On the botanic model of plant growth with intermediate vegetative-reproductive stage

The application of dynamic optimization to mathematical models of ontogenic biological growth has been the subject of much research [see e.g. . J. Theor. Biol. 33, 299-307]. Koz?owsky and Zió?ko [1988. Thor. Popul. Biol. 34, 118-129] and Zió?ko and Koz?owski [1995. IEEE Trans. Automat. Contr. 40(10), 1779-1783] presented a model with gradual transition from vegetative to reproductive growth. The central point of their model is a mixed state-control constraint on the rate of reproductive growth, which leads to a mixed vegetative-reproductive growth period. Their model is modified here in order to take into account the difference of photosynthesis use efficiency when energy is accumulated in the vegetative and in the reproductive organs of a plant, respectively. The simple assumption on correlation between photosynthesis and temperature permits us to modify the model in a form that is useful for changing climate. Unfortunately, the mathematical solution of the optimal control problem in Koz?owsky and Zió?ko (1988) and Zió?ko and Koz?owski (1995) is incorrect. The strict mathematical solution is presented here, the numerical example from is solved, and the results are compared. The influence of the length of the season and the relative photosynthesis use efficiency, as well as of the potential sink demand of the reproductive organs, on the location and duration of the mixed vegetative-reproduction period of growth is investigated numerically. The results show that the mixed growth period is increased and shifted toward the end of the season when the lengths of the season is increased. Additional details of the sensitivity analysis are also presented.     

A model for saccular cerebral aneurysm growth by collagen fibre remodelling

The first structural model for saccular cerebral aneurysm growth is proposed. It is assumed that the development of the aneurysm is accompanied by a loss of the media, and that only collagen fibres provide load-bearing capacity to the aneurysm wall. The aneurysm is modelled as an axisymmetric multi-layered membrane, exposed to an inflation pressure. Each layer is characterized by an orientation angle, which changes between different layers. The collagen fibres and fibroblasts within a specific layer are perfectly aligned. The growth and the morphological changes of the aneurysm are accomplished by the turnover of collagen. Fibroblasts are responsible for collagen production, and the related deformations are assumed to govern the collagen production rate. There are four key parameters in the model: a normalized pressure, the number of layers in the wall, an exponent in the collagen mass production rate law, and the pre-stretch under which the collagen is deposited. The influence of the model parameters on the aneurysmal response is investigated, and a stability analysis is performed. The model is able to predict clinical observations and mechanical test results, for example, in terms of predicted aneurysm size, shape, wall stress and wall thickness.     

Postnatal growth allometry of the extremities in Cebus albifrons and Cebus apella: A longitudinal and comparative study

Cebus albifrons and Cebus apella, partially sympatric capuchin monkeys from South America, are known to differ substantially in adult body mass and bodily proportions. C. apella possesses a robust, stocky build in contrast to the more gracile, relatively longer limbed body design of C. albifrons. Average birth weights and adult body lengths of these two congeners, however, are remarkably similar and do not serve to distinguish them. This study examines longitudinal growth rates and patterns of ontogenetic scaling in the extremities (humerus, radius, hand, femur, tibia, foot) in order to document the nature and magnitude of skeletal changes associated with increasing age and body mass. Our data indicate that the growth rates of the six skeletal components of the limbs differ only slightly and somewhat inconsistently between the two species. Body mass, however, increases at a consistently faster rate in C. apella. Relative to body mass, therefore, the extremities of C. albifrons scale much faster than those of C. apella. This implies that at any given postnatal body mass, C. albifrons is longer limbed than C. apella. Conversely, C. apella is heavier than C. albifrons at any given limb length or age. We suggest that such differences in body mass distribution are causally related to differences in locomotor behavior and foraging strategies. Specifically, the relatively long-limbed C. albifrons is probably more cursorial and tends to travel longer distances each day than C. apella. C. apella is a much more deliberate quadruped and is also characterized by especially vigorous and powerful foraging and feeding behaviors. We also compare our results to other (mostly cross-sectional) studies of skeletal growth allometry in nonhuman primates.     

