Mathematical modeling is a powerful tool for unraveling the complexities of the molecular regulatory networks underlying all aspects of cell physiology. To support this claim, we review our experiences modeling the cyclin-dependent kinase (CDK) network that controls events of the eukaryotic cell cycle. The model was derived from classic experiments on the biochemistry and molecular genetics of CDKs and their partner proteins. Because the dynamical properties of CDK activity depend in large part on positive and negative feedback loops in the regulatory network, it is difficult to predict its behavior by intuitive reasoning alone. Mathematical modeling is the correct tool for reliably determining the properties of the network in comparison with observed properties of dividing cells and for predicting the behavior of the control system under novel conditions. In this review, we describe six unexpected predictions of our 1993 model of the CDK control system in frog egg extracts and the remarkable experiments, performed much later, that verified all six predictions. The dynamical properties of the CDK network are consequences of feedback signals and ultrasensitive responses of regulatory proteins to CDK activity, and we describe the experimental evidence for the predicted ultrasensitivity. This case study illustrates the novel insights that mathematical modeling, analysis, and simulation can provide cell physiologists, and it points the way to a new "dynamical perspective" on molecular cell biology.
By way of surface receptor molecules and internal surveillance mechanisms, the living cell receives information about its external environment and internal state. In light of this information, the cell must determine its most appropriate course of action under the circumstances and initiate the relevant response pathways. Typical responses include growth and division, sexual reproduction, movement, differentiation and programmed cell death. Similar to a digital computer that uses bistable electrical switches to store and process information, the living cell uses bistable biochemical switches to implement its decision-making capabilities. In this review article, we describe some of the lines of thought that led, over the last 50 years, to our current understanding of cellular information processing, particularly related to cell growth, division and death.
Burst-firing in distinct subsets of thalamic relay (TR) neurons is thought to be a key requirement for the propagation of absence seizures. However, in the well-regarded Genetic Absence Epilepsy Rats from Strasbourg (GAERS) model as yet there has been no link described between burst-firing in TR neurons and spike-and-wave discharges (SWDs). GAERS ventrobasal (VB) neurons are a specific subset of TR neurons that do not normally display burst-firing during absence seizures in the GAERS model, and here, we assessed the underlying relationship of VB burst-firing with Ih and T-type calcium currents between GAERS and non-epileptic control (NEC) animals. In response to 200-ms hyperpolarizing current injections, adult epileptic but not pre-epileptic GAERS VB neurons displayed suppressed burst-firing compared to NEC. In response to longer duration 1,000-ms hyperpolarizing current injections, both pre-epileptic and epileptic GAERS VB neurons required significantly more hyperpolarizing current injection to burst-fire than those of NEC animals. The current density of the Hyperpolarization and Cyclic Nucleotide-activated (HCN) current (Ih) was found to be increased in GAERS VB neurons, and the blockade of Ih relieved the suppressed burst-firing in both pre-epileptic P15-P20 and adult animals. In support, levels of HCN-1 and HCN-3 isoform channel proteins were increased in GAERS VB thalamic tissue. T-type calcium channel whole-cell currents were found to be decreased in P7-P9 GAERS VB neurons, and also noted was a decrease in CaV3.1 mRNA and protein levels in adults. Z944, a potent T-type calcium channel blocker with anti-epileptic properties, completely abolished hyperpolarization-induced VB burst-firing in both NEC and GAERS VB neurons.
Building models of molecular regulatory networks is challenging not just because of the intrinsic difficulty of describing complex biological processes. Writing a model is a creative effort that calls for more flexibility and interactive support than offered by many of today's biochemical model editors. Our model editor MSMB - Multistate Model Builder - supports multistate models created using different modeling styles.
In this study, we focus on a recent stochastic budding yeast cell cycle model. First, we estimate the model parameters using extensive data sets: phenotypes of 110 genetic strains, single cell statistics of wild type and cln3 strains. Optimization of stochastic model parameters is achieved by an automated algorithm we recently used for a deterministic cell cycle model. Next, in order to test the predictive ability of the stochastic model, we focus on a recent experimental study in which forced periodic expression of CLN2 cyclin (driven by MET3 promoter in cln3 background) has been used to synchronize budding yeast cell colonies. We demonstrate that the model correctly predicts the experimentally observed synchronization levels and cell cycle statistics of mother and daughter cells under various experimental conditions (numerical data that is not enforced in parameter optimization), in addition to correctly predicting the qualitative changes in size control due to forced CLN2 expression. Our model also generates a novel prediction: under frequent CLN2 expression pulses, G1 phase duration is bimodal among small-born cells. These cells originate from daughters with extended budded periods due to size control during the budded period. This novel prediction and the experimental trends captured by the model illustrate the interplay between cell cycle dynamics, synchronization of cell colonies, and size control in budding yeast.
Endocrine therapy, targeting the oestrogen receptor pathway, is the most common treatment for oestrogen receptor-positive breast cancers. Unfortunately, these tumours frequently develop resistance to endocrine therapies. Among the strategies to treat resistant tumours are sequential treatment (in which second-line drugs are used to gain additional responses) and intermittent treatment (in which a 'drug holiday' is imposed between treatments). To gain a more rigorous understanding of the mechanisms underlying these strategies, we present a mathematical model that captures the transitions among three different, experimentally observed, oestrogen-sensitivity phenotypes in breast cancer (sensitive, hypersensitive and independent). To provide a global view of the transitions between these phenotypes, we compute the potential landscape associated with the model. We show how this oestrogen response landscape can be reshaped by population selection, which is a crucial force in promoting acquired resistance. Techniques from statistical physics are used to create a population-level state-transition model from the cellular-level model. We then illustrate how this population-level model can be used to analyse and optimize sequential and intermittent oestrogen-deprivation protocols for breast cancer. The approach used in this study is general and can also be applied to investigate treatment strategies for other types of cancer.
