The Ups and Downs of Modeling the Cell Cycle

Cell identity revealed by precise cell cycle state mapping links data modalities

Several methods for cell cycle inference from sequencing data exist and are widely adopted. In contrast, methods for classification of cell cycle state from imaging data are scarce. We have for the first time integrated sequencing and imaging derived cell cycle pseudo-times for assigning 449 imaged cells to 693 sequenced cells at an average resolution of 3.4 and 2.4 cells for sequencing and imaging data respectively. Data integration revealed thousands of pathways and organelle features that are correlated with each other, including several previously known interactions and novel associations. The ability to assign the transcriptome state of a profiled cell to its closest living relative, which is still actively growing and expanding opens the door for genotype-phenotype mapping at single cell resolution forward in time.

A comprehensive review of computational cell cycle models in guiding cancer treatment strategies

This article reviews the current knowledge and recent advancements in computational modeling of the cell cycle. It offers a comparative analysis of various modeling paradigms, highlighting their unique strengths, limitations, and applications. Specifically, the article compares deterministic and stochastic models, single-cell versus population models, and mechanistic versus abstract models. This detailed analysis helps determine the most suitable modeling framework for various research needs. Additionally, the discussion extends to the utilization of these computational models to illuminate cell cycle dynamics, with a particular focus on cell cycle viability, crosstalk with signaling pathways, tumor microenvironment, DNA replication, and repair mechanisms, underscoring their critical roles in tumor progression and the optimization of cancer therapies. By applying these models to crucial aspects of cancer therapy planning for better outcomes, including drug efficacy quantification, drug discovery, drug resistance analysis, and dose optimization, the review highlights the significant potential of computational insights in enhancing the precision and effectiveness of cancer treatments. This emphasis on the intricate relationship between computational modeling and therapeutic strategy development underscores the pivotal role of advanced modeling techniques in navigating the complexities of cell cycle dynamics and their implications for cancer therapy.

Missing data in amortized simulation-based neural posterior estimation

Amortized simulation-based neural posterior estimation provides a novel machine learning based approach for solving parameter estimation problems. It has been shown to be computationally efficient and able to handle complex models and data sets. Yet, the available approach cannot handle the in experimental studies ubiquitous case of missing data, and might provide incorrect posterior estimates. In this work, we discuss various ways of encoding missing data and integrate them into the training and inference process. We implement the approaches in the BayesFlow methodology, an amortized estimation framework based on invertible neural networks, and evaluate their performance on multiple test problems. We find that an approach in which the data vector is augmented with binary indicators of presence or absence of values performs the most robustly. Indeed, it improved the performance also for the simpler problem of data sets with variable length. Accordingly, we demonstrate that amortized simulation-based inference approaches are applicable even with missing data, and we provide a guideline for their handling, which is relevant for a broad spectrum of applications.

Computational simulation of cellular proliferation using a meshless method

BACKGROUND AND OBJECTIVE

During cell proliferation, cells grow and divide in order to obtain two new genetically identical cells. Understanding this process is crucial to comprehend other biological processes. Computational models and algorithms have emerged to study this process and several examples can be found in the literature. The objective of this work was to develop a new computational model capable of simulating cell proliferation. This model was developed using the Radial Point Interpolation Method, a meshless method that, to the knowledge of the authors, was never used to solve this type of problem. Since the efficiency of the model strongly depends on the efficiency of the meshless method itself, the optimal numbers of integration points per integration cell and of nodes for each influence-domain were investigated. Irregular nodal meshes were also used to study their influence on the algorithm.

METHODS

For the first time, an iterative discrete model solved by the Radial Point Interpolation Method based on the Galerkin weak form was used to establish the system of equations from the reaction-diffusion integro-differential equations, following a new phenomenological law proposed by the authors that describes the growth of a cell over time while dependant on oxygen and glucose availability. The discretization flexibility of the meshless method allows to explicitly follow the geometric changes of the cell until the division phase.

RESULTS

It was found that an integration scheme of 6 × 6 per integration cell and influence-domains with only seven nodes allows to predict the cellular growth and division with the best balance between the relative error and the computing cost. Also, it was observed that using irregular meshes do not influence the solution.

CONCLUSIONS

Even in a preliminary phase, the obtained results are promising, indicating that the algorithm might be a potential tool to study cell proliferation since it can predict cellular growth and division. Moreover, the Radial Point Interpolation Method seems to be a suitable method to study this type of process, even when irregular meshes are used. However, to optimize the algorithm, the integration scheme and the number of nodes inside the influence-domains must be considered.

Modeling Progression of Single Cell Populations Through the Cell Cycle as a Sequence of Switches

Cell cycle is a biological process underlying the existence and propagation of life in time and space. It has been an object for mathematical modeling for long, with several alternative mechanistic modeling principles suggested, describing in more or less details the known molecular mechanisms. Recently, cell cycle has been investigated at single cell level in snapshots of unsynchronized cell populations, exploiting the new methods for transcriptomic and proteomic molecular profiling. This raises a need for simplified semi-phenomenological cell cycle models, in order to formalize the processes underlying the cell cycle, at a higher abstracted level. Here we suggest a modeling framework, recapitulating the most important properties of the cell cycle as a limit trajectory of a dynamical process characterized by several internal states with switches between them. In the simplest form, this leads to a limit cycle trajectory, composed by linear segments in logarithmic coordinates describing some extensive (depending on system size) cell properties. We prove a theorem connecting the effective embedding dimensionality of the cell cycle trajectory with the number of its linear segments. We also develop a simplified kinetic model with piecewise-constant kinetic rates describing the dynamics of lumps of genes involved in S-phase and G2/M phases. We show how the developed cell cycle models can be applied to analyze the available single cell datasets and simulate certain properties of the observed cell cycle trajectories. Based on our model, we can predict with good accuracy the cell line doubling time from the length of cell cycle trajectory.

Characterizing and inferring quantitative cell cycle phase in single-cell RNA-seq data analysis

Cellular heterogeneity in gene expression is driven by cellular processes, such as cell cycle and cell-type identity, and cellular environment such as spatial location. The cell cycle, in particular, is thought to be a key driver of cell-to-cell heterogeneity in gene expression, even in otherwise homogeneous cell populations. Recent advances in single-cell RNA-sequencing (scRNA-seq) facilitate detailed characterization of gene expression heterogeneity and can thus shed new light on the processes driving heterogeneity. Here, we combined fluorescence imaging with scRNA-seq to measure cell cycle phase and gene expression levels in human induced pluripotent stem cells (iPSCs). By using these data, we developed a novel approach to characterize cell cycle progression. Although standard methods assign cells to discrete cell cycle stages, our method goes beyond this and quantifies cell cycle progression on a continuum. We found that, on average, scRNA-seq data from only five genes predicted a cell's position on the cell cycle continuum to within 14% of the entire cycle and that using more genes did not improve this accuracy. Our data and predictor of cell cycle phase can directly help future studies to account for cell cycle-related heterogeneity in iPSCs. Our results and methods also provide a foundation for future work to characterize the effects of the cell cycle on expression heterogeneity in other cell types.