A cellular growth model for root tips

Growth of the root tip is modeled using a one-dimensional string of cells. Each cell is characterized by three distinct phases, division, elongation-only or maturity. In this model two hypothetical phytohormones, one produced at the root tip and the other at the shoot, determine the behavior of the cell, and therefore the growth of the entire tip. While the division rate is taken to be a step function of the string coordinate, the growth rate of each cell is assumed to be piecewise linear and composed of linear functions of cell length. Thereafter, suitable operators for the calculation of the velocity and relative growth rate distributions are given. The results of the model are finally compared to measurements of Arabidopsis thaliana, Nicotiana tabacum and Pisum sativum roots.     

A stochastic computer model for simulating population growth

A model is described for investigating the interactions of age-specific birth and death rates, age distribution and density-governing factors determining the growth form of single-species populations. It employs Monte Carlo techniques to simulate the births and deaths of individuals while density-governing factors are represented by simple algebraic equations relating survival and fecundity to population density. In all respects the model's behavior agrees with the results of more conventional mathematical approaches, including the logistic model andLotka's Law, which predicts a relationship betwen age-specific rates, rate of increase and age distribution. Situations involving exponential growth, three different age-independent density functions affecting survival, three affecting fecundity and their nine combinations were tested. The one function meeting the assumptions of the logistic model produced a logistic growth curve embodying the correct values or r_m and K. The others generated sigmoid curves to which arbitrary logistic curves could be fitted with varying success. Because of populational time lags, two of the functions affecting fecundity produced overshoots and damped oscillations during the initial approach to the steady state. The general behavior of age-dependent density functions is briefly explored and a complex example is described that produces population fluctuations by an egg cannibalism mechanism similar to that found in the flour beetle Tribolium. The model is free of inherent time lags found in other discrete time models yet these may be easily introduced. Because it manipulates separate individuals, the model may be combined readily with the Monte Carlo simulation models of population genetics to study eco-genetic phenomena.     

A soybean growth model based on compensatory growth following defoliation

On the basis of an artificial defoliation experiment, a new growth model of soybean was formulated through a modification of Rudd's (1980) model with regard to his equations for dry matter allocation. Compensatory growth for leaf damage was modelled by a single process in which the dry matter allocation changes dynamically according to the severity of leaf damage. The sums of squared differences between simulations and experimental soybean yields were much smaller in our modified model than in Rudd's original model. The modified model gave a better simulation of yield loss due to defoliation that varied in time and intensity. The relationship between various times and intensities of defoliation and yield loss was shown, which is essential for establishing the dynamic economic injury level in IPM.     

A variational constitutive model for soft biological tissues

In this paper, a fully variational constitutive model of soft biological tissues is formulated in the finite strain regime. The model includes Ogden-type hyperelasticity, finite viscosity, deviatoric and volumetric plasticity, rate and microinertia effects. Variational updates are obtained via time discretization and pre-minimization of a suitable objective function with respect to internal variables. Genetic algorithms are used for model parameter identification due to their suitability for non-convex, high dimensional optimization problems. The material behavior predicted by the model is compared to available tests on swine and human brain tissue. The ability of the model to predict a wide range of experimentally observed behavior, including hysteresis, cyclic softening, rate effects, and plastic deformation is demonstrated.     