Although current textbook explanations of cell-cycle control in eukaryotes emphasize the periodic activation of cyclin-dependent protein kinases (CDKs), recent experimental observations suggest a significant role for the periodic activation and inactivation of a CDK-counteracting protein phosphatase 2A with a B55? subunit (PP2A:B55?), during mitotic cycles in frog-egg extracts and early embryos. In this paper, we extend an earlier mathematical model of embryonic cell cycles to include experimentally motivated roles for PP2A:B55? and its regulation by Greatwall kinase. Our model is consistent with what is already known about the regulation of CDK and PP2A:B55? in frog eggs, and it suggests a previously undescribed role for the Greatwall-PP2A:B55? interaction in creating a toggle switch for activation of the anaphase-promoting complex as embryonic cells exit mitosis and return to interphase.
Fifty years of genetic and molecular experiments have revealed a wealth of molecular interactions involved in the control of cell division. In light of the complexity of this control system, mathematical modeling has proved useful in analyzing biochemical hypotheses that can be tested experimentally. Stochastic modeling has been especially useful in understanding the intrinsic variability of cell cycle events, but stochastic modeling has been hampered by a lack of reliable data on the absolute numbers of mRNA molecules per cell for cell cycle control genes. To fill this void, we used fluorescence in situ hybridization (FISH) to collect single molecule mRNA data for 16 cell cycle regulators in budding yeast, Saccharomyces cerevisiae. From statistical distributions of single-cell mRNA counts, we are able to extract the periodicity, timing, and magnitude of transcript abundance during the cell cycle. We used these parameters to improve a stochastic model of the cell cycle to better reflect the variability of molecular and phenotypic data on cell cycle progression in budding yeast.
The free-living aquatic bacterium, Caulobacter crescentus, exhibits two different morphologies during its life cycle. The morphological change from swarmer cell to stalked cell is a result of changes of function of two bi-functional histidine kinases, PleC and CckA. Here, we describe a detailed molecular mechanism by which the function of PleC changes between phosphatase and kinase state. By mathematical modeling of our proposed molecular interactions, we derive conditions under which PleC, CckA and its response regulators exhibit bistable behavior, thus providing a scenario for robust switching between swarmer and stalked states. Our simulations are in reasonable agreement with in vitro and in vivo experimental observations of wild type and mutant phenotypes. According to our model, the kinase form of PleC is essential for the swarmer-to-stalked transition and to prevent premature development of the swarmer pole. Based on our results, we reconcile some published experimental observations and suggest novel mutants to test our predictions.
Breast cancer cells develop resistance to endocrine therapies by shifting between estrogen receptor (ER)-regulated and growth factor receptor (GFR)-regulated survival signaling pathways. To study this switch, we propose a mathematical model of crosstalk between these pathways. The model explains why MCF7 sub-clones transfected with HER2 or EGFR show three GFR-distribution patterns, and why the bimodal distribution pattern can be reversibly modulated by estrogen. The model illustrates how transient overexpression of ER activates GFR signaling and promotes estrogen-independent growth. Understanding this survival-signaling switch can help in the design of future therapies to overcome resistance in breast cancer.
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.
Top-down analyses in systems biology can automatically find correlations among genes and proteins in large-scale datasets. However, it is often difficult to design experiments from these results. In contrast, bottom-up approaches painstakingly craft detailed models that can be simulated computationally to suggest wet lab experiments. However, developing the models is a manual process that can take many years. These approaches have largely been developed independently. We present LINKER, an efficient and automated data-driven method that can analyze molecular interactomes to propose extensions to models that can be simulated. LINKER combines teleporting random walks and k-shortest path computations to discover connections from a source protein to a set of proteins collectively involved in a particular cellular process. We evaluate the efficacy of LINKER by applying it to a well-known dynamic model of the cell division cycle in Saccharomyces cerevisiae. Compared to other state-of-the-art methods, subnetworks computed by LINKER are heavily enriched in Gene Ontology (GO) terms relevant to the cell cycle. Finally, we highlight how networks computed by LINKER elucidate the role of a protein kinase (Cdc5) in the mitotic exit network of a dynamic model of the cell cycle.
Progression through the eukaryotic cell cycle is characterized by specific transitions, where cells move irreversibly from stage i-1 of the cycle into stage i. These irreversible cell cycle transitions are regulated by underlying bistable switches, which share some common features. An inhibitory protein stalls progression, and an activatory protein promotes progression. The inhibitor and activator are locked in a double-negative feedback loop, creating a one-way toggle switch that guarantees an irreversible commitment to move forward through the cell cycle, and it opposes regression from stage i to stage i-1. In many cases, the activator is an enzyme that modifies the inhibitor in multiple steps, whereas the hypo-modified inhibitor binds strongly to the activator and resists its enzymatic activity. These interactions are the basis of a reaction motif that provides a simple and generic account of many characteristic properties of cell cycle transitions. To demonstrate this assertion, we apply the motif in detail to the G1/S transition in budding yeast and to the mitotic checkpoint in mammalian cells. Variations of the motif might support irreversible cellular decision-making in other contexts.
