Denaturation: An example of a catastrophe III. Phase diagrams for multistate transformations

A catastrophe-theoretic approach for modelling two-state transconformation reactions, developed previously by the authors, is generalized here to treat multistate transitions. The manner in which phase-type diagrams arise is shown. An application is made to the denaturation of lysozyme and the problem of viral assembly is discussed.     

State transitions: an example of acclimation to low-light stress

State 1-State 2 transitions ('state transitions') are a rapid physiological adaptation mechanism that adjusts the way absorbed light energy is distributed between photosystem I and photosystem II. They occur in both green plants and cyanobacteria, although the light-harvesting complexes involved are very different. Which aspects of the mechanism are conserved in green plants and cyanobacteria and which may be different, are discussed. It is shown that phycobilisome mobility is necessary for state transitions in cyanobacteria. A conserved cyanobacterial gene (rpaC) that plays a very specific role in state transitions has been identified. There is still debate about the physiological role of state transitions. Comparison of the growth properties of the rpaC deletion mutant with the wild-type gives us a way of directly addressing the question. It was found that state transitions are physiologically important only at very low light intensities: they play no role in protection from photoinhibition. Thus state transitions are a way to maximize the efficiency of light-harvesting at low light intensities.     

Cooperative response of chemically excitable membrane. II. Two-state models and their limitations

Various types of two-state models, classified by the type of direct receptorionophore coupling, were formulated based on the previously presented generalized two-state model of cooperativity (Kijima &; Kijima, 1978) and their dose-response relationships were examined. Hill coefficient at the mid-point of dose-response curve n_H^o the measure of the cooperativity of curves, is restricted for partial agonists in any two-state models because n_H^o is expressed by the product of two terms, one of which decreases when the other increases. In the independent gating unit model in which the channel opens only when the independent gating units are all in the activated state, the restriction of n_H^o is the most stringent: it never exceeds 2. In 2 ÷ 1·39 even for full agonist. It appears to be incompatible with most of the cooperative responses observed on chemically excitable membrane. In the basic model or one protomer-one channel model, n_H^o never exceeds 2·0 when 〈p〉_∞, the maximum fraction of open-channel, is less than $\text{2}\text{3}$. In the cooperative gating unit model, n_H^o is the least restricted, which is less than 2·8 when 〈p〉_∞ ≤ 0·5, but if the number of gating units, N in a receptor is practically reasonably small (N ≤ 12), n_H^o ≤ 2·0 when 〈p〉_∞ ≤ 0·58. It is discussed whether or not several representative drug-receptive membranes can be accounted for by two-state models. Response of the insect sugar receptor is out of the above limitations of two-state models and can be accounted for by three-state model. The origin of cooperative interaction can be inferred by the shapes of dose-response curves. Cooperative dose-response curves of two dimensional lattices or oligomerc systems with large number of protomers weakly interacting by long range forces bend upward more markedly at lower region than the curves of strongly interacting oligomers, when curves with the same n_H^o are compared.     

Steady-state head-to-tail polymerization of actin or microtubules. II. Two-state and three-state kinetic cycles

In a previous paper, bioenergetic aspects of head-to-tail polymerization for a two-state actin ATPase cycle were discussed. In section 2, here, the steady-state polymer length distribution for this case is derived. The distribution has the same mathematical form as at equilibrium, but the parameters are different. In section 3, both bioenergetic topics and the polymer length distribution are considered for the more general and realistic case of a three-state actin ATPase cycle. Again, the mathematical form of the steady-state distribution is the same as at equilibrium, but the parameters are more complicated. In section 4, the question is examined of how much the mean and variance of a polymer length distribution, obtained from a finite experimental sample of polymer (aggregate) molecules, would be expected to deviate from the true mean and variance (from an infinite sample). Also considered briefly in section 4 is the effect of hard polymer-polymer interactions on the equilibrium polymer length distribution, at finite polymer concentrations.     

Sodium in gramicidin: an example of a permion.

The reaction path and free energy profile of Na+ were computed in the interior of the channel protein gramicidin, with the program MOIL. Gramicidin was represented in atomic detail, but surrounding water and lipid molecules were not included. Thus, only short range interactions were investigated. The permeation path of the ion was an irregular spiral, far from a straight line. Permeation cannot be described by motions of a single Na+ ion. The minimal energy path includes significant motion of water and channel atoms as well as motion of the permeating ion. We think of permeation as motion of a permion, a quasi-particle that includes the many body character of the permeation process, comparable with quasi-particles like holes, phonons, and electrons of solid-state physics. Na+ is accompanied by a plug of water molecules, and motions of water, Na+, and the atoms of gramicidin are highly correlated. The permion moves like a linear polymer made of waters and ion linked and moving coherently along a zigzag line, following the reptation mechanism of polymer transport. The effective mass, free energy, and memory kernel (of the integral describing time-dependent friction) of short range interactions were calculated. The effective mass of the permion (properly normalized) is much less than Na+. Friction varies substantially along the path. The free energy profile has two deep minima and several maxima. In certain regions, the dominant motions along the reaction path are those of the channel protein, not the permeating ion: there, ion waits while the other atoms move. At these waiting sites, the permion's motion along the reaction path is a displacement of the atoms of gramicidin that prepare the way for the Na+ ion.     

