Identifying prognostic structural features in tissue sections of colon cancer patients using point pattern analysis.

Diagnosis and prognosis of cancer are informed by the architecture inherent in cancer patient tissue sections. This architecture is typically identified by pathologists, yet advances in computational image analysis facilitate quantitative assessment of this structure. In this article, we develop a spatial point process approach to describe patterns in cell distribution within tissue samples taken from colorectal cancer (CRC) patients. In particular, our approach is centered on the Palm intensity function. This leads to taking an approximate-likelihood technique in fitting point processes models. We consider two Neyman-Scott point processes and a void process, fitting these point process models to the CRC patient data. We find that the parameter estimates of these models may be used to quantify the spatial arrangement of cells. Importantly, we observe characteristic differences in the spatial arrangement of cells between patients who died from CRC and those alive at follow up.

A signaling visualization toolkit to support rational design of combination therapies and biomarker discovery: SiViT.

Targeted cancer therapy aims to disrupt aberrant cellular signalling pathways. Biomarkers are surrogates of pathway state, but there is limited success in translating candidate biomarkers to clinical practice due to the intrinsic complexity of pathway networks. Systems biology approaches afford better understanding of complex, dynamical interactions in signalling pathways targeted by anticancer drugs. However, adoption of dynamical modelling by clinicians and biologists is impeded by model inaccessibility. Drawing on computer games technology, we present a novel visualization toolkit, SiViT, that converts systems biology models of cancer cell signalling into interactive simulations that can be used without specialist computational expertise. SiViT allows clinicians and biologists to directly introduce for example loss of function mutations and specific inhibitors. SiViT animates the effects of these introductions on pathway dynamics, suggesting further experiments and assessing candidate biomarker effectiveness. In a systems biology model of Her2 signalling we experimentally validated predictions using SiViT, revealing the dynamics of biomarkers of drug resistance and highlighting the role of pathway crosstalk. No model is ever complete: the iteration of real data and simulation facilitates continued evolution of more accurate, useful models. SiViT will make accessible libraries of models to support preclinical research, combinatorial strategy design and biomarker discovery.

NRF2 Regulates HER1 Signaling Pathway to Modulate the Sensitivity of Ovarian Cancer Cells to Lapatinib and Erlotinib.

NF-E2-related factor 2 (NRF2) regulates the transcription of a battery of metabolic and cytoprotective genes. NRF2 and epidermal growth factor receptors (EGFRs/HERs) are regulators of cellular proliferation and determinants of cancer initiation and progression. NRF2 and HERs confer cancers with resistance to several therapeutic agents. Nevertheless, there is limited understanding of the regulation of HER expression and activation and the link between NRF2 and HER signalling pathways. We show that NRF2 regulates both basal and inducible expression of HER1, as treatment of ovarian cancer cells (PEO1, OVCAR3, and SKOV3) with NRF2 activator tBHQ inducing HER1, while inhibition of NRF2 by siRNA knockdown or with retinoid represses HER1. Furthermore, treatment of cells with tBHQ increased total and phosphorylated NRF2, HER1, and AKT levels and compromised the cytotoxic effect of lapatinib or erlotinib. Treatment with siRNA or retinoid antagonised the effect of tBHQ on NRF2 and HER1 levels and enhanced the sensitivity of ovarian cancer cells to lapatinib or erlotinib. Pharmacological or genetic inhibition of NRF2 and/or treatment with lapatinib or erlotinib elevated cellular ROS and depleted glutathione. This extends the understanding of NRF2 and its regulation of HER family receptors and opens a strategic target for improving cancer therapy.

Kinetic modelling of in vitro data of PI3K, mTOR1, PTEN enzymes and on-target inhibitors Rapamycin, BEZ235, and LY294002.

