Stability of cyclic gene models for systems involving repression

We ccnsider a Goodwin-type model for cyclic gene systems involving endproduct repression. The model is described by a very general system of functic nal differential equations which include as special cases continuous analogues of cyclic models studied previously via computer simulation by other investigators (Fraser & Tiwari, 1974). We establish global stability of equilibrium solutions with arguments which are valid for any number (odd or even) of genes in the cyclic loop.     

From single cells to tissue architecture—a bottom-up approach to modelling the spatio-temporal organisation of complex multi-cellular systems

Collective phenomena in multi-cellular assemblies can be approached on different levels of complexity. Here, we discuss a number of mathematical models which consider the dynamics of each individual cell, so-called agent-based or individual-based models (IBMs). As a special feature, these models allow to account for intracellular decision processes which are triggered by biomechanical cell-cell or cell-matrix interactions. We discuss their impact on the growth and homeostasis of multi-cellular systems as simulated by lattice-free models. Our results demonstrate that cell polarisation subsequent to cell-cell contact formation can be a source of stability in epithelial monolayers. Stroma contact-dependent regulation of tumour cell proliferation and migration is shown to result in invasion dynamics in accordance with the migrating cancer stem cell hypothesis. However, we demonstrate that different regulation mechanisms can equally well comply with present experimental results. Thus, we suggest a panel of experimental studies for the in-depth validation of the model assumptions.     

Timing of events in mitosis

BACKGROUND: Regulation of the major transitions in the cell cycle, such as G1/S, G2/M, and metaphase to anaphase, are increasingly well understood. However, we have a poor understanding of the timing of events within each phase of the cell cycle, such as S phase or early mitosis. Two extreme models of regulation are possible. A "regulator-controlled model" in which the order of events is governed by the activation of a series of cytoplasmic regulators, such as kinases, phosphatases, or proteases; or a "substrate-controlled model" in which temporal regulation is determined by the differential responses of the cellular machinery to a common set of activators. RESULTS: We have tried to distinguish between these two models by examining the timing of both biochemical and morphological events in Xenopus egg extracts during mitosis. Several proteins respond with different delays to the activation of Cdc2. We have found that the timing of phosphorylation is largely unchanged when these proteins are exposed to extracts that have been in mitosis for various periods of time. Similarly, when Xenopus interphase nuclei are added to extracts at different times after the G2/M transition, they undergo all the expected morphological changes in the proper sequence and with very similar kinetics. CONCLUSIONS: Our results suggest that during early mitosis (from prophase to metaphase) the timing of biochemical events (such as phosphorylation) and morphological events (such as structural changes in the nucleus) is at least partly controlled by the responses of the substrates themselves to a common set of signals.     

Cell cycle dynamics inferred from the static properties of cells in balanced growth

The duration of a morphological phase of the cell cycle is reflected in the steady state distribution of the sizes of cells in that phase. Relationships presented here provide a method for estimating the timing and variability of any cell cycle phase. It is shown that the mean size of cells initiating and finishing any phase can be estimated from (1) the frequency of cells exhibiting the distinguishing morphological or autoradiographic features of the phase; (2) the mean size of cells in the phase; and (3) their coefficient of variation. The calculations are based on a submodel of the Koch-Schaechter Growth Controlled Model which assumes that (i) the distribution of division sizes is Gaussian; (ii) there is no correlation in division sizes between successive generations; and (iii) every cell division gives rise to two daughter cells of equal size. The calculations should be useful for a wider range of models, however, because the extrapolation factors are not sensitive to the chosen model. Criteria are proposed to allow the user to check the method's applicability for any experimental case. The method also provides a more efficient test of the dependence of growth on cell size than does the Collins-Richmond method. This is because the method uses the mean and coefficient of variation of the size of the total population, in conjunction with those of the cells in a final phase of the cell cycle, to test potential growth laws. For Escherichia coli populations studied by electron microscopy, an exponential growth model provided much better agreement than did a linear growth model. The computer simulations were used to generate rules for three types of cell phases: those that end at cell division, those that start at cell division, and those totally contained within a single cell cycle. For the last type, additional criteria are proposed to establish if the phase is well enough contained for the formulae and graphs to be used. The most useful rule emerging from these computer studies is that the fraction of the cell cycle time occupied by a phase is the product of the frequency of the phase and the ratio of the mean size of cells in that phase to the mean size of all cells in the population. A further advantage of the techniques presented here is that they use the 'extant' distributions that were actually measured, and not hypothesized distributions nor the special distributions needed for Collins-Richmond method that can only be calculated from the observed distributions of dividing or newborn cells on the basis of an assumed growth law.     