The eukaryotic cell cycle is characterized by alternating oscillations in the activities of cyclin-dependent kinase (Cdk) and the anaphase-promoting complex (APC). Successful completion of the cell cycle is dependent on the precise, temporally ordered appearance of these activities. A modest level of Cdk activity is sufficient to initiate DNA replication, but mitosis and APC activation require an elevated Cdk activity. In present-day eukaryotes, this temporal order is provided by a complex network of regulatory proteins that control both Cdk and APC activities via sharp thresholds, bistability, and time delays. Using simple computational models, we show here that these dynamical features of cell-cycle organization could emerge in a control system driven by a single Cdk/cyclin complex and APC wired in a negative-feedback loop. We show that ordered phosphorylation of cellular proteins could be explained by multisite phosphorylation/dephosphorylation and competition of substrates for interconverting kinase (Cdk) and phosphatase. In addition, the competition of APC substrates for ubiquitylation can create and maintain sustained oscillations in cyclin levels. We propose a sequence of models that gets closer and closer to a realistic model of cell-cycle control in yeast. Since these models lack the elaborate control mechanisms characteristic of modern eukaryotes, they suggest that bistability and time delay may have characterized eukaryotic cell divisions before the current cell-cycle control network evolved in all its complexity.
Cancers of the breast and other tissues arise from aberrant decision-making by cells regarding their survival or death, proliferation or quiescence, damage repair or bypass. These decisions are made by molecular signalling networks that process information from outside and from within the breast cancer cell and initiate responses that determine the cells survival and reproduction. Because the molecular logic of these circuits is difficult to comprehend by intuitive reasoning alone, we present some preliminary mathematical models of the basic decision circuits in breast cancer cells that may aid our understanding of their susceptibility or resistance to endocrine therapy.
The reciprocal differentiation of T helper 17 (T(H)17) cells and induced regulatory T (iT(reg)) cells plays a critical role in both the pathogenesis and resolution of diverse human inflammatory diseases. Although initial studies suggested a stable commitment to either the T(H)17 or the iT(reg) lineage, recent results reveal remarkable plasticity and heterogeneity, reflected in the capacity of differentiated effectors cells to be reprogrammed among T(H)17 and iT(reg) lineages and the intriguing phenomenon that a group of naïve precursor CD4(+) T cells can be programmed into phenotypically diverse populations by the same differentiation signal, transforming growth factor beta. To reconcile these observations, we have built a mathematical model of T(H)17/iT(reg) differentiation that exhibits four different stable steady states, governed by pitchfork bifurcations with certain degrees of broken symmetry. According to the model, a group of precursor cells with some small cell-to-cell variability can differentiate into phenotypically distinct subsets of cells, which exhibit distinct levels of the master transcription-factor regulators for the two T cell lineages. A dynamical control system with these properties is flexible enough to be steered down alternative pathways by polarizing signals, such as interleukin-6 and retinoic acid and it may be used by the immune system to generate functionally distinct effector cells in desired fractions in response to a range of differentiation signals. Additionally, the model suggests a quantitative explanation for the phenotype with high expression levels of both master regulators. This phenotype corresponds to a re-stabilized co-expressing state, appearing at a late stage of differentiation, rather than a bipotent precursor state observed under some other circumstances. Our simulations reconcile most published experimental observations and predict novel differentiation states as well as transitions among different phenotypes that have not yet been observed experimentally.
The mitotic checkpoint prevents a eukaryotic cell from commencing to separate its replicated genome into two daughter cells (anaphase) until all of its chromosomes are properly aligned on the metaphase plate, with the two copies of each chromosome attached to opposite poles of the mitotic spindle. The mitotic checkpoint is exquisitely sensitive in that a single unaligned chromosome, 1 of a total of ~50, is sufficient to delay progression into anaphase; however, when the last chromosome comes into alignment on the metaphase plate, the mitotic checkpoint is quickly satisfied, and the replicated chromosomes are rapidly partitioned to opposite poles of the dividing cell. The mitotic checkpoint is also curious in the sense that, before metaphase alignment, chromosomes that are not being pulled in opposite directions by the mitotic spindle activate the checkpoint, but during anaphase, these same tensionless chromosomes can no longer activate the checkpoint. These and other puzzles associated with the mitotic checkpoint are addressed by a proposed molecular mechanism, which involves two positive feedback loops that create a bistable response of the checkpoint to chromosomal tension.
Unlike many mutants that are completely viable or inviable, the CLB2-db? clb5? mutant of Saccharomyces cerevisiae is inviable in glucose but partially viable on slower growth media such as raffinose. On raffinose, the mutant cells can bud and divide but in each cycle there is a chance that a cell will fail to divide (telophase arrest), causing it to exit the cell cycle. This effect gives rise to a stochastic phenotype that cannot be explained by a deterministic model. We measure the inter-bud times of wild type and mutant cells growing on raffinose and compute statistics and distributions to characterize the mutants behavior. We convert a detailed deterministic model of the budding yeast cell cycle to a stochastic model and determine the extent to which it captures the stochastic phenotype of the mutant strain. Predictions of the mathematical model are in reasonable agreement with our experimental data and suggest directions for improving the model. Ultimately, the ability to accurately model stochastic phenotypes may prove critical to understanding disease and therapeutic interventions in higher eukaryotes.
