A mathematical model of periodic processes in membranes (with application to cell cycle regulation)

A mathematical model of the regulation of the cell cycle by the plasma membrane is suggested. The model is based on the hypothesis that structural transitions of the cell membrane play an important role in the regulation of cell division. Conditions of transition from the proliferating state to the resting state and back are investigated. Possible qualitative differences between models of the cell cycle of a normal and a tumour cell are pointed out.     

Membrane model of the regulation of proliferation: the theory and interpretation of an experiment

The role of cell surface physical organization in the cell cycle regulation is analyzed within the framework of the earlier proposed theory (Chernavskii et al., 1982). Two models of cell surface are considered: hard-frame fluid-mosaic model (latticemosaic) and the fluid-mosaic one. The former deals with normal cells. The existence of integral carcasse or "frame" which is formed by the essential part of cross-linked membrane components and may have at least two different conformational states is hypothesized. The second model describes membranes of tumour cells. With the latter theory any mitogen (excluding the restoration of nutrient depletion) reduces the mechanical tensile strength of the frame and stimulates the general structural rearrangement of the plasma membrane. There are only two conformational transitions during the cell cycle which serve as signals for the beginning of S and M phases. If the values of tensile strength are great enough and therefore the conformational transitions are impossible, the cells pass into the resting (prereplicative--G01, or premitotical--G02) state. Three types of experiments are interpreted in the proposed theory: a) on differences in the action of growth factors on normal and tumour cell cycle, b) on the necessary condition for mitogenicity of lectins, c) on the stimulation of proliferation by mechanical deformation of cells.     

The rate and topography of cell wall synthesis during the division cycle of Escherichia coli using N-acetylglucosamine as a peptidoglycan label

The rates of synthesis of peptidoglycan and protein during the division cycle of Escherichia coli were measured by the membrane elution technique using cells differentially labelled with N-acetylglucosamine and leucine. During the first part of the division cycle the ratio of the rates of protein and peptidoglycan synthesis was constant. The rate of peptidoglycan synthesis, relative to the rate of protein synthesis, increased during the latter part of the division cycle. These results support a simple, bipartite model of cell surface increase in rod-shaped cells. Prior to the start of constriction the cell surface increases only by lateral wall extension. After cell constriction starts, the cell surface increases by both lateral wall and pole growth. The increase in surface area is partitioned between the lateral wall and the pole so that the volume of the cell increases exponentially. No variation in cell density occurs, because the increase in surface allows a continuous exponential increase in cell volume that accommodates the exponential increase in cell mass. The results are consistent with the constant density of the growing cell and the surface stress model for the regulation of cell surface synthesis. In addition, the elution pattern suggests that the membrane elution method does work by having the cells effectively bound to the membrane by their poles.     

The surface membrane as a regulator of animal cell division

Summary The surface membrane of an animal cell is proposed to be the target for regulation of cell division. It undergoes regular periodic changes during the cell division cycle. Interference with these changes by cell-cell surface contacts is proposed to prevent the normal progression of events, and thereby can change the metabolic pattern so as to put the cells into a resting state. Through external influences, cells can escape from this resting state; when this occurs surface changes are the earliest ones observed. Cells that have become malignant, particularly after virus infection, show marked changes in their surface properties. Infection is proposed to prevent the surface changes that lead to the resting state. Recent evidence from in vitro experiments is summarized, and some speculations are made on the connection between the surface and processes of division such as nuclear replication. Presented in the Symposium on Regulation in Tumor Cells at the 22nd Annual Meeting of the Tissue Culture Association. Lake Placid, New York. This work was supported by Public Health Service Grant CA-A1-1195 and Grant E-555 from the American Cancer Society.     

Rate and topography of cell wall synthesis during the division cycle of Salmonella typhimurium.

