi-A isotherms agree with the experimental ones for various pulmonary surfactant components and the average deviation is about 9.2%.     

Structural changes in the transition state of protein folding: alternative interpretations of curved chevron plots.

The interpretation of folding rates is often rationalized within the context of transition state theory. This means that the reaction rate is linked to an activation barrier, the height of which is determined by the free energy difference between a ground state (the starting point) and an apparent transition state. Changes in the folding kinetics are thus caused by effects on either the ground state, the transition state, or both. However, structural changes of the transition state are rarely discussed in connection with experimental data, and kinetic anomalies are commonly ascribed to ground state effects alone, e.g., depletion or accumulation of structural intermediates upon addition of denaturant. In this study, we present kinetic data which are best described by transition state changes. We also show that ground state effects and transition state effects are in general difficult to distinguish kinetically. The analysis is based on the structurally homologous proteins U1A and S6. Both proteins display two-state behavior, but there is a marked difference in their kinetics. S6 exhibits a classical V-shaped chevron plot (log observed rate constant vs denaturant concentration), whereas U1A's chevron plot is symmetrically curved, like an inverted bell curve. However, S6 is readily mutated to display U1A-like kinetics. The seemingly drastic effects of these mutations are readily ascribed to transition state movements where large kinetic differences result from relatively small alterations of a common free energy profile and broad activation barriers.     

Contribution of the 6-120 disulfide bond of alpha-lactalbumin to the stabilities of its native and molten globule states.

The unfolding and refolding of a derivative of alpha-lactalbumin, in which the disulfide bond between Cys6 and Cys120 is selectively reduced and S-carboxymethylated, are investigated by equilibrium and kinetic circular dichroism measurements. The native conformation of this derivative is known to be essentially identical to that of intact alpha-lactalbumin. The equilibrium unfolding of the derivative involves a stable intermediate, which is also similar to the molten globule state of the disulfide intact protein. The results of stopped-flow circular dichroism experiments show that the same intermediate is formed rapidly as a transient intermediate in kinetic refolding. The conformational stabilities for the native and intermediate states have been estimated and compared with the stabilities for the corresponding states of intact alpha-lactalbumin. The stabilization of the native state by the disulfide has been interpreted in terms of a decrease in chain entropy in the unfolded state and elimination of the strain imposed on the disulfide bond in the native state. The molten globule state is also stabilized by the disulfide bond, although the degree of stabilization of the molten globule state is smaller than of the native state. The results suggest that, in the molten globule state, some ordered structures are present within the loop moiety formed by the 6-120 disulfide.     

pH-induced denaturation of proteins: a single salt bridge contributes 3-5 kcal/mol to the free energy of folding of T4 lysozyme

The energetics of a salt bridge formed between the side chains of aspartic acid 70 (Asp70) and histidine 31 (His31) of T4 lysozyme have been examined by nuclear magnetic resonance techniques. The pKa values of the residues in the native state are perturbed from their values in the unfolded protein such that His31 has a pKa value of 9.1 in the native state and 6.8 in the unfolded state at 10 degrees C in moderate salt. Similarly, the aspartate pKa is shifted to a value of about 0.5 in the native state from its value of 3.5-4.0 in the unfolded state. These shifts in pKa show that the salt bridge is stabilized 3-5 kcal/mol. This implies that the salt bridge stabilizes the native state by 3-5 kcal/mol as compared to the unfolded state. This is reflected in the thermodynamic stability of mutants of the protein in which Asp70, His31, or both are replaced by asparagine. These observations and consideration of the thermodynamic coupling of protonation state to folding of proteins suggest a mechanism of acid denaturation in which the unfolded state is progressively stabilized by protonation of its acid residues as pH is lowered below pH 4. The unfolded state is stabilized only if acidic groups in the folded state have lower pKa values than in the unfolded state. When the pH is sufficiently low, the acid groups of both the native and unfolded states are fully protonated, and the apparent unfolding equilibrium constant becomes pH independent. Similar arguments apply to base-induced unfolding.(ABSTRACT TRUNCATED AT 250 WORDS)     

Mapping the interactions present in the transition state for unfolding/folding of FKBP12.

