Mechanism of self-assembly of tobacco mosaic virus protein. I. Nucleation-controlled kinetics of polymerization.

The polymerization of tobacco mosaic virus protein has been found to proceed through metastable states under conditions where initially one of the two polymerization-linked protons is bound. These metastable polymers have been characterized and are found to be helical rods, which resemble the structure of equilibrium helical rods that form when both polymerization-linked protons are bound. At pH 6.5 and 20 °C the true equilibrium distribution of these helical rods has been shown to consist of sedimenting species that are much smaller, 24 to 34 S, than described previously, 100 to 200 S. The larger, non-equilibrium rods are produced by an overshoot in polymerization that results from the slow formation of 20 S nuclei followed by a very rapid elongation reaction. Generally, this sequence of rate processes is sensitive to the rate at which a reaction is initiated. In the present case it is the rate of heating or the rate of change of the pH that determines the reaction path and therefore the rate of attainment of equilibrium. In addition to the formation of metastable helical rods during polymerization overshoot, metastable 20 S aggregates can form when either equilibrium or non-equilibrium helical rods are depolymerized by cooling to 5 to 7 °C at pH 6.5. These 20 S aggregates are presumably two-turn disks or helices and can serve as nuclei for helical rod formation in subsequent polymerization reactions. Both helical rod and 20 S metastability are extremely sensitive to pH but, under carefully controlled conditions, the metastability is quite reproducible and reproducible nucleation-controlled polymerization kinetics can be observed even when polymerization-depolymerization cycling is carried out between branches of a hysteresis loop. Temperature- or pH-induced polymerization of tobacco mosaic virus protein can be made to proceed by the slow formation of 20 S, two-turn helix, nuclei followed by the rapid addition of one or more species comprising the 4 S protein. These results confirm a previously proposed kinetic mechanism for the non-equilibrium polymerization reaction (Scheele &; Schuster, 1974).     

Polymerization of optical isomers of phenylalanine N-carboxyanhydride by various secondary amines

In the polymerization of phenylalanine NCA initiated by some secondary amines, the two enatimorphs of phenylalanine NCA were polymerized with the same rate, which was almost twice as high, as that found for the racemic mixture. This stereoselectivity was observed only when the polymerization was initiated by secondary amines which are sterically crowded and reluctant to undergo a nucleophilic addition to NCA. Poly(DL -phenylalanine) produced in the stereoselective polymerization had a higher molecular weight than that produced in nonstereoselective polymerization. These findings point to the possibility that the stereoselectivity arises only in those polymerizations which are propagated by the activated monomers and not in the propagation involving the terminal amine of the growing polymer. A possible mechanism for the stereoselective polymerization is proposed and examined.     

The effect of overshooting the target strain on estimating viscoelastic properties from stress relaxation experiments

BACKGROUND: Tendon's mechanical behaviors have frequently been quantified using the quasi-linear viscoelastic (QLV) model. The QLV parameters are typically estimated by fitting the model to a single-step stress relaxation experiment. Unfortunately, overshoot of the target strain occurs to some degree in most experiments. This has never been formally investigated even though failing to measure, minimize, or compensate for overshoot may cause large errors in the estimation of parameters. Therefore, the objective of this study was to investigate the effect of overshoot on the estimation of QLV parameters. METHOD OF APPROACH: A simulated experiment was first performed to quantify the effect of different amounts of overshoot on the estimated QLV parameters. Experimental data from tendon was then used to determine if the errors associated with overshoot could be reduced when a direct fit is used (i.e., the actual strain history was used in the curve fit). RESULTS: We found that both the elastic and viscous QLV parameters were incorrectly estimated if overshoot was not properly accounted for in the fit. Furthermore, the errors associated with overshoot were partially reduced when overshoot was accounted for using a direct fit. CONCLUSIONS: A slow ramp rate is recommended to limit the amount of overshoot and a direct fit is recommended to limit the errors associated with overshoot, although other approaches such as adjusting the control system to limit overshoot could also be utilized.     

An asymptotic model of unsteady airway reopening

We consider a simple physical model for the reopening of a collapsed lung airway involving the unsteady propagation of a long bubble of air, driven at a prescribed flow-rate, into a liquid-filled channel formed by two flexible membranes that are held under large longitudinal tension and are confined between two parallel rigid plates. This system is described theoretically using an asymptotic approximation, valid for uniformly small membrane slopes, which reduces to a fourth-order nonlinear evolution equation for the channel width ahead of the bubble tip, from which the time-evolution of the bubble pressure pb* and bubble speed may be determined. The model shows that there can be a substantial delay between the time at which the bubble starts to grow in volume and the time at which its tip starts to move. Under certain conditions, the start of the bubble's motion is accompanied by a transient overshoot in pb*, as seen previously in experiment; the model predicts that the overshoot is greatest in narrow channels when the bubble is driven with a large volume flux. It is also shown how the threshold pressure for steady bubble propagation in wide channels has distinct contributions from the capillary pressure drop across the bubble tip and viscous dissipation in the channel ahead of the bubble.     

