In silico optimization and low structured kinetic model of poly[(R)-3-hydroxybutyrate] synthesis by Cupriavidus necator DSM 545 by fed-batch cultivation on glycerol

Glycerol was utilized by Cupriavidus necator DSM 545 for production of poly-3-hydroxybutyrate (PHB) in fed-batch fermentation. Maximal specific growth rates (0.12 and 0.3 h⁻¹) and maximal specific non-growth PHB production rate (0.16 g g⁻¹ h⁻¹) were determined from two experiments (inocula from exponential and stationary phase). Saturation constants for nitrogen (0.107 and 0.016 g L⁻¹), glycerol (0.05 g L⁻¹), non-growth related PHB synthesis (0.011 g L⁻¹) and nitrogen/PHB related inhibition constant (0.405 g L⁻¹), were estimated. Five relations for specific growth rate were tested using mathematical models. In silico performed optimization procedures (varied glycerol/nitrogen ratio and feeding) has resulted in a PHB content of 70.9%, shorter cultivation time (23 h) and better PHB yield (0.347 g g⁻¹). Initial concentration of biomass 16.8 g L⁻¹ and glycerol concentration in broth between 3 and 5 g L⁻¹ were decisive factors for increasing of productivity.     

Cell proliferation drives neural crest cell invasion of the intestine

A general mathematical model of cell invasion is developed and validated with an experimental system. The model incorporates two basic cell functions: non-directed (diffusive) motility and proliferation to a carrying capacity limit. The model is used here to investigate cell proliferation and motility differences along the axis of an invasion wave. Mathematical simulations yield surprising and counterintuitive predictions. In this general scenario, cells at the invasive front are proliferative and migrate into previously unoccupied tissues while those behind the front are essentially nonproliferative and do not directly migrate into unoccupied tissues. These differences are not innate to the cells, but are a function of proximity to uninvaded tissue. Therefore, proliferation at the invading front is the critical mechanism driving apparently directed invasion. An appropriate system to experimentally validate these predictions is the directional invasion and colonization of the gut by vagal neural crest cells that establish the enteric nervous system. An assay using gut organ culture with chick-quail grafting is used for this purpose. The experimental results are entirely concordant with the mathematical predictions. We conclude that proliferation at the wavefront is a key mechanism driving the invasive process. This has important implications not just for the neural crest, but for other invasion systems such as epidermal wound healing, carcinoma invasion and other developmental cell migrations.     

Looking inside an invasion wave of cells using continuum models: proliferation is the key

Recently, a suite of cell migration assays were conducted to investigate the migration of neural crest (NC) cells along the gut during the development of the enteric nervous system (ENS). The NC cells colonise the gastro-intestinal tract as a rostro-caudal wave. Local behaviour was shown to be controlled by position relative to the leading edge of the wavefront. The assays involved chick-quail grafting techniques allowing the total invading population to be considered as a two-species system. A two-species continuum model with logistic proliferation and a migration mechanism is developed here to simulate the chick-quail graft experiments and provide a means of looking at the processes occurring within the invasion wave. Five migration mechanisms are considered--linear diffusion, two cases of nonlinear diffusion, chemokinesis and chemotaxis. The model results agree with the experimental observations, regardless of the specific type of migration mechanism. The results show that NC cell invasion is driven by proliferation and cell motility at the leading edge of the wave. Furthermore, logistic proliferation exerts the dominant control on the system. This observation is confirmed by analysing some simplified invasion models. Once the basic experiments were mathematically replicated, the mathematical models were used in turn to make some predictions that were yet to be experimentally tested. This involved conducting a sensitivity analysis of the system by interrupting the proliferation and/or migration ability of the leading edge. Numerical results show that the system is stable against these changes. Of the three experiments suggested, one was carried out and the experimental results were concordant with the theoretical predictions. The outcome of two other suggested experiments are predicted and left for future experimental validation.     

A Mathematical Model for the Effects of HER2 Overexpression on Cell Proliferation in Breast Cancer

We present a mathematical model to study the effects of HER2 over-expression on cell proliferation in breast cancer. The model illustrates the proliferative behavior of cells as a function of HER2 and EGFR receptors numbers, and the growth factor EGF. This mathematical model comprises kinetic equations describing the cell surface binding of EGF growth factor to EGFR and HER2 receptors, coupled to a model for the dependence of cell proliferation rate on growth factor receptors binding. The simulation results from this model predict: (1) a growth advantage associated with excess HER2 receptors; (2) that HER2-over-expression is an insufficient parameter to predict the proliferation response of cancer cells to epidermal growth factors; and (3) the EGFR receptor expression level in HER2-over-expressing cells plays a key role in mediating the proliferation response to receptor-ligand signaling. This mathematical model also elucidates the interaction and roles of other model parameters in determining cell proliferation rate of HER2-over-expressing cells.     

