4,324 research outputs found
Concentration fluctuations in growing and dividing cells:Insights into the emergence of concentration homeostasis
Intracellular reaction rates depend on concentrations and hence their levels are often regulated. However classical models of stochastic gene expression lack a cell size description and cannot be used to predict noise in concentrations. Here, we construct a model of gene product dynamics that includes a description of cell growth, cell division, size-dependent gene expression, gene dosage compensation, and size control mechanisms that can vary with the cell cycle phase. We obtain expressions for the approximate distributions and power spectra of concentration fluctuations which lead to insight into the emergence of concentration homeostasis. We find that (i) the conditions necessary to suppress cell division-induced concentration oscillations are difficult to achieve; (ii) mRNA concentration and number distributions can have different number of modes; (iii) two-layer size control strategies such as sizer-timer or adder-timer are ideal because they maintain constant mean concentrations whilst minimising concentration noise; (iv) accurate concentration homeostasis requires a fine tuning of dosage compensation, replication timing, and size-dependent gene expression; (v) deviations from perfect concentration homeostasis show up as deviations of the concentration distribution from a gamma distribution. Some of these predictions are confirmed using data for E. coli, fission yeast, and budding yeast
Parallel Load Balancing Strategies for Ensembles of Stochastic Biochemical Simulations
The evolution of biochemical systems where some chemical species are present with only a small number of molecules, is strongly influenced by discrete and stochastic effects that cannot be accurately captured by continuous and deterministic models. The budding yeast cell cycle provides an excellent example of the need to account for stochastic effects in biochemical reactions. To obtain statistics of the cell cycle progression, a stochastic simulation algorithm must be run thousands of times with different initial conditions and parameter values. In order to manage the computational expense involved, the large ensemble of runs needs to be executed in parallel. The CPU time for each individual task is unknown before execution, so a simple strategy of assigning an equal number of tasks per processor can lead to considerable work imbalances and loss of parallel efficiency. Moreover, deterministic analysis approaches are ill suited for assessing the effectiveness of load balancing algorithms in this context. Biological models often require stochastic simulation. Since generating an ensemble of simulation results is computationally intensive, it is important to make efficient use of computer resources. This paper presents a new probabilistic framework to analyze the performance of dynamic load balancing algorithms when applied to large ensembles of stochastic biochemical simulations. Two particular load balancing strategies (point-to-point and all-redistribution) are discussed in detail. Simulation results with a stochastic budding yeast cell cycle model confirm the theoretical analysis. While this work is motivated by cell cycle modeling, the proposed analysis framework is general and can be directly applied to any ensemble simulation of biological systems where many tasks are mapped onto each processor, and where the individual compute times vary considerably among tasks
Bifurcation analysis of a model of the budding yeast cell cycle
We study the bifurcations of a set of nine nonlinear ordinary differential
equations that describe the regulation of the cyclin-dependent kinase that
triggers DNA synthesis and mitosis in the budding yeast, Saccharomyces
cerevisiae. We show that Clb2-dependent kinase exhibits bistability (stable
steady states of high or low kinase activity). The transition from low to high
Clb2-dependent kinase activity is driven by transient activation of
Cln2-dependent kinase, and the reverse transition is driven by transient
activation of the Clb2 degradation machinery. We show that a four-variable
model retains the main features of the nine-variable model. In a three-variable
model exhibiting birhythmicity (two stable oscillatory states), we explore
possible effects of extrinsic fluctuations on cell cycle progression.Comment: 31 pages,13 figure
Boolean network model predicts cell cycle sequence of fission yeast
A Boolean network model of the cell-cycle regulatory network of fission yeast
(Schizosaccharomyces Pombe) is constructed solely on the basis of the known
biochemical interaction topology. Simulating the model in the computer,
faithfully reproduces the known sequence of regulatory activity patterns along
the cell cycle of the living cell. Contrary to existing differential equation
models, no parameters enter the model except the structure of the regulatory
circuitry. The dynamical properties of the model indicate that the biological
dynamical sequence is robustly implemented in the regulatory network, with the
biological stationary state G1 corresponding to the dominant attractor in state
space, and with the biological regulatory sequence being a strongly attractive
trajectory. Comparing the fission yeast cell-cycle model to a similar model of
the corresponding network in S. cerevisiae, a remarkable difference in
circuitry, as well as dynamics is observed. While the latter operates in a
strongly damped mode, driven by external excitation, the S. pombe network
represents an auto-excited system with external damping.Comment: 10 pages, 3 figure
Modelling Cell Cycle using Different Levels of Representation
Understanding the behaviour of biological systems requires a complex setting
of in vitro and in vivo experiments, which attracts high costs in terms of time
and resources. The use of mathematical models allows researchers to perform
computerised simulations of biological systems, which are called in silico
experiments, to attain important insights and predictions about the system
behaviour with a considerably lower cost. Computer visualisation is an
important part of this approach, since it provides a realistic representation
of the system behaviour. We define a formal methodology to model biological
systems using different levels of representation: a purely formal
representation, which we call molecular level, models the biochemical dynamics
of the system; visualisation-oriented representations, which we call visual
levels, provide views of the biological system at a higher level of
organisation and are equipped with the necessary spatial information to
generate the appropriate visualisation. We choose Spatial CLS, a formal
language belonging to the class of Calculi of Looping Sequences, as the
formalism for modelling all representation levels. We illustrate our approach
using the budding yeast cell cycle as a case study
Cell-size maintenance: universal strategy revealed
How cells maintain a stable size has fascinated scientists since the
beginning of modern biology, but has remained largely mysterious. Recently,
however, the ability to analyze single bacteria in real time has provided new,
important quantitative insights into this long-standing question in cell
biology
A Framework to Analyze the Performance of Load Balancing Schemes for Ensembles of Stochastic Simulations
Ensembles of simulations are employed to estimate the statistics of possible future states of a system, and are widely used in important applications such as climate change and biological modeling. Ensembles of runs can naturally be executed in parallel. However, when the CPU times of individual simulations vary considerably, a simple strategy of assigning an equal number of tasks per processor can lead to serious work imbalances and low parallel efficiency. This paper presents a new probabilistic framework to analyze the performance of dynamic load balancing algorithms for ensembles of simulations where many tasks are mapped onto each processor, and where the individual compute times vary considerably among tasks. Four load balancing strategies are discussed: most-dividing, all-redistribution, random-polling, and neighbor-redistribution. Simulation results with a stochastic budding yeast cell cycle model is consistent with the theoretical analysis. It is especially significant that there is a provable global decrease in load imbalance for the local rebalancing algorithms due to scalability concerns for the global rebalancing algorithms. The overall simulation time is reduced by up to 25%, and the total processor idle time by 85%
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