The pharmacodynamics of the p53-Mdm2 targeting drug Nutlin: the role of gene-switching noise

Molecular Targeting of the Most Functionally Complex Gene in Precision Oncology: p53

While chemotherapy is a key treatment strategy for many solid tumors, it is rarely curative, and most tumor cells eventually become resistant. Because of this, there is an unmet need to develop systemic treatments that capitalize on the unique mutational landscape of each patient's tumor. The most frequently mutated protein in cancer, p53, has a role in nearly all cancer subtypes and tumorigenesis stages and therefore is one of the most promising molecular targets for cancer treatment. Unfortunately, drugs targeting p53 have seen little clinical success despite promising preclinical data. Most of these drug compounds target specific aspects of p53 inactivation, such as through inhibiting negative regulation by the mouse double minute (MDM) family of proteins. These treatment strategies fail to address cancer cells' adaptation mechanisms and ignore the impact that p53 loss has on the entire p53 network. However, recent gene therapy successes show that targeting the p53 network and cellular dysfunction caused by p53 inactivation is now possible and may soon translate into successful clinical responses. In this review, we discuss p53 signaling complexities in cancer that have hindered the development and use of p53-targeted drugs. We also describe several current therapeutics reporting promising preclinical and clinical results.

Application of Sensitivity Analysis to Discover Potential Molecular Drug Targets

Mathematical modeling of signaling pathways and regulatory networks has been supporting experimental research for some time now. Sensitivity analysis, aimed at finding model parameters whose changes yield significantly altered cellular responses, is an important part of modeling work. However, sensitivity methods are often directly transplanted from analysis of technical systems, and thus, they may not serve the purposes of analysis of biological systems. This paper presents a novel sensitivity analysis method that is particularly suited to the task of searching for potential molecular drug targets in signaling pathways. Using two sample models of pathways, p53/Mdm2 regulatory module and IFN-β-induced JAK/STAT signaling pathway, we show that the method leads to biologically relevant conclusions, identifying processes suitable for targeted pharmacological inhibition, represented by the reduction of kinetic parameter values. That, in turn, facilitates subsequent search for active drug components.

A noninvasive iRFP713 p53 reporter reveals dynamic p53 activity in response to irradiation and liver regeneration in vivo

Genetically encoded probes are widely used to visualize cellular processes in vitro and in vivo. Although effective in cultured cells, fluorescent protein tags and reporters are suboptimal in vivo because of poor tissue penetration and high background signal. Luciferase reporters offer improved signal-to-noise ratios but require injections of luciferin that can lead to variable responses and that limit the number and timing of data points that can be gathered. Such issues in studying the critical transcription factor p53 have limited insight on its activity in vivo during development and tissue injury responses. Here, by linking the expression of the near-infrared fluorescent protein iRFP713 to a synthetic p53-responsive promoter, we generated a knock-in reporter mouse that enabled noninvasive, longitudinal analysis of p53 activity in vivo in response to various stimuli. In the developing embryo, this model revealed the timing and localization of p53 activation. In adult mice, the model monitored p53 activation in response to irradiation and paracetamol- or CCl4-induced liver regeneration. After irradiation, we observed potent and sustained activation of p53 in the liver, which limited the production of reactive oxygen species (ROS) and promoted DNA damage resolution. We propose that this new reporter may be used to further advance our understanding of various physiological and pathophysiological p53 responses.

Robust p53 recovery using chattering free sliding mode control and a gain-scheduled modified Utkin observer

p53 protein plays an essential role in protecting the genomic integrity of mammalian cells. A drastic decrease in the amount of p53 protein has been observed in cancerous cells. By using Nutlin-based small molecule drugs, the concentration of p53 can be restored to the desired level. This paper presents the drug-dosage design for p53 pathway, based on a control-oriented nonlinear model. A chattering free sliding mode control (CFSMC) strategy is employed to track the desired trajectory of p53 concentration for both of its dynamic behaviors, i.e., sustained and oscillatory responses. A gain-scheduled modified Utkin observer (GSMUO) is designed for robust state reconstruction and disturbance estimation. The simulation results show that CFSMC and GSMUO exhibit desired robustness and performance properties in the presence of parametric variations, an input disturbance and measurement noise. Moreover, a comprehensive simulation study, along with a detailed quantitative analysis is performed to compare CFSMC-GSMUO with four different techniques: a sliding mode control (SMC) with an equivalent control based sliding mode observer (SMO) and GSMUO, respectively, and a dynamic sliding mode control (DSMC) with SMO and GSMUO, respectively. The analysis demonstrates that the tracking error and utilization of the control energy is the least in the case of CFSMC-GSMUO as compared to its counterparts.