不同孔径CPC材料对大鼠骨髓间充质干细胞增殖的影响

目的：评价不同大小孔径的磷酸钙骨水泥（Calcium phosphate cement,CPC）材料对大鼠骨髓间充质干细胞（Bone mesenchymal stem cells,BMSCs）增殖能力的影响。方法：用盐析法制备三种不同孔径的（200-300μm、300-450μm、450-600μm）CPC材料,利用Micro-CT测量三种材料的平均孔径、孔隙率。无菌条件下取新生大鼠BMSCs原代培养并传代;将三组材料分别放置于24孔板内,每个材料接种5×104个细胞后,37℃、饱和湿度环境下静置培养。于接种后第1、4、7、14、21天用picogreen试剂盒测定细胞增值率;并在第14天、21天戊二醛固定材料并干燥喷金,扫描电镜观察材料表面细胞生长情况。结果：micro-CT测量结果显示：三种CPC材料孔径间相互连通,孔隙率均大于68%,平均孔径分别为235μm、422μm、505μm。细胞在三组材料上均呈对数增长趋势,在第14天到达平台期,在第1天三组细胞数量无明显差异,第4天450-600μm组细胞数量明显高于其余两组（P〈0.05）,在第7天细胞数量随孔径的增加而增加,3组间均有统计学差异（P〈0.05）,第14天和第21天200-300μm组细胞数量明显少于其余两组（P〈0.05）,300-450μm组和450-600μm组间无统计学差异（P〉0.05）。结论：孔径大小可影响大鼠BMSCs在多孔CPC材料上的增殖能力,随着孔径增大,细胞增殖力增高。本研究为进一步研究孔径结构对细胞的影响提供了实验依据。     

Mathematical modeling of cell growth in a 3D scaffold and validation of static and dynamic cultures

Tissue engineering, an immensely important field in contemporary clinical practices, aims at the repair or replacement of damaged tissues. The mathematical model proposed herein shows the distribution and growth of cells in their characteristic time in a 3D scaffold model. This study contributes to the progress of simulation techniques in static and dynamic cultures of bone tissue. Brinkman, nutrient transport, and cell growth equations are brought together to quantify the growth behavior of cells. However, when a static culture is being studied, the Brinkman equation is eliminated. The model was validated by experimental cell culture using 3‐(4,5‐dimethylthiazol‐2‐yl)‐2,5‐diphenyltetrazolium bromide assay and scanning electron microscopy. Then, static and dynamic cultures were compared to assess the cell density and cell distribution in the scaffold. Cell counting after 21 days of cell culture showed that the number of cells increased 42‐fold in static and 53.5‐fold in dynamic cultures, which was in good agreement with our model estimations (37‐fold increase in the number of cells in static and 49‐fold increase in dynamic cultures). In conclusion, our mathematical model could predict cell distribution and growth in the scaffold.     

A stochastic model for estimation of mutation rates in multiple-replication proliferation processes

In this paper we propose a stochastic model based on the branching process for estimation and comparison of the mutation rates in proliferation processes of cells or microbes. We assume in this model that cells or microbes (the elements of a population) are reproduced by generations and thus the model is more suitably applicable to situations in which the new elements in a population are produced by older elements from the previous generation rather than by newly created elements from the same current generation. Cells and bacteria proliferate by binary replication, whereas the RNA viruses proliferate by multiple replication. The model is in terms of multiple replications, which includes the special case of binary replication. We propose statistical procedures for estimation and comparison of the mutation rates from data of multiple cultures with divergent culture sizes. The mutation rate is defined as the probability of mutation per replication per genome and thus can be assumed constant in the entire proliferation process. We derive the number of cultures for planning experiments to achieve desired accuracy for estimation or desired statistical power for comparing the mutation rates of two strains of microbes. We establish the efficiency of the proposed method by demonstrating how the estimation of mutation rates would be affected when the culture sizes were assumed similar but actually diverge.      

Timing the changes of cyclin E cell content in G1 in exponentially growing cells

We present a method for measuring the content of immunocytochemically detected proteins in individual cells progressing through G(1) phase and its application in the analysis of cyclin E levels. The sequence of G(1) events is tracked under unaltered cycling conditions, in a cell line in the phase of balanced growth in vitro, to avoid the pitfalls of synchronization. Cells were pulse-labeled with BrdUrd and analyzed sequentially by multiparameter flow cytometry, focusing on the subpopulation of labeled cells progressively entering G(1). We use the time-from-birth ("age") of individual cells to track their position inside G(1). Using the average content of cyclin E in the whole population of G(1) cells as the internal reference for each sample, we analyzed the time course of the frequency histograms of cyclin E content within BrdUrd-labeled G(1) cells by exploiting the properties of the age distributions of asynchronous populations. This way we could calculate the average cyclin E content of cells in each age cohort. Cyclin E values were low until age 3 h, after which they rose gradually, reaching six times the value of newborn cells at the end of G(1).     

