A new computational growth model for sea urchin skeletons

A new computational model has been developed to simulate growth of regular sea urchin skeletons. The model incorporates the processes of plate addition and individual plate growth into a composite model of whole-body (somatic) growth. A simple developmental model based on hypothetical morphogens underlies the assumptions used to define the simulated growth processes. The data model is based on a Delaunay triangulation of plate growth center points, using the dual Voronoi polygons to define plate topologies. A spherical frame of reference is used for growth calculations, with affine deformation of the sphere (based on a Young-Laplace membrane model) to result in an urchin-like three-dimensional form. The model verifies that the patterns of coronal plates in general meet the criteria of Voronoi polygonalization, that a morphogen/threshold inhibition model for plate addition results in the alternating plate addition pattern characteristic of sea urchins, and that application of the Bertalanffy growth model to individual plates results in simulated somatic growth that approximates that seen in living urchins. The model suggests avenues of research that could explain some of the distinctions between modern sea urchins and the much more disparate groups of forms that characterized the Paleozoic Era.     

On the lag phase and initial decline of microbial growth curves

The lag phase is generally thought to be a period during which the cells adjust to a new environment before the onset of exponential growth. Characterizing the lag phase in microbial growth curves has importance in food sciences, environmental sciences, bioremediation and in understanding basic cellular processes. The goal of this work is to extend the analysis of cell growth curves and to better estimate the duration of the lag phase. A non-autonomous model is presented that includes actively duplicating cells and two subclasses of non-duplicating cells. The growth curves depend on the growth and death rate of these three subpopulations and on the initial proportion of each. A deterministic and a stochastic model are both developed and give the same results. A notable feature of the model is the decline of cells during the early stage of the growth curve, and the range of parameters when this decline occurs is identified. A limited growth model is also presented that accounts for the lag, exponential growth and stationary phase of microbial growth curves.     

Predicting Plant Height of Greenhouse Grown Crops with a Polynomial Growth Rate Model

A prediction model for the growth of plant height is developed, using polynomials in time to describe the growth rate. The growth rate is affected by forcing factors through the polynomial coefficients. A random slope model is used to describe the difference in growth rate for plants grown under similar conditions. Maximum likelihood estimates of model parameters are obtained and a selection procedure is employed to estimate the model complexity using Schwarz' bayesian criterion as a measure of predictive power. The procedure is applied to data sets for greenhouse grown poinsettias. The use of polynomials to describe the time effects on the growth rate makes the strategy versatile, and it can be used to predict the growth of many different crops. Many forcing factors of different types can be incorporated simultaneously in the model. Confidence of predictions are also quantifies, which is important when the results are applied in a practical situation, e.g. in climate control of commercial greenhouses.     

Kinetic study of hybridoma cell growth in continuous culture: II. Behavior of producers and comparison to nonproducers

A hybridoma cell line, AFP-27-P, was cultivated in continuous culture under glucose-limited conditions. The viable cell concentration, dead-cell concentration, and cell volume all varied with the dilution rate. A model previously developed for a nonproducing clone of the same cell line, AFP-27-NP, was extended to describe the behavior of the cells. The relationship between the specific growth rate and glucose concentration is described by a function similar to the Monod model. A threshold glucose concentration and a minimum specific growth rate are incorporated; the model is meaningful only at glucose concentration and a minimum specific growth rate are incorporated; the model is meaningful only at glucose concentrations and specific growth rates above these levels. The relationship between the death rate and the glucose concentration is described by an inverted Monod-type function. Furthermore, the yield coefficient based on glucose is constant in the lower range of specific growth rates and changes to a new constant value in the upper range of specific growth rates. No maintenance term for glucose consumption is used; in the plot of specific glucose consumption rate vs. specific growth rate, the line intercepts the specific growth rate at a value close to the minimum growth rate. The productivity of antibody as a function of the specific growth rate is described by a mixed type model with a noon-growth-associated term and a negative-growth-associated term. The values for the model parameters were determined from regression analysis of the steady state data.     

Growth models (including terminal and segmental branching) for topological binary trees

A growth model for topological trees is formulated as a generalization of the terminal and segmental growth model. For this parameterized growth model, expressions are derived for the partition probabilities (probabilities of subtree pairs of certain degrees). The probabilities of complete trees are easily derived from these partition probabilities.     

Experimental evaluation of a model for cometabolism: Prediction of simultaneous degradation of trichloroethylene and methane by a methanotrophic mixed culture

A model for cometabolism is verified experimentally for a defined methanotrophic mixed culture. The model includes the effects of cell growth, endogenous cell decay, product toxicity, and competitive inhibition with the assumption that cometabolic transformation rates are enhanced by reducing power obtained from oxidation of growth substrates. A theoretical transformation yield is used to quantify the enhancement resulting from growth substrate oxidation. A systematic method for evaluating model parameters independently is described. The applicability of the model is evaluated by comparing experimental data for methanotrophic cometabolism of TCE with model predictions from independently measured model parameters. Propagation of errors is used to quantify errors in parameter estimates and in the final prediction. The model successfully predicts TCE transformation and methane utilization for a wide range of concentrations of TCE (0.5 to 9 mg/L) and methane (0.05 to 6 mg/L). (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 56: 492-501, 1997.     

