A Phenomenologic-mathematical Model of Growth Dynamics

Starting point of the modelling procedure are measured courses of the body length increase of man (inverse problem) reaching from the time of conception up to the end of adolescence. First assumption: The whole growth process can be subdivided into independent partial processes for succeeding time periods of the individual's development each of them producess a more or less marked growth spurt. 2. Superposition of these partial processes means addition of the portions of body length which are generated by the spurts yielding in this manner the measured course of body length increase. 3. There is no change in dynamics for producing the several growth spurts, and this dynamics will be described by the differential equation of the logistic law of growth. These steps will be interpreted in control-theoretical terms. In this sense growth is a follow-up control process which is governed by the genetically fixed “biological program of growth” in form of a step function of reference values.     

A Model of Shoot: Root Partitioning with Optimal Growth

A shoot: root partitioning model is presented, which is a developmentof previous approaches in the area. The model incorporates asa physiologically reasonable apparent ‘goal’ forthe plant, the assumption that the partitioning of growth betweenthe shoot and root maximizes the plant specific growth ratein balanced exponential growth. The analysis is concerned principallywith plant growth being a function of carbon and nitrogen only,although it is indicated how other nutrients, or growth factors,may be incorporated. Plant growth is driven by the environmentalconditions, and partitioning is defined entirely in terms ofthe shoot: root ratio and carbon and nitrogen status of theplant. In its basic form the model requires the definition ofa single plant growth parameter, along with the shoot and rootspecific activities and structural composition. Shoot: root partitioning, specific growth rate, vegetative phase     

A Shoot:Root Partitioning Model

A model for partitioning newly-synthesized structural dry matterbetween shoot and root is developed. It is based on a postulatedpartitioning function, which depends upon the relative levelsof carbon and nitrogen substrates, with parameters determiningthe control point and also the degree of control. The modelis used to investigate the relationships between plant specificgrowth rate, shoot:root ratio, and the specific activities ofshoot and root (which depend upon environment), during steady-stateexponential growth; the transient behaviour of the model isalso explored and oscillations in these quantities are obtained. Shoot:root ratio, specific growth rate, mathematical model, partition of assimilates     

A Mechanistic Model of Carbohydrate Dynamics During Adventitious Root Development in Leafy Cuttings

The rooting of vegetatively propagated leafy cuttings involvesthe complex interaction of many processes. For this reason,the influence of carbohydrate status, nutrition, water and hormonalfactors on root formation is poorly understood at a mechanisticlevel. We present a mechanistic model of the growth of pre-formedroot initials on a cutting consisting of leaf, internode androots. The processes represented are leaf photosynthesis, starchmobilization, sugar transport, and sugar utilization for rootgrowth. The model provides a quantitative scheme for understandinghow root development depends on properties of cuttings suchas leaf area, internode length and initial carbohydrate content.The potential of the model to interpret rooting experimentson a whole-cutting basis is illustrated using published datafor cuttings of Triplochiton scleroxylon (a West African hardwood)with different leaf areas. Observed rooting times are reproducedin the model by varying the leaf photosynthetic rate per unitarea. The simulated starch and sugar dynamics during root growthare in qualitative agreement with observations. A sensitivityanalysis is performed to examine the effect of key parameterson the timing or success of rooting. The model provides a frameworkfor examining the role of other factors known to affect rooting,such as nutrient and water status, but requires further parameterisationbefore it can be used as a predictive tool in vegetative propagation. Model, carbohydrates, rooting, vegetative propagation     

A Multicompartment Mathematical Model of Cancer Stem Cell-Driven Tumor Growth Dynamics

Tumors are appreciated to be an intrinsically heterogeneous population of cells with varying proliferation capacities and tumorigenic potentials. As a central tenet of the so-called cancer stem cell hypothesis, most cancer cells have only a limited lifespan, and thus cannot initiate or reinitiate tumors. Longevity and clonogenicity are properties unique to the subpopulation of cancer stem cells. To understand the implications of the population structure suggested by this hypothesis—a hierarchy consisting of cancer stem cells and progeny non-stem cancer cells which experience a reduction in their remaining proliferation capacity per division—we set out to develop a mathematical model for the development of the aggregate population. We show that overall tumor progression rate during the exponential growth phase is identical to the growth rate of the cancer stem cell compartment. Tumors with identical stem cell proportions, however, can have different growth rates, dependent on the proliferation kinetics of all participating cell populations. Analysis of the model revealed that the proliferation potential of non-stem cancer cells is likely to be small to reproduce biologic observations. Furthermore, a single compartment of non-stem cancer cell population may adequately represent population growth dynamics only when the compartment proliferation rate is scaled with the generational hierarchy depth.     