Linking cell division to cell growth in a spatiotemporal model of the cell cycle

Cell division must be tightly coupled to cell growth in order to maintain cell size, yet the mechanisms linking these two processes are unclear. It is known that almost all proteins involved in cell division shuttle between cytoplasm and nucleus during the cell cycle; however, the implications of this process for cell cycle dynamics and its coupling to cell growth remains to be elucidated. We developed mathematical models of the cell cycle which incorporate protein translocation between cytoplasm and nucleus. We show that protein translocation between cytoplasm and nucleus not only modulates temporal cell cycle dynamics, but also provides a natural mechanism coupling cell division to cell growth. This coupling is mediated by the effect of cytoplasmic-to-nuclear size ratio on the activation threshold of critical cell cycle proteins, leading to the size-sensing checkpoint (sizer) and the size-independent clock (timer) observed in many cell cycle experiments.     

Involvement of cell proliferation in the process of follicular atresia in the guinea pig

Cell morphology and proliferation was investigated in the atretic follicles during estrous cycles in the guinea pig. Ovarian samples on days 1, 4, 8, 12 and 16 of the estrous cycle in the guinea pig were taken in the morning for histologic staining with hematoxylin and eosin (HE), and immunohistochemical staining of the protein proliferating cell nuclear antigen (PCNA). The results indicated that the granulosa cells degenerated and eliminated first in atretic follicles, while the fibroblast-like cells appeared in the innermost layer of theca interna cells. When the fibroblast-like cells migrated to the antrum, they proliferated and formed a new tissue in peripheral to the zona pellucida of the oocyte. Our results also revealed that the orientation of the theca interna cell arrangement changed twice during the process of atresia, and the loose connective tissue in the antrum was critical for follicular atresia. Therefore, follicular atresia was not a simple process of cell death and elimination, but coexisted with cell proliferation. To our knowledge, we have for the first time confirmed cell proliferation and the presence of new tissue in atretic follicles in guinea pigs.     

CAMBIUM, a process-based model of daily xylem development in Eucalyptus

In hardwoods such as Eucalyptus spp., xylem (wood) is a heterogeneous tissue consisting of multiple cell types. As such, xylem development involves multiple complex interactions. To describe and understand xylem development, and ultimately predict the resultant wood properties, a process-based approach to modelling wood property variation is potentially very useful. In this paper, a new model (CAMBIUM), which incorporates concepts of these processes, is described. CAMBIUM predicts how wood density and fibre and vessel anatomical properties vary from pith-to-bark at a daily time step as a function of changing environmental conditions and a set of simulated physiological processes. Simulations from an existing process-based model of stand development (CABALA) are used as inputs. A key feature of CAMBIUM is a model of the interaction between different xylem cell types. Some weaknesses were identified in the ability of the model to simulate vessel spatial patterns and frequencies, emphasizing the complexities inherent in this aspect of angiosperm wood formation. The model was, however, able to provide realistic estimates of short-term variation and temporal ranges in eucalypt fibre diameter and secondary wall development and wood density.     

Modelling and analysis of time-lags in some basic patterns of cell proliferation

 In this paper, we present a systematic approach for obtaining qualitatively and quantitatively correct mathematical models of some biological phenomena with time-lags. Features of our approach are the development of a hierarchy of related models and the estimation of parameter values, along with their non-linear biases and standard deviations, for sets of experimental data. We demonstrate our method of solving parameter estimation problems for neutral delay differential equations by analyzing some models of cell growth that incorporate a time-lag in the cell division phase. We show that these models are more consistent with certain reported data than the classic exponential growth model. Although the exponential growth model provides estimates of some of the growth characteristics, such as the population-doubling time, the time-lag growth models can additionally provide estimates of: (i) the fraction of cells that are dividing, (ii) the rate of commitment of cells to cell division, (iii) the initial distribution of cells in the cell cycle, and (iv) the degree of synchronization of cells in the (initial) cell population. Received: 15 September 1997/Revised version: 1 April 1998     

In silico prediction of the effects of mutations in the human UDP-galactose 4′-epimerase gene: Towards a predictive framework for type III galactosemia