A model for growth of Saccharomyces cerevisiae containing a recombinant plasmid in selective media

A major problem in the use of plasmids as recombinant vectors is the problem of plasmid-free cell generation from plasmid shedding and subsequent growth. A common technique for controlling the population of plasmidfree cells is the use of selective media against these cells using an auxotrophic host and a plasmid that has the ability to produced the essential metabolite. A distributed model describing the growth of Saccharomyces cerevisiae containing a recombinant plasmid in selective media was developed. The model allows for growth and production of a metabolite by the plasmid-carrying strain and growth of the plasmid-free cells on resulting metabolite concentrations. Through a determination of system constants and numerical solution to the equations, experimental batch and continuous culture results for cell concentration transients could be simulated by the model. The results indicated that despite selective pressure, plasmid-free cell growth was significant.     

A general model for detecting genetic determinants underlying longitudinal traits with unequally spaced measurements and nonstationary covariance structure

A mixture model for determining quantitative trait loci (QTL) affecting growth trajectories has been proposed in the literature. In this article, we extend this model to a more general situation in which longitudinal traits for each subject are measured at unequally spaced time intervals, different subjects have different measurement patterns, and the residual correlation within subjects is nonstationary. We derive an EM-simplex hybrid algorithm to estimate the allele frequencies, Hardy-Weinberg disequilibrium, and linkage disequilibrium between QTL in the original population and parameters contained in the growth equation and in the covariance structure. A worked example of head circumference growth in 145 children is used to validate our extended model. A simulation study is performed to examine the statistical properties of the parameter estimation obtained from this example. Finally, we discuss the implications and extensions of our model for detecting QTL that affect growth trajectories.     

Kinetic study of hybridoma cell growth in continuous culture. I. A model for non-producing cells

The kinetic behavior of a nonproducing hybridoma clone AFP-27-NP was investigated in continuous culture under glucose-limited conditions. A total of more than 21, 000 h of cultures were operated at dilution rates ranging from 0.01 to 0.06 h(-1). The viable cell concentrations, dead cell concentrations, and cell volumes all varied with the dilution rate. A steady-state model was developed based on the biomass concentration and the glucose concentration. The specific growth rate as a function of glucose concentration is described by a model similar to the Monod model with a threshold glucose concentration and a minimum specific growth rate incorporated; the model is meaningful only at glucose concentrations and specific growth rates above these levels. A death rate is included in the model which is described by an inverted Monod-type function of glucose concentration. The yield coefficient based on glucose is constant in the lower range of specific growth rates and changes to a new constant value in the upper region of specific growth rates. No maintenance term for glucose consumption was needed; in the plot of specific glucose consumption rate vs. specific growth rate, the line intercepted the specific growth rate axis at a value close to the minimum growth rate. The values for the model parameters were determined from regression analysis of the steady-state data. The model predictions and experimental results fit very well.     

A model for noninhibitory microbial growth

A model for noninhibitory microbial growth has been developed which is superior to the Monod model in that it can predict the decline in steady-state growth yields at both the slow and the fast specific growth rates. The model parameters are evaluated from data obtained for steady-state, phenol-limited Pseudomonas putida growth using a conventional 1-dm(3) cheniostat. The model also has been successfully applied to Mor and Fiechter's data for cheniostat yeast cultures.     

A population balance model for fish population dynamics

A population balance model of fish population dynamics for batch systems was developed. A growth rate expression was introduced and coupled with the population balance. Solutions of the model provide predictions of such fish size distribution characteristics as average size, standard deviation and coefficient of variation. A growth diffusivity mechanism was found to be inapplicable to systems where a terminal size is reached. A study of the two parameter growth rate expression was conducted, illustrating that conditions conducive to high growth rates also resulted in broadening of size distributions. The model was compared to data found in the literature to demonstrate its predictive capabilities.     

A mathematical model of in vitro cancer cell growth and treatment with the antimitotic agent curacin A

A mathematical model of cancer cell growth and response to treatment with the experimental antimitotic agent curacin A is presented. Rate parameters for the untreated growth of MCF-7/LY2 breast cancer and A2780 ovarian cell lines are determined from in vitro growth studies. Subsequent growth studies following treatments with 2.5, 25 and 50 nanomolar (nM), concentrations of curacin A are used to determine effects on the cell cycle and cell viability. The model's system of ordinary differential equations yields an approximate analytical solution which predicts the minimum concentration necessary to prevent growth. The model shows that cell growth is arrested when the apoptotic rate is greater than the mitotic rate and that the S-phase transition rate acts to amplify this effect. Analysis of the data suggests that curacin A is rapidly absorbed into both cell lines causing an increase in the S-phase transition and a decrease in the M-phase transition. The model also indicates that the rate of apoptosis remains virtually constant for MCF-7/LY2 while that of A2780 increases 38% at 2.5 nM and 59% at 50 nM as compared to the untreated apoptotic rate.     