Lack of understanding of endocrine resistance remains one of the major challenges for breast cancer researchers, clinicians, and patients. Current reductionist approaches to understanding the molecular signaling driving resistance have offered mostly incremental progress over the past 10 years. As the field of systems biology has begun to mature, the approaches and network modeling tools being developed and applied therein offer a different way to think about how molecular signaling and the regulation of critical cellular functions are integrated. To gain novel insights, we first describe some of the key challenges facing network modeling of endocrine resistance, many of which arise from the properties of the data spaces being studied. We then use activation of the unfolded protein response (UPR) following induction of endoplasmic reticulum stress in breast cancer cells by antiestrogens, to illustrate our approaches to computational modeling. Activation of UPR is a key determinant of cell fate decision making and regulation of autophagy and apoptosis. These initial studies provide insight into a small subnetwork topology obtained using differential dependency network analysis and focused on the UPR gene XBP1. The XBP1 subnetwork topology incorporates BCAR3, BCL2, BIK, NF?B, and other genes as nodes; the connecting edges represent the dependency structures amongst these nodes. As data from ongoing cellular and molecular studies become available, we will build detailed mathematical models of this XBP1-UPR network.
Progression through the cell division cycle is orchestrated by a complex network of interacting genes and proteins. Some of these proteins are known to fluctuate periodically during the cell cycle, but a systematic study of the fluctuations of a broad sample of cell-cycle proteins has not been made until now. Using time-lapse fluorescence microscopy, we profiled 16 strains of budding yeast, each containing GFP fused to a single gene involved in cell cycle regulation. The dynamics of protein abundance and localization were characterized by extracting the amplitude, period, and other indicators from a series of images. Oscillations of protein abundance could clearly be identified for Cdc15, Clb2, Cln1, Cln2, Mcm1, Net1, Sic1, and Whi5. The period of oscillation of the fluorescently tagged proteins is generally in good agreement with the inter-bud time. The very strong oscillations of Net1 and Mcm1 expression are remarkable since little is known about the temporal expression of these genes. By collecting data from large samples of single cells, we quantified some aspects of cell-to-cell variability due presumably to intrinsic and extrinsic noise affecting the cell cycle.
The timing of DNA synthesis, mitosis and cell division is regulated by a complex network of biochemical reactions that control the activities of a family of cyclin-dependent kinases. The temporal dynamics of this reaction network is typically modeled by nonlinear differential equations describing the rates of the component reactions. This approach provides exquisite details about molecular regulatory processes but is hampered by the need to estimate realistic values for the many kinetic constants that determine the reaction rates. It is difficult to estimate these kinetic constants from available experimental data. To avoid this problem, modelers often resort to qualitative modeling strategies, such as Boolean switching networks, but these models describe only the coarsest features of cell cycle regulation. In this paper we describe a hybrid approach that combines the best features of continuous differential equations and discrete Boolean networks. Cyclin abundances are tracked by piecewise linear differential equations for cyclin synthesis and degradation. Cyclin synthesis is regulated by transcription factors whose activities are represented by discrete variables (0 or 1) and likewise for the activities of the ubiquitin-ligating enzyme complexes that govern cyclin degradation. The discrete variables change according to a predetermined sequence, with the times between transitions determined in part by cyclin accumulation and degradation and as well by exponentially distributed random variables. The model is evaluated in terms of flow cytometry measurements of cyclin proteins in asynchronous populations of human cell lines. The few kinetic constants in the model are easily estimated from the experimental data. Using this hybrid approach, modelers can quickly create quantitatively accurate, computational models of protein regulatory networks in cells.
Low voltage-activated T-type calcium (Ca) channels contribute to the normal development of the heart and are also implicated in pathophysiological states such as cardiac hypertrophy. Functionally distinct T-type Ca channel isoforms can be generated by alternative splicing from each of three different T-type genes (Ca(V)3.1, Ca(V)3.2,Ca(V)3.3), although it remains to be described whether specific splice variants are associated with developmental states and pathological conditions. We aimed to identify and functionally characterize Ca(V)3.2 T-type Ca channel alternatively spliced variants from newborn animals and to compare with adult normotensive and spontaneously hypertensive rats (SHR). DNA sequence analysis of full-length Ca(V)3.2 cDNA generated from newborn heart tissue identified ten major regions of alternative splicing, the more common variants of which were analyzed by quantitative real-time PCR (qRT-PCR) and also subject to functional examination by whole-cell patch clamp. The main findings are that: (1) cardiac Ca(V)3.2 T-type Ca channels are subject to considerable alternative splicing, (2) there is preferential expression of Ca(V)3.2(-25) splice variant channels in newborn rat heart with a developmental shift in adult heart that results in approximately equal levels of expression of both (+25) and (-25) exon variants, (3) in the adult stage of hypertensive rats there is a both an increase in overall Ca(V)3.2 expression and a shift towards expression of Ca(V)3.2(+25) containing channels as the predominant form, and (4) alternative splicing confers a variant-specific voltage-dependent facilitation of Ca(V)3.2 channels. We conclude that Ca(V)3.2 alternative splicing generates significant T-type Ca channel structural and functional diversity with potential implications relevant to cardiac developmental and pathophysiological states.