Incoherent Inputs Enhance the Robustness of Biological Oscillators

Robust biological oscillators retain the critical ability to function in the presence of environmental perturbations. Although central architectures that support robust oscillations have been extensively studied, networks containing the same core vary drastically in their potential to oscillate, and it remains elusive what peripheral modifications to the core contribute to this functional variation. Here, we have generated a complete atlas of two- and three-node oscillators computationally, then systematically analyzed the association between network structure and robustness. We found that, while certain core topologies are essential for producing a robust oscillator, local structures can substantially modulate the robustness of oscillations. Notably, local nodes receiving incoherent or coherent inputs respectively promote or attenuate the overall network robustness in an additive manner. We validated these relationships in larger-scale networks reflective of real biological oscillators. Our findings provide an explanation for why auxiliary structures not required for oscillation are evolutionarily conserved and suggest simple ways to evolve or design robust oscillators.

Parameter estimation in models of biological oscillators: an automated regularised estimation approach

BACKGROUND

Dynamic modelling is a core element in the systems biology approach to understanding complex biosystems. Here, we consider the problem of parameter estimation in models of biological oscillators described by deterministic nonlinear differential equations. These problems can be extremely challenging due to several common pitfalls: (i) a lack of prior knowledge about parameters (i.e. massive search spaces), (ii) convergence to local optima (due to multimodality of the cost function), (iii) overfitting (fitting the noise instead of the signal) and (iv) a lack of identifiability. As a consequence, the use of standard estimation methods (such as gradient-based local ones) will often result in wrong solutions. Overfitting can be particularly problematic, since it produces very good calibrations, giving the impression of an excellent result. However, overfitted models exhibit poor predictive power. Here, we present a novel automated approach to overcome these pitfalls. Its workflow makes use of two sequential optimisation steps incorporating three key algorithms: (1) sampling strategies to systematically tighten the parameter bounds reducing the search space, (2) efficient global optimisation to avoid convergence to local solutions, (3) an advanced regularisation technique to fight overfitting. In addition, this workflow incorporates tests for structural and practical identifiability.

RESULTS

We successfully evaluate this novel approach considering four difficult case studies regarding the calibration of well-known biological oscillators (Goodwin, FitzHugh-Nagumo, Repressilator and a metabolic oscillator). In contrast, we show how local gradient-based approaches, even if used in multi-start fashion, are unable to avoid the above-mentioned pitfalls.

CONCLUSIONS

Our approach results in more efficient estimations (thanks to the bounding strategy) which are able to escape convergence to local optima (thanks to the global optimisation approach). Further, the use of regularisation allows us to avoid overfitting, resulting in more generalisable calibrated models (i.e. models with greater predictive power).

Dynamics and control of the ERK signaling pathway: Sensitivity, bistability, and oscillations

Cell signaling is the process by which extracellular information is transmitted into the cell to perform useful biological functions. The ERK (extracellular-signal-regulated kinase) signaling controls several cellular processes such as cell growth, proliferation, differentiation and apoptosis. The ERK signaling pathway considered in this work starts with an extracellular stimulus and ends with activated (double phosphorylated) ERK which gets translocated into the nucleus. We model and analyze this complex pathway by decomposing it into three functional subsystems. The first subsystem spans the initial part of the pathway from the extracellular growth factor to the formation of the SOS complex, ShC-Grb2-SOS. The second subsystem includes the activation of Ras which is mediated by the SOS complex. This is followed by the MAPK subsystem (or the Raf-MEK-ERK pathway) which produces the double phosphorylated ERK upon being activated by Ras. Although separate models exist in the literature at the subsystems level, a comprehensive model for the complete system including the important regulatory feedback loops is missing. Our dynamic model combines the existing subsystem models and studies their steady-state and dynamic interactions under feedback. We establish conditions under which bistability and oscillations exist for this important pathway. In particular, we show how the negative and positive feedback loops affect the dynamic characteristics that determine the cellular outcome.

Systems Level Modeling of the Cell Cycle Using Budding Yeast

Proteins involved in the regulation of the cell cycle are highly conserved across all eukaryotes, and so a relatively simple eukaryote such as yeast can provide insight into a variety of cell cycle perturbations including those that occur in human cancer. To date, the budding yeast Saccharomyces cerevisiae has provided the largest amount of experimental and modeling data on the progression of the cell cycle, making it a logical choice for in-depth studies of this process. Moreover, the advent of methods for collection of high-throughput genome, transcriptome, and proteome data has provided a means to collect and precisely quantify simultaneous cell cycle gene transcript and protein levels, permitting modeling of the cell cycle on the systems level. With the appropriate mathematical framework and sufficient and accurate data on cell cycle components, it should be possible to create a model of the cell cycle that not only effectively describes its operation, but can also predict responses to perturbations such as variation in protein levels and responses to external stimuli including targeted inhibition by drugs. In this review, we summarize existing data on the yeast cell cycle, proteomics technologies for quantifying cell cycle proteins, and the mathematical frameworks that can integrate this data into representative and effective models. Systems level modeling of the cell cycle will require the integration of high-quality data with the appropriate mathematical framework, which can currently be attained through the combination of dynamic modeling based on proteomics data and using yeast as a model organism.

Adder and a coarse-grained approach to cell size homeostasis in bacteria

Cell size control and homeostasis is a long-standing subject in biology. Recent experimental work provides extensive evidence for a simple, quantitative size homeostasis principle coined adder (as opposed to sizer or timer). The adder principle provides unexpected insights into how bacteria maintain their size without employing a feedback mechanism. We review the genesis of adder and recent cell size homeostasis study on evolutionarily divergent bacterial organisms and beyond. We propose new coarse-grained approaches to understand the underlying mechanisms of cell size control at the whole cell level.

