Biomedical subjects
Publications and source records attributed to K A Dill.
We attempt to give an alternate point of view of the analysis by Roterman et al. (J. Biolmol. Struct. Dyn. 7,415 (1989]. In particular, we argue for the use of flexible geometry and explicit inclusion of solvent effects in analyzing phi, psi maps of peptides.
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The denatured "state" of a protein is a distribution of many different molecular conformations, the averages of which are measured by experiments. The properties of this ensemble depend sensitively on the solution conditions. There is now considerable evidence that even in strong denaturants such as 6M GuHC1 and 9M urea, some structure may remain in protein chains. Under milder or physiological conditions, the denatured states of most proteins appear to be highly compact with extensive secondary structure. Both theoretical and experimental studies suggest that hydrophobic interactions, chain conformational entropies, and electrostatic forces are dominant in determining this structure. The denaturation reaction of many proteins in GuHC1 or urea can be most simply modelled as a two-state transition between the native structure and a relatively compact denatured state, which then undergoes a gradual increase in radius on further addition of denaturant. However, when a protein acquires a large net charge in acids or bases, it can have two stable denatured populations, one compact and the other more highly unfolded. The prediction and elucidation of the structural details of the non-native states of proteins may ultimately prove to be as difficult as predicting the native structures, particularly for D0, the denatured state under physiological conditions. Just as with the native state, the structure of this biologically important denatured state appears to depend on the amino acid sequence. The development of synthetic, peptide and protein fragment models of the denatured state and the recent progress in NMR spectroscopy provide bases for optimism that new insights will be gained into this poorly understood realm of protein biochemistry.
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We develop a theory for the effects of charge on the stabilization of globular proteins. The folding process is modeled as occurring through a fictitious intermediate state along a two-part thermodynamic pathway in which the molecule (i) increases its density and then (ii) rearranges its ionic groups to the protein surface. The equilibrium for the binding of protons in salt solutions is assumed to be driven by the electrical potential due to the charge distribution, in addition to the intrinsic binding affinity and bulk proton concentration. The potential is calculated for inside and outside a porous sphere model of the protein using the Poisson-Boltzmann relation, wherein the interior dielectric constant is taken to be a linear function of the chain density. The model predicts the slope of the titration curves for native myoglobin in agreement with experiments by Breslow and Gurd (1962). From the similar experiments on the unfolded state, and from the experiments of Privalov et al. (1986) on the intrinsic viscosity of the unfolded molecules, the theory shows that the unfolded state has a much higher density than a chain in a theta solvent and that the density increases with ionic strength. In addition, from the free energy of proton binding to the protein, we also calculate the electrostatic contributions to protein stability, a major contribution deriving from changes in ionization. We consider the example of the stability of myoglobin as a function of pH, ionic strength, and ionic groups buried in the native protein structure. We show that although maximum stability of most proteins should occur at their isoelectric point, the burial of nontitratable groups should lead to maximum stabilities at pH values other than the isoelectric point.
The principal forces of protein folding--hydrophobicity and conformational entropy--are nonspecific. A long-standing puzzle has, therefore, been: What forces drive the formation of the specific internal architectures in globular proteins? We find that any self-avoiding flexible polymer molecule will develop large amounts of secondary structure, helices and parallel and antiparallel sheets, as it is driven to increasing compactness by any force of attraction among the chain monomers. Thus structure formation arises from the severity of steric constraints in compact polymers. This steric principle of organization can account for why short helices are stable in globular proteins, why there are parallel and anti-parallel sheets in proteins, and why weakly unfolded proteins have some secondary structure. On this basis, it should be possible to construct copolymers, not necessarily using amino acids, that can collapse to maximum compactness in incompatible solvents and that should then have structural organization resembling that of proteins.
Using an elementary physical model for protein folding, of self-avoiding short copolymer chains on two-dimensional square lattices, we address two questions regarding the evolution and origins of globular proteins. (i) How will protein native structures and stabilities be affected by single-and double-site mutations? (ii) What is the probability that a randomly chosen sequence of amino acids will be compact and globular under folding conditions? For a large number of different sequences, we search the conformational space exhaustively to find unequivocally the "native" conformation(s), of global minimum free energy, for each sequence. We find that replacing nonpolar residues in the core by polar residues is generally destabilizing, that surface sites are less sensitive than core sites, that some mutations increase the degeneracy of native states, and that overall it is most probable that a mutation will be neutral, having no effect on the native structure. These results support a "Continuity Principle," that small changes in sequence seldom have large effects on structure or stability of the native state. The simulations also show that (i) the number of "convergent" sequences (different sequences coding for the same native structure) is extremely large and (ii) most sequences become quite dense under folding conditions. This implies that the probability of formation of a globular protein from a random sequence of amino acids by prebiotic or mutational methods is significantly greater than zero.