Mathematical Modelling of p53 Signalling during DNA Damage Response: A Survey

No gene has garnered more interest than p53 since its discovery over 40 years ago. In the last two decades, thanks to seminal work from Uri Alon and Ghalit Lahav, p53 has defined a truly synergistic topic in the field of mathematical biology, with a rich body of research connecting mathematic endeavour with experimental design and data. In this review we survey and distill the extensive literature of mathematical models of p53. Specifically, we focus on models which seek to reproduce the oscillatory dynamics of p53 in response to DNA damage. We review the standard modelling approaches used in the field categorising them into three types: time delay models, spatial models and coupled negative-positive feedback models, providing sample model equations and simulation results which show clear oscillatory dynamics. We discuss the interplay between mathematics and biology and show how one informs the other; the deep connections between the two disciplines has helped to develop our understanding of this complex gene and paint a picture of its dynamical response. Although yet more is to be elucidated, we offer the current state-of-the-art understanding of p53 response to DNA damage.

Landscape and flux quantify the stochastic transition dynamics for p53 cell fate decision

The p53 transcription factor is a key mediator in cellular responses to various stress signals including DNA repair, cell cycle arrest, and apoptosis. In this work, we employ landscape and flux theory to investigate underlying mechanisms of p53-regulated cell fate decisions. Based on a p53 regulatory network, we quantified the potential landscape and probabilistic flux for the p53 system. The landscape topography unifies and quantifies three cell fate states, including the limit cycle oscillations (representing cell cycle arrest), high p53 state (characterizing apoptosis), and low p53 state (characterizing the normal proliferative state). Landscape and flux results provide a quantitative explanation for the biphasic dynamics of the p53 system. In the oscillatory phase (first phase), the landscape attracts the system into the ring valley and flux drives the system cyclically moving, leading to cell cycle arrest. In the fate decision-making phase (second phase), the ring valley shape of the landscape provides an efficient way for cells to return to the normal proliferative state once DNA damage is repaired. If the damage is unrepairable with larger flux, the system may cross the barrier between two states and switch to the apoptotic state with a high p53 level. By landscape-flux decomposition, we revealed a trade-off between stability (guaranteed by landscape) and function (driven by flux) in cellular systems. Cells need to keep a balance between appropriate speed to repair DNA damage and appropriate stability to survive. This is further supported by flux landscape analysis showing that flux may provide the dynamical origin of phase transition in a non-equilibrium system by changing landscape topography.

Dynamic behavior of the p53-Mdm2 core module under the action of drug Nutlin and dual delays

Nutlin is a family of p53-targeting drugs. It is able to bind to Mdm2, thereby accelerate the accumulation of p53 that is a prominent tumor suppressor. An integrated module of the Nutlin PBK and p53 pathway is composed of positive feedback mediated by Mdm2 mRNA as well as the drug Nutlin and negative feedback mediated by Mdm2 protein. The main research content of our paper is how the time delay of protein synthesis, response time delay of Nutlin drug, the degradation rate of Mdm2, the degradation rate of p53 depended on Mdm2 and the actual dose of Nutlin in the cell affect the oscillatory behavior caused by Hopf bifurcation in the integrated network system of Nutlin PBK and p53 pathways. The stability of the unique positive equilibrium point and the existence of Hopf bifurcation are studied by taking the time delays as the bifurcation parameters and applying bifurcation theory. Based on the normal form theory and central manifold theorem, explicit criteria to determine the Hopf bifurcation direction and stability of the bifurcated periodic solution are established. It is found that the time delays and key parameters in the integrated network system of Nutlin PBK and p53 pathways play an important role in the amplitude and period of p53 oscillation according to the results from the numerical simulation and theoretical calculation. These results may provide us with a better understanding of the biological functions of the p53 pathway and some clues for cancer treatment.