The rates of synthesis of peptidoglycan and protein during the division cycle of Salmonella typhimurium have been measured by using the membrane elution technique and differentially labeled diaminopimelic acid and leucine. The cells were labeled during unperturbed exponential growth and then bound to a nitrocellulose membrane by filtration. Newborn cells were eluted from the membrane with fresh medium. The radioactivity in the newborn cells in successive fractions was determined. As the cells are eluted from the membrane as a function of their cell cycle age at the time of labeling, the rate of incorporation of the different radioactive compounds as a function of cell cycle age can be determined. During the first part of the division cycle, the ratio of the rates of protein and peptidoglycan synthesis was constant. During the latter part of the division cycle, there was an increase in the rate of peptidoglycan synthesis relative to the rate of protein synthesis. These results support a simple, bipartite model of cell surface increase in rod-shaped cells. Before the start of constriction, the cell surface increased only by cylindrical extension. After cell constriction started, the cell surface increased by both cylinder and pole growth. The increase in surface area was partitioned between the cylinder and the pole so that the volume of the cell increased exponentially. No variation in cell density occurred because the increase in surface allowed a continuous exponential increase in cell volume that accommodated the exponential increase in cell mass. Protein was synthesized exponentially during the division cycle. The rate of cell surface increase was described by a complex equation which is neither linear nor exponential.     

Mathematical modeling of fission yeast Schizosaccharomyces pombe cell cycle: exploring the role of multiple phosphatases

Cell cycle is the central process that regulates growth and division in all eukaryotes. Based on the environmental condition sensed, the cell lies in a resting phase G0 or proceeds through the cyclic cell division process (G1??S??G2??M). These series of events and phase transitions are governed mainly by the highly conserved Cyclin dependent kinases (Cdks) and its positive and negative regulators. The cell cycle regulation of fission yeast Schizosaccharomyces pombe is modeled in this study. The study exploits a detailed molecular interaction map compiled based on the published model and experimental data. There are accumulating evidences about the prominent regulatory role of specific phosphatases in cell cycle regulations. The current study emphasizes the possible role of multiple phosphatases that governs the cell cycle regulation in fission yeast S. pombe. The ability of the model to reproduce the reported regulatory profile for the wild-type and various mutants was verified though simulations.     

Changes in mitochondrial mass,membrane potential,and cellular adenosine triphosphate content during the cell cycle of human leukemic (HL-60) cells

Oxidative phosphorylation within the inner mitochondrial membrane generates the majority of cellular adenosine triphosphate (ATP) required for normal physiological functions (including regulation of cell volume and solute concentration, maintenance of cellular architecture, and synthesis of essential macromolecules). Its efficient functioning depends on the maintenance of an electrochemical gradient and is tightly coupled to the energetic demands of the cell and/or tissue. Commitment to and completion of the cell division cycle are sensitive to changes in the availability of mitochondrially derived ATP, although the relationship between cell cycle and mitochondrial physiology is poorly understood. Using vital, mitochondrial-specific fluorochromes to differentiate between mitochondrial mass (10-N-nonyl acridine orange) and mitochondrial membrane potential (Rhodamine123), together with a quantification of total cellular ATP levels, it was possible to generate profiles of these mitochondrial characteristics in HL-60 cells at different stages of their cell cycle. The data suggest that the availability of ATP changes in a cell cycle-specific manner and cannot be predicted by changes in mitochondrial mass or membrane potential. Furthermore, transition points in the cell cycle where ATP availability is low with respect to the amount of functional inner mitochondrial membrane have been observed. We suggest that these cell cycle phase transitions are sensitive to inhibition of mitochondrial activity because the basal levels of available ATP at these points are nearer to a theoretical “minimal threshold” below which cell cycle progression is inhibited. J. Cell. Physiol. 180:91–96, 1999. © 1999 Wiley-Liss, Inc.     

