A structured erythropoiesis model with nonlinear cell maturation velocity and hormone decay rate

We develop a quasilinear structured model that describes the regulation of erythropoiesis, the process in which red blood cells are developed. In our model, the maturation velocity of precursor cells is assumed to be a function of the erythropoietin hormone, and the decay rate of this hormone is assumed to be a function of the number of precursor cells, unlike other models which assume these parameters to be constants. Existence-uniqueness results are established and convergence of a finite difference approximation to the unique solution of the model is obtained. The finite difference scheme is then used to investigate the effects of these nonlinear parameters on the model dynamics. Our results show that a velocity of precursor cells maturation rate which is an increasing function of the hormone level and a decay rate of the hormone which is an increasing function of the number of precursor cells have a stabilizing effect on the dynamics of the model. While assuming that one parameter is a function and letting the other be a constant stabilizes the oscillations in the mature cells level, the effect is more significant when both parameters are taken to be functions. A study of robustness with respect to the forms of these functions and parameter sensitivity is also carried out.     

Preferential invasion of reticulocytes during late-stage Plasmodium berghei infection accounts for reduced circulating reticulocyte levels

Insufficient circulating reticulocytes have been observed during severe malarial anaemia in both human and murine infection, and are often attributed to reduced production of red cell precursors. However, a number of Plasmodium species display a preference for invading reticulocytes rather than erythrocytes. Thus, the reduction in circulating reticulocyte numbers may arise as a result both of increased parasitization and lysis of reticulocytes, as well as decreased production. We have analysed both circulating reticulocyte numbers and the percentage of infected reticulocytes during murine Plasmodium berghei infection. We found a large reduction in circulating numbers when compared with an equivalent chemically induced anaemia. However, mathematical analysis of parasite and red cell numbers revealed the preference of P. berghei for reticulocytes to be approximately 150-fold over that for erythrocytes, leading to increased destruction of reticulocytes. Although erythropoietic suppression is evident during the first week of P. berghei infection, this preferential infection and destruction of reticulocytes is sufficient to mediate ongoing reduced levels of circulating reticulocytes during the latter stages of infection, following compensatory erythropoiesis in response to haemolytic anaemia.     

Theoretical model of thalassemic erythrocyte shape transformation

Our earlier model of reticulocyte shape transformation [Pawlowski, P.H., Burzynska, B., Zielenkiewicz, P., 2006. Theoretical model of reticulocyte to erythrocyte shape transformation. J. Theor. Biol. 243, 24-38] was applied to explain the morphological properties of thalassemic erythrocytes. Modification of the standard set of parameters of the model, describing minimal cell volume, membrane bending rigidity, and membrane tension, allowed for simulation of development of α- and β-thalassemic cells from splenectomized and nonsplenectomized individuals. This resulted in observation of thin rim discocytes, tailed erythrocytes and oval forms, as well as in differentiation of time of the cell shape metamorphosis. A comparative analysis of the susceptibility of thalassemic and normal erythrocytes to undergo deformation as well of their stability was performed.     

温室作物生物量积累率二阶差分模型

为了研究温室作物生物量积累的变化过程,本文构建了一类二阶差分模型,该模型具有有界性、单调性与全局渐近稳定性.对实验数据的模拟表明,该模型能很好解释温室黄瓜生物量轨迹运动趋势与干重积累率增长特性,比原有的生长模型拟合效果好.     