A multiscale model for eccentric and concentric cardiac growth through sarcomerogenesis

We present a novel computational model for maladaptive cardiac growth in which kinematic changes of the cardiac chambers are attributed to alterations in cytoskeletal architecture and in cellular morphology. We adopt the concept of finite volume growth characterized through the multiplicative decomposition of the deformation gradient into an elastic part and a growth part. The functional form of its growth tensor is correlated to sarcomerogenesis, the creation and deposition of new sarcomere units. In response to chronic volume-overload, an increased diastolic wall strain leads to the addition of sarcomeres in series, resulting in a relative increase in cardiomyocyte length, associated with eccentric hypertrophy and ventricular dilation. In response to chronic pressure-overload, an increased systolic wall stress leads to the addition of sacromeres in parallel, resulting in a relative increase in myocyte cross sectional area, associated with concentric hypertrophy and ventricular wall thickening. The continuum equations for both forms of maladaptive growth are discretized in space using a nonlinear finite element approach, and discretized in time using the implicit Euler backward scheme. We explore a generic bi-ventricular heart model in response to volume- and pressure-overload to demonstrate how local changes in cellular morphology translate into global alterations in cardiac form and function.     

A balanced model for biofilms developed at different growth and detachment forces

In a steady state biofilm culture, dissolved organic carbon (DOC) distribution between catabolism and anabolism can be described by a ratio of the DOC channeled into carbon dioxide (S_CO2) to the DOC converted into biomass (S_g). Based on a balanced oxidative reaction of DOC, a S_CO2/S_g-dependent observed growth yield (Y_obs) model was developed for biofilm culture and was verified with literature data. Growth and detachment forces are two decisive factors in biofilm process. The detachment force (D_f) normalized with respect to the growth force (G_f) was introduced to describe the interaction between the biofilm growth and detachment processes. Biofilm metabolism and structure were closely related to the D_f/G_f-ratio, and biofilm community could metabolically respond to changes in growth and detachment forces. A proper balance between growth and detachment forces is crucial for development of a compact and stable biofilm. The proposed D_f/G_f concept provides a theoretical basis for experimental data obtained at different growth and detachment forces to be interpreted in a unified sense. Biofilm structure may be manipulated by controlling the D_f/G_f ratio.     

A minimal medium for growth of Pasteurella multocida

Abstract We developed a minimal medium supporting the growth of both toxigenic and nontoxigenic strains of Pasteurella multocida to optical densities of > 0.5 (600 nm ). P. multocida P1059 (ATCC 15742), one of a number of strains which can cause fowl cholera, was used as the model strain in this study. The medium was composed of 17 ingredients including cysteine, glutamic acid, leucine, methionine, inorganic salts, nicotinamide, pantothenate, thiamine, and an energy source. Leucine was not required for growth but was stimulatory, and thiamine could be replaced by adenine. An additional 46 strains of P. multocida were tested, and 40 out of 46 (87%) strains grew as well as strain P1059 through a minimum of 10 serial transfers. P. multocida toxin (PMT) was produced when cells of a known toxigenic strain (P4261) were cultivated in the minimal medium. No growth of Pasteurella haemolytica or Pasteurella trehalosi strains was observed in this minimal medium.     

A simple model for polyproline II structure in unfolded states of alanine-based peptides

The striking similarity between observed circular dichroism spectra of nonprolyl homopolymers and that of regular left-handed polyproline II (P_II) helices prompted Tiffany and Krimm to propose in 1968 that unordered peptides and unfolded proteins are built of P_II segments linked by sharp bends. A large body of experimental evidence, accumulated over the past three decades, provides compelling evidence in support of the original hypothesis of Tiffany and Krimm. Of particular interest are the recent experiments of Shi et al. who find significant P_II structure in a short unfolded alanine-based peptide. What is the physical basis for P_II helices in peptide and protein unfolded states? The widely accepted view is that favorable chain-solvent hydrogen bonds lead to a preference for dynamical fluctuations about noncooperative P_II helices in water. Is this preference simply a consequence of hydrogen bonding or is it a manifestation of a more general trend for unfolded states which are appropriately viewed as chains in a good solvent? The prevalence of closely packed interiors in folded proteins suggests that under conditions that favor folding, water—which is a better solvent for itself than for any polypeptide chain—expels the chain from its midst, thereby maximizing chain packing. Implicit in this view is a complementary idea: under conditions that favor unfolding, chain-solvent interactions are preferred and in a so-called good solvent, chain packing density is minimized. In this work we show that minimization of chain packing density leads to preferred fluctuations for short polyalanyl chains around canonical, noncooperative P_II-like conformations. Minimization of chain packing is modeled using a purely repulsive soft-core potential between polypeptide atoms. Details of chain-solvent interactions are ignored. Remarkably, the simple model captures the essential physics behind the preference of short unfolded alanine-based peptides for P_II helices. Our results are based on a detailed analysis of the potential energy landscape which determines the system''s structural and thermodynamic preferences. We use the inherent structure formalism of Stillinger and Weber, according to which the energy landscape is partitioned into basins of attraction around local minima. We find that the landscape for the experimentally studied seven-residue alanine-based peptide is dominated by fluctuations about two noncooperative structures: the left-handed polyproline II helix and its symmetry mate.     

