Instability and oscillatory behavior of membrane-chemical reaction systems

The stability problem of a chemical system consisting of reversible reactions is analyzed with the aid of computer calculations. The system is based on the model proposed by Edelstein and exhibits oscillations of chemical species. The analysis shows that the oscillatory character is of limit cycle type. The results are applied to the construction of a membrane-chemical reaction system, which shows characteristic instability behavior. This is useful as a model of cell division.     

Actin concentration and monomer-polymer ratio in developing chicken skeletal muscle

The actin concentration and monomer-polymer ratio in developing chicken skeletal muscle were determined by means of a DNase I inhibition assay. The concentration of G-actin in embryonic muscle was much higher than the critical concentration for polymerization of purified actin. As muscle development progressed, the amount of total actin remarkably increased, whereas the concentration of G-actin markedly decreased, and finally in adults reached the critical concentration for polymerization of purified actin. When the monomeric actin in the soluble fraction of embryonic muscle was purified, the critical concentration for polymerization of the embryonic actin decreased to the same value as that of adult skeletal muscle actin. On the other hand, there was no difference between the crude and purified actin in the type of actin. They consisted of alpha-, beta-, and gamma-actins; their amounts were in the order, beta greater than gamma greater than alpha. Furthermore, polymerization of the monomeric actin in the soluble fraction of embryonic muscle was induced by the addition of myosin or HMM. The large amount of monomeric actin in the embryonic skeletal muscle may be due to the presence of some factor(s) which inhibits actin polymerization and also to an insufficiency of myosin.     

On the mechanism of actin monomer-polymer subunit exchange at steady state

The rate of exchange of G-actin with subunits of F-actin and the rate of hydrolysis of ATP in solutions of F-actin at steady state have been measured simultaneously. Subunit exchange kinetics were analyzed by both a treadmill model and an exchange-diffusion model. The best fit to a treadmill model of the data obtained in 0.5 mM MgCl2 and 0.2 mM ATP at 30 degrees C gave a treadmill efficiency (net monomers incorporated per ATP hydrolyzed) of 0.26, in good agreement with the previously reported s-value of 0.25 (Wegner, A. (1976) J. Mol. Biol. 108, 139-150) for similar ionic conditions. However, in this and other conditions with excess free divalent cations (Ca2+ or Mg2+), the observed exchange kinetics were in better agreement with an exchange-diffusion model than with a treadmilling model over the entire time course of the experiment. In the absence of excess divalent cations (50 mM KCl), exchange was too slow to be analyzed adequately by either model. Using the measured filament length distribution and the observed fit of the exchange-diffusion model to the data in 0.5 mM MgCl2, an on-rate constant of 2.8 x 10(6) M-1 S-1 and an off-rate constant of 5.8 s-1 were calculated. These values, while in good agreement with previously measured pre-steady state polymerization rate constants under different ionic conditions (Pollard, T. D., and Mooseker, M. S. (1981) J. Cell Biol. 88, 654-659), are about 30-fold higher than the rate constants predicted from the rate of ATP hydrolysis at steady state. To rationalize these discrepancies, a model is proposed in which a segment of F-actin subunits at one or both ends of the filament contains bound ATP at steady state.     

Concentration dependence in three-component systems in sedimentation equilibrium in buoyant density gradients

The data on the band widths and band shapes of several DNA's at various concentrations in sedimentation equilibrium in a CsCl density gradient have recently become available. In the present report, these literature data are treated in the following manner: (1) based on a theory of isotope-substitution, calculations are made of the molecular weights at infinite dilution, and (2) to explain the concentration dependence of band widths and band shapes, a theory of charge and hydration is put forth, and it is shown that by retaining the terms involving the charge of the macromolecules, it is possible to account for most of the concentration dependence.     