Cellular aspects of the distinct M protein and SfbI anchoring pathways in Streptococcus pyogenes

Wall-anchored surface proteins are critical for the in vivo survival of Streptococcus pyogenes. Cues in the signal sequence direct the membrane translocation of surface proteins: M protein to the septum, and SfbI to the poles. Both proteins are subsequently anchored to the wall by the membrane bound enzyme sortase A. However, the cellular features of these pathways are not fully understood. Here we show that M protein and SfbI are anchored simultaneously throughout the cell cycle. M protein is rapidly anchored at the septum, and in part of the cell cycle, is anchored simultaneously at the mother and daughter septa. Conversely, SfbI accumulates gradually on peripheral peptidoglycan, resulting in a polar distribution. Sortase is not required for translocation of M protein or SfbI at their respective locations. Methicillin-induced unbalanced peptidoglycan synthesis diminishes surface M protein but not SfbI. Furthermore, overexpression of the division regulator DivIVA also diminishes surface M protein but increases SfbI. These results demonstrate a close connection between the regulation of cell division and protein anchoring. Better understanding of the spatial regulation of surface anchoring may lead to the identification of novel targets for the development of anti-infective agents, given the importance of surface molecules for pathogenesis.     

Cell Cycle Control by a Minimal Cdk Network

In present-day eukaryotes, the cell division cycle is controlled by a complex network of interacting proteins, including members of the cyclin and cyclin-dependent protein kinase (Cdk) families, and the Anaphase Promoting Complex (APC). Successful progression through the cell cycle depends on precise, temporally ordered regulation of the functions of these proteins. In light of this complexity, it is surprising that in fission yeast, a minimal Cdk network consisting of a single cyclin-Cdk fusion protein can control DNA synthesis and mitosis in a manner that is indistinguishable from wild type. To improve our understanding of the cell cycle regulatory network, we built and analysed a mathematical model of the molecular interactions controlling the G1/S and G2/M transitions in these minimal cells. The model accounts for all observed properties of yeast strains operating with the fusion protein. Importantly, coupling the model’s predictions with experimental analysis of alternative minimal cells, we uncover an explanation for the unexpected fact that elimination of inhibitory phosphorylation of Cdk is benign in these strains while it strongly affects normal cells. Furthermore, in the strain without inhibitory phosphorylation of the fusion protein, the distribution of cell size at division is unusually broad, an observation that is accounted for by stochastic simulations of the model. Our approach provides novel insights into the organization and quantitative regulation of wild type cell cycle progression. In particular, it leads us to propose a new mechanistic model for the phenomenon of mitotic catastrophe, relying on a combination of unregulated, multi-cyclin-dependent Cdk activities.     

Cell membranes after malignant transformation. Part I: Dynamic stability at low surface tension

A hydrodynamic cell model is introduced to analyze the dynamic stability of the cell membrane after malignant transformation. The cell membrane is considered as a two-dimensional charged interface between intra- and extra-cellular fluids. Employing a first order stability analysis, conditions are established under which growth of surface fluctuations can occur (leading to microvilli formation or cell division). The system is unstable if the total surface tension, i.e. the pure surface tension plus the free energy of formation of the double layers, is negative. Following that criterion, cell division is promoted in cancer cells; moreover, as cancer cells are more fluid than normal cells, they will divide more rapidly. The model also predicts that microvilli (protrusions of the cell membrane) will have a diameter of the order of the dominant wavelengths of perturbation (0.1 - 1 mu) which supports the view that such protrusions are consequences of amplified cell surface fluctuations.     

Cell surface changes and Rous sarcoma virus gene expression in synchronized cells

We have investigated whether cell surface changes associated with growth control and malignant transformation are linked to the cell cycle. Chicken embryo cells synchronized by double thymidine block were examined for cell-cycle-dependent alterations in membrane function (measured by transport of 2-deoxyglucose, uridine, thymidine, and mannitol), in cell surface morphology (examined by scanning electron microscopy), and in the ability of tumor virus gene expression to induce a transformation-specific change in membrane function. We reach the following conclusions: (a) The high rate of 2-deoxyglucose transport seen in transformed cells and the low rates of 2-deoxyglucose and uridine transport characteristic of density-inhibited cells do not occur in normal growing cells as they traverse the cell cycle. (b) Although there are cell cycle-dependent changes in surface morphology, they are not reflected in corresponding changes in membrane function. (c) Tumor virus gene expression can alter cell membrane function at any stage in the cell cycle and without progression through the cell cycle.     