Substrate regulation of the sarcoplasmic reticulum ATPase. Transient kinetic studies.

The rate of phosphorylation of the Ca2+-dependent ATPase of sarcoplasmic reticulum vesicles by ITP and ATP was studied using a millisecond mixing and quenching device. The rate of phosphorylation was slower when the vesicles were preincubated in a Ca2+-free medium than when preincubated with Ca2+, regardless of the substrate used and of the pH of the medium. When the vesicles were preincubated with Ca2+ at pH 7.4 an overshoot of phosphorylation was observed in the presence of ITP. The overshoot was abolished when the pH of the medium was decreased to 6.0 or when the vesicles were preincubated in a Ca2+-free medium. Using vesicles preincubated with Ca2+ the apparent Km for ITP found was 2.5 mM at pH 6.0 and 1.0 mM at pH 7.4. The Vmax observed (77 mumol g-1 s-1) did not change with the pH of the medium. Both at pH 6.0 and 7.4 the apparent Km for ATP was 3 microM when preincubated in a Ca2+-free medium. At pH 6.0 the Vmax for ATP varied from 96 to 33 mumol g-1 s-1 depending on whether the vesicles were preincubated in the presence or absence of Ca2+. At pH 7.4 the Vmax for ATP was 90 mumol g-1 s-1 in both conditions. The rate of phosphorylation of the vesicles was dependent on the relative Ca2+ and Mg2+ concentrations of the reaction medium regardless of the substrate used.     

The effect of the propagation coefficient on size distribution in micellar systems

In this study the effect of the propagation coefficient on the molar distribution function in a modified shell model for micellar systems was examined. The sharpness of the micelle size distribution boundary was found to depend less on the degree of polymerization, n, than on the propagation coefficient, P. Although Kegeles (J. Phys. Chem. 83 (1979) 1728) has reported a marked sharpening of the distribution boundary when P = 2.0. we found the boundary to be fairly broad at this point. However, as values of the propagation coefficient were increased from 3 to 10, the micelle distribution boundary became increasingly sharp. The possibility of such a change in the reaction boundary arising from a structural transition, accompanied by a change in the rate of dissociation of monomer from the shell, is also discussed.     

Difference in polymerization and steady-state dynamics of free and gelsolin-capped filaments formed by alpha- and beta-isoactins

The polymerization of scallop β-like actin is significantly slower than that of skeletal muscle α-actin. To reveal which steps of polymerization contribute to this difference, we estimated the efficiency of nucleation of the two actins, the rates of filament elongation at spontaneous and gelsolin-nucleated polymerization and the turnover rates of the filament subunits at steady-state. Scallop actin nucleated nearly twice less efficient than rabbit actin. In actin filaments with free ends, when dynamics at the barbed ends overrides that at the pointed ends, the relative association rate constants of α- and β-actin were similar, whereas the relative dissociation rate constant of β-ATP-actin subunits was 2- to 3-fold higher than that of α-actin. The 2- to 3-fold faster polymerization of skeletal muscle versus scallop Ca-actin was preserved with gelsolin-capped actin filaments when only polymerization at the pointed end is possible. With gelsolin-induced polymerization, the rate constants of dissociation of ATP-actin subunits from the pointed ends were similar, while the association rate constant of β-actin to the pointed filament ends was twice lower than that of α-actin. This difference may be of physiological relevance for functional intracellular sorting of actin isoforms.     

