Set-back model of division-synchronization: optimal spacing of thermal shocks that accelerate cell cycling.

Monte Carlo simulations have been used to predict the dependence of synchrony on the timing of periodic thermal shocks that synchronize division by cell cycle set-backs. In many of the simulations each set-back augmented the subsequent rate of progression of individual cells through the division cycle. In this study a subtle error in previous synchronization simulations was corrected. The simulations show that whether or not set-backs affect subsequent cell-cycling rates the degree of synchrony attained is acutely dependent on the spacing of thermal shocks administered once per division. Set-back-dependent increases in division-cycling rates usually decrease the difference between maximum and minimum synchrony. According to the simulations the more cell cycle rates between shocks are augmented by set-back the shorter the optimum time span between shocks. Whether or not set-backs affect subsequent division-cycling rates the intershock time span providing maximum synchrony allows cell number to precisely double.     

Butterfly edge effects are predicted by a simple model in a complex landscape

Edge responses have been studied for decades and form a critical component of our understanding of how organisms respond to landscape structure and habitat fragmentation. Until recently, however, the lack of a general, conceptual framework has made it difficult to make sense of the patterns and variability reported in the edge literature. We present a test of an edge effects model which predicts that organisms should avoid edges with less-preferred habitat, show increased abundance near edges with preferred habitat or habitat containing complementary resources, and show no response to edges with similar-quality habitat that offers only supplementary resources. We tested the predictions of this model against observations of the edge responses of 15 butterfly species at 12 different edge types within a complex, desert riparian landscape. Observations matched model predictions more than would be expected by chance for the 211 species/edge combinations tested over 3 years of study. In cases where positive or negative edge responses were predicted, observed responses matched those predictions 70% of the time. While the model tends to underpredict neutral results, it was rare that an observed edge response contradicted that predicted by the model. This study also supported the two primary ecological mechanisms underlying the model, although not equally. We detected a positive relationship between habitat preferences and the slope of the observed edge response, suggesting that this basic life history trait underlies edge effects and influences their magnitude. Empirical evidence also suggested the presence of complementary resources underlies positive edge responses, but only when completely confined to the adjacent habitat. This multi-species test of a general edge effects model at multiple edge types shows that resource-based mechanisms can explain many edge responses and that a modest knowledge of life history attributes and resource availability is sufficient for predicting and understanding many edge responses in complex landscapes. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Asymmetric cell division: plane but not simple

The polarity of sensory bristles on the thorax of Drosophila is linked to the orientation of the asymmetric cell divisions that partition cell fate determinants in this lineage. The orientation of these divisions is under the control of the Frizzled pathway that generates planar polarity in a number of cell types.     

Partial synchronization of cell division in root meristem induced by 5-aminouracil

5-aminouracil induces a partial synchronization of mitoses in barley, onion and garlic root tips. The highest degree of synchronization has been achieved in garlic where the mitotic index reached the value of about 36%, while in onion and barley the values equalled about 20%. The concentration causing the maximal synchronization in barley (400–750 ppm) was many times higher than in garlic (62.5 ppm) and onion (100 ppm). The occurrence of micronuclei was evaluated in garlic, under the conditions when synchronization was maximal. It was increased nearly tenfold as compared with the control.     

The role of lipid and antioxidant exchanges in cell division synchronization (mathematical model)

Cell-cycle synchronization of two diffusecoupled cells has been studied in the framework of the membrane model for the cell division cycle, proposed by Chernavskii et al. (1977). It has been shown semianalytically (using the averaging principle) and by computer stimulation that a) if the duration of theG1-phase (T _G1 ) for two identical cells is comparable with the duration of the remaining cycle (T _S+G2+M ), the lipid (L)-exchange results in a synchronization with phase difference =0. The antioxidant (A)-exchange leads to a phase-locking with =T ₀/2 (whereT ₀ is the cell cycle period; b) ifT _G1 T _S+G2+M (orT _G1 T _S+G2+M ) theL-exchange makes synchronization possible both with =0 and =T ₀/2 while theA-exchange results in phase-locking with confined to the region 0 toT ₀/2; c) for non-identical cells differing in the values of kinetic parameters, the locking band narrows as the population density increases (when some model parameters are close to the bifurcation thresholds). We expect that the cells selected artificially at a definite phase of cycle might maintain the synchronous division for a long time if the lipid exchange between cells were stimulated.     

A simple mechanistic model of sprout spacing in tumour-associated angiogenesis

This paper develops a simple mathematical model of the sitting of capillary sprouts on an existing blood vessel during the initiation of tumour-induced angiogenesis. The model represents an inceptive attempt to address the question of how unchecked sprouting of the parent vessel is avoided at the initiation of angiogenesis, based on the idea that feedback regulation processes play the dominant role. No chemical interaction between the proangiogenic and antiangiogenic factors is assumed. The model is based on corneal pocket experiments, and provides a mathematical analysis of the initial spacing of angiogenic sprouts.     