In order for the cells genome to be passed intact from one generation to the next, the events of the cell cycle (DNA replication, mitosis, cell division) must be executed in the correct order, despite the considerable molecular noise inherent in any protein-based regulatory system residing in the small confines of a eukaryotic cell. To assess the effects of molecular fluctuations on cell-cycle progression in budding yeast cells, we have constructed a new model of the regulation of Cln- and Clb-dependent kinases, based on multisite phosphorylation of their target proteins and on positive and negative feedback loops involving the kinases themselves. To account for the significant role of noise in the transcription and translation steps of gene expression, the model includes mRNAs as well as proteins. The model equations are simulated deterministically and stochastically to reveal the bistable switching behavior on which proper cell-cycle progression depends and to show that this behavior is robust to the level of molecular noise expected in yeast-sized cells (approximately 50 fL volume). The model gives a quantitatively accurate account of the variability observed in the G1-S transition in budding yeast, which is governed by an underlying sizer+timer control system.
Many aspects of cell physiology are controlled by protein kinases and phosphatases, which together determine the phosphorylation state of targeted substrates. Some of these target proteins are themselves kinases or phosphatases or other components of a regulatory network characterized by feedback and feed-forward loops. In this review we describe some common regulatory motifs involving kinases, phosphatases, and their substrates, focusing particularly on bistable switches involved in cellular decision processes. These general principles are applied to cell cycle transitions, with special emphasis on the roles of regulated phosphatases in orchestrating progression from one phase to the next of the DNA replication-division cycle.
Models of regulatory networks become more difficult to construct and understand as they grow in size and complexity. Large models are usually built up from smaller models, representing subsets of reactions within the larger network. To assist modelers in this composition process, we present a formal approach for model composition, a wizard-style program for implementing the approach, and suggested language extensions to the Systems Biology Markup Language to support model composition. To illustrate the features of our approach and how to use the JigCell Composition Wizard, we build up a model of the eukaryotic cell cycle "engine" from smaller pieces.
Diets rich in fruits and vegetables are associated with lower risk of cancer which may be conferred in part by the antioxidant properties of these foods. However, antioxidant supplementation or increased consumption of antioxidant-rich foods has been reported to have inconsistent effects on DNA damage. The present work (the DART study) investigated the extent of inter-individual variation in DNA damage, the capacity for base excision repair (BER) and the responses of both variables to supplementation with an antioxidant supplement for 6 weeks. There was a wide inter-individual variation in endogenous lymphocyte DNA strand breaks (8-fold variation), in damage after a challenge with H2O2 (16-fold variation) and in DNA repair (41-fold variation) measured using the comet assay. When stratified into tertiles according to the pre-supplementation level of endogenous DNA damage, there was a statistically significant decrease in DNA damage after supplementation in the tertile with the highest pre-supplementation level of damage. There was no effect of supplementation on BER. Endogenous DNA damage level before supplementation was significantly different (P = 0.037) between the three genotypes for the Val16Ala single nucleotide polymorphism in manganese superoxide dismutase (rs4880) with individuals homozygous/wild type showing less damage than those carrying the alanine variant.
The signal-response characteristics of a living cell are determined by complex networks of interacting genes, proteins, and metabolites. Understanding how cells respond to specific challenges, how these responses are contravened in diseased cells, and how to intervene pharmacologically in the decision-making processes of cells requires an accurate theory of the information-processing capabilities of macromolecular regulatory networks. Adopting an engineers approach to control systems, we ask whether realistic cellular control networks can be decomposed into simple regulatory motifs that carry out specific functions in a cell. We show that such functional motifs exist and review the experimental evidence that they control cellular responses as expected.
Systems biology takes an interdisciplinary approach to the systematic study of complex interactions in biological systems. This approach seeks to decipher the emergent behaviors of complex systems rather than focusing only on their constituent properties. As an increasing number of examples illustrate the value of systems biology approaches to understand the initiation, progression, and treatment of cancer, systems biologists from across Europe and the United States hope for changes in the way their field is currently perceived among cancer researchers. In a recent EU-US workshop, supported by the European Commission, the German Federal Ministry for Education and Research, and the National Cancer Institute of the NIH, the participants discussed the strengths, weaknesses, hurdles, and opportunities in cancer systems biology.
Models of regulatory networks become more difficult to construct and understand as they grow in size and complexity. Modelers naturally build large models from smaller components that each represent subsets of reactions within the larger network. To assist modelers in this process, we present model aggregation, which defines models in terms of components that are designed for the purpose of being combined.
The innate immunity signaling process is controlled by numerous positive and negative regulators. The interleukin-1 receptor-associated kinase M (IRAK-M) is one of the negative regulators that contribute to the attenuation of NFkappaB activation. The molecular mechanism involved, however, is poorly defined. In this report, we observed that IRAK-M selectively suppresses the NIK-IKKalpha-mediated alternative NFkappaB pathway. Deletion of IRAK-M led to NIK stabilization, favored the formation of the IKKalpha/IKKalpha homodimer instead of the IKKalpha/IKKbeta heterodimer, and enhanced RelB nuclear distribution. In contrast, p65 nuclear localization and phosphorylation was not affected by IRAK-M deficiency. IRAK-M-deficient cells exhibited increased expression of selected cytokines such as IL-6 and GM-CSF, as well as quickened resynthesis of IkappaBalpha. The increased expression of IL-6 and GM-CSF was ablated when RelB expression was knocked down using specific siRNA. We also demonstrated that the observed inhibitory effect of IRAK-M was primarily limited to the TLR2 ligand, instead of TLR4. Taken together, our findings suggest that IRAK-M negatively regulates the alternative NFkappaB pathway in a ligand-specific manner.