Computational strategies for a system-level understanding of metabolism

Cell metabolism is the biochemical machinery that provides energy and building blocks to sustain life. Understanding its fine regulation is of pivotal relevance in several fields, from metabolic engineering applications to the treatment of metabolic disorders and cancer. Sophisticated computational approaches are needed to unravel the complexity of metabolism. To this aim, a plethora of methods have been developed, yet it is generally hard to identify which computational strategy is most suited for the investigation of a specific aspect of metabolism. This review provides an up-to-date description of the computational methods available for the analysis of metabolic pathways, discussing their main advantages and drawbacks. In particular, attention is devoted to the identification of the appropriate scale and level of accuracy in the reconstruction of metabolic networks, and to the inference of model structure and parameters, especially when dealing with a shortage of experimental measurements. The choice of the proper computational methods to derive in silico data is then addressed, including topological analyses, constraint-based modeling and simulation of the system dynamics. A description of some computational approaches to gain new biological knowledge or to formulate hypotheses is finally provided.

A data-driven, mathematical model of mammalian cell cycle regulation

Few of >150 published cell cycle modeling efforts use significant levels of data for tuning and validation. This reflects the difficultly to generate correlated quantitative data, and it points out a critical uncertainty in modeling efforts. To develop a data-driven model of cell cycle regulation, we used contiguous, dynamic measurements over two time scales (minutes and hours) calculated from static multiparametric cytometry data. The approach provided expression profiles of cyclin A2, cyclin B1, and phospho-S10-histone H3. The model was built by integrating and modifying two previously published models such that the model outputs for cyclins A and B fit cyclin expression measurements and the activation of B cyclin/Cdk1 coincided with phosphorylation of histone H3. The model depends on Cdh1-regulated cyclin degradation during G1, regulation of B cyclin/Cdk1 activity by cyclin A/Cdk via Wee1, and transcriptional control of the mitotic cyclins that reflects some of the current literature. We introduced autocatalytic transcription of E2F, E2F regulated transcription of cyclin B, Cdc20/Cdh1 mediated E2F degradation, enhanced transcription of mitotic cyclins during late S/early G2 phase, and the sustained synthesis of cyclin B during mitosis. These features produced a model with good correlation between state variable output and real measurements. Since the method of data generation is extensible, this model can be continually modified based on new correlated, quantitative data.

Introductory review of computational cell cycle modeling

Recent advances in the modeling of the cell cycle through computer simulation demonstrate the power of systems biology. By definition, systems biology has the goal to connect a parts list, prioritized through experimental observation or high-throughput screens, by the topology of interactions defining intracellular networks to predict system function. Computer modeling of biological systems is often compared to a process of reverse engineering. Indeed, designed or engineered technical systems share many systems-level properties with biological systems; thus studying biological systems within an engineering framework has proven successful. Here we review some aspects of this process as it pertains to cell cycle modeling.

Dynamics of the cell-cycle network under genome-rewiring perturbations

The cell-cycle progression is regulated by a specific network enabling its ordered dynamics. Recent experiments supported by computational models have shown that a core of genes ensures this robust cycle dynamics. However, much less is known about the direct interaction of the cell-cycle regulators with genes outside of the cell-cycle network, in particular those of the metabolic system. Following our recent experimental work, we present here a model focusing on the dynamics of the cell-cycle core network under rewiring perturbations. Rewiring is achieved by placing an essential metabolic gene exclusively under the regulation of a cell-cycle's promoter, forcing the cell-cycle network to function under a multitasking challenging condition; operating in parallel the cell-cycle progression and a metabolic essential gene. Our model relies on simple rate equations that capture the dynamics of the relevant protein-DNA and protein-protein interactions, while making a clear distinction between these two different types of processes. In particular, we treat the cell-cycle transcription factors as limited 'resources' and focus on the redistribution of resources in the network during its dynamics. This elucidates the sensitivity of its various nodes to rewiring interactions. The basic model produces the correct cycle dynamics for a wide range of parameters. The simplicity of the model enables us to study the interface between the cell-cycle regulation and other cellular processes. Rewiring a promoter of the network to regulate a foreign gene, forces a multitasking regulatory load. The higher the load on the promoter, the longer is the cell-cycle period. Moreover, in agreement with our experimental results, the model shows that different nodes of the network exhibit variable susceptibilities to the rewiring perturbations. Our model suggests that the topology of the cell-cycle core network ensures its plasticity and flexible interface with other cellular processes, without a need for an optimal setting of the kinetic parameters.

Optimization and model reduction in the high dimensional parameter space of a budding yeast cell cycle model

Background

Parameter estimation from experimental data is critical for mathematical modeling of protein regulatory networks. For realistic networks with dozens of species and reactions, parameter estimation is an especially challenging task. In this study, we present an approach for parameter estimation that is effective in fitting a model of the budding yeast cell cycle (comprising 26 nonlinear ordinary differential equations containing 126 rate constants) to the experimentally observed phenotypes (viable or inviable) of 119 genetic strains carrying mutations of cell cycle genes.

Results

Starting from an initial guess of the parameter values, which correctly captures the phenotypes of only 72 genetic strains, our parameter estimation algorithm quickly improves the success rate of the model to 105–111 of the 119 strains. This success rate is comparable to the best values achieved by a skilled modeler manually choosing parameters over many weeks. The algorithm combines two search and optimization strategies. First, we use Latin hypercube sampling to explore a region surrounding the initial guess. From these samples, we choose ∼20 different sets of parameter values that correctly capture wild type viability. These sets form the starting generation of differential evolution that selects new parameter values that perform better in terms of their success rate in capturing phenotypes. In addition to producing highly successful combinations of parameter values, we analyze the results to determine the parameters that are most critical for matching experimental outcomes and the most competitive strains whose correct outcome with a given parameter vector forces numerous other strains to have incorrect outcomes. These “most critical parameters” and “most competitive strains” provide biological insights into the model. Conversely, the “least critical parameters” and “least competitive strains” suggest ways to reduce the computational complexity of the optimization.

Conclusions

Our approach proves to be a useful tool to help systems biologists fit complex dynamical models to large experimental datasets. In the process of fitting the model to the data, the tool identifies suggestive correlations among aspects of the model and the data.

Caveats in modeling a common motif in genetic circuits

From a coarse-grained perspective, the motif of a self-activating species, activating a second species that acts as its own repressor, is widely found in biological systems, in particular in genetic systems with inherent oscillatory behavior. Here we consider a specific realization of this motif as a genetic circuit, termed the bistable frustrated unit, in which genes are described as directly producing proteins. Upon an improved resolution in time, we focus on the effect that inherent time scales on the underlying scale can have on the bifurcation patterns on a coarser scale. Time scales are set by the binding and unbinding rates of the transcription factors to the promoter regions of the genes. Depending on the ratio of these rates to the decay times of both proteins, the appropriate averaging procedure for obtaining a coarse-grained description changes and leads to sets of deterministic equations, which considerably differ in their bifurcation structure. In particular, the desired intermediate range of regular limit cycles fades away when the binding rates of genes are not fast as compared to the decay time of the proteins. Our analysis illustrates that the common topology of the widely found motif alone does not imply universal features in the dynamics.