The structure of the transition state for folding/unfolding of the immunophilin FKBP12 has been characterised using a combination of protein engineering techniques, unfolding kinetics, and molecular dynamics simulations. A total of 34 mutations were made at sites throughout the protein to probe the extent of secondary and tertiary structure in the transition state. The transition state for folding is compact compared with the unfolded state, with an approximately 30 % increase in the native solvent-accessible surface area. All of the interactions are substantially weaker in the transition state, as probed by both experiment and molecular dynamics simulations. In contrast to some other proteins of this size, no element of structure is fully formed in the transition state; instead, the transition state is similar to that found for smaller, single-domain proteins, such as chymotrypsin inhibitor 2 and the SH3 domain from alpha-spectrin. For FKBP12, the central three strands of the beta-sheet, beta-strand 2, beta-strand 4 and beta-strand 5, comprise the most structured region of the transition state. In particular Val101, which is one of the most highly buried residues and located in the middle of the central beta-strand, makes approximately 60 % of its native interactions. The outer beta-strands and the ends of the central beta-strands are formed to a lesser degree. The short alpha-helix is largely unstructured in the transition state, as are the loops. The data are consistent with a nucleation-condensation model of folding, the nucleus of which is formed by side-chains within beta-strands 2, 4 and 5, and the C terminus of the alpha-helix. The precise residues involved in the nucleus differ in the two simulated transition state ensembles, but the interacting regions of the protein are conserved. These residues are distant in the primary sequence, demonstrating the importance of tertiary interactions in the transition state. The two independently derived transition state ensembles are structurally similar, which is consistent with a Bronsted analysis confirming that the transition state is an ensemble of states close in structure.     

The mechanism of folding of globular proteins. Equilibria and kinetics of conformational transitions of penicillinase from Staphylococcus aureus involving a state of intermediate conformation.

1. The thermodynamically reversible unfolding and refolding of penicillinase between the native and fully unfolded states were followed by using guanidinium chloride as denaturant. 2. The equilibria, studied by optical rotation, u.v. absorption, viscosity and enzyme activity, show the presence of a state of intermediate conformation, termed state H, which is stable at 20 degrees C in 0.8 M-guanidinium chloride. 3. The physical properties of this state show that it is slightly expanded with an intrinsic viscosity of 8 ml-g-1, that the 13 tyrosine residues, which are distributed through the primary sequence, are maximally exposed to the solvent and that the helix content is the same as that of the native state. 4. The kinetics of the transition between the native state, state H and the fully unfolded state were followed by u.v. absorption and by optical rotation. They are interpreted as showing that state H lies on the folding pathway between the native and fully unfolded states. 5. The transition between the native state and state H exhibits monophasic unfolding kinetics and biphasic refolding kinetics. This indicates that there must be at least two intermediate states in this process, at least one of which lies on the folding pathway which may also involve cul-de-sac paths. 6. The results are discussed in terms of a mechanism involving rapid stabilization of nucleation regions in a moderately compact but internally solvated structure, with 'native format' [Anfinsen (1973) Science 181, 233-230] secondary structure stabilized by tertiary interaction. The final and rate-limiting step in refolding involves shuffling of these structural elements into the native state. 7. This model is discussed in relation to folding in vivo.     

Is the molten globule a third thermodynamic state of protein? The example of α-lactalbumin

Thermal and denaturant-induced transitions of the acid molten globule state of bovine α-lactalbumin (acid [A] state) are analyzed by scanning calorimetry, titration calorimetry, viscosimetry, and derivative spectroscopy. A denaturant-induced heat effect of the A state is shown by a calorimetric difference titration of the A-state versus unfolded (reduced) α-lactalbumin. However, changes of viscosity and derivative spectra do not parallel the heat effect. At thermal denaturation monitored by derivative spectroscopy and scanning microcalorimetry the presence of a gradual transition in α-lactalbumin A state is shown. The results are consistent with the existence of tertiary interactions in the A state and the absence of a cooperative unfolding transition of the molten globule. The results do not support the idea that the molten globule is a third thermodynamic state. Proteins 30:43–48, 1998. © 1998 Wiley-Liss, Inc.     