黄土高原刺槐细根生长模型

通过室分析方法建立了细根表面积密度随土层深度变化的房室模型,并根据黄土高原人工刺槐林细根的调查数据,从数值上验证了模型S=Ah~B（C＋Dh＋Eh~2＋Fh~3）是房室模型的简化形式,还进一步建立了黄土高原刺槐细根生长关于土层深度和时间的动态生长模型.经验证,该模型能准确地计算黄土高原不同水分生态区及不同时间和土层的刺槐细根表面积密度,具有很高的应用价值.     

A 3D Hybrid Model for Tissue Growth: The Interplay between Cell Population and Mass Transport Dynamics

To provide theoretical guidance for the design and in vitro cultivation of bioartificial tissues, we have developed a multiscale computational model that can describe the complex interplay between cell population and mass transport dynamics that governs the growth of tissues in three-dimensional scaffolds. The model has three components: a transient partial differential equation for the simultaneous diffusion and consumption of a limiting nutrient; a cellular automaton describing cell migration, proliferation, and collision; and equations that quantify how the varying nutrient concentration modulates cell division and migration. The hybrid discrete-continuous model was parallelized and solved on a distributed-memory multicomputer to study how transport limitations affect tissue regeneration rates under conditions encountered in typical bioreactors. Simulation results show that the severity of transport limitations can be estimated by the magnitude of two dimensionless groups: the Thiele modulus and the Biot number. Key parameters including the initial seeding mode, cell migration speed, and the hydrodynamic conditions in the bioreactor are shown to affect not only the overall rate, but also the pattern of tissue growth. This study lays the groundwork for more comprehensive models that can handle mixed cell cultures, multiple nutrients and growth factors, and other cellular processes, such as cell death.     

Human Growth and Body Weight Dynamics: An Integrative Systems Model

Quantifying human weight and height dynamics due to growth, aging, and energy balance can inform clinical practice and policy analysis. This paper presents the first mechanism-based model spanning full individual life and capturing changes in body weight, composition and height. Integrating previous empirical and modeling findings and validated against several additional empirical studies, the model replicates key trends in human growth including A) Changes in energy requirements from birth to old ages. B) Short and long-term dynamics of body weight and composition. C) Stunted growth with chronic malnutrition and potential for catch up growth. From obesity policy analysis to treating malnutrition and tracking growth trajectories, the model can address diverse policy questions. For example I find that even without further rise in obesity, the gap between healthy and actual Body Mass Indexes (BMIs) has embedded, for different population groups, a surplus of 14%–24% in energy intake which will be a source of significant inertia in obesity trends. In another analysis, energy deficit percentage needed to reduce BMI by one unit is found to be relatively constant across ages. Accompanying documented and freely available simulation model facilitates diverse applications customized to different sub-populations.     

The Effect of Coumarin on Root Growth and Root Histology

The effect of coumarin on the root growth was studied on roots from intact plants, isolated roots and isolated elongating zones. All material was cultivated aseptically. A new method was developed for sterile culture of intact plants in flowing nutrient medium. The effects on cell division and cell elongation were studied separately. An effect on both these processes can be established at all concentrations that affect the root growth. The concentration-growth curve has an “all-or-none” appearance. Coumarin inhibits the transverse divisions in all cell layers; the perivascular layers seem to be more sensitive. Also the mitotic activity that is involved in the initiation of laterals is inhibited. The longitudinal divisions within the stele are enhanced. Coumarin decreases the cell length in all cell layers, most likely with greater relative sensitivity in the perivascular layers. Studies on the time course of cell elongation in both attached corn roots and isolated elongating zones reveal that the decrease in cell length is caused exclusively by a decrease in the maximal rate of elongation, whereas the duration of the elongation is unchanged. With each decrease of the cell length, the cell diameter is increased. The two changes are intimately connected within the greater part of the active region of concentration. Studies on the time course of the radial expansion in isolated elongating zones show a strict connection in time between cell elongation and radial expansion. The radial expansion leads to unchanged or increased cell volume at most concentrations and for most cell types. Coumarin causes an inhibition of the longitudinally directed processes and a stimulation of the radially directed ones. This is interpreted as indicating that the formative system is disengaged or reorientated, i.e., the polarity of the cells is changed. Through experiments partly with isolated elongating zones and partly by disruption of the linear phase by means of mannitol, the inhibitory effect of coumarin could be localized to the first non-linear phase of the elongation. The results were compared with earlier findings in the literature. The microtubuli are proposed as a conceivable main Component in the formative system common to both cell division and cell elongation. These are assumed to be affected by changes in the SH/SS balance produced by coumarin.     