The tensor-based model of plant growth applied to leaves of Arabidopsis thaliana: A two-dimensional computer model

Plant organs grow in coordinated and continuous way. Such growth is of a tensor nature, hence there is an infinite number of different directions of growth rate in each point of the growing organ. Three mutually orthogonal directions of growth can be recognized in which growth achieves extreme values (principal directions of growth [PDGs]). Models based on the growth tensor have already been successfully applied to the root and shoot apex. This paper presents the 2D model of growth applied to the arabidopsis leaf. The model employs the growth tensor method with a non-stationary velocity field. The postulated velocity functions are confirmed by growth measurements with the aid of the replica method.     

A quantitative genetic model for growth,shape, reaction norms,and other infinite-dimensional characters

Infinite-dimensional characters are those in which the phenotype of an individual is described by a function, rather than by a finite set of measurements. Examples include growth trajectories, morphological shapes, and norms of reaction. Methods are presented here that allow individual phenotypes, population means, and patterns of variance and covariance to be quantified for infinite-dimensional characters. A quantitative-genetic model is developed, and the recursion equation for the evolution of the population mean phenotype of an infinite-dimensional character is derived. The infinite-dimensional method offers three advantages over conventional finite-dimensional methods when applied to this kind of trait: (1) it describes the trait at all points rather than at a finite number of landmarks, (2) it eliminates errors in predicting the evolutionary response to selection made by conventional methods because they neglect the effects of selection on some parts of the trait, and (3) it estimates parameters of interest more efficiently.     

A simple model for the dynamics of a host-parasite-hyperparasite interaction

Hyperparasites can play a crucial role in the control of a host-parasite interaction if they are successfully established in the community. We investigated the specific traits of the hyperparasite and those of the release event which allow a successful regulation of primary parasite populations. This study has been motivated by the case study of chestnut-Cryphonectria parasitica-Cryphonectria Hypovirus interaction. We use a model of SIR/SIS type which assumes a limited diffusion of the parasite. Our model emphasizes the thresholds for invasion linked to the ecological specificities of both the pathogen and the hyperparasite (transmission rates and virulence) and to the initial conditions of the system (population sizes of the different categories). The predictions are consistent with data on the observed spread of the virus. "Mild" strains of the hyperparasite, characterized by a high vertical transmission rate and low virulence, are more prone to establish than "severe" strains. It also demonstrates that the horizontal transmission of the virus, which is controlled by a vegetative incompatibility system in the fungus, is not the unique constraint for the virus establishment. This study may contribute to theoretical and practical aspects of the biological control of plant diseases with a hyperparasite and to the ecology of biological invasions.     

Maintenance energy: a general model for energy-limited and energy-sufficient growth

The new model proposed to account for the energy requirement for growth includes both a constant maintenance energy term (m) independent of the specific growth rate and a term (m′) which decreases linearly with increase in specific growth rate and becomes zero at the maximum specific growth rate. The available data for testing the model do not deviate significantly from the relations predicted. Consistent values of the maximum growth yield (Y _G) can be derived, irrespective of whether the cultures are energy limited or energy sufficient. Attention is drawn to the possibility that the constant maintenance energy term may be estimated from the maximum specific growth rate.