Robustness analysis of cellular systems using the genetic tug-of-war method

Robustness is one of the principles of design inherent to biological systems. Cellular robustness can be measured as limits of intracellular parameters such as gene expression levels. We have recently developed an experimental approach coined as genetic Tug-Of-War (gTOW), which we used to perform robustness analysis in yeast. Using gTOW, we were able to measure the upper limit of expression of gene targets. In this review, we first elaborate on how the gTOW method compares to current mathematical simulation models prevalently used in the determination of robustness. We then explain the experimental principles underlying gTOW and its associated tools, and we provide concrete examples of robustness analysis using gTOW, i.e. cell cycle and HOG pathway gene expression analysis. Finally, we list a series of Q&As related to the experimental utilization of gTOW and we describe the potential impact of gTOW and its relevance to the understanding of biological systems.

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.

ELECTRONIC SUPPLEMENTARY MATERIAL

The online version of this article (doi:10.1007/s11693-011-9090-7) contains supplementary material, which is available to authorized users.

Synchronization ability of coupled cell-cycle oscillators in changing environments

BACKGROUND

The biochemical oscillator that controls periodic events during the Xenopus embryonic cell cycle is centered on the activity of CDKs, and the cell cycle is driven by a protein circuit that is centered on the cyclin-dependent protein kinase CDK1 and the anaphase-promoting complex (APC). Many studies have been conducted to confirm that the interactions in the cell cycle can produce oscillations and predict behaviors such as synchronization, but much less is known about how the various elaborations and collective behavior of the basic oscillators can affect the robustness of the system. Therefore, in this study, we investigate and model a multi-cell system of the Xenopus embryonic cell cycle oscillators that are coupled through a common complex protein, and then analyze their synchronization ability under four different external stimuli, including a constant input signal, a square-wave periodic signal, a sinusoidal signal and a noise signal.

RESULTS

Through bifurcation analysis and numerical simulations, we obtain synchronization intervals of the sensitive parameters in the individual oscillator and the coupling parameters in the coupled oscillators. Then, we analyze the effects of these parameters on the synchronization period and amplitude, and find interesting phenomena, e.g., there are two synchronization intervals with activation coefficient in the Hill function of the activated CDK1 that activates the Plk1, and different synchronization intervals have distinct influences on the synchronization period and amplitude. To quantify the speediness and robustness of the synchronization, we use two quantities, the synchronization time and the robustness index, to evaluate the synchronization ability. More interestingly, we find that the coupled system has an optimal signal strength that maximizes the synchronization index under different external stimuli. Simulation results also show that the ability and robustness of the synchronization for the square-wave periodic signal of cyclin synthesis is strongest in comparison to the other three different signals.

CONCLUSIONS

These results suggest that the reaction process in which the activated cyclin-CDK1 activates the Plk1 has a very important influence on the synchronization ability of the coupled system, and the square-wave periodic signal of cyclin synthesis is more conducive to the synchronization and robustness of the coupled cell-cycle oscillators. Our study provides insight into the internal mechanisms of the cell cycle system and helps to generate hypotheses for further research.

A Short-Term Advantage for Syngamy in the Origin of Eukaryotic Sex: Effects of Cell Fusion on Cell Cycle Duration and Other Effects Related to the Duration of the Cell Cycle-Relationship between Cell Growth Curve and the Optimal Size of the Species, and Circadian Cell Cycle in Photosynthetic Unicellular Organisms

The origin of sex is becoming a vexatious issue for Evolutionary Biology. Numerous hypotheses have been proposed, based on the genetic effects of sex, on trophic effects or on the formation of cysts and syncytia. Our approach addresses the change in cell cycle duration which would cause cell fusion. Several results are obtained through graphical and mathematical analysis and computer simulations. (1) In poor environments, cell fusion would be an advantageous strategy, as fusion between cells of different size shortens the cycle of the smaller cell (relative to the asexual cycle), and the majority of mergers would occur between cells of different sizes. (2) The easiest-to-evolve regulation of cell proliferation (sexual/asexual) would be by modifying the checkpoints of the cell cycle. (3) A regulation of this kind would have required the existence of the G2 phase, and sex could thus be the cause of the appearance of this phase. Regarding cell cycle, (4) the exponential curve is the only cell growth curve that has no effect on the optimal cell size in unicellular species; (5) the existence of a plateau with no growth at the end of the cell cycle explains the circadian cell cycle observed in unicellular algae.

NONLINEAR DYNAMICS OF CELL CYCLES WITH STOCHASTIC MATHEMATICAL MODELS

Cell cycles are fundamental components of all living organisms and their systematic studies extend our knowledge about the interconnection between regulatory, metabolic, and signaling networks, and therefore open new opportunities for our ultimate efficient control of cellular processes for disease treatments, as well as for a wide variety of biomedical and biotechnological applications. In the study of cell cycles, nonlinear phenomena play a paramount role, in particular in those cases where the cellular dynamics is in the focus of attention. Quantification of this dynamics is a challenging task due to a wide range of parameters that require estimations and the presence of many stochastic effects. Based on the originally deterministic model, in this paper we develop a hierarchy of models that allow us to describe the nonlinear dynamics accounting for special events of cell cycles. First, we develop a model that takes into account fluctuations of relative concentrations of proteins during special events of cell cycles. Such fluctuations are induced by varying rates of relative concentrations of proteins and/or by relative concentrations of proteins themselves. As such fluctuations may be responsible for qualitative changes in the cell, we develop a new model that accounts for the effect of cellular dynamics on the cell cycle. Finally, we analyze numerically nonlinear effects in the cell cycle by constructing phase portraits based on the newly developed model and carry out a parametric sensitivity analysis in order to identify parameters for an efficient cell cycle control. The results of computational experiments demonstrate that the metabolic events in gene regulatory networks can qualitatively influence the dynamics of the cell cycle.

An atlas of gene regulatory networks reveals multiple three-gene mechanisms for interpreting morphogen gradients

Although >450 different topologies can achieve the same multicellular patterning function, they can be grouped into six main classes, which operate using different underlying dynamics.

Alternative designs for the same functions can therefore split into two types: (a) topology alterations that retain the same underlying dynamics and (b) alterations that utilize a completely different underlying dynamical mechanism.

This segregation of networks into distinct dynamical mechanisms can be revealed by the shape of the topology atlas itself.

Cell–cell communication is not usually part of the causal mechanism underlying a band-pass response during morphogen interpretation, but it can tune the result or increase robustness.