The phosphatidylinositide 3-kinases (PI3K) and mammalian target of rapamycin-1 (mTOR1) are two key targets for anti-cancer therapy. Predicting the response of the PI3K/AKT/mTOR1 signalling pathway to targeted therapy is made difficult because of network complexities. Systems biology models can help explore those complexities but the value of such models is dependent on accurate parameterisation. Motivated by a need to increase accuracy in kinetic parameter estimation, and therefore the predictive power of the model, we present a framework to integrate kinetic data from enzyme assays into a unified enzyme kinetic model. We present exemplar kinetic models of PI3K and mTOR1, calibrated on in vitro enzyme data and founded on Michaelis-Menten (MM) approximation. We describe the effects of an allosteric mTOR1 inhibitor (Rapamycin) and ATP-competitive inhibitors (BEZ235 and LY294002) that show dual inhibition of mTOR1 and PI3K. We also model the kinetics of phosphatase and tensin homolog (PTEN), which modulates sensitivity of the PI3K/AKT/mTOR1 pathway to these drugs. Model validation with independent data sets allows investigation of enzyme function and drug dose dependencies in a wide range of experimental conditions. Modelling of the mTOR1 kinetics showed that Rapamycin has an IC50 independent of ATP concentration and that it is a selective inhibitor of mTOR1 substrates S6K1 and 4EBP1: it retains 40% of mTOR1 activity relative to 4EBP1 phosphorylation and inhibits completely S6K1 activity. For the dual ATP-competitive inhibitors of mTOR1 and PI3K, LY294002 and BEZ235, we derived the dependence of the IC50 on ATP concentration that allows prediction of the IC50 at different ATP concentrations in enzyme and cellular assays. Comparison of drug effectiveness in enzyme and cellular assays showed that some features of these drugs arise from signalling modulation beyond the on-target action and MM approximation and require a systems-level consideration of the whole PI3K/PTEN/AKT/mTOR1 network in order to understand mechanisms of drug sensitivity and resistance in different cancer cell lines. We suggest that using these models in a systems biology investigation of the PI3K/AKT/mTOR1 signalling in cancer cells can bridge the gap between direct drug target action and the therapeutic response to these drugs and their combinations.

A novel mechanism of action of HER2 targeted immunotherapy is explained by inhibition of NRF2 function in ovarian cancer cells.

Nuclear erythroid related factor-2 (NRF2) is known to promote cancer therapeutic detoxification and crosstalk with growth promoting pathways. HER2 receptor tyrosine kinase is frequently overexpressed in cancers leading to uncontrolled receptor activation and signaling. A combination of HER2 targeting monoclonal antibodies shows greater anticancer efficacy than the single targeting antibodies, however, its mechanism of action is largely unclear. Here we report novel actions of anti-HER2 drugs, Trastuzumab and Pertuzumab, involving NRF2.HER2 targeting by antibodies inhibited growth in association with persistent generation of reactive oxygen species (ROS), glutathione (GSH) depletion, reduction in NRF2 levels and inhibition of NRF2 function in ovarian cancer cell lines. The combination of antibodies produced more potent effects than single antibody alone; downregulated NRF2 substrates by repressing the Antioxidant Response (AR) pathway with concomitant transcriptional inhibition of NRF2. We showed the antibody combination produced increased methylation at the NRF2 promoter consistent with repression of NRF2 antioxidant function, as HDAC and methylation inhibitors reversed such produced transcriptional effects. These findings demonstrate a novel mechanism and role for NRF2 in mediating the response of cancer cells to the combination of Trastuzumab and Pertuzumab and reinforce the importance of NRF2 in drug resistance and as a key anticancer target.

NRF2 Regulates HER2 and HER3 Signaling Pathway to Modulate Sensitivity to Targeted Immunotherapies.

NF-E2 related factor-2 (NRF2) is an essential transcription factor for multiple genes encoding antioxidants and detoxification enzymes. NRF2 is implicated in promoting cancer therapeutic resistance by its detoxification function and crosstalk with proproliferative pathways. However, the exact mechanism of this intricate connectivity between NRF2 and growth factor induced proliferative pathway remains elusive. Here, we have demonstrated that pharmacological activation of NRF2 by tert-butylhydroquinone (tBHQ) upregulates the HER family receptors, HER2 and HER3 expression, elevates pAKT levels, and enhances the proliferation of ovarian cancer cells. Preactivation of NRF2 also attenuates the combined growth inhibitory effects of HER2 targeting monoclonal antibodies, Pertuzumab and Trastuzumab. Further, tBHQ caused transcriptional induction of HER2 and HER3, while SiRNA-mediated knockdown of NRF2 prevented this and further caused transcriptional repression and enhanced cytotoxicity of the HER2 inhibitors. Hence, NRF2 regulates both HER2 and HER3 receptors to influence cellular responses to HER2 targeting monoclonal antibodies. This deciphered crosstalk mechanism reinforces the role of NRF2 in drug resistance and as a relevant anticancer target.