The asymmetric cell division cycle of Caulobacter crescentus is orchestrated by an elaborate gene-protein regulatory network, centered on three major control proteins, DnaA, GcrA and CtrA. The regulatory network is cast into a quantitative computational model to investigate in a systematic fashion how these three proteins control the relevant genetic, biochemical and physiological properties of proliferating bacteria. Different controls for both swarmer and stalked cell cycles are represented in the mathematical scheme. The model is validated against observed phenotypes of wild-type cells and relevant mutants, and it predicts the phenotypes of novel mutants and of known mutants under novel experimental conditions. Because the cell cycle control proteins of Caulobacter are conserved across many species of alpha-proteobacteria, the model we are proposing here may be applicable to other genera of importance to agriculture and medicine (e.g., Rhizobium, Brucella).
Nucleotide excision repair (NER) is responsible for repairing bulky helix-distorting DNA lesions and is essential for the maintenance of genomic integrity. Severe hereditary impairment of NER leads to cancers such as those in xeroderma pigmentosum, and more moderate reductions in NER capacity have been associated with an increased cancer risk. Diet is a proven modifier of cancer risk but few studies have investigated the potential relationships between diet and NER. In the present study, the plasmid-based host cell reactivation assay was used to measure the NER capacity in peripheral blood mononuclear cells from fifty-seven volunteers aged 18-30 years before and after 6 weeks of supplementation with micronutrients (selenium and vitamins A, C and E). As a control, nine individuals remained unsupplemented over the same period. Volunteers were genotyped for the following polymorphisms in NER genes: ERCC5 Asp1104His (rs17655); XPC Lys939Gln (rs2228001); ERCC2 Lys751Gnl (rs13181); XPC PAT (an 83 bp poly A/T insertion-deletion polymorphism in the XPC gene). NER capacity varied 11-fold between individuals and was inversely associated with age and endogenous DNA strand breaks. For the first time, we observed an inverse association between adiposity and NER. No single polymorphism was associated with the NER capacity, although significant gene-gene interactions were observed between XPC Lys939Gln and ERCC5 Asp1104His and XPC Lys939Gln and ERCC2 Lys751Gnl. While there was no detectable effect of micronutrient supplementation on NER capacity, there was evidence that the effect of fruit intake on the NER capacity may be modulated by the ERCC2 Lys751Gnl single nucleotide polymorphism.
Repetitive cell cycles, which are essential to the perpetuation of life, are orchestrated by an underlying biochemical reaction network centered around cyclin-dependent protein kinases (Cdks) and their regulatory subunits (cyclins). Oscillations of Cdk1/CycB activity between low and high levels during the cycle trigger DNA replication and mitosis in the correct order. Based on computational modeling, we proposed that the low and the high kinase activity states are alternative stable steady states of a bistable Cdk-control system. Bistability is a consequence of system-level feedback (positive and double-negative feedback signals) in the underlying control system. We have also argued that bistability underlies irreversible transitions between low and high Cdk activity states and thereby ensures directionality of cell cycle progression.
The activity of a protein can be reversibly modulated by post-translational, covalent modifications, such as phosphorylation and dephosphorylation. In many cases, the modulated protein may be phosphorylated by the same kinase on many different amino acid residues. Such multisite phosphorylations may occur progressively (during a single binding event of kinase to substrate) or distributively (the kinase dissociates from its substrate after each phosphorylation reaction). If a protein is phosphorylated by a distributive multisite mechanism, then the net activity of a population of these protein molecules can be a highly nonlinear function of the ratio of activities of the kinase and phosphatase enzymes. If the multiply phosphorylated protein is embedded in a positive feedback loop with its kinase and/or phosphatase, then the network may exhibit robust bistable behavior. Using numerical simulations and bifurcation theory, we study the properties of a particular bistable reaction network motivated by the antagonistic relationship between cyclin-dependent kinase and its multiply phosphorylated target, Cdh1, which is involved in the degradation of cyclin molecules. We characterize the bistable switch in terms of (i) the mechanism of distributive phosphorylation (ordered or disordered), (ii) the number of phosphorylation sites on the target protein, (iii) the effect of phosphorylation on the target protein (abrupt or progressive inactivation), and (iv) the effects of stochastic fluctuations in small cells with limited numbers of kinase, phosphatase and target proteins.
Multicellular organisms shape development and remove aberrant cells by programmed cell death ("apoptosis"). Because defective cell death (too little or too much) is implicated in various diseases (like cancer and autoimmunity), understanding how apoptosis is regulated is an important goal of molecular cell biologists. To this end, we propose a mathematical model of the intrinsic apoptotic pathway that captures three key dynamical features: a signal threshold to elicit cell death, irreversible commitment to the response, and a time delay that is inversely proportional to signal strength. Subdividing the intrinsic pathway into three modules (initiator, amplifier, executioner), we use computer simulation and bifurcation theory to attribute signal threshold and time delay to positive feedback in the initiator module and irreversible commitment to positive feedback in the executioner module. The model accounts for the behavior of mutants deficient in various genes and is used to design experiments that would test its basic assumptions. Finally, we apply the model to study p53-induced cellular responses to DNA damage. Cells first undergo cell cycle arrest and DNA repair, and then apoptosis if the damage is beyond repair. The model ascribes this cell-fate transition to a transformation of p53 from "helper" to "killer" forms.
We demonstrate how to model macromolecular regulatory networks with JigCell and the Parameter Estimation Toolkit (PET). These software tools are designed specifically to support the process typically used by systems biologists to model complex regulatory circuits. A detailed example illustrates how a model of the cell cycle in frog eggs is created and then refined through comparison of simulation output with experimental data. We show how parameter estimation tools automatically generate rate constants that fit a model to experimental data.