Understanding how gene regulatory networks (GRNs) achieve particular biological functions is a central question in systems biology. Systems biology promises to go beyond a case-by-case understanding of individual networks to map out the complete design space of mechanistic possibilities that underlie biological functions. Can such maps serve as useful theoretical frameworks in which to explore the general design principles for these functions? Towards addressing these questions, we created the first design space for a morphogen interpretation function.

In order to generate a design space for such a function, we enumerated all possible wiring designs of GRNs consisting of three genes and tested their ability to perform one particular morphogen interpretation function; stripe formation, as it represents a simplified form of the much studied French flag problem and is a commonly found gene expression pattern (Figure 1A). We found that only 5% of GRNs had the ability to generate a single stripe of gene expression when simulated with a fixed morphogen input in a one-dimensional model.

We hypothesized that the core mechanisms for producing the stripe of gene expression should be represented by topologies that contain only the necessary and sufficient gene–gene interactions for that function. Hence, we utilized the notions of complexity and neighborhood to generate a complexity atlas. GRNs of such an atlas (represented by nodes) are considered neighbors if they differ by a single gene–gene interaction (neighboring GRN nodes are connected by edges). Such a metagraph (graph of graphs) can then be reorganized using complexity (number of gene–gene interactions) to determine a GRNs position in the y axis, whereas GRNs are spaced in the x axis with the aim of reducing edge crossing (Figure 5A). This reorganization reveals a striking structure, where ‘stalactites' of complexity can be seen protruding from the bottom of the atlas. Each of these stalactites converges on a single ‘core' topology that by extensive analysis we find represents a distinct mechanism.

The mechanisms employ a diverse range of distinct space–time behaviors, and the underlying core topologies display design features such as modularity and feed-forward. We mapped the mechanisms to the complexity atlas by analyzing how each particular GRN of the atlas was working. The GRNs functioning via the different mechanisms are highlighted by the different colors in Figure 5A. Mechanisms thus occupy large regions of separated topology space, suggesting them to be discrete. Analyzing transitions between mechanisms through parameter space confirms this to be the case.

We find that three of the mechanisms are employed in real patterning systems, including both blastoderm patterning in Drosophila and mesoderm specification in Xenopus (Figure 5B). The remaining three mechanisms are thus candidates for employment in other patterning systems. We explored the performance features of these mechanisms, which suggest that some have features such as robustness to parameter variation that make them highly likely to be employed in particular patterning contexts.

Only one of the six-core mechanisms absolutely requires cell–cell communication for functionality, prompting us to predict that cell–cell communication will rarely be responsible for the basic dose response of morphogen interpretation networks. However, we show how cell–cell communication has an important role in robust stripe generation in the face of a noisy morphogen input and in fine tuning the quantitative details of stripe patterning.

In summary, the complexity atlas approach is an amendable approach to any system with a clear genotype–function relationship. We demonstrate how certain functions such as morphogen interpretation may have a range of potential solutions in contrast to previous studies that analyzed more constrained functions. Furthermore, we demonstrate how such an approach can be utilized to define a ‘design space' for a given biological function that describes the different mechanistic possibilities and how they relate to one another (Figure 5). Such a design space can be used practically as a guide to discern which patterning mechanisms are likely be at work in a particular context throwing up less intuitive possibilities with powerful performance features.

The interpretation of morphogen gradients is a pivotal concept in developmental biology, and several mechanisms have been proposed to explain how gene regulatory networks (GRNs) achieve concentration-dependent responses. However, the number of different mechanisms that may exist for cells to interpret morphogens, and the importance of design features such as feedback or local cell–cell communication, is unclear. A complete understanding of such systems will require going beyond a case-by-case analysis of real morphogen interpretation mechanisms and mapping out a complete GRN ‘design space.' Here, we generate a first atlas of design space for GRNs capable of patterning a homogeneous field of cells into discrete gene expression domains by interpreting a fixed morphogen gradient. We uncover multiple very distinct mechanisms distributed discretely across the atlas, thereby expanding the repertoire of morphogen interpretation network motifs. Analyzing this diverse collection of mechanisms also allows us to predict that local cell–cell communication will rarely be responsible for the basic dose-dependent response of morphogen interpretation networks.

A general framework for modeling growth and division of mammalian cells

BACKGROUND

Modeling the cell-division cycle has been practiced for many years. As time has progressed, this work has gone from understanding the basic principles to addressing distinct biological problems, e.g., the nature of the restriction point, how checkpoints operate, the nonlinear dynamics of the cell cycle, the effect of localization, etc. Most models consist of coupled ordinary differential equations developed by the researchers, restricted to deal with the interactions of a limited number of molecules. In the future, cell-cycle modeling--and indeed all modeling of complex biologic processes--will increase in scope and detail.

RESULTS

A framework for modeling complex cell-biologic processes is proposed here. The framework is based on two constructs: one describing the entire lifecycle of a molecule and the second describing the basic cellular machinery. Use of these constructs allows complex models to be built in a straightforward manner that fosters rigor and completeness. To demonstrate the framework, an example model of the mammalian cell cycle is presented that consists of several hundred differential equations of simple mass action kinetics. The model calculates energy usage, amino acid and nucleotide usage, membrane transport, RNA synthesis and destruction, and protein synthesis and destruction for 33 proteins to give an in-depth look at the cell cycle.

CONCLUSIONS

The framework presented here addresses how to develop increasingly descriptive models of complex cell-biologic processes. The example model of cellular growth and division constructed with the framework demonstrates that large structured models can be created with the framework, and these models can generate non-trivial descriptions of cellular processes. Predictions from the example model include those at both the molecular level--e.g., Wee1 spontaneously reactivates--and at the system level--e.g., pathways for timing-critical processes must shut down redundant pathways. A future effort is to automatically estimate parameter values that are insensitive to changes.

Modeling oscillatory control in NF-κB, p53 and Wnt signaling

Oscillations are commonly observed in cellular behavior and span a wide range of timescales, from seconds in calcium signaling to 24 hours in circadian rhythms. In between lie oscillations with time periods of 1-5 hours seen in NF-κB, p53 and Wnt signaling, which play key roles in the immune system, cell growth/death and embryo development, respectively. In the first part of this article, we provide a brief overview of simple deterministic models of oscillations. In particular, we explain the mechanism of saturated degradation that has been used to model oscillations in the NF-κB, p53 and Wnt systems. The second part deals with the potential physiological role of oscillations. We use the simple models described earlier to explore whether oscillatory signals can encode more information than steady-state signals. We then discuss a few simple genetic circuits that could decode information stored in the average, amplitude or frequency of oscillations. The presence of frequency-detector circuit downstream of NF-κB or p53 would be a strong clue that oscillations are important for the physiological response of these signaling systems.