Quantitative analysis of NRF2 pathway reveals key elements of the regulatory circuits underlying antioxidant response and proliferation of ovarian cancer cells.

Cells are constantly exposed to Reactive Oxygen Species (ROS) produced both endogenously to meet physiological requirements and from exogenous sources. While endogenous ROS are considered as important signalling molecules, high uncontrollable ROS are detrimental. It is unclear how cells can achieve a balance between maintaining physiological redox homeostasis and robustly activate the antioxidant system to remove exogenous ROS. We have utilised a Systems Biology approach to understand how this robust adaptive system fulfils homeostatic requirements of maintaining steady-state ROS and growth rate, while undergoing rapid readjustment under challenged conditions. Using a panel of human ovarian and normal cell lines, we experimentally quantified and established interrelationships between key elements of ROS homeostasis. The basal levels of NRF2 and KEAP1 were cell line specific and maintained in tight correlation with their growth rates and ROS. Furthermore, perturbation of this balance triggered cell specific kinetics of NRF2 nuclear-cytoplasmic relocalisation and sequestration of exogenous ROS. Our experimental data were employed to parameterise a mathematical model of the NRF2 pathway that elucidated key response mechanisms of redox regulation and showed that the dynamics of NRF2-H2O2 regulation defines a relationship between half-life, total and nuclear NRF2 level and endogenous H2O2 that is cell line specific.

Systems analysis of drug-induced receptor tyrosine kinase reprogramming following targeted mono- and combination anti-cancer therapy.

The receptor tyrosine kinases (RTKs) are key drivers of cancer progression and targets for drug therapy. A major challenge in anti-RTK treatment is the dependence of drug effectiveness on co-expression of multiple RTKs which defines resistance to single drug therapy. Reprogramming of the RTK network leading to alteration in RTK co-expression in response to drug intervention is a dynamic mechanism of acquired resistance to single drug therapy in many cancers. One route to overcome this resistance is combination therapy. We describe the results of a joint in silico, in vitro, and in vivo investigations on the efficacy of trastuzumab, pertuzumab and their combination to target the HER2 receptors. Computational modelling revealed that these two drugs alone and in combination differentially suppressed RTK network activation depending on RTK co-expression. Analyses of mRNA expression in SKOV3 ovarian tumour xenograft showed up-regulation of HER3 following treatment. Considering this in a computational model revealed that HER3 up-regulation reprograms RTK kinetics from HER2 homodimerisation to HER3/HER2 heterodimerisation. The results showed synergy of the trastuzumab and pertuzumab combination treatment of the HER2 overexpressing tumour can be due to an independence of the combination effect on HER3/HER2 composition when it changes due to drug-induced RTK reprogramming.

Customizing the therapeutic response of signaling networks to promote antitumor responses by drug combinations.

Drug resistance, de novo and acquired, pervades cellular signaling networks (SNs) from one signaling motif to another as a result of cancer progression and/or drug intervention. This resistance is one of the key determinants of efficacy in targeted anti-cancer drug therapy. Although poorly understood, drug resistance is already being addressed in combination therapy by selecting drug targets where SN sensitivity increases due to combination components or as a result of de novo or acquired mutations. Additionally, successive drug combinations have shown low resistance potential. To promote a rational, systematic development of combination therapies, it is necessary to establish the underlying mechanisms that drive the advantages of combination therapies, and design methods to determine drug targets for combination regimens. Based on a joint systems analysis of cellular SN response and its sensitivity to drug action and oncogenic mutations, we describe an in silico method to analyze the targets of drug combinations. Our method explores mechanisms of sensitizing the SN through a combination of two drugs targeting vertical signaling pathways. We propose a paradigm of SN response customization by one drug to both maximize the effect of another drug in combination and promote a robust therapeutic response against oncogenic mutations. The method was applied to customize the response of the ErbB/PI3K/PTEN/AKT pathway by combination of drugs targeting HER2 receptors and proteins in the down-stream pathway. The results of a computational experiment showed that the modification of the SN response from hyperbolic to smooth sigmoid response by manipulation of two drugs in combination leads to greater robustness in therapeutic response against oncogenic mutations determining cancer heterogeneity. The application of this method in drug combination co-development suggests a combined evaluation of inhibition effects together with the capability of drug combinations to suppress resistance mechanisms before they become clinically manifest.