Solution structure of the state 1 conformer of GTP-bound H-Ras protein and distinct dynamic properties between the state 1 and state 2 conformers

Ras small GTPases undergo dynamic equilibrium of two interconverting conformations, state 1 and state 2, in the GTP-bound forms, where state 2 is recognized by effectors, whereas physiological functions of state 1 have been unknown. Limited information, such as static crystal structures and (31)P NMR spectra, was available for the study of the conformational dynamics. Here we determine the solution structure and dynamics of state 1 by multidimensional heteronuclear NMR analysis of an H-RasT35S mutant in complex with guanosine 5'-(β, γ-imido)triphosphate (GppNHp). The state 1 structure shows that the switch I loop fluctuates extensively compared with that in state 2 or H-Ras-GDP. Also, backbone (1)H,(15)N signals for state 2 are identified, and their dynamics are studied by utilizing a complex with c-Raf-1. Furthermore, the signals for almost all the residues of H-Ras·GppNHp are identified by measurement at low temperature, and the signals for multiple residues are found split into two peaks corresponding to the signals for state 1 and state 2. Intriguingly, these residues are located not only in the switch regions and their neighbors but also in the rigidly structured regions, suggesting that global structural rearrangements occur during the state interconversion. The backbone dynamics of each state show that the switch loops in state 1 are dynamically mobile on the picosecond to nanosecond time scale, and these mobilities are significantly reduced in state 2. These results suggest that multiconformations existing in state 1 are mostly deselected upon the transition toward state 2 induced by the effector binding.     

Some perspectives on modeling leukemia

A diffusion model of leukemia is presented. The space-occupying effects of leukemic cells during leukemic expansion is investigated. The analyses and simulations of the model suggest that acute leukemia is a state in which positions inhabited by colonies of normal cells are invaded by emerging colonies of abnormal cells. Normal cells are then driven to a state of extinction as leukemic cells evolve toward high and dominant steady state levels.     

Some properties of pyruvate and 2-oxoglutarate oxidation by blowfly flight-muscle mitochondria

1. High rates of state 3 pyruvate oxidation are dependent on high concentrations of inorganic phosphate and a predominance of ADP in the intramitochondrial pool of adenine nucleotides. The latter requirement is most marked at alkaline pH values, where ATP is profoundly inhibitory. 2. Addition of CaCl(2) during state 4, state 3 (Chance & Williams, 1955) or uncoupled pyruvate oxidation causes a marked inhibition in the rate of oxygen uptake when low concentrations of mitochondria are employed, but may lead to an enhancement of state 4 oxygen uptake when very high concentrations of mitochondria are used. 3. These properties are consistent with the kinetics of the NAD-linked isocitrate dehydrogenase (EC 1.1.1.41) from this tissue, which is activated by isocitrate, citrate, ADP, phosphate and H(+) ions, and inhibited by ATP, NADH and Ca(2+). 4. Studies of the redox state of NAD and cytochrome c show that addition of ADP during pyruvate oxidation causes a slight reduction, whereas addition during glycerol phosphate oxidation causes a ;classical' oxidation. Nevertheless, it is concluded that pyruvate oxidation is probably limited by the respiratory chain in state 4 and by the NAD-linked isocitrate dehydrogenase in state 3. 5. The oxidation of 2-oxoglutarate by swollen mitochondria is also stimulated by high concentrations of ADP and phosphate, and is not uncoupled by arsenate.     

On the reality of transition state dissociation constants

Transition state dissociation constants are currently considered, utilizing stopped flow equipment. The underlying theory is briefly reviewed, relating the ideas to steady state kinetics of enzyme systems. The ideas are further analyzed under the consideration of chemical relaxation. Test conditions are described which would allow an investigation of the concepts of transition state dissociation constants by chemical relaxation techniques. A discussion concerning the way in which the concepts of transition state dissociation constants relate to other theories which assume short-lived, but real, dissociation constants is included. The theory is rigorously analyzed (in a second part), revealing the nature of the assumption of a transition state dissociation constant: While they may be written in a formal manner, they are not based on reality—on kinetic grounds direct interconversions between transition states are practically impossible. This applies also to transition state dissociation constants involving protons.     

Reversal of an epigenetic switch governing cell chaining in Bacillus subtilis by protein instability