The enzyme UDP-galactose 4′-epimerase (GALE) catalyses the reversible epimerisation of both UDP-galactose and UDP-N-acetyl-galactosamine. Deficiency of the human enzyme (hGALE) is associated with type III galactosemia. The majority of known mutations in hGALE are missense and private thus making clinical guidance difficult. In this study a bioinformatics approach was employed to analyse the structural effects due to each mutation using both the UDP-glucose and UDP-N-acetylglucosamine bound structures of the wild-type protein. Changes to the enzyme's overall stability, substrate/cofactor binding and propensity to aggregate were also predicted. These predictions were found to be in good agreement with previous in vitro and in vivo studies when data was available and allowed for the differentiation of those mutants that severely impair the enzyme's activity against UDP-galactose. Next this combination of techniques were applied to another twenty-six reported variants from the NCBI dbSNP database that have yet to be studied to predict their effects. This identified p.I14T, p.R184H and p.G302R as likely severely impairing mutations. Although severely impaired mutants were predicted to decrease the protein's stability, overall predicted stability changes only weakly correlated with residual activity against UDP-galactose. This suggests other protein functions such as changes in cofactor and substrate binding may also contribute to the mechanism of impairment. Finally this investigation shows that this combination of different in silico approaches is useful in predicting the effects of mutations and that it could be the basis of an initial prediction of likely clinical severity when new hGALE mutants are discovered.     

Using a stem cell and progeny model to illustrate the relationship between cell cycle times of in vivo human tumour cell tissue populations, in vitro primary cultures and the cell lines derived from them

There is increasing evidence that the growth of human tumours is driven by a small proportion of tumour stem cells with self-renewal properties. Multiplication of these cells leads to loss of self-renewal and after division for a finite number of times the cells undergo programmed cell death. Cell cycle times of human cancers have been measured in vivo and shown to vary in the range from two days to several weeks, depending on the individual. Cells cultured directly from tumours removed at surgery initially grow at a rate comparable to the in vivo rate but continued culture leads to the generation of cell lines that have shorter cycle times (1–3 days). It has been postulated that the more rapidly growing sub-population exhibits some of the properties of tumour stem cells and are the precursors of a slower growing sub-population that comprise the bulk of the tumour. We have previously developed a mathematical model to describe the behaviour of cell lines and we extend this model here to describe the behaviour of a system with two cell populations with different kinetic characteristics and a precursor–product relationship. The aim is to provide a framework for understanding the behaviour of cancer tissue that is sustained by a minor population of proliferating stem cells.     

In silico investigation of novel biological pathways: The role of CD200 in regulation of T cell priming in experimental autoimmune encephalomyelitis

The use of simulation to investigate biological domains will inevitably lead to the need to extend existing simulations as new areas of these domains become more fully understood. Such simulation extensions can entail the incorporation of additional cell types, molecules or molecular pathways, all of which can exert a profound influence on the simulation behaviour. Where the biological domain is not well characterised, a structured development methodology must be employed to ensure that the extended simulation is well aligned with its predecessor. We develop and discuss such a methodology, relying on iterative simulation development and sensitivity analysis. The utility of this methodology is demonstrated using a case study simulation of experimental autoimmune encephalomyelitis (EAE), a murine T cell-mediated autoimmune disease model of multiple sclerosis, where it is used to investigate the activity of an additional regulatory pathway. We discuss how application of this methodology guards against creating inappropriate simulation representations of the biology when investigating poorly characterised biological mechanisms.     

Estrous cycle-controlled cell proliferation in the adrenal cortex of female rats

Summary In a total of 120 rats the number of ³H-Tdr-labelled nuclei of the adrenocortex was counted during various phases of the estrous cycle. In two separate experiments cyclic variations in the number of DNA synthesizing cells were found. The labelling index of the zona glomerulosa showed a significant maximum in proestrus whereas in zona fasciculata a minimum was revealed in estrus. In the glomerulosa the maximum of labelled cells was followed by a mitotic peak in estrus. Due to very low numbers of labelled cells no rhythm was found in the reticularis. The possible endocrine regulations of this endogenous rhythm of adrenocortical cell replication are discussed.The authors wish to express their appreciation for the expert assistance in the statistical evaluation of data rendered by Dr. Trieb and for the reliable technical aid by Mr. Majer     

Effect of an inhibitor of noradrenaline uptake,desipramine, on cell proliferation in the intestinal crypt epithelium

The intestinal mucosa receives an adrenergic innervation for which there is no commonly accepted function. However, in recent years, cell kinetic studies have raised the possibility that this innervation may be an important regulator of crypt cell proliferation. The effects of noradrenaline released from adrenergic nerves is terminated principally by re-uptake of the amine into the nerve and this process can be inhibited by the antidepressant drug, desipramine. In this report desipramine is shown to accelerate crypt cell proliferation in intact, but not in chemically sympathectomized rats, thus adding support to the notion that regulation of crypt cell division is an important function of the sympathetic nervous system.