Evidence that F-actin can hydrolyze ATP independent of monomer-polymer end interactions

The rate of ATP hydrolysis in solutions of F-actin at steady state in 50 mM KC1, 0.1 mM CaC12 was inhibited by AMP and ADP. The inhibition was competitive with ATP (Km of about 600 microM) with Ki values of 9 microM for AMP and 44 microM for ADP. ATP hydrolysis was inhibited greater than 95% by 1 mM AMP. AMP had no effect on the time course of actin polymerization, ATP hydrolysis during polymerization, or the critical actin concentration. Simultaneous measurements of G-actin/F-actin subunit exchange and nucleotide exchange showed that nucleotide exchange occurred much more rapidly than subunit exchange; during the experiment over 50% of the F-actin-bound nucleotide was replaced when less than 1% of the F-actin subunits had exchanged. When AMP was present it was incorporated into the polymer, preventing incorporation of ADP from ATP in solution. F-actin with bound Mg2+ was much less sensitive to AMP than F-actin with bound Ca2+. These data provide evidence for an ATP hydrolysis cycle associated with direct exchange of F-actin-bound ADP for ATP free in solution independent of monomer-polymer end interactions. This exchange and hydrolysis of nucleotide may be enhanced when Ca2+ is bound to the F-actin protomers.     

Statistical evaluation of ways to analyze nonideal systems by sedimentation equilibrim

Three equations describing sedimentation equilibrium are examined and tested for their ability to analyze data. The testing procedure using simulated data is similar to that described previously (Holladay, L. A., and Sophianopoulos, A. J. (1972) J. Biol. Chem.247, 427–439) and used with another equation. The equations examined here are found to be of much less statistical reliability and of a more restricted range of application than the previously examined equation. The equation described previously, (Holladay, L. A., and Sophianopoulos, A. J. (1972) J. Biol. Chem.247, 427–439) is also used here to examine the conditions necessary to detect isodesmic systems of more than four components. The self-association of lysozyme reported previously (Sophianopoulos, A. J., and Van Holde, K. E. (1964) J. Biol. Chem.239, 2516–2524) is reexamined at pH 8.2, 0.15 ionic strength, and 13°C. The tentative conclusion is that the system is mainly a monomer-dimer, with a small, uncertain amount of tetramer possibly present. Under the above conditions the second virial coefficient, B, is estimated to lie in the range 0–4.4 × 10^?6 mole·dl·g^?2, the dimerization constant. K₂₁, lies in the range 2.3–2.7 × 10^?3m, and the tetramerdimer constant, K₄₂, is in the range 1.5–15 × 10^?3m.     

A diffusion driven instability in systems that separate particles by velocity sedimentation.

Velocity sedimentation has been used extensively to separate particles according to the magnitude of their sedimentation velocity in suitable media. This technique has been used over a wide range of particle size from protein molecules, viruses, subcellular particles to whole cells. Successful separation demands that collective particle motion should not occur. In practice it is observed that such systems may, under certain circumstances, suffer from a particular type of instability which destroys the normal dependence of sedimentation velocity on particle size and density. The aim of this paper is to identify the critical parameters that determine the development of this instability. Stability criteria are deduced and predictions of the theory compared with published observations. Satisfactory agreement between theory and observation is obtained. It is concluded that the simple stability criterion, namely that stable sedimentation will occur if the total density gradient is in the direction of the sedimenting force, grossly overestimates the particle load that can be separated in practice. Some specific recommendations for optimum particle loading are included. Earlier theoretical and experimental works are briefly reviewed.     

Perfusion systems for hybridoma cells based on sedimentation in chambers and erlenmeyer flasks

Abstract: An inclined sedimentation chamber and a modified 250-ml Erlenmeyer flask have been used as separation devices for perfusion fermentations with hybridoma cells. The maximum cell density is increased 2–16-fold compared to batch fermentations when the separation units are used. When the sedimentation chamber is used, IgG is continuously produced and the daily production is increased by a factor 3.7 compared to batch fermentation.     

The direct analysis of sedimentation equilibrium results obtained with polymerizing systems.