Bacillus subtilis forms long chains of cells during growth and biofilm formation. Cell separation is mediated by autolysins, whose genes are under the negative control of a heteromeric complex composed of the proteins SinR and SlrR. Formation of the SinR-SlrR complex is governed by a self-reinforcing, double-negative feedback loop in which SinR represses the gene for SlrR and SlrR, by forming the SinR-SlrR complex, titrates SinR and prevents it from repressing slrR. The loop is a bistable switch and exists in a SlrR(LOW) state in which autolysin genes are on, and a SlrR(HIGH) state in which autolysin genes are repressed by SinR-SlrR. Cells in the SlrR(LOW) state are driven into the SlrR(HIGH) state by SinI, an antirepressor that binds to and inhibits SinR. However, the mechanism by which cells in the SlrR(HIGH) state revert back to the SlrR(LOW) state is unknown. We report that SlrR is proteolytically unstable and present evidence that self-cleavage via a LexA-like autopeptidase and ClpC contribute to its degradation. Cells producing a self-cleavage-resistant mutant of SlrR exhibited more persistent chaining during growth and yielded biofilms with enhanced structural complexity. We propose that degradation of SlrR allows cells to switch from the SlrR(HIGH) to the SlrR(LOW) state.     

Non-equilibrium thermodynamics of temporally oscillating chemical reactions.

Two thermodynamic quantities are introduced: the entropy change due to a variation of chemical affinity from a steady, state. to some other state and the corresponding entropy production. The entropy change is always negative definite except at the steady state and is capable of being a Liapunov function. The phase-plane behaviour of the entropy production along the trajectory generated by kinetic equations is investigated in connection with the stability of steady state. The examples taken on that occasion are the Volterra-Lotka and Prigogine-Lefever models. The non-equilibrium thermodynamic properties common to the oscillating reactions in two-variable system are in general considered with an emphasis on the thermodynamic analysis for the direction of rotation of the trajectory generated by the two-variable kinetic equations.     

A semiparametric transition model with latent traits for longitudinal multistate data

SUMMARY: We propose a general multistate transition model. The model is developed for the analysis of repeated episodes of multiple states representing different health status. Transitions among multiple states are modeled jointly using multivariate latent traits with factor loadings. Different types of state transition are described by flexible transition-specific nonparametric baseline intensities. A state-specific latent trait is used to capture individual tendency of the sojourn in the state that cannot be explained by covariates and to account for correlation among repeated sojourns in the same state within an individual. Correlation among sojourns across different states within an individual is accounted for by the correlation between the different latent traits. The factor loadings for a latent trait accommodate the dependence of the transitions to different competing states from a same state. We obtain the semiparametric maximum likelihood estimates through an expectation-maximization (EM) algorithm. The method is illustrated by studying repeated transitions between independence and disability states of activities of daily living (ADL) with death as an absorbing state in a longitudinal aging study. The performance of the estimation procedure is assessed by simulation studies.     

A State Space Transformation Can Yield Identifiable Models for Tracer Kinetic Studies with Enrichment Data

Tracer studies are analyzed almost universally by multicompartmental models where the state variables are tracer amounts or activities in the different pools. The model parameters are rate constants, defined naturally by expressing fluxes as fractions of the source pools. We consider an alternative state space with tracer enrichments or specific activities as the state variables, with the rate constants redefined by expressing fluxes as fractions of the destination pools. Although the redefinition may seem unphysiological, the commonly computed fractional synthetic rate actually expresses synthetic flux as a fraction of the product mass (destination pool). We show that, for a variety of structures, provided the structure is linear and stationary, the model in the enrichment state space has fewer parameters than that in the activities state space, and is hence better both to study identifiability and to estimate parameters. The superiority of enrichment modeling is shown for structures where activity model unidentifiability is caused by multiple exit pathways; on the other hand, with a single exit pathway but with multiple untraced entry pathways, activity modeling is shown to be superior. With the present-day emphasis on mass isotopes, the tracer in human studies is often of a precursor, labeling most or all entry pathways. It is shown that for these tracer studies, models in the activities state space are always unidentifiable when there are multiple exit pathways, even if the enrichment in every pool is observed; on the other hand, the corresponding models in the enrichment state space have fewer parameters and are more often identifiable. Our results suggest that studies with labeled precursors are modeled best with enrichments.     