The dynamics of single-substrate continuous cultures: the role of ribosomes

When a chemostat is perturbed from its steady state, it displays complex dynamics. For instance, if the identity of the growth-limiting substrate is switched abruptly, the substrate concentration and cell density undergo a pronounced excursion from the steady state that can last several days. These dynamics occur because certain physiological variables respond slowly. In the literature, several physiological variables have been postulated as potential sources of the slow response. These include transport enzymes, biosynthetic enzymes, and ribosomes. We have been addressing this problem by systematically exploring the role of these variables. In previous work Shoemaker et al. (J. Theor. Biol., 222 (2003) 307-322), we studied the role of transport enzymes, and we showed that transients starting from low transport enzyme levels could be quantitatively captured by a model taking due account of transport enzyme synthesis. However, there is some experimental data indicating that slow responses occur even if the initial enzyme levels are high. Here, we analyse this data to show that in these cases, the sluggish response is most probably due to slow adjustment of the ribosome levels. To test this hypothesis, we extend our previous model by accounting for the evolution of both the transport enzyme and the ribosomes. Based on a kinetic analysis of the data in the literature, we assume that the specific protein synthesis rate is proportional to the ribosome level, and the specific ribosome synthesis rate is autocatalytic. Simulations of the model show remarkable agreement with experimentally observed steady states and the transients. Specifically, the model predictions are in good agreement with (1) the steady-state profiles of the cell density, substrate concentration, RNA, proteins, and transport enzymes, (2) the instantaneous specific substrate uptake, growth, and respiration rates in response to a continuous-to-batch shift, and (3) the transient profiles of the cell density, substrate concentration, and RNA in response to feed switches and dilution rate shifts. Time-scale analysis of the model reveals that every transient response is a combination of two fundamental (and simpler) dynamics, namely, substrate-sufficient batch dynamics and cell-sufficient fed-batch dynamics. We obtain further insight into the transient response by analysing the equations describing these fundamental dynamics. The analysis reveals that in feed switches or dilution rate shift-ups, the transport enzyme reaches a maximum before RNA achieves its maximum, and in dilution rate shift-downs the cell density reaches a maximum before RNA achieves a minimum.     

Structured coalescent processes from a modified Moran model with large offspring numbers

Structured coalescent processes are derived for the finite island model under a migration mechanism that conserves the subpopulation sizes. The underlying population model is a modified Moran model in which the reproducing individual can have very many offspring with some probability. Convergence to a structured coalescent process results when assuming that migration follows a coalescent timescale which can be much shorter than the usual Wright–Fisher timescale. Three different limit processes are possible depending on the coalescent timescale, two of which allow multiple mergers of ancestral lines. The expected time to most recent common ancestor, and the expected total size of the genealogy, of balanced and unbalanced samples can be very similar, even when migration is low, if the coalescent process allows multiple mergers. The expected total size increases almost linearly with sample size in some cases. The results have implications for inference about genetic population structure.     

A mathematical model of iron metabolism

A mathematical model of iron metabolism is presented. It comprises the following iron pools within the body: transferrin-bound iron in the plasma, iron in circulating red cells and their bone marrow precursors, iron in mucosal, parenchymal and reticuloendothelial cells. The control exerted by a hormone, called erythropoietin, on bone marrow utilization of iron for hemoglobin synthesis is taken into account. The model so obtained consists of a system of functional differential equations of retarded type. Most model parameters can be estimated from radiotracer experiments, others can be measured and numerical values can be assigned to the remaining ones making few reasonable assumptions according to the available physiological knowledge. Iron metabolism behavior under different therapeutical treatments was simulated. Model predictions were compared to experimental data collected in clinical routine.This work has been partially supported by C.N.R. (Italy) through grants N. 80.01227.07 and N. 81.00888.07     

Parametric study of radiofrequency ablation in the clinical practice with the use of two-compartment numerical models

The objective of the current work was to simulate radiofrequency ablation (RFA) with theoretical and realistic computational models, which correspond to single-compartment models and clinical scenarios. A 3D model in a cubic region of 12 cm edge was studied representing either a homogeneous model or real clinical scenarios in three human tissues, i.e., liver, lung and kidney. An active electrode was placed at the center of the model. Various tumor sizes (1–3 cm) and source voltages (10–30 V) were investigated for the second case of a two-compartment model. In the case of a 3-cm tumor in diameter, the electrical and thermal problems (at steady state) were solved to calculate the temperature distribution within the tumor and tissue. Lesion volume was quantified using the Arrhenius equation and the isothermals of 50 and 60 °C. The physical properties of all materials were constant during the simulations, i.e., no changes with temperature were considered. It was found that tumor conductivity was low to achieve significant damage in the tumor; in all clinical scenarios, saline-enhanced RFA was necessary and led to a more efficient tumor destruction. It was also shown that highly perfused tissues, such as liver and kidney, block the energy deposition within them, in contrast to lung, and, thus, require a further saline enhancement. Finally, the effect of perfusion on lesion size was studied, and it was concluded that tumor perfusion was more significant than surrounding tissue perfusion.     