Theory is presented in relation to sedimentation equilibrium results obtained with polymerizing systems, which permits evaluation of the activity of the monomer as a function of total weight concentration. In contrast to established methods, the suggested procedure does not involve the solution of simultaneous equations which are sums of exponentials or the determination of weight-average molecular weights. A major advantage of the method is that it avoids errors inherent in differentiation and integration steps. An extrapolation to infinite filution is involved, but this is to a defined limit and is uncomplicated by the existence of critical points in the relevant plot. The method is capable of detecting possible volume changes inherent on polymer formation, of treating systems where activity coefficients of solute species are functions of total concentration and of describing the system in terms of relevant equilibrium constants. These points and comparisons with existing methods of analysis are illustrated with numerical examples and with results obtained with lysozyme at pH 6.7. The lysozyme results are interpretable in terms of either a non-ideal monomer-dimer system or a monomer-dimer-trimer system.     

A quantitative treatment of reversible monomer-polymer exchange reactions with microtubules and other biopolymers

We present a quantitative solution to the problem of equilibrium exchange of radioactive monomers into biological polymers. This solution avoids approximations used in earlier attempts to handle the problem. The analysis therefore provides a better theoretical basis for evaluating data for head-to-tail polymerization in biopolymers such as F-actin and microtubules. A discussion of the model's implications concerning head-to-tail polymerization and an extension of the analysis to drug action on biopolymer assembly is included.     

Analysis of heterologous interacting systems by sedimentation velocity: curve fitting algorithms for estimation of sedimentation coefficients, equilibrium and kinetic constants

Analytical ultracentrifugation (AUC) has played and will continue to play an important role in the investigation of protein-protein, protein-DNA and protein-ligand interactions. A major advantage of AUC over other methods is that it allows the analysis of systems free in solution in nearly any buffer without worry about spurious interactions with a supporting matrix. Large amounts of high-quality data can be acquired in relatively short times. Advances in software for the treatment of AUC data over the last decade have eliminated many of the tedious aspects of AUC data analysis, allowing relatively rapid analysis of complicated systems that were previously unapproachable. A software package called sedanal is described that can perform global fits to AUC sedimentation velocity data obtained for both interacting and non-interacting, macromolecular multi-species, multi-component systems, by combining data from multiple runs over a range of sample concentrations and component ratios. Interaction parameters include both forward and reverse rate constants, or equilibrium constants, for each reaction, as well as concentration dependence of both sedimentation and diffusion coefficients. sedanal fits to time-difference data to eliminate time-independent systematic errors inherent in AUC data. The sedanal software package is based on the use of finite-element numerical solutions of the Lamm equation.     

Modulation of monomer-polymer equilibrium of phosphorylated smooth muscle myosin: effects on actin activation

Actin activation of the adenosinetriphosphatase (ATPase) of phosphorylated gizzard myosin at low (2 mM) free Mg2+ concentration and 50 mM total ionic strength continues to increase on raising the free Ca2+ concentration near pCa 3. Similar levels of activity can be obtained by increasing the free Mg2+ concentration to a higher (in excess of 4 mM free) concentration. In the presence of micromolar concentrations of free Ca2+ and low free Mg2+ concentration, the actin-activated adenosine 5'-triphosphate (ATP) hydrolysis exhibits an initial rapid rate which progressively slows to a final, lower but more linear rate. In the presence of high divalent cation concentrations, the fast rate of ATP hydrolysis is maintained during the entire ATPase assay. The ionic conditions which favor the slow rate of ATP hydrolysis are correlated with increased proportions of folded myosin monomers while higher rates of ATP hydrolysis are correlated with increased levels of aggregated myosin. Elevating the thin filament proteins to saturating concentrations does not abolish the change in ATPase rate or the final distribution of myosin aggregates and monomers; however, the stability of the myosin aggregates is enhanced by the presence of thin filament proteins in low divalent cation conditions. The nonlinear profile of the actin-activated ATP hydrolysis in low divalent cation concentrations is eliminated by utilizing nonfilamentous, phosphorylated heavy meromyosin. The data presented indicate that Ca2+ and Mg2+ alter monomer-polymer equilibrium of stably phosphorylated myosin. The alteration of monomer-polymer equilibrium by Ca2+ at low Mg2+ concentration modulates ATPase rates.