Operability of Continuous Bioprocesses: Static Behavior of a Large Class of Unstructured Models

The complete static behavior of a large class of unstructured models of continuous bioprocesses is classified using elementary concepts of the singularity theory and continuation techniques. The class consists of models for which the cell growth rate is proportional to the rate of utilization of limiting substrate while the kinetics of cell growth, utilization of limiting substrate and synthesis of the desired non-biomass product are allowed to assume general forms of substrate and product. This class of models was used extensively in the literature to model fermentation processes. Global analytical conditions are derived that allow the construction of a practical picture in the multidimensional parameter space delineating the different static behavior these models can predict, including unique steady states, coexistence of wash-out conditions with non-trivial steady states and multistability resulting from hysteresis. These general results are applied to a number of experimentally validated models of fermentation processes, and allow the study of the effect of kinetic and operating parameters on the stability characteristics of these models. Practical criteria are also derived for the safe operation of the bioprocesses.     

Space-Limited Mitosis in the Glazier–Graner–Hogeweg Model

The Glazier–Graner–Hogeweg (GGH) model is a cellular automata framework for representing the time evolution of cellular systems, appealing because unlike many other individual-cell-based models it dynamically simulates changes in cell shape and size. Proliferation has seen some implementation into this modelling framework, but without consensus in the literature as to how this behaviour is best represented. Additionally, the majority of published GGH model implementations which feature proliferation do so in order to simulate a certain biological situation where mitosis is important, but without analysis of how these proliferation routines operate on a fundamental level. Here, a method of proliferation for the GGH model which uses separate cell phenotypes to differentiate cells which have entered or just left the mitotic phase of the cell cycle is presented and demonstrated to correctly predict logistic growth on a macroscopic scale (in accordance with experimental evidence). Comparisons between model simulations and the generalised logistic growth model provide an interpretation of the latter’s ‘shape parameter’, and the proliferation routine used here is shown to offer the modeller somewhat predictable control over the proliferation rate, important for ensuring temporal consistency between different cellular behaviours in the model. All results are found to be insensitive to the inclusion of active cell motility. The implications of these simulated proliferation assays towards problems in cell biology are also discussed.     

Models for clutch size and sex ratio with sibling interaction

General models are constructed to predict sex ratio and clutch size simultaneously for those organisms in which members of a clutch interact to affect each other's fitness. The same set of underlying factors can be shown to predict both optimal sex ratios and clutch sizes. The presence or absence of these factors enables different life histories or models to be classified. Previous sibling interaction sex ratio and clutch size models are special cases of the general model. The circumstances in which it is wrong to consider clutch size and sex ratio in isolation are identified. A distinction is made between those models that maximise sex ratio or clutch size with respect to a single clutch and those that consider either several clutches or lifetime fitness.     

极光(aurora)激酶在细胞有丝分裂和肿瘤形成中的重要功能

极光激酶（aurora kinases）是负责调控细胞有丝分裂的一类重要的丝氨酸／苏氨酸激酶。在不同的模式生物中,极光激酶各家族成员的结构和功能都高度保守。近年来,随着极光激酶相关研究的不断深入,人们逐渐认识到极光激酶在细胞有丝分裂以及肿瘤形成中的重要功能。在细胞有丝分裂中,极光激酶参与了诸如中心体成熟分离、纺锤体组装和维持、染色体分离以及胞质分裂等多个事件。异常表达的极光激酶往往会导致细胞在有丝分裂的过程中出现大量的异常现象。此外,极光激酶还参与了肿瘤形成的过程,已经发现一些靶向作用于极光的小分子具有显著的抑癌作用。本文围绕哺乳动物的三种极光激酶,重点讨论了它们在细胞有丝分裂中的动态定位、生物学功能以及时空上的调节方式,并分析了异常表达的极光激酶参与肿瘤形成的可能途径,提出了肿瘤治疗的新思路。     