Stabilizing patterning in the Drosophila segment polarity network by selecting models in silico

The segmentation of Drosophila is a prime model to study spatial patterning during embryogenesis. The spatial expression of segment polarity genes results from a complex network of interacting proteins whose expression products are maintained after successful segmentation. This prompted us to investigate the stability and robustness of this process using a dynamical model for the segmentation network based on Boolean states. The model consists of intra-cellular as well as inter-cellular interactions between adjacent cells in one spatial dimension. We quantify the robustness of the dynamical segmentation process by a systematic analysis of mutations. Our starting point consists in a previous Boolean model for Drosophila segmentation. We define mathematically the notion of dynamical robustness and show that the proposed model exhibits limited robustness in gene expression under perturbations. We applied in silico evolution (mutation and selection) and discover two classes of modified gene networks that have a more robust spatial expression pattern. We verified that the enhanced robustness of the two new models is maintained in differential equations models. By comparing the predicted model with experiments on mutated flies, we then discuss the two types of enhanced models. Drosophila patterning can be explained by modelling the underlying network of interacting genes. Here we demonstrate that simple dynamical considerations and in silico evolution can enhance the model to robustly express the expected pattern, helping to elucidate the role of further interactions.

Fragilities caused by dosage imbalance in regulation of the budding yeast cell cycle

Cells can maintain their functions despite fluctuations in intracellular parameters, such as protein activities and gene expression levels. This commonly observed biological property of cells is called robustness. On the other hand, these parameters have different limitations, each reflecting the property of the subsystem containing the parameter. The budding yeast cell cycle is quite fragile upon overexpression of CDC14, but is robust upon overexpression of ESP1. The gene products of both CDC14 and ESP1 are regulated by 1∶1 binding with their inhibitors (Net1 and Pds1), and a mathematical model predicts the extreme fragility of the cell cycle upon overexpression of CDC14 and ESP1 caused by dosage imbalance between these genes. However, it has not been experimentally shown that dosage imbalance causes fragility of the cell cycle. In this study, we measured the quantitative genetic interactions of these genes by performing combinatorial “genetic tug-of-war” experiments. We first showed experimental evidence that dosage imbalance between CDC14 and NET1 causes fragility. We also showed that fragility arising from dosage imbalance between ESP1 and PDS1 is masked by CDH1 and CLB2. The masking function of CLB2 was stabilization of Pds1 by its phosphorylation. We finally modified Chen's model according to our findings. We thus propose that dosage imbalance causes fragility in biological systems.

Normal cell functioning is dependent on balance between protein interactions and gene regulations. Although the balance is often perturbed by environmental changes, mutations, and noise in biochemical reactions, cellular systems can maintain their function despite these perturbations. This property of cells, called robustness, is now considered to be a design principle of biological systems and has become a central theme for systems biology. We previously developed an experimental method designated “genetic tug-of-war,” in which we assessed the robustness of cellular systems upon overexpression of certain genes, especially that of the budding yeast cell cycle. Although the yeast cell cycle can be maintained despite significant overexpression of most genes within the system, the cell cycle halts upon just two-fold overexpression of M phase phosphatase CDC14. In this study, we experimentally showed that this fragility is caused by dosage imbalance between CDC14 and NET1. Interestingly, fragility of regulation of separase gene ESP1, potentially caused by dosage imbalance, was masked by regulation of other factors such as CDH1 and CLB2. We thus propose that dosage imbalance causes fragility in biological systems.

A quantitative systems view of the spindle assembly checkpoint

The idle assembly checkpoint acts to delay chromosome segregation until all duplicated sister chromatids are captured by the mitotic spindle. This pathway ensures that each daughter cell receives a complete copy of the genome. The high fidelity and robustness of this process have made it a subject of intense study in both the experimental and computational realms. A significant number of checkpoint proteins have been identified but how they orchestrate the communication between local spindle attachment and global cytoplasmic signalling to delay segregation is not yet understood. Here, we propose a systems view of the spindle assembly checkpoint to focus attention on the key regulators of the dynamics of this pathway. These regulators in turn have been the subject of detailed cellular measurements and computational modelling to connect molecular function to the dynamics of spindle assembly checkpoint signalling. A review of these efforts reveals the insights provided by such approaches and underscores the need for further interdisciplinary studies to reveal in full the quantitative underpinnings of this cellular control pathway.

Systems biology of the cell cycle of Saccharomyces cerevisiae: From network mining to system-level properties

Following a brief description of the operational procedures of systems biology (SB), the cell cycle of budding yeast is discussed as a successful example of a top-down SB analysis. After the reconstruction of the steps that have led to the identification of a sizer plus timer network in the G1 to S transition, it is shown that basic functions of the cell cycle (the setting of the critical cell size and the accuracy of DNA replication) are system-level properties, detected only by integrating molecular analysis with modelling and simulation of their underlying networks. A detailed network structure of a second relevant regulatory step of the cell cycle, the exit from mitosis, derived from extensive data mining, is constructed and discussed. To reach a quantitative understanding of how nutrients control, through signalling, metabolism and transcription, cell growth and cycle is a very relevant aim of SB. Since we know that about 900 gene products are required for cell cycle execution and control in budding yeast, it is quite clear that a purely systematic approach would require too much time. Therefore lines for a modular SB approach, which prioritises molecular and computational investigations for faster cell cycle understanding, are proposed. The relevance of the insight coming from the cell cycle SB studies in developing a new framework for tackling very complex biological processes, such as cancer and aging, is discussed.

Computational systems biology of the cell cycle

One of the early success stories of computational systems biology was the work done on cell-cycle regulation. The earliest mathematical descriptions of cell-cycle control evolved into very complex, detailed computational models that describe the regulation of cell division in many different cell types. On the way these models predicted several dynamical properties and unknown components of the system that were later experimentally verified/identified. Still, research on this field is far from over. We need to understand how the core cell-cycle machinery is controlled by internal and external signals, also in yeast cells and in the more complex regulatory networks of higher eukaryotes. Furthermore, there are many computational challenges what we face as new types of data appear thanks to continuing advances in experimental techniques. We have to deal with cell-to-cell variations, revealed by single cell measurements, as well as the tremendous amount of data flowing from high throughput machines. We need new computational concepts and tools to handle these data and develop more detailed, more precise models of cell-cycle regulation in various organisms. Here we review past and present of computational modeling of cell-cycle regulation, and discuss possible future directions of the field.