A Dynamic Growth Model of Vegetative Soya Bean Plants: Model Structure and Behaviour under Varying Root Temperature and Nitrogen Concentration

A differential equation model of vegetative growth of the soyabean plant (Glycine max (L.) Merrill cv. ‘Ransom’)was developed to account for plant growth in a phytotron systemunder variation of root temperature and nitrogen concentrationin nutrient solution. The model was tested by comparing modeloutputs with data from four different experiments. Model predictionsagreed fairly well with measured plant performance over a widerange of root temperatures and over a range of nitrogen concentrationsin nutrient solution between 0.5 and 10.0 mmol in the phytotron environment. Sensitivity analyses revealedthat the model was most sensitive to changes in parameters relatingto carbohydrate concentration in the plant and nitrogen uptakerate. Key words: Glycine max (L.) Merrill, dry matter, nitrogen uptake, partitioning, photosynthesis, respiration, sensitivity analysis     

The Dynamics of Territory Acquisition: A Model of Two Coexisting Strategies

Two potential strategies for acquiring territories are (1) fighting and taking over a territory from its owner, or (2) waiting until a territory owner dies and then taking its place. In this paper we explore territory acquisition using these two strategies, using a population dynamical model. Factors expected to affect the predominance of each strategy are injury rate, rate of successful territory takeover, birth and death rates on the territory, and birth and death rates while non-territorial. We explore the effects of these parameters on numbers of territorial and nonterritorial fighters and waiters. Waiters predominate when injury rate, birth rate of nonterritorial individuals, and death rate of territory owners are high. Fighters predominate when rate of successful territory takeover, death rate of nonterritorial individuals, and birth rate of territory owners are high. We present supportive evidence for these preditions from the literature.     

高梁根系生长发育规律及动态模拟

高粱［Ｓｏｒｇｈｕｍｂｉｃｏｌｏｒ（Ｌ．）Ｍｏｅｎｃｈ］又名蜀粟，有悠久的栽培历史和独特的抗逆性及适应性，在我国旱作农区，凡不适于玉米、小麦栽培的干旱或半干旱瘠薄耕地，种植高粱均能获得较高和较稳定的籽粒产量［１］，高粱这种抗逆性较强的特点与其有发达的根系系统有关，但由于研究方法和手段的原因，在国内对高粱根系研究开展的还较少，本试验在大田条件下系统研究高粱根系生长发育规律，并与玉米根系进行比较，为进一步开展高粱抗逆性研究和抗旱育种提供依据。１　材料和方法试验于１９９６年在中国科学院石家庄农业现代化…     

The Root Cap: Cell Dynamics, Cell Differentiation and Cap Function

The root cap is a universal feature of angiosperm, gymnosperm, and pteridophyte roots. Besides providing protection against abrasive damage to the root tip, the root cap is also involved in the simultaneous perception of a number of signals – pressure, moisture, gravity, and perhaps others – that modulate growth in the main body of the root. These signals, which originate in the external environment, are transduced by the cap and are then transported from the cap to the root. Root gravitropism is one much studied response to an external signal. In the present paper, consideration is given to the structure of the root cap and, in particular, to how the meristematic initial cells of both the central cap columella and the lateral portion of the cap which surrounds the columella are organized in relation to the production of new cells. The subsequent differentiation and development of these cells is associated with their displacement through the cap and their eventual release, as “border cells”, from the cap periphery. Mutations, particularly in Arabidopsis, are increasingly playing a part in defining not only the pattern of genetic activity within different cells of the cap but also in revealing how the corresponding wild-type proteins relate to the range of functions of the cap. Notable in this respect have been analyses of the early events of root gravitropism. The ability to image auxin and auxin permeases within the cap and elsewhere in the root has also extended our understanding of this growth response. Images of auxin distribution may, in addition, help extend ideas concerning the positional controls of cell division and cell differentiation within the cap. However, firm information relating to these controls is scarce, though there are intriguing suggestions of some kind of physiological link between the border cells surrounding the cap and mitotic activity in the cap meristem. Open questions concern the structure and functional interrelationships between the root and the cap which surmounts it, and also the means by which the cap transduces the environmental signals that are of critical importance for the growth of the individual roots, and collectively for the shaping of the root system.     

