Autocatalytic Growth Research Articles

Growth and metabolism of cells and tissue of jack pine (Pinus banksiana). 4. Changes in amino acids in callus and in seedlings of similar genetic origin

Growth rates of callus from hypocotyls and radicles of jack pine (Pinus banksiana Lamb.) seedlings were associated with the differential release and adherence of daughter cells. From 18 to 40% of the N in the medium was assimilated through the increasing surface area of callus and contributed nearly 6% of the total gain in dry weight. Sequential changes in free amino acid N leading to final size were similar for callus from both plant parts. Changes in N correlated significantly with growth rates and callus density (dry weight per cubic centimetre). When free amino acid N was expressed as a percentage of the total soluble N, correlations signified the relative proportions of the amino acid pool that gave different growth-rate forms. The balance of N metabolism during the autocatalytic growth of hypocotyl callus was under the influence of free glutamine, whereas the exponential growth of radicle callus was dominated by the synthesis of asparagine N. In callus from both plant parts 80 to 87% of the net gain in N was recovered in the bound (protein and nucleic acid) fraction. Percentage of free glutamine N decreased with the increase in bound N.Ways in which free amino acid N interacted with growth rates indicated that final size may be usefully defined not merely as an extreme of a growth function but in more sequential kinetic terms supported by a series of correlation coefficients. Correlations revealed the specific points at which free amino acids interacted strongly with rates.When amino acid N in callus was compared with N in seedlings from which callus was derived, the trends were strikingly similar. In seedlings the succession of amino acids was linked more to the uptake of N from the gametophyte by cotyledons and daughter cells in growing tissues rather than to their morphogenesis. Differences related mainly to the greater ability of the seedling to synthesize protein and to maintain higher levels of total soluble N than in callus.

A solvable model in population dynamics

Two specific rate transforms for an autocatalytic growth process G(x)=−tan(αlogx) and G(x)=−tanh(αlogx) have been proposed. Both deterministic and stochastic solutions are given. The characteristic behavior of the growth, which periodically increases and declines, has been described by considering only one half period. Exact analytic solution of the equivalent Schrödinger equation for the Fokker-Planck equation of the problem has been obtained and expression for the probability distribution function is deduced. Finally, a possible biological application of the model has been given.

Mechanism of chemical instability for periodic precipitation phenomena

A mechanism of chemical instability of autocatalytic reactions coupled with diffusion is proposed for spatially periodic precipitation phenomena (such as Liesegang rings or bands). We postulate that precipitation is preceded by colloid formation; electric double layers surround the colloid particles, and at sufficient concentration of colloid, autocatalytic growth of particles and formation of new particles occur owing to an increased product of ion concentrations within the double layer with an increased colloid concentration. A linear stability analysis of the reaction-diffusion equations for this mechanism predicts (1) formation of macroscopic inhomogeneities (spatial structures) due to the onset of instability in the absence of imposed external gradients and prior to the appearance of any visible bands; (2) ranges of the characteristic length scales and time scales of the initial structure pattern; (3) phase relations of concentrations of ionic species and colloid; (4) variation of characteristic length scales with initial concentrations, and rate and diffusion coefficients of ions and colloid; (5) a mechanism for secondary structure of precipitation bands; (6) the possibility of revert structure (decreasing distance between bands away from the origin of an imposed gradient); and (7) the suggestion that the imposition of a concentration gradient, as in a Liesegang experiment, polarizes and may alter the shape of the periodic precipitation structure but is not the basic cause of that structure. The quantitative nature of the structure requires solution of the nonlinear reaction-diffusion equations which is not attempted. The predictions of the proposed mechanism are in substantial agreement with experiments. We report on some experiments which provide evidence for items (1), (6), and (7); for the remaining items we refer to experiments reported in the literature. We conclude with a critique of the Ostwald theory of Liesegang rings, which does not predict revert spacing nor secondary structure. We provide additional experimental evidence against the requirements of this theory of an imposed concentration gradient that in time brings about supersaturation followed by precipitation.

Nitrification Rate in Biological Processes

At least four reaction rate equations have been proposed to describe the process of nitrification. A more precise understanding of this reaction rate is needed to optimize the design of the process. The proposed equations which include the Monod, zero-order, first-order, and autocatalytic growth are reviewed. An experimental study is described which was designed to better understand the process reaction rate. The study involved a thin film biological reactor fed with a synthetic medium developed for the study of nitrification. This simple model was used to provide flexibility and control over such parameters as hydraulics, slime layer thickness, contact time, and wall growth problems. The rate determination was developed by varying both initial concentration and contact time. Results indicate that the reaction rate is zero-order between an initial ammonia nitrogen concentration of 2.5 mg/l - 673 mg/l.

Precipitation behavior of α-solid solutions of the Fe-Sn system

The solubility limit for tin in a-iron was established from lattice parameters determined by X-ray measurements. The precipitation processes in α-Fe-Sn solid solutions are of both continuous and discontinuous types. The discontinuous precipitation cells form at grain boundaries, subgrain boundaries, and in the matrix. They contain no lamellae, but rather either crystallographically oriented, ordered, needle-shaped particles or a mass of irregular precipitated particles. The linear growth law and the results of X-ray diffraction studies confirm the discontinuous character. The activation energy of the process lies in the range of that for volume diffusion of substitutional elements in a-iron. The application of the Zener equation yields effective diffusion coefficients which lie in the range of the bulk diffusion coefficients. A dislocation mechanism is evidently responsible for the autocatalytic growth of the discontinuous precipitation in α-Fe-Sn alloys. At high annealing temperatures a continuous precipitation process sets in at grain and subgrain boundaries and in the grains themselves.

The autocatalytic growth model. I. Critical analysis of the conceptual framework.

Because of the important role which the ‘autocatalytic’ or ‘logistic’ equation has played in determining the direction of a good deal of research both in demography and in the study of individual growth phenomena, a critical and comparative evaluation of those leading ideas inRobertson's (1923) book which pertain to this equation and of some of the criticisms levelled against it seemed to be of interest. The present paper shows that, contrary to common belief,Robertson did not really assume that the autocatalytic reactions to which he compared growth processes, took place in closed systems (viz., cells). On the other hand, he does not seem to have found a satisfactory representation of how the growth phenomena of the individual cells in an organism might interact to yield the overall growth of the organism as a whole. Nor is the manner in which he made his equation account for the openness of the individual cells free from possible criticism. An alternative equation is here proposed, which will be discussed in another paper. The properties of the solutions of this equation are such that the autocatalytic theory might never have gained a foothold if this, more realistic, equation would have been the object of the initial studies.

Autocatalytic growth of a mutant due to accumulation of unstable phenylalanine precursor.

Autocatalytic growth of a mutant due to accumulation of unstable phenylalanine precursor.

The Autocatalytic Growth-Curve

The "curve of autocatalytic growth" (and also the generalized logistic) is essentially the hyperbolic tangent. Use of this fact simplifies the theoretical and practical handling of the equation. Demonstration of a good fit of the autocatalytic curve to a given growth-curve is no proof that the growth is autocatalytic, since the autocatalytic curve can be made to fit curves of similar appearance but very different nature. The variety of forms which the autocatalytic curve can assume is evidence of the futility of such an attempted proof.

An Application of the Autocatalytic Growth Curve to Microbial Metabolism

An Application of the Autocatalytic Growth Curve to Microbial Metabolism