Prediction of Growth: A Hierarchical Bayesian Approach

A nonparametric hierarchical growth curve model is proposed. Different levels in the model hierarchy are intended to correspond to different sources of variation in an individual's growth. The nonparametric character of the model offers considerable flexibility in fitting the growth curves to empirical data. Here the emphasis is on prediction, and for this purpose the adopted Bayesian inferential approach seems particularly natural and efficient. A Markov chain Carlo method is used to perform the numerical computations. As an illustration of the techniques, we consider the growth of children, during their first two years.     

A kinetic model for microbial growth on liquid hydrocarbons

A kinetic model is presented to explain microbial growth using liquid n-alkanes as substrate. The model is based on the assumption that growth occurs on the soluble alkane and that the metabolite produced by the growing cells helps the dissolution of liquid alkanes in the aqueous medium. Growth curves based on that model fit well with growth data for batch and continuous culture reported by various authors. The model also explains the differences between the relative length of exponential and linear phases of growth reported earlier.     

A mathematical model for examining growth and sporulation processes of Bacillus subtilis

A mathematical model for the growth process of the bacterium Bacillus subtilis is described. The model is a highly structured one. The driving motivation for development of the model and explicit accounting of major interactions of metabolic networks in the model is related to our eventual goal that the model will be used in the analysis of complex biological patterns. Bacillus subtilis was chosen in our study due to the interesting sporulation process that these cells undergo in response to adverse environmental conditions including nutrient limitation. Sporulation process in B. subtilis represents a primordial prototype of cellular differentiation in higher cellular systems. Thus a model for the B. subtilis growth process should prove extremely useful for understanding questions of developmental biology. The model is capable of simulating the transition between the exponential and stationary phase of growth in a batch culture. Since during the transition period the growth process and the metabolism become decoupled and many transient processes are taking place, such predictions are a severe test for the validity of any model. A strategy to examine the leading hypothesis on B. subtills sporulation implementing GTP as a component which signals sporulation initiation is described.     

A new model for periphyton growth in running waters

A new model for biofilm growth is based on a logistic approach but accounts for detachment of the biofilm by the running water and the existence of a threshold point for growth. Above a critical current velocity, development of periphyton is not stable. A stability analysis shows the existence of a fold catastrophe in the model and the amplification of water velocity fluctuations by the algal biomass.     

A mechanistic model of the aerobic growth of Saccharomyces cerevisiae.

A two-stage deterministic model of the growth of Saccharomyces cerevisiae is presented. The cell cycle of this organism was used to suggest the basic model structure. The model represents the preparatory processes of substrate uptake and conversion separately from replication and division. The regulation of the fraction of the culture devoted to each of these broad areas of metabolism, and the overall growth rate, is related to the nature and availability of the energy substrate. The simulation of respiration and glycolysis is achieved by including two alternative energy producing pathways. The regulation of these pathways is described in terms of the postulated primary regulation of the proportion of the culture required for substrate uptake and conversion, and the overall kinetic constants for each pathway. This regulation is dictated primarily by the growth rate rather than the nature or concentration of the energy substrate. The model successfully describes both batch and continuous growth of S. cerevisiae under conditons of glucose limitation and oxygen excess. A preliminary assessment indicates that adjustment of the relevant parameters will allow the model to describe the growth of S. cerevisiae on other sugars and under oxygen limitation. Similarly the model could be expected to describe the growth characteristics of other yeast species.     

Hydrocarbon fermentations using Candida lipolytica. II. A model for cell growth kinetics

A mechanistic model is presented for the growth kinetics of a yeast grown by submerged aerobic fermentation using a liquid hydrocarbon as sole carbon source. The model is based on the assumption that cell growth is governed by the extent of probable cell attachment at the hydrocarbon oil-droplet surfaces in a four-phase dispersion. An analytical expression has been developed for the model. It is shown that for the case of relatively small oil droplets, the model predicts the present and previous experimental data for growth of yeasts (Candida species) in n-alkane systems. The model is further examined for maximal growth in terms of substrate dilution rate and agitation power consumption for a continuous fermentation process.     

Identification of quantitative trait nucleotides that regulate cancer growth: a simulation approach

A general growth model derived from basic cellular properties can be used to describe the dynamic process of cancer growth with mathematical equations. It has been recognized that cancer growth is under genetic control, with a multitude of interacting genes each segregating in a Mendelian fashion and displaying environmental sensitivity. In this article, we integrate the mathematical aspects of the pervasive growth model into a statistical framework for the identification of quantitative trait nucleotides that underlie cancer growth. This integrative framework is constructed with a single nucleotide polymorphism-based haplotype blocking analysis. Simulation studies have been performed to demonstrate the usefulness of the model. The proposed model provides a generic platform model for testing and detecting specific DNA sequence variants that regulates the timing of cancer emergence, growth and differentiation.