A Mathematical Model for BRASSINOSTEROID INSENSITIVE1-Mediated Signaling in Root Growth and Hypocotyl Elongation

Brassinosteroid (BR) signaling is essential for plant growth and development. In Arabidopsis (Arabidopsis thaliana), BRs are perceived by the BRASSINOSTEROID INSENSITIVE1 (BRI1) receptor. Root growth and hypocotyl elongation are convenient downstream physiological outputs of BR signaling. A computational approach was employed to predict root growth solely on the basis of BRI1 receptor activity. The developed mathematical model predicts that during normal root growth, few receptors are occupied with ligand. The model faithfully predicts root growth, as observed in bri1 loss-of-function mutants. For roots, it incorporates one stimulatory and two inhibitory modules, while for hypocotyls, a single inhibitory module is sufficient. Root growth as observed when BRI1 is overexpressed can only be predicted assuming that a decrease occurred in the BRI1 half-maximum response values. Root growth appears highly sensitive to variation in BR concentration and much less to reduction in BRI1 receptor level, suggesting that regulation occurs primarily by ligand availability and biochemical activity.     

The Root Cap: Cell Dynamics, Cell Differentiation and Cap Function

The root cap is a universal feature of angiosperm, gymnosperm, and pteridophyte roots. Besides providing protection against abrasive damage to the root tip, the root cap is also involved in the simultaneous perception of a number of signals – pressure, moisture, gravity, and perhaps others – that modulate growth in the main body of the root. These signals, which originate in the external environment, are transduced by the cap and are then transported from the cap to the root. Root gravitropism is one much studied response to an external signal. In the present paper, consideration is given to the structure of the root cap and, in particular, to how the meristematic initial cells of both the central cap columella and the lateral portion of the cap which surrounds the columella are organized in relation to the production of new cells. The subsequent differentiation and development of these cells is associated with their displacement through the cap and their eventual release, as border cells, from the cap periphery. Mutations, particularly in Arabidopsis, are increasingly playing a part in defining not only the pattern of genetic activity within different cells of the cap but also in revealing how the corresponding wild-type proteins relate to the range of functions of the cap. Notable in this respect have been analyses of the early events of root gravitropism. The ability to image auxin and auxin permeases within the cap and elsewhere in the root has also extended our understanding of this growth response. Images of auxin distribution may, in addition, help extend ideas concerning the positional controls of cell division and cell differentiation within the cap. However, firm information relating to these controls is scarce, though there are intriguing suggestions of some kind of physiological link between the border cells surrounding the cap and mitotic activity in the cap meristem. Open questions concern the structure and functional interrelationships between the root and the cap which surmounts it, and also the means by which the cap transduces the environmental signals that are of critical importance for the growth of the individual roots, and collectively for the shaping of the root system. Current address (Peter W. Barlow): School of Biological Sciences, University of Bristol, Woodland Road, Bristol BS8 1UG, UK     

Root Hairs as a Model System for Studying Plant Cell Growth

Root hairs are tip-growing projections that form on specializedepidermal cells. Physiological studies are identifying key transportersrequired for hair growth, and drug studies have been instructivein defining the role of the cytoskeleton in cell morphogenesis.Genetic analysis is identifying proteins involved in cell growthand the phenotypes of the mutants are instructive in definingthe precise function of these proteins in cellular morphogenesis.Recent progress in our understandings of cell growth using thearabidopsis root hair as a model system is reviewed. Copyright2001 Annals of Botany Company Arabidopsis, root hair, trichoblast, actin, microtubules, cell wall, genetics, calcium, potassium, phosphorus     

Physics of Root Growth

THE elongation of a plant cell involves the yielding of the cell wall under the action of tensile stresses in the wall¹. The rate of elongation, R, can be expressed simply as R=mW, where m is the extensibility of thé cell wall material and W is the wall pressure. Changes in either m or W have been used to explain the effect of biochemical factors on the growth rate of plant cells^2,3. Cell growth is also affected by the physical environment and this becomes particularly important in the case of plant roots where soil water potential and the mechanical resistance of the soil to deformation can become rate controlling. Working with 3-5 day old radicles of Pisum sativum, growing in soil cores, we have obtained values of wall pressure in terms of these two properties and we find that the rate of root elongation can be described by a simple extensibility equation.     

The Population Dynamics and Community Ecology of Root Hemiparasitic Plants

Root hemiparasitic plants and their host plants interact directly, through parasitism, as well as indirectly, through scramble competition for resources. To understand the population dynamics and community ecology of root hemiparasitic plants and their hosts, models of resource-based competition have been extended to include resource parasitism. Parasitism provides a mechanism for parasitic plants to overcome deficits in their ability to compete for soil resources. The interaction ranges from competitive to exploiter-victim, depending on whether the benefits of parasitism overshadow the costs of competition. These models predict that as productivity in the system increases, parasitic plants should become more abundant. In diverse host communities, differences in the impact that parasites have on their hosts and the benefits that they receive from parasitizing different hosts may lead to nontransitive competitive relationships and a sort of apparent competition. The possible dynamics include paper-rock-scissors oscillations and indirect mutualisms between parasitic plants and their hosts that allow them to form coalitions that can exclude competitive dominants.