Feedforward and feedback regulation of the MAPK and PI3K oscillatory circuit in breast cancer.

Although the theoretical possibility of oscillations in MAPK signalling has long been described, experimental validation has proven more elusive. In this study we observed oscillations in MAPK and PI3K signalling in breast cancer cells in response to epidermal growth factor receptor-family stimulation. Using systems level analysis with a kinetic model, we demonstrate that receptor amplification, loss of transcriptional feedback, or pathway crosstalk, are responsible for oscillations in MAPK and PI3K signalling. Transcriptional profiling reveals architectural motifs likely to be responsible for feedback control of oscillations. Overexpression of the HER2 oncogene and inhibition of transcriptional feedback increase the amplitude of oscillations and provide experimental validation of the computational findings.

Characterising the tumour morphological response to therapeutic intervention: an ex vivo model.

In cancer, morphological assessment of histological tissue samples is a fundamental part of both diagnosis and prognosis. Image analysis offers opportunities to support that assessment through quantitative metrics of morphology. Generally, morphometric analysis is carried out on two-dimensional tissue section data and so only represents a small fraction of any tumour. We present a novel application of three-dimensional (3D) morphometrics for 3D imaging data obtained from tumours grown in a culture model. Minkowski functionals, a set of measures that characterise geometry and topology in n-dimensional space, are used to quantify tumour topology in the absence of and in response to therapeutic intervention. These measures are used to stratify the morphological response of tumours to therapeutic intervention. Breast tumours are characterised by estrogen receptor (ER) status, human epidermal growth factor receptor (HER)2 status and tumour grade. Previously, we have shown that ER status is associated with tumour volume in response to tamoxifen treatment ex vivo. Here, HER2 status is found to predict the changes in morphology other than volume as a result of tamoxifen treatment ex vivo. Finally, we show the extent to which Minkowski functionals might be used to predict tumour grade. Minkowski functionals are generalisable to any 3D data set, including in vivo and cellular systems. This quantitative topological analysis can provide a valuable link among biomarkers, drug intervention and tumour morphology that is complementary to existing, non-morphological measures of tumour response to intervention and could ultimately inform patient treatment.

Engineering simulations for cancer systems biology.

Computer simulation can be used to inform in vivo and in vitro experimentation, enabling rapid, low-cost hypothesis generation and directing experimental design in order to test those hypotheses. In this way, in silico models become a scientific instrument for investigation, and so should be developed to high standards, be carefully calibrated and their findings presented in such that they may be reproduced. Here, we outline a framework that supports developing simulations as scientific instruments, and we select cancer systems biology as an exemplar domain, with a particular focus on cellular signalling models. We consider the challenges of lack of data, incomplete knowledge and modelling in the context of a rapidly changing knowledge base. Our framework comprises a process to clearly separate scientific and engineering concerns in model and simulation development, and an argumentation approach to documenting models for rigorous way of recording assumptions and knowledge gaps. We propose interactive, dynamic visualisation tools to enable the biological community to interact with cellular signalling models directly for experimental design. There is a mismatch in scale between these cellular models and tissue structures that are affected by tumours, and bridging this gap requires substantial computational resource. We present concurrent programming as a technology to link scales without losing important details through model simplification. We discuss the value of combining this technology, interactive visualisation, argumentation and model separation to support development of multi-scale models that represent biologically plausible cells arranged in biologically plausible structures that model cell behaviour, interactions and response to therapeutic interventions.

Features of the reversible sensitivity-resistance transition in PI3K/PTEN/AKT signalling network after HER2 inhibition.