Inhibition and relaxation of sea urchin sperm flagella by vanadate

Direct measurements of the stiffness (elastic bending resistance) of demembranated sera urchin sperm flagella were made in the presence of MgATP2- and vanadate. Under these conditions, the flagellum is in a relaxed state, with a stiffness of approximately 0.9 x 10(-21) N m2, which is approximately 5% of the stiffness obtained in the rigor state in the absence of MgATP2-. MgADP- dose not substitute for MgATP2- in producing relaxed state. A progressive inhibition of movement is observed after addition of MgATP2- to flagella preincubated with vanadate, in which new bend generation, propagation, and relaxation by straightening are distinguished, depending on the ratio of MgATP2- and vanadate. At appropriate concentrations of vanadate, increase of the velocity of bend propagation is observed at a very low concentration of MgATP2- that is not enough to induce spontaneous beating. Vanadate enhances competitive inhibition of beat frequency by MgADP- but not by ADP3-, ATP4-, or Pi. These observations, and the uncompetitive inhibition of beat frequency by vanadate, indicate that vanadate can only bind to dynein-nucleotide complexes induced by MgATP2- and MgADP-. The state accessible by MgATP2- binding must be a state in which the cross-bridges are detached and the flagellum is relaxed. The state accessible by MgADP- binding must be a cross-bridged state. Bound vanadate prevents the transition between these two states. Inhibition and relaxation by banadate in the presence of MgATP2- results from the specific affinity of vanadate for a state in which nucleotide is bound, rather than a specific affinity for the deteched state.     

Methionine oxidation of monomeric lambda repressor: the denatured state ensemble under nondenaturing conditions

Although poorly understood, the properties of the denatured state ensemble are critical to the thermodynamics and the kinetics of protein folding. The most relevant conformations to cellular protein folding are the ones populated under physiological conditions. To avoid the problem of low expression that is seen with unstable variants, we used methionine oxidation to destabilize monomeric lambda repressor and predominantly populate the denatured state under nondenaturing buffer conditions. The denatured ensemble populated under these conditions comprises conformations that are compact. Analytical ultracentrifugation sedimentation velocity experiments indicate a small increase in Stokes radius over that of the native state. A significant degree of alpha-helical structure in these conformations is detected by far-UV circular dichroism, and some tertiary interactions are suggested by near-UV circular dichroism. The characteristics of the denatured state populated by methionine oxidation in nondenaturing buffer are very different from those found in chemical denaturant.     

Swelling activation of K-Cl cotransport in LK sheep erythrocytes: a three-state process

K-Cl cotransport in LK sheep erythrocytes is activated by osmotic swelling and inhibited by shrinkage. The mechanism by which changes in cell volume are transduced into changes in transport was investigated by measuring time courses of changes in transport after osmotic challenges in cells with normal and reduced Mg concentrations. When cells of normal volume and normal Mg are swollen, there is a delay of 10 min or more before the final steady-state flux is achieved, as there is for swelling activation of K-Cl cotransport in erythrocytes of other species. The delay was shown to be independent of the extent of swelling. There was also a delay after shrinkage inactivation of cotransport. Reducing cellular Mg concentration activates cotransport. Swelling of low-Mg cells activates cotransport further, but with no measurable delay. In contrast, there is a delay in shrinkage inactivation of cotransport in low-Mg cells. The results are interpreted in terms of a three-state model: [formula see text] in which A state, B state, and C state transporters have relatively slow, intermediate, and fast transport rates, respectively. Most transporters in shrunken cells with normal Mg are in the A state. Swelling converts transporters to the B state in the rate-limiting process, followed by rapid conversion to the C state. Reducing cell Mg also promotes the A-- >B conversion. Swelling of low-Mg cells activates transport rapidly because of the initial predominance of B state transporters. The results support the following conclusions about the rate constants of the three-state model: k21 is the rate constant for a Mg-promoted process that is inhibited by swelling; k12 is not volume sensitive. Both k23 and k32 are increased by swelling and reduced by shrinkage; they are rate constants for a single process, whereas k12 and k21 are rate constants for separate processes. Finally, the A-->B conversion entails an increase in Jmax of the transporters, and the B-->C conversion entails an increase in the affinity of the transporters for K.     

State transitions by molecules

In our previous paper, we described a method by which a state machine is implemented by a single-stranded DNA molecule whose 3'-end sequence encodes the current state of the machine. Successive state transitions are performed in such a way that the current state is annealed onto an appropriate portion of DNA encoding the transition table of the state machine and the next state is copied to the 3'-end by extension with polymerase. In this paper, we first show that combined with parallel overlap assembly, a single series of successive transitions can solve NP-complete problems. This means that the number of necessary laboratory steps is independent from the problem size. We then report the results of two experiments concerning the implementation of our method. One is on isothermal reactions which greatly increase the efficiency of state transitions compared with reactions controlled by thermal cycles. The other is on the use of unnatural bases for avoiding out-of-frame annealing. The latter result can also be applied to many DNA-based computing paradigms.