Time-resolved solution X-ray scattering of tobacco mosaic virus coat protein: kinetics and structure of intermediates

The kinetics of assembly and disassembly of tobacco mosaic virus coat protein (TMVP) following temperature jumps have been studied by small-angle X-ray scattering and turbidimetry. The structures of the principal aggregates of TMVP oligomers (A protein), intermediate size (helix I) and large size helical rods (helix II), have been characterized by their average radii of gyration of thickness, cross section, and shape obtained from the corresponding regimes of the small-angle scattering pattern. This structural information was obtained within seconds after the temperature-induced initiation of either polymerization or depolymerization and allowed us to detect transient intermediates. This methodology made it possible to observe and characterize the structure of a principal intermediate. Taken together with other kinetic information, these data suggest that polymerization of TMVP under virus self-assembly conditions may proceed via a single-layered helical nucleus that contains about 20 subunits. Previous studies have shown that overshoot polymerization of TMVP can occur and results in metastable long helical viruslike rods which subsequently depolymerize and then form short helical rods, depending on the conditions of the final equilibrium state. The longer rods (helix II) are overshoot polymers which form within seconds and contain 17 1/3 subunits per turn (helix IIB), in contrast to the subunit packing arrangement of 16 1/3 subunits per turn found in the shorter helical rods (helix IA). The latter packing arrangement is the one found in TMV. An overall polymerization scheme is proposed for the formation of these two helical forms of TMVP.     

Kinetic analysis of chemotactic peptide-induced actin polymerization in neutrophils

Definition of the kinetics of ligand-activated actin polymerization in the neutrophil is important for ultimately understanding the mechanisms utilized for regulation of actin polymerization in this non-muscle cell. To better define the kinetics of formyl peptide (fMLP)-induced actin polymerization in neutrophils we determined F-actin content at 5 second intervals after activation of human neutrophils with a range (10(-11)-10(-9) M) of fMLP concentrations. The state of actin polymerization was monitored by quantifying F-actin content with NBD phallacidin binding in both flow cytometric and extraction assays. Results demonstrate three successive kinetic periods of fMLP-induced actin polymerization in neutrophils, a lag period, a 5 second period when rate of polymerization is maximal, and a period of declining rate of actin polymerization as F-actin content approaches a maximum. The duration of the lag period, the maximum rate of polymerization, and the maximum extent of polymerization all depend upon the fMLP concentration. The lag period varies from 0 to 12 seconds and is followed in 5-10 seconds by a 5 second burst of actin polymerization when the rate is as great as 9% increase in F-actin content per second. After the 5 second burst of polymerization, the rate of polymerization rapidly declines. The study defines three distinct kinetic periods of fMLP-induced actin polymerization during which important rate-limiting biochemical events occur. The mechanistic and motile implications of kinetic periods are discussed.     

Free radical copolymerization kinetics of γ-methyl-α-methylene-γ-butyrolactone (MeMBL)

The propagation kinetics and copolymerization behavior of the biorenewable monomer γ-methyl-α-methylene-γ-butyrolactone (MeMBL) are studied using the pulsed laser polymerization (PLP)/size exclusion chromatography (SEC) technique. The propagation rate coefficient for MeMBL is 15% higher than that of its structural analogue, methyl methacrylate (MMA), with a similar activation energy of 21.8 kJ·mol(-1). When compared to MMA, MeMBL is preferentially incorporated into copolymers when reacted with styrene (ST), MMA, and n-butyl acrylate (BA); the monomer reactivity ratios fit from bulk MeMBL/ST, MeMBL/MMA, and MeMBL/BA copolymerizations are r(MeMBL) = 0.80 ± 0.04 and r(ST) = 0.34 ± 0.04, r(MeMBL) = 3.0 ± 0.3 and r(MMA) = 0.33 ± 0.01, and r(MeMBL) = 7.0 ± 2.0 and r(BA) = 0.16 ± 0.03, respectively. In all cases, no significant variation with temperature was found between 50 and 90 °C. The implicit penultimate unit effect (IPUE) model was found to adequately fit the composition-averaged copolymerization propagation rate coefficient, k(p,cop), for the three systems.     

Tobacco mosaic virus protein: kinetic and equilibrium studies on the pH-dependent transition. A-protein yields double disc.

Concentration dependent and temperature dependent stopped-flow experiments on the transition A-protein→double disc show a triphasic reaction consisting of a nucleation phase, a propagation phase and a slow redistribution of polymer size which involves the dissociation of “overshoot” aggregates into double discs and smaller aggregates. No first order rate process is observed under the present experimental conditions. Equilibrium circular dichroism data and preliminary kinetic data at various temperatures indicate a change at about 21°C which might be correlated to a partial transition double disc→helix parallelled by a further shift in the equilibrium of double disc formation; from both data the thermodynamic and activation parameters for the A-protein→double disc transition are estimated.     