Evolution of Dispersal in a Structured Metapopulation Model in Discrete Time

In this article, a structured metapopulation model in discrete time with catastrophes and density-dependent local growth is introduced. The fitness of a rare mutant in an environment set by the resident is defined, and an efficient method to calculate fitness is presented. With this fitness measure evolutionary analysis of this model becomes feasible. This article concentrates on the evolution of dispersal. The effect of catastrophes, dispersal cost, and local dynamics on the evolution of dispersal is investigated. It is proved that without catastrophes, if all population–dynamical attractors are fixed points, there will be selection for no dispersal. A new mechanism for evolutionary branching is also found: Even though local population sizes approach fixed points, catastrophes can cause enough temporal variability, so that evolutionary branching becomes possible.     

Cannibalism as a life boat mechanism

Under certain conditions a cannibalistic population can survive when food for the adults is too scarce to support a non-cannibalistic population. Cannibalism can have this lifeboat effect if (i) the juveniles feed on a resource inaccessible to the adults; and (ii) the adults are cannibalistic and thus incorporate indirectly the inaccessible resource. Using a simple model we conclude that the mechanism works when, at low population densities, the average yield, in terms of new offspring, due to the energy provided by one cannibalized juvenile is larger than one.     

Temperature is the key factor explaining interannual variability of Daphnia development in spring: a modelling study

Plankton succession during spring/early summer in temperate lakes is characterised by a highly predictable pattern: a phytoplankton bloom is grazed down by zooplankton (Daphnia) inducing a clear-water phase. This sequence of events is commonly understood as a cycle of consumer-resource dynamics, i.e. zooplankton growth is driven by food availability. Here we suggest, using a modelling study based on a size-structured Daphnia population model, that temperature and not food is the dominant factor driving interannual variability of Daphnia population dynamics during spring. Simply forcing this model with a seasonal temperature regime typical for temperate lakes is sufficient for generating the distinctive seasonal trajectory of Daphnia abundances observed in meso-eutrophic temperate lakes. According to a scenario analysis, a forward shift of the vernal temperature increase by 60 days will advance the timing of the Daphnia maximum on average by 54 days, while a forward shift in the start of the spring bloom by 60 days will advance the Daphnia maximum only by less than a third (17 days). Hence, the timing of temperature increase was more important for the timing of Daphnia development than the timing of the onset of algal growth. The effect of temperature is also large compared to the effect of applying different Daphnia mortality rates (0.055 or 0.1 day(-1), 38 days), an almost tenfold variation in phytoplankton carrying capacity (25 days) and a tenfold variation in Daphnia overwintering abundance (3 days). However, the standing stock of Daphnia at its peak was almost exclusively controlled by the phytoplankton carrying capacity of the habitat and seems to be essentially independent of temperature. Hence, whereas food availability determines the standing stock of Daphnia at its spring maximum, temperature appears to be the most important factor driving the timing of the Daphnia maximum and the clear-water phase in spring.     

捕食者-食饵交错扩散模型的整体解

应用能量估计方法和Bootstrap技巧证明含有两类竞争的食饵种群和一类捕食者种群的三种群捕食者-食饵扩散模型在空间维数小于6时古典解的整体存在性.     