Gene expression regulation at the translational level: contribution of marine organisms

Gene expression regulation is crucial for organism survival. Each step has to be regulated, from the gene to the protein. mRNA can be stored in the cell without any direct translation. This process is used by the cell to control protein synthesis rapidly at the right place, at the right time. Protein synthesis costs a lot of energy for the cell, so that a precise control of this process is required. Translation initiation represents an important step to regulate gene expression. Many factors that can bind mRNA and recruit different partners are involved in the inhibition or stimulation of protein synthesis. Oceans contain an important diversity of organisms that are used as important models to analyse gene expression at the translational level. These are useful to study translational control in different physiological processes for instance cell cycle (meiosis during meiotic maturation of starfish oocytes, mitosis following fertilization of sea urchin eggs) or to understand nervous system mechanisms (aplysia). All these studies will help finding novel actors involved in translational control and will thus be useful to discover new targets for therapeutic treatments against human diseases.     

Genome-wide selection of unique and valid oligonucleotides

Functional genomics methods are used to investigate the huge amount of information contained in genomes. Numerous experimental methods rely on the use of oligo- or polynucleotides. Nucleotide strand hybridization forms the underlying principle for these methods. For all these techniques, the probes should be unique for analyzed genes. In addition to being unique for the studied genes, the probes should fulfill a large number of criteria to be usable and valid. The criteria include for example, avoidance of self-annealing, suitable melting temperature and nucleotide composition. We developed a method for searching unique and valid oligonucleotides or probes for genes so that there is not even a similar (approximate) occurrence in any other location of the whole genome. By using probe size 25, we analyzed 17 complete genomes representing a wide range of both prokaryotic and eukaryotic organisms. More than 92% of all the genes in the investigated genomes contained valid oligonucleotides. Extensive statistical tests were performed to characterize the properties of unique and valid oligonucleotides. Unique and valid oligonucleotides were relatively evenly distributed in genes except for the beginning and end, which were somewhat overrepresented. The flanking regions in eukaryotes were clearly underrepresented among suitable oligonucleotides. In addition to distributions within genes, the effects on codon and amino acid usage were also studied.     

A resource for benchmarking the usefulness of protein structure models

ABSTRACT: BACKGROUND: Increasingly, biologists and biochemists use computational tools to design experiments to probe the function of proteins and/or to engineer them for a variety of different purposes. The most effective strategies rely on the knowledge of the three-dimensional structure of the protein of interest. However it is often the case that an experimental structure is not available and that models of different quality are used instead. On the other hand, the relationship between the quality of a model and its appropriate use is not easy to derive in general, and so far it has been analyzed in detail only for specific application RESULTS: This paper describes a database and related software tools that allow testing of a given structure based methods on models of a protein representing different levels of accuracy. The comparison of the results of a computational experiment on the experimental structure and on a set of its decoy models will allow developers and users to assess which is the specific threshold of accuracy required to perform the task effectively. CONCLUSIONS: The ModelDB server automatically builds decoy models of different accuracy for a given protein of known structure and provides a set of useful tools for their analysis. Pre-computed data for a non-redundant set of deposited protein structures are available for analysis and download in the ModelDB database.     

Neutron-scattering studies of the structure of chromatin core particles in solution

The structure of the nucleosome core particle in solution has been studied by neutron scattering using the full-contrast variation technique, which reduces the experimental spectra to three fundamental scatter functions holding information on shape and structure. Systematic calculations of the fundamental scatter functions expected from proposed core-particle models have been compared with the observed functions and show that the neutron-scattering criteria severely restrict the number of models which can be valid for the structure in solution. The best model for the core particle in solution has a hydrophobic histone core about which 1.7 ± 0.1 turns of DNA are wrapped at a pitch between 3.0 and 3.5 nm. This core contains most of the histone and has an average thickness of 4 nm and diameter 6.4–7.5 nm. While solution scattering is not able to specify uniquely the actual shape of the core to high resolution, all models which are possible for the shape of the core to a resolution justified by the data have been considered. It is clear that cylindrical or wedge shapes compatible with the above dimensions are valid structures. A hole probably penetrates the histone core, but the data do not allow a diameter greater than 1 nm. Available evidence suggests that about a quarter of the total histone is outside the core.     