Modeling spatial and temporal dynamics of chemotactic networks

When stimulated by chemoattractants, eukaryotic cells respond through a combination of temporal and spatial dynamics. These responses come about because of the interaction of a large number of signaling components. The complexity of these systems makes it hard to understand without a means of systematically generating and testing hypotheses. Computer simulations have proved to be useful in testing conceptual models. Here we outline the steps required to develop these models.

Search for steady states of piecewise-linear differential equation models of genetic regulatory networks

Analysis of the attractors of a genetic regulatory network gives a good indication of the possible functional modes of the system. In this paper we are concerned with the problem of finding all steady states of genetic regulatory networks described by piecewise-linear differential equation (PLDE) models. We show that the problem is NP-hard and translate it into a propositional satisfiability (SAT) problem. This allows the use of existing, efficient SAT solvers and has enabled the development of a steady state search module of the computer tool Genetic Network Analyzer (GNA). The practical use of this module is demonstrated by means of the analysis of a number of relatively small bacterial regulatory networks as well as randomly generated networks of several hundreds of genes.

Deactivation of Src family kinases: hypothesis testing using a Monte Carlo sensitivity analysis of systems-level properties

Src family tyrosine kinases play a key role in many cellular signalling networks, but due to the high complexity of these networks their precise function remains elusive. Many factors involved in Src regulation, such as specific kinases and phosphatases, are still unknown. Mathematical models have been constructed to improve the understanding of the system and its dynamic behavior. Using a computational random parameter search, we characterized and compared the dynamics of three alternative models in order to assess their likelihoods. For this, we investigated how systems-level properties such as bistability and excitable behavior relate to kinetic and physiological parameters and how robust these properties were. Our results suggest the existence of a putative negative feedback loop in the Src system. A previously suggested role for PTPalpha in the deactivation of Src was not supported by the model.

Systems biology by the rules: hybrid intelligent systems for pathway modeling and discovery

BACKGROUND

Expert knowledge in journal articles is an important source of data for reconstructing biological pathways and creating new hypotheses. An important need for medical research is to integrate this data with high throughput sources to build useful models that span several scales. Researchers traditionally use mental models of pathways to integrate information and development new hypotheses. Unfortunately, the amount of information is often overwhelming and these are inadequate for predicting the dynamic response of complex pathways. Hierarchical computational models that allow exploration of semi-quantitative dynamics are useful systems biology tools for theoreticians, experimentalists and clinicians and may provide a means for cross-communication.

RESULTS

A novel approach for biological pathway modeling based on hybrid intelligent systems or soft computing technologies is presented here. Intelligent hybrid systems, which refers to several related computing methods such as fuzzy logic, neural nets, genetic algorithms, and statistical analysis, has become ubiquitous in engineering applications for complex control system modeling and design. Biological pathways may be considered to be complex control systems, which medicine tries to manipulate to achieve desired results. Thus, hybrid intelligent systems may provide a useful tool for modeling biological system dynamics and computational exploration of new drug targets. A new modeling approach based on these methods is presented in the context of hedgehog regulation of the cell cycle in granule cells. Code and input files can be found at the Bionet website: www.chip.ord/~wbosl/Software/Bionet.

CONCLUSION

This paper presents the algorithmic methods needed for modeling complicated biochemical dynamics using rule-based models to represent expert knowledge in the context of cell cycle regulation and tumor growth. A notable feature of this modeling approach is that it allows biologists to build complex models from their knowledge base without the need to translate that knowledge into mathematical form. Dynamics on several levels, from molecular pathways to tissue growth, are seamlessly integrated. A number of common network motifs are examined and used to build a model of hedgehog regulation of the cell cycle in cerebellar neurons, which is believed to play a key role in the etiology of medulloblastoma, a devastating childhood brain cancer.

A mechanosensory system controls cell shape changes during mitosis

Essential life processes are heavily controlled by a variety of positive and negative feedback systems. Cytokinesis failure, ultimately leading to aneuploidy, is appreciated as an early step in tumor formation in mammals and is deleterious for all cells. Further, the growing list of cancer predisposition mutations includes a number of genes whose proteins control mitosis and/or cytokinesis. Cytokinesis shape control is also an important part of pattern formation and cell-type specialization during multi-cellular development. Inherently mechanical, we hypothesized that mechanosensing and mechanical feedback are fundamental for cytokinesis shape regulation. Using mechanical perturbation, we identified a mechanosensory control system that monitors shape progression during cytokinesis. In this review, we summarize these findings and their implications for cytokinesis regulation and for understanding the cytoskeletal system architecture that governs shape control.

Whole-cell modeling framework in which biochemical dynamics impact aspects of cellular geometry

A mathematical framework for modeling biological cells from a physicochemical perspective is described. Cells modeled within this framework consist of at least two regions, including a cytosolic volume encapsulated by a membrane surface. The cytosol is viewed as a well-stirred chemical reactor capable of changing volume while the membrane is assumed to be an oriented 2-D surface capable of changing surface area. Two physical properties of the cell, namely volume and surface area, are determined by (and determine) the reaction dynamics generated from a set of chemical reactions designed to be occurring in the cell. This framework allows the modeling of complex cellular behaviors, including self-replication. This capability is illustrated by constructing two self-replicating prototypical whole-cell models. One protocell was designed to be of minimal complexity; the other to incorporate a previously reported well-known mechanism of the eukaryotic cell cycle. In both cases, self-replicative behavior was achieved by seeking stable physically possible oscillations in concentrations and surface-to-volume ratio, and by synchronizing the period of such oscillations to the doubling of cytosolic volume and membrane surface area. Rather than being enforced externally or artificially, growth and division occur naturally as a consequence of the assumed chemical mechanism operating within the framework.

The role of modelling in identifying drug targets for diseases of the cell cycle

The cell cycle is implicated in diseases that are the leading cause of mortality and morbidity in the developed world. Until recently, the search for drug targets has focused on relatively small parts of the regulatory network under the assumption that key events can be controlled by targeting single pathways. This is valid provided the impact of couplings to the wider scale context of the network can be ignored. The resulting depth of study has revealed many new insights; however, these have been won at the expense of breadth and a proper understanding of the consequences of links between the different parts of the network. Since it is now becoming clear that these early assumptions may not hold and successful treatments are likely to employ drugs that simultaneously target a number of different sites in the regulatory network, it is timely to redress this imbalance. However, the substantial increase in complexity presents new challenges and necessitates parallel theoretical and experimental approaches. We review the current status of theoretical models for the cell cycle in light of these new challenges. Many of the existing approaches are not sufficiently comprehensive to simultaneously incorporate the required extent of couplings. Where more appropriate levels of complexity are incorporated, the models are difficult to link directly to currently available data. Further progress requires a better integration of experiment and theory. New kinds of data are required that are quantitative, have a higher temporal resolution and that allow simultaneous quantitative comparison of the concentration of larger numbers of different proteins. More comprehensive models are required and must accommodate not only substantial uncertainties in the structure and kinetic parameters of the networks, but also high levels of ignorance. The most recent results relating network complexity to robustness of the dynamics provide clues that suggest progress is possible.