A numerical solution of the mechanical bidomain model

Introduction: The mechanical bidomain model predicts forces on integrin proteins in the membrane. It has been solved analytically for idealized examples, but a numerical algorithm is needed to address realistic problems. Methods: The bidomain equations are approximated using finite differences. An ischemic region is modeled as a circular area having no active tension, surrounded by normal tissue. Results: The membrane force is large in the ischemic border zone, but is small elsewhere. Strain is distributed widely throughout the ischemic region and surrounding tissue. Conclusion: This calculation provides a testable prediction for the mechanism of mechanotransduction and remodeling in cardiac tissue.     

Long-term stability from fixation probabilities in finite populations: new perspectives for ESS theory

For mixed strategies in finite populations, long-term stability is defined with respect to the probability of fixation of a mutant. Under weak selection, necessary and sufficient conditions are obtained using a diffusion approximation of the Wright-Fisher model or exact solutions for the Moran model. These differ from the usual ESS conditions if the strategies affect fertility instead of viability, leading to a game matrix depending on the population size, or if the mutant mixed strategy uses a new pure strategy. In this case, the mutant deviation must not exceed some threshold value depending on the population size. In a diploid population, long-term stability may not occur unless there is partial dominance. In the case of sex allocation, continuous stability of an even sex ratio is ascertained. If sex allocation is random, an evolutionary decrease of the variance is predicted.     

Modeling growth and succinoglucan production by Agrobacterium radiobacter NCIB 9042 in batch cultures

Wild-type Agrobacterium radiobacter NCIB 9042 has been cultivated in batch cultures on a synthetic medium which was adapted for growth and succinoglucan production. Experiments were carried out in a 4-L stirred-tank aerated reactor. Glucose, biomass, polysaccharide, protein, and inorganic- and organic-nitrogen concentrations were measured, and oxygen consumption and CO(2) production rates were obtained by a gas-balance technique. Nitrogen balance shows that inorganic nitrogen is entirely recovered into proteins. The carbon balance is satisfied with in +/-5%. Stoichiometric equations for biomass growth and succinoglucan synthesis were established. The biosyntheticpolymer pathways including ATP and cofactor consumption were investigated. From previous studies, a (P/O) value of 1.66 is selected for oxygen sufficient cultures. The actual ATP requirements of 25.4 mmol ATP/g succinoglucan (38.5 mol ATP/mol succinoglucan), determined by a metabolic analysis, is 2.39 times the stoichiometric value. Experimental results were modeled by a system of differential equations. The exponential growth phase was described by a nitrogen-limited Monod equation. Subsequent succinoglucan synthesis followed a slightly modified Luedeking-Piret relation partitioning internal and external polysaccharide. Experimentally determined coefficients are compared with published results for continuous culture of A. radiobacter NCIB 11883.     

高寒内陆河流域植被覆盖增加对地下水补给的影响

地下水是干旱区内陆河流域的主要基础性资源,对流域生态安全、可持续发展等具有重要意义。干旱/半干旱区的地下水补给比湿润地区更易受到地表覆盖条件的影响。为揭示干旱区内陆河流域植被覆盖增加对地下水补给的影响,以巴音河中下游为例,针对土壤和水评价工具(SWAT)模型未有效考虑降水、地形等因素对植被覆盖影响的缺陷,改进SWAT模型,采用全球地表卫星叶面积指数(GLASS LAI)数据代替其LAI计算模块,再结合SWAT土地利用更新模块,准确刻画区域植被覆盖变化。将改进后的SWAT模型与模块化有限拆分地下水流耦合(MODFLOW)模型耦合,准确模拟并分析植被覆盖增加对流域地下水补给的影响。结果表明：基于植被动态变化的土壤和水评价工具与模块化有限拆分地下水流耦合模型(DVSWAT-MODFLOW)模型的月蒸散发及月地下水位模拟效果较好;巴音河中下游2019年林地及草地面积以及LAI较2001年明显增加;2019年植被覆盖情况对应的年际及月际尺度地下水补给量较2001年分别减少了6.1—26.52 mm以及0—15.03 mm;植被覆盖增加对年际尺度地下水补给量的影响强弱在一定程度上取决于年降水量,对...