Mean-field statistical thermodynamics theory has recently been developed to account for the partitioning of solutes from aqueous mobile phases into reversed-phase liquid chromatography stationary phases. Several predictions are tested here against an extensive data base of nearly 350 sets of experiments. In agreement with theory, we find that (i) the dependence of retention on mobile phase composition can often be suitably linearized through use of a type of composition plot recently suggested by Dill, (ii) retention measurements can be used to determine the binary interaction constants of solutes with solvents, and (iii) ET-30 solvent probe experiments appear to provide a direct measure of the binary interaction constants. This work suggests that the simple random-mixing approximation for solutes with solvents is often useful even for complex chromatographic solutions.
Statistical thermodynamic theory has recently been developed to account for the stabilities of globular proteins. Here we extend that work to predict the dependence on temperature. Folding is assumed to be driven by solvophobic interactions and opposed by the conformational entropy. The temperature dependence of the solvophobic interaction is taken from the transfer experiments on amino acids by Tanford and Nozaki and on model solutes by Gill and Wadsö. One long-standing puzzle has been why proteins denature upon heating, since the solvophobic force to fold strengthens with increasing temperature. This is resolved by the theory, which predicts two first-order phase transitions. "Cold denaturation" is driven principally by the weakening of the solvophobic interaction, but normal denaturation is driven principally by the gain of conformational entropy of the chain. Predictions of the thermodynamic state functions are in reasonable agreement with the calorimetric experiments of Privalov and Khechinashvili. Comparison of the theory with experiments suggests that there may be an additional enthalpic driving force toward folding which is not due to the solvophobic interactions.
We have measured the membrane/water partition coefficients of benzene into lipid bilayers as a function of the surface density of the phospholipid chains. A simple 2H NMR method was used for the measurement of surface densities; it is shown to give results similar to those obtained from more demanding X-ray diffraction measurements. We observe that benzene partitioning into the bilayer is dependent not only on the partitioning chemistry, characterized by the oil/water partition coefficient, but also on the surface density of the bilayer chains. Increasing surface density leads to solute exclusion: benzene partitioning decreases by an order of magnitude as the surface density increases from 50% to 90% of its maximum value, a range readily accessible in bilayers and biomembranes under physiological conditions. This effect is independent of the nature of the agent used to alter surface density: temperature, cholesterol, and phospholipid chain length were tested here. These observations support the recent statistical thermodynamic theory of solute partitioning into chain molecule interphases, which predicts that the expulsion of solute is due to entropic effects of the orientational ordering among the phospholipid chains. We conclude that the partitioning of solutes into bilayer membranes, which are interfacial phases, is of a fundamentally different nature than partitioning into bulk oil and octanol phases.
We develop theory for the lateral interactions among the zwitterionic head groups of phospholipids in monolayers and bilayers, particularly phosphatidylcholine (PC) and phosphatidylethanolamine (PE). With the P- end of the head group anchored at the water/hydrocarbon interface, a balance of two effects dictates the angle that the P--N+ dipole makes with respect to the plane of the bilayer: N+ is driven toward water due to the (Born) electrostatic free energy, but the hydrophobic effect drives the methyl and methylene groups around the N+ charge toward the hydrocarbon. The only adjustable parameter of the model is the average fluctuation of the oil/water interface or, alternatively, the dielectric constant of the hydrocarbon phase. The model predicts that at 5 degrees C the head group dipole should lie largely in the bilayer plane, in accord with X-ray, neutron diffraction, and NMR studies. The theory makes the novel prediction that the N+ end of the dipole becomes increasingly submerged in hydrocarbon with increasing temperature, leading to strongly enhanced lateral repulsion between PC head groups. This prediction is in good agreement with second and third viral coefficients of monolayer lateral pressures, and with the temperature dependence of the former. The theoretical model is consistent with head group fluctuations measured by neutron diffraction of PC and PE bilayers. Because PE has a smaller hydrophobic cluster near N+, its lateral repulsion should be much smaller and less temperature dependent than for PC, also in agreement with equation-of-state measurements. This suggests why at high density PE monolayers have higher melting temperatures than PC monolayers and more propensity for reversed curvature.