PLK1 与妇科肿瘤的研究进展

人类肿瘤生成过程由很多复杂环节组成,其主要现象表现为细胞分裂增殖的失调控生长。细胞分裂都必须按照正常细胞程序的每一个步骤进行才能保证机体的正常运转,细胞周期依赖分子PLK1是调节正常细胞有丝分裂、胞质分裂,以及对DNA受损伤后进行一系列反应调节的重要因子。它在细胞周期中的作用已有多位学者共同认识,当细胞失调控时检测到PLK1存在过量的表达,同时大量研究表明,人类PLK1基因不仅在多种已发现的恶性肿瘤中有此现象,而且在一些肿瘤中,它关系到这些肿瘤的发生发展及预后,被认为其可能成为一种新的肿瘤标志物,还可作为肿瘤定向分子靶向治疗中的一个有效目的基因的靶点,并且近年来对PLK1在肿瘤基因蛋白靶向治疗方面的药物研究开发已经成为学者研究的一个热点方向,该文对近年来PLK1在肿瘤生成中的作用,特别是其与妇科肿瘤关系方面的一些研究进展予以以下阐述。     

Influence of temperature on cell membranes and cell cycles of mammals

Within the membrane model of cell division regulation the following effects are considered: (1) cell accumulation in the S-phase of the cycle at a temporary increase of the temperature; (2) cells coming out of the rest state into proliferation as temperature increases.Some mechanisms are suggested explaining selective death of transformed cells under hyperthermia and the change of lipid composition in membranes under a long-period cell cultivation at a non-optimal temperature.     

Meiotic weakness: the first division

Cell division is probably the most dramatic event in the life of a cell : the entire genetic material has to be equally distributed into the two daughter cells. Segregation errors have severe consequences and lead to either cell death or the generation of aneuploid cells and may cause the formation of tumors or tumor promoting mutations in somatic cells. In meiosis, they provoke the generation of aneuploid embryos and/or spontaneous abortions. Trisomies in humans, such as trisomy 21, are due to the missegregation of one chromosome in the first meiotic division in the oocyte. This review deals with the molecular mechanisms regulating the two meiotic divisions required for the generation of female haploid germ cells. Here we focus mainly on spindle assembly, and cell cycle regulation especially during the first meiotic division in mouse oocytes (excellent reviews have been written on the peculiar aspects of cell cycle regulation in meiosis II, such as the CSF arrest).     

Random transitions,size control,and inheritance in cell population dynamics

A general model of cell population dynamics is derived and analyzed. The model uses the continuous structure variables age and size, and thus distinguishes individual cells with respect to such properties as cycle length and division size. The model allows the occurrence of random transitions as cells progress through the cell cycle, the control of cell size upon cell cycle events, and the inheritance of properties from mother to daughter cells. The concepts of asynchronous exponential growth, α-curves, β-curves, mother-daughter transit time correlations, and sister-sister transit time correlations are formalized. The existence and uniqueness of solutions to the model is proved.     

Normal versus abnormal cell proliferation. A unitary and analytical overview

The most recent findings on the molecular and cellular characterization of normal and abnormal cell proliferation are summarized. They include molecular spectroscopy, nucleic acid conformation, protein modifications, premature chromosome condensation, nucleoli changes, nuclear and cell morphometry, image analysis, flow microfluorimetry, and time-lapse cinematography. Biophysical and biochemical evidence in favor or against two cycles of chromatin condensation, followed by two abrupt random decondensations, per cell cycle are presented. Other biphasic changes at the molecular and cellular levels that favor the existence of two random transitions, or restriction points, per cell cycle are discussed. A comprehensive unitary model of the cell cycle is then outlined; this model is able to explain most findings on continuously dividing cells and on quiescent cells induced to proliferate. Within this analytical framework the physical-chemical and biological properties are given, in either normal or tumor cells, for the various types of "noncycling" cells that are here viewed as necessary steps in mammalian cell growth rather than separates states. The implications of the coupling of higher-order chromatin structure with cell geometry and growth, high in fibroblast-like cells but low in transformed cells, are also discussed. Molecular mechanisms likely responsible for the chromatin conformational changes occurring at the G0 leads to G1, G1 leads to S, G2 leads to M transitions are finally discussed in terms of polyelectrolyte theory.