Systems biology approaches that combine experimental data and theoretical modelling to understand cellular signalling network dynamics offer a useful platform to investigate the mechanisms of resistance to drug interventions and to identify combination drug treatments. Extending our work on modelling the PI3K/PTEN/AKT signalling network (SN), we analyse the sensitivity of the SN output signal, phospho-AKT, to inhibition of HER2 receptor. We model typical aberrations in this SN identified in cancer development and drug resistance: loss of PTEN activity, PI3K and AKT mutations, HER2 overexpression, and overproduction of GSK3ß and CK2 kinases controlling PTEN phosphorylation. We show that HER2 inhibition by the monoclonal antibody pertuzumab increases SN sensitivity, both to external signals and to changes in kinetic parameters of the proteins and their expression levels induced by mutations in the SN. This increase in sensitivity arises from the transition of SN functioning from saturation to non-saturation mode in response to HER2 inhibition. PTEN loss or PIK3CA mutation causes resistance to anti-HER2 inhibitor and leads to the restoration of saturation mode in SN functioning with a consequent decrease in SN sensitivity. We suggest that a drug-induced increase in SN sensitivity to internal perturbations, and specifically mutations, causes SN fragility. In particular, the SN is vulnerable to mutations that compensate for drug action and this may result in a sensitivity-to-resistance transition. The combination of HER2 and PI3K inhibition does not sensitise the SN to internal perturbations (mutations) in the PI3K/PTEN/AKT pathway: this combination treatment provides both synergetic inhibition and may prevent the SN from acquired mutations causing drug resistance. Through combination inhibition treatments, we studied the impact of upstream and downstream interventions to suppress resistance to the HER2 inhibitor in the SN with PTEN loss. Comparison of experimental results of PI3K inhibition in the PTEN upstream pathway with PDK1 inhibition in the PTEN downstream pathway shows that upstream inhibition abrogates resistance to pertuzumab more effectively than downstream inhibition. This difference in inhibition effect arises from the compensatory mechanism of an activation loop induced in the downstream pathway by PTEN loss. We highlight that drug target identification for combination anti-cancer therapy needs to account for the mutation effects on the upstream and downstream pathways.

Compensatory effects in the PI3K/PTEN/AKT signaling network following receptor tyrosine kinase inhibition.

Overcoming de novo and acquired resistance to anticancer drugs that target signaling networks is a formidable challenge for drug design and effective cancer therapy. Understanding the mechanisms by which this resistance arises may offer a route to addressing the insensitivity of signaling networks to drug intervention and restore the efficacy of anticancer therapy. Extending our recent work identifying PTEN as a key regulator of Herceptin sensitivity, we present an integrated theoretical and experimental approach to study the compensatory mechanisms within the PI3K/PTEN/AKT signaling network that afford resistance to receptor tyrosine kinase (RTK) inhibition by anti-HER2 monoclonal antibodies. In a computational model representing the dynamics of the signaling network, we define a single control parameter that encapsulates the balance of activities of the enzymes involved in the PI3K/PTEN/AKT cycle. By varying this control parameter we are able to demonstrate both distinct dynamic regimes of behavior of the signaling network and the transitions between those regimes. We demonstrate resistance, sensitivity, and suppression of RTK signals by the signaling network. Through model analysis we link the sensitivity-to-resistance transition to specific compensatory mechanisms within the signaling network. We study this transition in detail theoretically by variation of activities of PTEN, PI3K, AKT enzymes, and use the results to inform experiments that perturb the signaling network using combinatorial inhibition of RTK, PTEN, and PI3K enzymes in human ovarian carcinoma cell lines. We find good alignment between theoretical predictions and experimental results. We discuss the application of the results to the challenges of hypersensitivity of the signaling network to RTK signals, suppression of drug resistance, and efficacy of drug combinations in anticancer therapy.

Cancer systems biology.

Cancer is a complex and heterogeneous disease, not only at a genetic and biochemical level, but also at a tissue, organism, and population level. Multiple data streams, from reductionist biochemistry in vitro to high-throughput "-omics" from clinical material, have been generated with the hope that they encode useful information about phenotype and, ultimately, tumour behaviour in response to drugs. While these data stand alone in terms of the biology they represent, there is the enticing prospect that if incorporated into systems biology models, they can help understand complex systems behaviour and provide a predictive framework as an additional tool in understanding how tumours change and respond to treatment over time. Since these biological data are heterogeneous and frequently qualitative rather than quantitative, at the present time a single systems biology approach is unlikely to be effective; instead, different computational and mathematical approaches should be tailored to different types of data, and to each other, in order to test and re-test hypotheses. In time, these models might converge and result in usable tractable models which accurately represent human cancer. Likewise, biologists and clinicians need to understand what the requirements of systems biology are so that compatible data are produced for computational modelling. In this review, we describe some theoretical approaches (data-driven and process-driven) and experimental methodologies which are being used in cancer research and the clinical context where they might be applied.

Modelling fungal colonies and communities: challenges and opportunities.