Few crucial links assure checkpoint efficiency in the yeast cell-cycle network

MOTIVATION

The ability of cells to complete mitosis with high fidelity relies on elaborate checkpoint mechanisms. We study S- and M-phase checkpoint responses in silico in the budding yeast with a stochastic dynamical model for the cell-cycle. We aim to provide an unbiased functional classification of network interactions that reflect the contribution of each link to checkpoint efficiency in the presence of cellular fluctuations.

RESULTS

We developed an algorithm BNetDyn to compute stochastic dynamical trajectories for an input gene network and its structural perturbations. User specified output measures like the mutual information between trigger and output nodes are then evaluated on the stationary state of the Markov process. Systematic perturbations of the yeast cell-cycle model by Li et al. classify each link according to its effect on checkpoint efficiencies and stabilities of the main cell-cycle phases. This points to the crosstalk in the cascades downstream of the SBF/MBF transcription activator complexes as determinant for checkpoint optimality; a finding that consistently reflects recent experiments. Finally our stochastic analysis emphasizes how dynamical stability in the yeast cell-cycle network crucially relies on backward inhibitory circuits next to forward induction.

AVAILABILITY

C++ source code and network models can be downloaded at http://www.vital-it.ch/Software/

Cell cycle: bistability is needed for robust cycling

Xenopus egg extracts have distinct Cdk-active and Cdk-inactive states at intermediate cyclin concentrations, a phenomenon known as bistability. A new study shows that this behavior is important for robust cell cycling.

Dynamical principles of two-component genetic oscillators

Genetic oscillators based on the interaction of a small set of molecular components have been shown to be involved in the regulation of the cell cycle, the circadian rhythms, or the response of several signaling pathways. Uncovering the functional properties of such oscillators then becomes important for the understanding of these cellular processes and for the characterization of fundamental properties of more complex clocks. Here, we show how the dynamics of a minimal two-component oscillator is drastically affected by its genetic implementation. We consider a repressor and activator element combined in a simple logical motif. While activation is always exerted at the transcriptional level, repression is alternatively operating at the transcriptional (Design I) or post-translational (Design II) level. These designs display differences on basic oscillatory features and on their behavior with respect to molecular noise or entrainment by periodic signals. In particular, Design I induces oscillations with large activator amplitudes and arbitrarily small frequencies, and acts as an “integrator” of external stimuli, while Design II shows emergence of oscillations with finite, and less variable, frequencies and smaller amplitudes, and detects better frequency-encoded signals (“resonator”). Similar types of stimulus response are observed in neurons, and thus this work enables us to connect very different biological contexts. These dynamical principles are relevant for the characterization of the physiological roles of simple oscillator motifs, the understanding of core machineries of complex clocks, and the bio-engineering of synthetic oscillatory circuits.

Periodic variations in protein abundances are at the heart of important cellular processes, with common examples being the circadian rhythms or the cell cycle. What is the molecular basis of this behavior? Recent reports showed how simple architectures, based on the interaction of a few molecular components, are capable of inducing oscillatory dynamics. These structures are also of interest for the understanding of complex cellular oscillators, as they appear to be core constituents of them. The authors carefully analyze one of these architectures and uncover how different genetic implementations of such structures strikingly influence its dynamical behavior. They consider two genetic implementations of a repressor and activator element combined in a simple logical motif. While activation is transcriptionally implemented in both cases, repression may act either transcriptionally or post-translationally. These differences in design originate drastic changes in the way oscillations are produced, in the tolerance to molecular noise, or in the circuit response to external stimuli. Similar aspects have been discussed in relation to neural dynamics; therefore this work is able to connect two very different biological scenarios. Thus, simple genetic motifs exploit not only their connectivity pattern but their design to act as information processing units within living cells.

Cell-cycle control of gene expression in budding and fission yeast

Cell-cycle control of transcription seems to be a universal feature of proliferating cells, although relatively little is known about its biological significance and conservation between organisms. The two distantly related yeasts Saccharomyces cerevisiae and Schizosaccharomyces pombe have provided valuable complementary insight into the regulation of periodic transcription as a function of the cell cycle. More recently, genome-wide studies of proliferating cells have identified hundreds of periodically expressed genes and underlying mechanisms of transcriptional control. This review discusses the regulation of three major transcriptional waves, which roughly coincide with three main cell-cycle transitions (initiation of DNA replication, entry into mitosis, and exit from mitosis). I also compare and contrast the transcriptional regulatory networks between the two yeasts and discuss the evolutionary conservation and possible roles for cell cycle-regulated transcription.

Reconstruction of genetic circuits

The complex genetic circuits found in cells are ordinarily studied by analysis of genetic and biochemical perturbations. The inherent modularity of biological components like genes and proteins enables a complementary approach: one can construct and analyse synthetic genetic circuits based on their natural counterparts. Such synthetic circuits can be used as simple in vivo models to explore the relation between the structure and function of a genetic circuit. Here we describe recent progress in this area of synthetic biology, highlighting newly developed genetic components and biological lessons learned from this approach.

Mitotic-Exit Control as an Evolved Complex System

The exit from mitosis is the last critical decision during a cell-division cycle. A complex regulatory system has evolved to evaluate the success of mitotic events and control this decision. Whereas outstanding genetic work in yeast has led to rapid discovery of a large number of interacting genes involved in the control of mitotic exit, it has also become increasingly difficult to comprehend the logic and mechanistic features embedded in the complex molecular network. Our view is that this difficulty stems in part from the attempt to explain mitotic-exit control using concepts from traditional top-down engineering design, and that exciting new results from evolutionary engineering design applied to networks and electronic circuits may lend better insights. We focus on four particularly intriguing features of the mitotic-exit control system and attempt to examine these features from the perspective of evolutionary design and complex system engineering.

How cells coordinate growth and division

Size is a fundamental attribute impacting cellular design, fitness, and function. Size homeostasis requires a doubling of cell mass with each division. In yeast, division is delayed until a critical size has been achieved. In metazoans, cell cycles can be actively coupled to growth, but in certain cell types extracellular signals may independently induce growth and division. Despite a long history of study, the fascinating mechanisms that control cell size have resisted molecular genetic insight. Recently, genetic screens in Drosophila and functional genomics approaches in yeast have macheted into the thicket of cell size control.