A critical goal in cell biology is to develop a systems-level perspective of eukaryotic cell cycle controls. Among these controls, a complex signaling network (called checkpoints) arrests progression through the cell cycle when there is a threat to genomic integrity such as unreplicated or damaged DNA. Understanding the regulatory principles of cell cycle checkpoints is important because loss of checkpoint regulation may be a requisite step on the roadway to cancer. Mathematical modeling has proved to be a useful guide to cell cycle regulation by revealing the importance of bistability, hysteresis and time lags in governing cell cycle transitions and checkpoint mechanisms. In this report, we propose a mathematical model of the frog egg cell cycle including effects of unreplicated DNA on progression into mitosis. By a stepwise approach utilizing parameter estimation tools, we build a model that is grounded in fundamental behaviors of the cell cycle engine (hysteresis and time lags), includes new elements in the signaling network (Myt1 and Chk1 kinases), and fits a large and diverse body of data from the experimental literature. The model provides a validated framework upon which to build additional aspects of the cell cycle checkpoint signaling network, including those control signals in the mammalian cell cycle that are commonly mutated in cancer.
The DNA replication-division cycle of eukaryotic cells is controlled by a complex network of regulatory proteins, called cyclin-dependent kinases, and their activators and inhibitors. Although comprehensive and accurate deterministic models of the control system are available for yeast cells, reliable stochastic simulations have not been carried out because the full reaction network has yet to be expressed in terms of elementary reaction steps. As a first step in this direction, we present a simplified version of the control system that is suitable for exact stochastic simulation of intrinsic noise caused by molecular fluctuations and extrinsic noise because of unequal division. The model is consistent with many characteristic features of noisy cell cycle progression in yeast populations, including the observation that mRNAs are present in very low abundance (approximately 1 mRNA molecule per cell for each expressed gene). For the control system to operate reliably at such low mRNA levels, some specific mRNAs in our model must have very short half-lives (<1 min). If these mRNA molecules are longer-lived (perhaps 2 min), then the intrinsic noise in our simulations is too large, and there must be some additional noise suppression mechanisms at work in cells.
There is increasing evidence that solid cancers contain cancer-initiating cells (CICs) that are capable of regenerating a tumor that has been surgically removed and/or treated with chemotherapy and/or radiation therapy. Currently, cell surface markers, like CD133 or CD44, are used to identify CICs in vitro; however, these markers cannot be used to identify and track CICs in vivo. The 26S proteasome is the main regulator of many processes within a proliferating cell, and its activity may be altered depending on the phenotype of a cell.
The eukaryotic cell cycle requires precise temporal coordination of the activities of hundreds of executor proteins (EPs) involved in cell growth and division. Cyclin-dependent protein kinases (Cdks) play central roles in regulating the production, activation, inactivation and destruction of these EPs. From genome-scale data sets of budding yeast, we identify 126 EPs that are regulated by Cdk1 both through direct phosphorylation of the EP and through phosphorylation of the transcription factors that control expression of the EP, so that each of these EPs is regulated by a feed-forward loop (FFL) from Cdk1. By mathematical modelling, we show that such FFLs can activate EPs at different phases of the cell cycle depending of the effective signs (+ or -) of the regulatory steps of the FFL. We provide several case studies of EPs that are controlled by FFLs exactly as our models predict. The signal-transduction properties of FFLs allow one (or a few) Cdk signal(s) to drive a host of cell cycle responses in correct temporal sequence.
Low-voltage-activated, or T-type, calcium (Ca(2+)) channels are believed to play an essential role in the generation of absence seizures in the idiopathic generalized epilepsies (IGEs). We describe a homozygous, missense, single nucleotide (G to C) mutation in the Ca(v)3.2 T-type Ca(2+) channel gene (Cacna1h) in the genetic absence epilepsy rats from Strasbourg (GAERS) model of IGE. The GAERS Ca(v)3.2 mutation (gcm) produces an arginine to proline (R1584P) substitution in exon 24 of Cacna1h, encoding a portion of the III-IV linker region in Ca(v)3.2. gcm segregates codominantly with the number of seizures and time in seizure activity in progeny of an F1 intercross. We have further identified two major thalamic Cacna1h splice variants, either with or without exon 25. gcm introduced into the splice variants acts "epistatically," requiring the presence of exon 25 to produce significantly faster recovery from channel inactivation and greater charge transference during high-frequency bursts. This gain-of-function mutation, the first reported in the GAERS polygenic animal model, has a novel mechanism of action, being dependent on exonic splicing for its functional consequences to be expressed.
Many genes with crucial roles in zinc homeostasis in mammals respond to fluctuating zinc supply through unknown mechanisms, and uncovering these mechanisms is essential to understanding the process at cellular and systemic levels. We detected zinc-dependent binding of a zinc-induced protein to a specific sequence, the zinc transcriptional regulatory element (ZTRE), in the SLC30A5 (zinc transporter ZnT5) promoter and showed that substitution of the ZTRE abrogated the repression of a reporter gene in response to zinc. We identified the ZTRE in other genes, including (through an unbiased search) the CBWD genes and (through targeted analysis) in multiple members of the SLC30 family, including SLC30A10, which is repressed by zinc. The function of the CBWD genes is currently unknown, but roles for homologs in metal homeostasis are being uncovered in bacteria. We demonstrated that CBWD genes are repressed by zinc and that substitution of the ZTRE in SLC30A10 and CBWD promoter-reporter constructs abrogates this response. Other metals did not affect expression of the transcriptional regulator, binding to the ZTRE or promoter-driven reporter gene expression. These findings provide the basis for elucidating how regulation of a network of genes through this novel mechanism contributes to zinc homeostasis and how the cell orchestrates this response.