This contribution, based on a Special Interest Group session held during IMC9, focuses on physiological based models of filamentous fungal colony growth and interactions. Fungi are known to be an important component of ecosystems, in terms of colony dynamics and interactions within and between trophic levels. We outline some of the essential components necessary to develop a fungal ecology: a mechanistic model of fungal colony growth and interactions, where observed behaviour can be linked to underlying function; a model of how fungi can cooperate at larger scales; and novel techniques for both exploring quantitatively the scales at which fungi operate; and addressing the computational challenges arising from this highly detailed quantification. We also propose a novel application area for fungi which may provide alternate routes for supporting scientific study of colony behaviour. This synthesis offers new potential to explore fungal community dynamics and the impact on ecosystem functioning.

A novel ataxia-telangiectasia mutated autoregulatory feedback mechanism in murine embryonic stem cells.

Ataxia-telangiectasia mutated (ATM) is known to play a central role in effecting the DNA damage response that protects somatic cells from potentially harmful mutations, and in this role it is a key anti-cancer agent. However, it also promotes repair of therapeutic damage (e.g. radiotherapy) and so frustrates the efficacy of some treatments. A better understanding of the mechanisms of ATM regulation is therefore important both in prevention and treatment of disease. While progress has been made in elucidating the key signal transduction pathways that mediate damage response in somatic cells, relatively little is known about whether these function similarly in pluripotent embryonic stem (ES) cells where ATM is also implicated in our understanding of adult stem cell ageing and in improvements in regenerative medicine. There is some evidence that different mechanisms may operate in ES cells and that our understanding of the mechanisms of ATM regulation is therefore incomplete. We investigated the behaviour of the damage response signalling pathway in mouse ES cells. We subjected the cells to the DNA-damaging agent doxorubicin, a drug that induces double-strand breaks, and measured ATM expression levels. We found that basal ATM gene expression was unaffected by doxorubicin treatment. However, following ATM kinase inhibition using a specific ATM inhibitor, we observed a significant increase in ATM and ataxia-telangiectasia and Rad3 related transcription. We demonstrate the use of a dynamical modelling approach to show that these results cannot be explained in terms of known mechanisms. Furthermore, we show that the modelling approach can be used to identify a novel feedback process that may underlie the anomalies in the data. The predictions of the model are consistent both with our in vitro experiments and with in vivo studies of ATM expression in somatic cells in mice, and we hypothesize that this feedback operates in both somatic and ES cells in vivo. The results point to a possible new target for ATM inhibition that overcomes the restorative potential of the proposed feedback.

Modelling interactions in fungi.

Indeterminate organisms have received comparatively little attention in theoretical ecology and still there is much to be understood about the origins and consequences of community structure. The fungi comprise an entire kingdom of life and epitomize the indeterminate growth form. While interactions play a significant role in shaping the community structure of indeterminate organisms, to date most of our knowledge relating to fungi comes from observing interaction outcomes between two species in two-dimensional arena experiments. Interactions in the natural environment are more complex and further insight will benefit from a closer integration of theory and experiment. This requires a modelling framework capable of linking genotype and environment to community structure and function. Towards this, we present a theoretical model that replicates observed interaction outcomes between fungal colonies. The hypotheses underlying the model propose that interaction outcome is an emergent consequence of simple and highly localized processes governing rates of uptake and remobilization of resources, the metabolic cost of production of antagonistic compounds and non-localized transport of internal resources. The model may be used to study systems of many interacting colonies and so provides a platform upon which the links between individual-scale behaviour and community-scale function in complex environments can be built.

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.

Biomass recycling and the origin of phenotype in fungal mycelia.

Fungi are one of the most important and widespread components of the biosphere, and are essential for the growth of over 90% of all vascular plants. Although they are a separate kingdom of life, we know relatively little about the origins of their ubiquitous existence. This reflects a wider ignorance arising from their status as indeterminate organisms epitomized by extreme phenotypic plasticity that is essential for survival in complex environments. Here we show that the fungal phenotype may have its origins in the defining characteristic of indeterminate organisms, namely their ability to recycle locally immobilized internal resources into a mobilized form capable of being directed to new internal sinks. We show that phenotype can be modelled as an emergent phenomenon resulting from the interplay between simple local processes governing uptake and remobilization of internal resources, and macroscopic processes associated with their transport. Observed complex growth forms are reproduced and the sensitive dependence of phenotype on environmental context may be understood in terms of nonlinearities associated with regulation of the recycling apparatus.