Effects of asymmetric division on a stochastic model of the cell division cycle

The stochastic model of cell division formulated by Alt and Tyson is generalized to the case of imprecise binary fission. Closed-form expressions are derived for the generation-time distribution, the birth-size and division-size distributions, the beta curve, and the correlation coefficient of generation times of sister cells. The theoretical results are compared to observations of cell division statistics in a culture of fission yeast.     

Effects of directional environmental change on extinction dynamics in experimental microbial communities are predicted by a simple model

Global temperatures are expected to rise between 1.1 and 6.4°C over the next 100 years, although the exact rate will depend on future greenhouse emissions, and will vary spatially. Temperature can alter an individual's metabolic rate, and consequently birth and death rates. In declining populations, these alterations may manifest as changes in the rate of that population's decline, and subsequently the timing of extinction events. Predicting such events could therefore be of considerable use. We use a small‐scale experimental system to investigate how the rate of temperature change can alter a population's time to extinction, and whether it is possible to predict this event using a simple phenomenological model that incorporates information about population dynamics at a constant temperature, published scaling of metabolic rates, and temperature. In addition, we examine 1) the relative importance of the direct effects of temperature on metabolic rate, and the indirect effects (via temperature driven changes in body size), on predictive accuracy (defined as the proximity of the predicted date of extinction to the mean observed date of extinction), 2) the combinations of model parameters that maximise accuracy of predictions, and 3) whether substituting temperature change through time with mean temperature produces accurate predictions. We find that extinction occurs earlier in environments that warm faster, and this can be accurately predicted (R² > 0.84). Increasing the number of parameters that were temperature‐dependent increased the model's accuracy, as did scaling these temperature‐dependent parameters with either the direct effects of temperature alone, or with the direct and indirect effects. Using mean temperature through time instead of actual temperature produces less accurate predictions of extinction. These results suggest that simple phenomenological models, incorporating metabolic theory, may be useful in understanding how environmental change can alter a population's rate of extinction. Synthesis Understanding how populations will respond to future climatic change is a key goal in ecology, however the exact rate of future warming will vary both spatially and temporally. Consequently, mathematical models must be used to understand the potential range of future population dynamics under various warming scenarios. We use a combination of experimentation and modelling to show that the effects of varying rates of environmental change on population dynamics can be predicted by a simple model. However, the accuracy of these predictions depends upon, amongst other things, a detailed knowledge of how temperature will change over time, rather than approximating this change to mean temperature.     

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.     

The criterion of cell division synchronization for assessing the stressor exposure of a Salmonella typhi population

Criterion of the synchronization (CS) of cells division for S. typhi population is proposed. The criterion is based on the assumption of the normal distribution of cells with different generation time in the population after stressor (shock) action. CS is equal to the ratio of the dispersion of the generation time of cells in the population to the average generation time of the whole population and determined from the parameters of the mathematical model. The quantitative values of the parameters of the mathematical model were obtained by the minimization of error between the calculation and experimental data. CS was used for the evaluation and choice of the optimum stressor action in the synchronization of the division of S. typhi.     

Regulation of plant cell wall stiffness by mechanical stress: a mesoscale physical model

Journal of Mathematical Biology - A crucial question in developmental biology is how cell growth is coordinated in living tissue to generate complex and reproducible shapes. We address this issue...     

Drosophila mechanoreceptors as a model for studying asymmetric cell division

Asymmetric cell division (ACD) is one of the processes creating the overall diversity of cell types in multicellular organisms. The essence of this process is that the daughter cells exit from it being different from both the parental cell and one another in their ability to further differentiation and specialization. The large bristles (macrochaetae) that are regularly arranged on the surface of the Drosophila adult function as mechanoreceptors, and since their development requires ACD, they have been extensively used as a model system for studying the genetic control of this process. Each macrochaete is composed of four specialized cells, the progeny resulting from several ACDs from a single sensory organ precursor (SOP) cell, which differentiates from the ectodermal cells of the wing imaginal disc in the third-instar larva and pupa. In this paper we review the experimental data on the genes and their products controlling the ACDs of the SOP cell and its daughter cells, and their further specialization. We discuss the main mechanisms determining the time when the cell enters ACD, as well as the mechanisms providing for the structural characteristics of asymmetric division, namely, polar distribution of protein determinants (Numb and Neuralized), orientation of the division spindle relative to these determinants, and unequal segregation of the determinants specifying the direction of daughter cell development.     

Cell growth and division: a deterministic/probabilistic model of the cell cycle

A model of the cell cycle, incorporating a deterministic cell-size monitor and a probabilistic component, is investigated. Steady-state distributions for cell size and generation time are calculated and shown to be globally asymptotically stable. These distributions are used to calculate various statistical quantities, which are then compared to known experimental data. Finally, the results are compared to distributions calculated from a Monte-Carlo simulation of the model.