Actin polymerization. The mechanism of action of cytochalasin D

Fluorescence changes using actin covalently labeled with N-(1-pyrenyl)iodoacetamide have been used to determine the effect of cytochalasin D on actin polymerization. A mechanism for the effect of cytochalasin D on actin polymerization is presented, which explains the experimental observation of a cytochalasin D-induced increase in the initial rate of polymerization and a decrease in the final extent of the reaction. Central to this mechanism is the Mg2+-dependent formation of cytochalasin D-induced dimers. The dimers serve as nuclei to enhance the polymerization rate. Binding of Mg2+ to a low affinity site on the dimer induces a conformational change which can be observed as a rapid fluorescence increase. A subsequent time-dependent fluorescence decrease observed prior to polymerization appears to represent ATP hydrolysis resulting in dissociation of the dimer and release of actin monomers containing ADP. We postulate that a slow rate of exchange of ATP for bound ADP relative to hydrolysis results in the accumulation of monomers containing ADP. As these monomers have a high critical concentration, the final extent of polymerization is reduced dramatically. The Mg2+ dependence of the final extent of polymerization in the presence of cytochalasin D is also explained in the context of this mechanism.     

The overshoot phenomenon in cotransport

Based on simplified equations, the overshoot curve experimentally observed with Na⁺-linked cotransport of neutral substrate (sugars or amino acids) has been simulated by computer. The approach is in principle similar to that of previous approaches (Weiss, S.D., McNamara, P.D. and Segal, S. (1981) J. Theor. Biol. 91, 597–608), but more general; in particular, it includes the effect of electrical membrane potential difference, and the quantitative relationship between height of peak and certain transport parameters, such as maximum rate, dissociation constant of ternary complex, electric charge of translocator, respectively. In addition, it tests two alternative models with respect to the rate-determining step: the translocation, on the one hand, and the association/dissociation of the ligands at the translocator site, on the other. The major findings are the following: (1) An overshoot can be obtained similar to that usually found experimentally, provided that maximum rate and affinity between translocator and transport of solute exceed certain minimum values. (2) The overshoot effect with Na-linked cotransport is enhanced by a negative membrane potential (inside relative to outside) and decreased by a positive potential. In the first case, the peak is higher and occurs faster. In the latter case, the peak is lower and delayed. (3) The effect of an electric potential difference on the overshoot curve does not depend appreciably on the charge of the empty translocator, except if the translocation of the latter is strongly rate-limiting. (4) To obtain an overshoot curve, it is not necessary that the translocation step be rate-limiting, contrary to what has been postulated previously (Läuger, P. (1980) J. Membrane Biol. 57, 163–178).     

Pseudo-Inductive Behaviour of the Membrane Potential of Chara corallina under Galvanostatic Conditions: A TIME-VARIANT CONDUCTANCE PROPERTY OF POTASSIUM CHANNELS

The membrane potential of Chara corallina Klein ex Willd, emR.D.W. displays an oscillatory behaviour in response to an appliedcurrent step. The relative amplitude and the frequency of oscillationof the overshoot increase with the strength of the current. Increasing temperature from 10 °C to 30 °C decreasesboth the relative overshoot amplitude and the static membraneresistance. The activation energy calculated from the Arrheniusplot of the frequency of the overshoot has a value of 36.1±2.3kJ mol_–1. Raising the external pH from 5.0 to 6.0 decreases the relativeamplitude of the overshoot and increases the steady state membraneresistance. Treating the cells for 30 s with 0.1 mol m_–3 N-ethylmaleimideinduces a rapid fall in both static membrane resistance andovershoot. These results are interpreted in terms of changes in potassiumchannels conductance. Key words: Chara corallina, Membrane potential, Potassium channels conductance     

Plasmid repopulation kinetics in Staphylococcus aureus

We have analyzed the kinetic route by which the indirectly controlled Staphylococcus aureus plasmid, pT181, responds to and corrects fluctuations in copy number. The kinetics of copy number correction from low to steady-state levels (termed repopulation) were determined using two different methods of copy number reduction. Thermosensitive replication (Tsr) mutants of pT181 were grown at nonpermissive temperatures to lower copy number and then shifted to a permissive temperature to allow repopulation. After the downshift, both wild-type and copy mutant plasmids, with active inhibitors, exhibited a burst of exponential replication that resulted in a two- to threefold overshoot of normal steady-state copy numbers. This was followed by inhibition of replication and eventual reestablishment of the steady-state replication rate. Similar replication kinetics were observed when these plasmids were introduced into naive cells by high-frequency transduction. By contrast, a pT181 copy mutant with a nonfunctional inhibitor-target regulation did not overshoot its steady-state copy number, but instead repopulated asymptotically. These results suggest that at low copy numbers, pT181 and its derivatives replicate at near-maximal rates and overshoot prior to the establishment of an inhibitory concentration of repressor. The maximal replication rate is independent of the plasmid's cop genotype. As the copy number increases, inhibitor accumulates and eventually reduces the replication rate. In the absence of an active inhibitor, the steady-state copy number is established at a level that must be limited by some other invariant factor.     