The General Theory of Mapping Functions for Random Genetic Recombination

The general theory of mapping functions for random genetic recombination is derived without reference to physical models. The results are of particular relevance to asymmetric recombination (preferential recombination of the alleles of either parent) and include the effects of lethal lesions. It is noted that the assumption of randomness determines the mapping functions uniquely so that they are independent of the specifications of any stochastic physical model of recombination. In particular, the functions derived from physical models by Haldane, Wu, Wood and Verhoef and de Haan are special cases of those derived here. A general principle for the testing of genetic linkage is formulated which is valid for both symmetric and asymmetric recombination.     

Cell Growth and Size Homeostasis in Silico

Cell growth in size is a complex process coordinated by intrinsic and environmental signals. In a research work performed by a different group, size distributions of an exponentially growing population of mammalian cells were used to infer cell-growth rate in size. The results suggested that cell growth was neither linear nor exponential, but subject to size-dependent regulation. To explain the observed growth pattern, we built a mathematical model in which growth rate was regulated by the relative amount of mRNA and ribosomes in a cell. Under the growth model and a stochastic division rule, we simulated the evolution of a population of cells. Both the sampled growth rate and size distribution from this in silico population agreed well with experimental data. To explore the model space, alternative growth models and division rules were studied. This work may serve as a starting point to understand the mechanisms behind cell growth and size regulation using predictive models.     

Cell Growth and Size Homeostasis in Silico

Cell growth in size is a complex process coordinated by intrinsic and environmental signals. In a research work performed by a different group, size distributions of an exponentially growing population of mammalian cells were used to infer cell-growth rate in size. The results suggested that cell growth was neither linear nor exponential, but subject to size-dependent regulation. To explain the observed growth pattern, we built a mathematical model in which growth rate was regulated by the relative amount of mRNA and ribosomes in a cell. Under the growth model and a stochastic division rule, we simulated the evolution of a population of cells. Both the sampled growth rate and size distribution from this in silico population agreed well with experimental data. To explore the model space, alternative growth models and division rules were studied. This work may serve as a starting point to understand the mechanisms behind cell growth and size regulation using predictive models.     

Identification of potential regulatory sites of the Na+,K+-ATPase by kinetic analysis

Kinetic models are presented that allow the Na(+),K(+)-ATPase steady-state turnover number to be estimated at given intra- and extracellular concentrations of Na(+), K(+), and ATP. Based on experimental transient kinetic data, the models utilize either three or four steps of the Albers-Post scheme, that is, E(2) --> E(1), E(1) --> E(2)P (or E(1) --> E(1)P and E(1)P --> E(2)P), and E(2)P --> E(2), which are the major rate-determining steps of the enzyme cycle. On the time scale of these reactions, the faster binding steps of Na(+), K(+), and ATP to the enzyme are considered to be in equilibrium. Each model was tested by comparing calculations of the steady-state turnover from rate constants and equilibrium constants for the individual partial reactions with published experimental data of the steady-state activity at varying Na(+) and K(+) concentrations. To provide reasonable agreement between the calculations and the experimental data, it was found that Na(+)/K(+) competition for cytoplasmic binding sites was an essential feature required in the model. The activity was also very dependent on the degree of K(+)-induced stimulation of the reverse reaction E(1) --> E(2). Taking into account the physiological substrate concentrations, the models allow the most likely potential sites of short-term Na(+),K(+)-ATPase regulation to be identified. These were found to be (a) the cytoplasmic Na(+) and K(+) binding sites, via changes in Na(+) or K(+) concentration or their dissociation constants, (b) ATP phosphorylation (as a substrate), via a change in its rate constant, and (c) the position of the E(2)<==>E(1) equilibrium.