We have reviewed the general principles of interfacial constraint on highly concentrated polymers near sharp interfaces. First, chains are constrained by their inability to penetrate the boundary. Second, at high concentration, polymers are also constrained by interactions with neighboring chains. Third, one additional constraint depends on the chain length: (a) for long chains, a symmetry condition arises from the indistinguishability of segments k and k + 1, whereas (b) for shorter molecules, wherein the segments are distinguishable, the length of the chains is fixed. Subject to these restraints, chains at equilibrium will be configured to maximize their entropy, and hence their configurational disorder. The physical properties of chains at interfaces are often quite different from those of bulk polymers. In most such systems, the conformational ordering is dissipated within only 5-10 A from the interface, but some physical properties depend on effects that are propagated over much longer distances. The currently available theory is found to be in quite good general agreement with a large number of conformational and mixing properties of polymers at interfaces, in semicrystalline polymers, in alkane crystals, in stationary phases used in reversed-phase liquid chromatography, and in amphiphilic aggregates including bilayer membranes and micelles.
Theory and experiment have recently converged to permit a coherent description of the molecular organization of the hydrocarbon tails within surfactant micelles, monolayers, bilayers and other amphiphilic aggregates. The theory is reviewed here, presented in simple form, and is compared to experiments. It is concluded that molecular organization arises from the interfacial localization of amphiphilic chain molecules whose equilibrium conformations are as random as permitted by packing and intramolecular constraints.
Using lattice statistical mechanics, we develop theory to account for the folding of a heteropolymer molecule such as a protein to the globular and soluble state. Folding is assumed to be driven by the association of solvophobic monomers to avoid solvent and opposed by the chain configurational entropy. Theory predicts a phase transition as a function of temperature or solvent character. Molecules that are too short or too long or that have too few solvophobic residues are predicted not to fold. Globular molecules should have a largely solvophobic core, but there is an entropic tendency for some residues to be "out of place", particularly in small molecules. For long chains, molecules comprised of globular domains are predicted to be thermodynamically more stable than spherical molecules. The number of accessible conformations in the globular state is calculated to be an exceedingly small fraction of the number available to the random coil. Previous estimates of this number, which have motivated kinetic theories of folding, err by many tens of orders of magnitude.
DNase a has a broad, asymmetric fluorescence emission peak centered at 341 nm. Binding of Ca2+ of Mg2+ to DNase shifted the peak to 342 nm and caused a 10% fluorescence enhancement. Half of the maximum change occurred at 6 x 10(-5) M Ca2+ or at 6 x 10(-4) M Mg2+. The change in fluorescence is most likely due to a conformational change in DNase which occurs when Ca2+ or Mg2+ is bound to the nonspecific tight Ca2+ binding site on DNase. The kinetics of the fluorescence change, followed by stopped flow techniques, show a fast phase (65%) and a slow phase (35%). At 1 mM Ca2+, the half-time for the fast phase is 17 ms, and for the slow phase, 3.5 min. Both phases of the reaction are first order in DNase and independent of Ca2+ at concentrations above 1 mM. DNase incubated with Ca2+ undergoes a slow (t 1/2 approximately equal to 6 min) 1.5-fold increase in activity. This activation follows pseudo-first order kinetics and is not due to the presence of additional Ca2+ in the substrate. The simplest hypothesis which accounts for these data, and previously reported studies on the effect of Ca2+ on DNase, is that DNase exists in 3 conformational states at 25 degrees C and pH 7.5. The kinetics are consistent with a mechanism which can be diagrammed as: (formula: see text) where A, A, and B represent three conformational states of DNase.
The configurations of the hydrocarbon chains in micelles are severely constrained by the space-filling requirements of the chain segments, by the continuity of the chains, and by the micellar geometry. A statistical theory that takes full account of these constraints is developed by using a lattice model. The chain ends are deduced to be nonuniformly distributed, with maximal incidence approximately midway between the center of the micelle and the outer surface. Whereas the chain disorder near the outside of the hydrophobic core may approach that of a liquid, crowding of the chains near the core center imposes a degree of order approaching that in a crystal. These results are at variance with the prevailing view that the micellar interior resembles a "liquid hydrocarbon droplet." Also discussed are the effects of curvature on the chain configurations in monolayers and bilayers. It is found, for example, that the "disorder gradients" in inner and outer half-bilayers of small vesicles should be substantially different. Implications of these results are discussed.
Using the lattice model for a liquid, we treat the packing of short-chain molecules in interphases such as bilayer membranes. The constant density in the interphase imposes intermolecular constraints on the configurations of the flexible chains. The statistical theory here presented predicts a diffuse distribution of chain ends near the bilayer midplane; no adjustable parameters are required. Inasmuch as some of the chains terminate relatively near the polar interface, the number of chains reaching deeper planar layers is diminished. Consequently, configurational freedom increases with depth. This is the source of the well-known disorder gradient.