Kinetics of the cooperative association of T4 tail sheath protein P18 to polysheaths

The polymerization of the monomeric sheath protein P18 to polysheath was followed by light scattering in 1 mM sodium phosphate buffer, pH 7 at a MgCl2 concentration of 5 mM. Sigmoidal kinetics were observed in the case of spontaneous nucleation. These were well fitted by a mechanism involving a slow nucleation step (rate constant kN = 10(-2) M-1 S-1) followed by propagation steps (k = 10(5) M-1 S-1) in which P18 protomers are added to the ends of the polysheath particles. When sonicated polysheaths or contracted sheaths were added as seeds exponential time courses were observed. From the pseudo first order rate constant and the concentration of seeds the above value for the rate constant of propagation was confirmed. The ability of contracted sheaths to nucleate polysheath formation lends support to the conclusion that polysheaths and contracted sheaths have identical structures and differ in their length distributions only. These were measured from electromicrographs and from the distribution of sedimentation coefficients. Poisson type, kinetically controlled size distributions were found after polymerization of polysheath. An extremely slow redistribution towards an exponential distribution was detected. The spontaneous slow formation of polysheaths is much slower than the formation of extended sheath are core baseplates. Extended sheath is a metastable assembly produce of P18 which either dissociates of contracts to form contracted sheath. Polysheaths and contracted sheaths are extremely stable products but their immediate formation is hindered by high nucleation difficulties.     

Initiation of the microgene polymerization reaction with non-repetitive homo-duplexes

Microgene Polymerization Reaction (MPR) is used as an experimental system to artificially simulate evolution of short, non-repetitive homo-duplex DNA into multiply-repetitive products that can code for functional proteins. Blunt-end ligation by DNA polymerase is crucial in expansion of homo-duplexes (HDs) into head-to-tail multiple repeats in MPR. The propagation mechanism is known, but formation of the initial doublet (ID) by juxtaposing two HDs and polymerization through the gap has been ambiguous. Initiation events with pairs of HDs using Real-Time PCR were more frequent at higher HD concentrations and slightly below the melting temperature. A process molecularity of about 3.1, calculated from the amplification efficiency and the difference in PCR cycles at which propagation was detected at varying HD concentrations, led to a simple mechanism for ID formation: the gap between two HDs is bridged by a third. Considering thermodynamic aspects of the presumed intermediate “nucleation complex” can predict relative propensity for the process with other HDs.     

Reactions of nitroimidazoles with free radicals--enhancement of reaction by u.v. irradiation

The free-radical reactivity of the nitroimidazole derivatives metronidazole, misonidazole, benznidazole and ornidazole was investigated by observing their effect on the polymerization of acrylamide in aqueous solution. Free-radical polymerization was initiated by the thermal decomposition of potassium peroxydisulphate at 50 degrees C. Measurement of the polymerization rate showed an inhibitory effect of the nitroimidazoles which was greatly enhanced when the system was irradiated with u.v. light near their absorption maximum of 320-325 nm. Analysis of the competitive kinetics of the system enabled calculation of the rate constant for reaction of the ground state and photoexcited nitroimidazole with the polyacrylamide free radicals. No significant difference between the various nitroimidazoles could be found in the dark reaction, but in the u.v.-irradiated system the order of reactivity (misonidazole greater than benznidazole greater than metronidazole approximately equal to ornidazole) was the same as the reported relative mutagenic, cytotoxic and radiosensitizing potency of the compounds. These results imply that the excited states of the nitroimidazoles are important to their activity in radical-radical reactions.     

Kinetics of Repeat Propagation in the Microgene Polymerization Reaction

Repetitive DNA is a periodic copolymer with the intrinsic property of exponential propagation to longer repeats. Microgene polymerization reaction (MPR) is a model system in which a short nonrepetitive homo-duplex DNA evolves to multiple repetitive products during heat-cool cycles. The mechanism underlying this process involves staggered annealing of complementary DNA strands of variable lengths and polymerase-mediated filling-in of the generated overhangs. MPR is considered here as a process sharing common features with two polymerization types, chain-growth and step-growth, and significant distinctions from both types were highlighted. The involved reaction stages were formulated and a kinetic model was derived and tested experimentally. The model can quantitatively explain MPR propagation and be used as a good approximation for this phenomenon.