CD4+ T cells have several subsets of functional phenotypes, which play critical yet diverse roles in the immune system. Pathogen-driven differentiation of these subsets of cells is often heterogeneous in terms of the induced phenotypic diversity. In vitro recapitulation of heterogeneous differentiation under homogeneous experimental conditions indicates some highly regulated mechanisms by which multiple phenotypes of CD4+ T cells can be generated from a single population of naïve CD4+ T cells. Therefore, conceptual understanding of induced heterogeneous differentiation will shed light on the mechanisms controlling the response of populations of CD4+ T cells under physiological conditions.
The innate immune system, acting as the first line of host defense, senses and adapts to foreign challenges through complex intracellular and intercellular signaling networks. Endotoxin tolerance and priming elicited by macrophages are classic examples of the complex adaptation of innate immune cells. Upon repetitive exposures to different doses of bacterial endotoxin (lipopolysaccharide) or other stimulants, macrophages show either suppressed or augmented inflammatory responses compared to a single exposure to the stimulant. Endotoxin tolerance and priming are critically involved in both immune homeostasis and the pathogenesis of diverse inflammatory diseases. However, the underlying molecular mechanisms are not well understood. By means of a computational search through the parameter space of a coarse-grained three-node network with a two-stage Metropolis sampling approach, we enumerated all the network topologies that can generate priming or tolerance. We discovered three major mechanisms for priming (pathway synergy, suppressor deactivation, activator induction) and one for tolerance (inhibitor persistence). These results not only explain existing experimental observations, but also reveal intriguing test scenarios for future experimental studies to clarify mechanisms of endotoxin priming and tolerance.
How breast cancer cells respond to the stress of endocrine therapies determines whether they will acquire a resistant phenotype or execute a cell-death pathway. After a survival signal is successfully executed, a cell must decide whether it should replicate. How these cell-fate decisions are regulated is unclear, but evidence suggests that the signals that determine these outcomes are highly integrated. Central to the final cell-fate decision is signaling from the unfolded protein response, which can be activated following the sensing of stress within the endoplasmic reticulum. The duration of the response to stress is partly mediated by the duration of inositol-requiring enzyme-1 activation following its release from heat shock protein A5. The resulting signals appear to use several B-cell lymphoma-2 family members to both suppress apoptosis and activate autophagy. Changes in metabolism induced by cellular stress are key components of this regulatory system, and further adaptation of the metabolome is affected in response to stress. Here we describe the unfolded protein response, autophagy, and apoptosis, and how the regulation of these processes is integrated. Central topologic features of the signaling network that integrate cell-fate regulation and decision execution are discussed.
Cell cycle progression in eukaryotes is regulated by periodic activation and inactivation of a family of cyclin-dependent kinases (Cdks). Entry into mitosis requires phosphorylation of many proteins targeted by mitotic Cdk, and exit from mitosis requires proteolysis of mitotic cyclins and dephosphorylation of their targeted proteins. Mitotic exit in budding yeast is known to involve the interplay of mitotic kinases (Cdk and Polo kinases) and phosphatases (Cdc55/PP2A and Cdc14), as well as the action of the anaphase promoting complex (APC) in degrading specific proteins in anaphase and telophase. To understand the intricacies of this mechanism, we propose a mathematical model for the molecular events during mitotic exit in budding yeast. The model captures the dynamics of this network in wild-type yeast cells and 110 mutant strains. The model clarifies the roles of Polo-like kinase (Cdc5) in the Cdc14 early anaphase release pathway and in the G-protein regulated mitotic exit network.
The eukaryotic cell cycle is regulated by a complicated chemical reaction network. Although many deterministic models have been proposed, stochastic models are desired to capture noise in the cell resulting from low numbers of critical species. However, converting a deterministic model into one that accurately captures stochastic effects can result in a complex model that is hard to build and expensive to simulate. In this paper, we first apply a hybrid (mixed deterministic and stochastic) simulation method to such a stochastic model. With proper partitioning of reactions between deterministic and stochastic simulation methods, the hybrid method generates the same primary characteristics and the same level of noise as Gillespies stochastic simulation algorithm, but with better efficiency. By studying the results generated by various partitionings of reactions, we developed a new strategy for hybrid stochastic modeling of the cell cycle. The new approach is not limited to using mass-action rate laws. Numerical experiments demonstrate that our approach is consistent with characteristics of noisy cell cycle progression, and yields cell cycle statistics in accord with experimental observations.
Related JoVE Video
Journal of Visualized Experiments
What is Visualize?
JoVE Visualize is a tool created to match the last 5 years of PubMed publications to methods in JoVE's video library.
How does it work?
We use abstracts found on PubMed and match them to JoVE videos to create a list of 10 to 30 related methods videos.
Video X seems to be unrelated to Abstract Y...
In developing our video relationships, we compare around 5 million PubMed articles to our library of over 4,500 methods videos. In some cases the language used in the PubMed abstracts makes matching that content to a JoVE video difficult. In other cases, there happens not to be any content in our video library that is relevant to the topic of a given abstract. In these cases, our algorithms are trying their best to display videos with relevant content, which can sometimes result in matched videos with only a slight relation.