Two-state expansion and collapse of a polypeptide

The initial phase of folding for many proteins is presumed to be the collapse of the polypeptide chain from expanded to compact, but still denatured, conformations. Theory and simulations suggest that this collapse may be a two-state transition, characterized by barrier-crossing kinetics, while the collapse of homopolymers and random heteropolymers is continuous and multi-phasic. A new rapid-mixing flow technique has been used to resolve the late stages of polypeptide collapse, at time scales >/=45 microseconds. We have used a laser temperature-jump with fluorescence spectroscopy to resolve the complete time-course of the collapse of denatured cytochrome c with nanosecond time resolution. We find the process to be exponential in time and thermally activated, with an apparent activation energy approximately 9 k(B)T (after correction for solvent viscosity). These results indicate that polypeptide collapse is kinetically a two-state transition. Because of the observed free energy barrier, the time scale of polypeptide collapse is dramatically slower than is predicted by Langevin models for homopolymer collapse.     

Two-state expansion and collapse of a polypeptide

The initial phase of folding for many proteins is presumed to be the collapse of the polypeptide chain from expanded to compact, but still denatured, conformations. Theory and simulations suggest that this collapse may be a two-state transition, characterized by barrier-crossing kinetics, while the collapse of homopolymers is continuous and multi-phasic. We have used a laser temperature-jump with fluorescence spectroscopy to measure the complete time-course of the collapse of denatured cytochrome c with nanosecond time resolution. We find the process to be exponential in time and thermally activated, with an apparent activation energy approximately 9 k(B)T (after correction for solvent viscosity). These results indicate that polypeptide collapse is kinetically a two-state transition. Because of the observed free energy barrier, the time scale of polypeptide collapse is dramatically slower than is predicted by Langevin models for homopolymer collapse.     

Volume changes accompanying thermal denaturation of deoxyribonucleic acid. II. Denaturation at alkaline pH

The change in apparent molal volume ? of DNA on thermal denaturation in carbonate buffer at pH 11.0 has been determined by the dilatometric method. It was found that ? increases sigmoidally during the helix–coil transition. Several methods, including a colorimetric technique that closely simulates the conditions used in the dilatometric experiments, were employed to estimate the protons lost by the DNA during the transition. These measurements indicated that the extent of the proton loss depends on the counterion present, increasing in the order Li⁺ < Na⁺ < K⁺ < Cs⁺. The major part of the volume changes observed during the denaturation is due to the volume changes expected to accompany the transfer of protons from the bases guanine and thym ne to carbonate ions. As has been previously reported for the denaturation of DNA at neutral pH, the volume change directly due to the change in shape of the polymer molecules is so small as to be experimentally undetectable.     

Genetic loci ordering instability: an example.

In attempting to establish the order of genetic loci by constructing a map from pairwise linkage data, one assumes that the loci satisfy a linear-order relation. If the data utilized in the construction are not consistent with the linear-order assumption, then a very small change in the data may lead to a large qualitative change in the map. An example of such an instability is presented in this paper.     

Cytofluorometric studies on conformation of nucleic acids in situ. II. Denaturation of deoxyribonucleic acid.

Thermal denaturation of deoxyribonucleic acid (DNA) in situ in individual unbroken cells is studied by a cytofluorometric method. This method allows us to investigate DNA denaturation in the presence of divalent cations at concentrations reported to be necessary to maintain native structure of nuclear chromatin. Under these conditions the pattern of DNA denaturation is very different than when studied in the presence of ethylenediaminetetraacetate or citrate. The results suggest that with divalent cations present, the histone basic charges are more uniformly distributed along whole nuclear DNA. Various cell types exhibit great differences in sensitivity to DNA denaturation when assayed in the presence of 1 mM MgCl2. Human lymphocytes, monocytes and certain kinds of human leukemic cells show differences large enough to be used as a parameter for their recognition in mixed samples. Possible applications of the method in basic research on chromatin conformation and as a tool for cell recognition in diagnostic cytology or in the classification of human leukemia are proposed.