Effect of pharmacodynamical interaction between nutlin-3a and aspirin in the activation of p53

BACKGROUND AND OBJECTIVE

p53, an anti-tumour protein, is significantly inactivated in most tumours. A small molecule of nutlin-3a is used to activate its function by repressing (Mouse double minute 2 homolog) Mdm2 protein which inhibits its activity. In cancer patients, a high risk of drug-drug interactions (DDIs) is observed owing to their multi-dosing prescriptions, which may lead them to harmful effects. In the presented work, we have aimed to investigate the effect of pharmacodynamical interaction between two anti-cancer drugs, nutlin-3a and aspirin in the activation of p53 protein.

METHODS

We have adapted control system techniques and designed a Proportional-Integral-Derivative (PID) controller. This controller is used to activate p53 protein. A drug interaction parameter is used to incorporate the effect of both drugs. Extensive simulation is performed using two different doses of aspirin, i.e. a low and a high dose of aspirin.

RESULTS

The result shows no harmful effects of pharmacodynamical interaction when a low dose is administered along with nutlin-3a. When a high dose of aspirin is administered it acts as input disturbance and leads to undesirable over-expression of p53 protein. This can further harm other growth cells, thus inducing harmful effects. A comparative analysis is also tabulated with different dosing regimens which shows that a combination of nutlin-3a and a low dose of aspirin provides better results than a high dose of aspirin.

CONCLUSION

Overall, the work provides an insight to the activation of p53 protein in cancer patients under the presence of pharmacodynamical interaction and might contribute to the effective management of cancer patients.

Nutlin-3a Enhances Natural Killer Cell-Mediated Killing of Neuroblastoma by Restoring p53-Dependent Expression of Ligands for NKG2D and DNAM-1 Receptors

In this study, we explored whether Nutlin-3a, a well-known, nontoxic small-molecule compound antagonizing the inhibitory interaction of MDM2 with the tumor suppressor p53, may restore ligands for natural killer (NK) cell-activating receptors (NK-AR) on neuroblastoma cells to enhance the NK cell-mediated killing. Neuroblastoma cell lines were treated with Nutlin-3a, and the expression of ligands for NKG2D and DNAM-1 NK-ARs and the neuroblastoma susceptibility to NK cells were evaluated. Adoptive transfer of human NK cells in a xenograft neuroblastoma-bearing NSG murine model was assessed. Two data sets of neuroblastoma patients were explored to correlate p53 expression with ligand expression. Luciferase assays and chromatin immunoprecipitation analysis of p53 functional binding on PVR promoter were performed. Primary neuroblastoma cells were also treated with Nutlin-3a, and neuroblastoma spheroids obtained from one high-risk patient were assayed for NK-cell cytotoxicity. We provide evidence showing that the Nutlin-3a-dependent rescue of p53 function in neuroblastoma cells resulted in (i) increased surface expression of ligands for NK-ARs, thus rendering neuroblastoma cell lines significantly more susceptible to NK cell-mediated killing; (ii) shrinkage of human neuroblastoma tumor masses that correlated with overall survival upon adoptive transfer of NK cells in neuroblastoma-bearing mice; (iii) and increased expression of ligands in primary neuroblastoma cells and boosting of NK cell-mediated disaggregation of neuroblastoma spheroids. We also found that p53 was a direct transcription factor regulating the expression of PVR ligand recognized by DNAM-1. Our findings demonstrated an immunomodulatory role of Nutlin-3a, which might be prospectively used for a novel NK cell-based immunotherapy for neuroblastoma.

Piece-wise linear models of biological systems-Application, analysis, and comparison with nonlinear models using the example of the p53 regulatory module

In this paper, we propose to use a linear system with switching methodology for description and analysis of complex biological systems. We show advantages of the proposed approach over the one usually used, which is based on ODE. We propose the detailed methodology of a full analysis of developed models, including analytical determination of the location and type of equilibrium points, finding an analytical solution, stability and bifurcation analysis. We illustrate the above with the example of the well-known p53 signalling pathway comparing the results with the results of a nonlinear, ODE-based version of the proposed model. The complex methodology proposed by us, especially due to the definition of model structure, which is easy to understand for biologists and medics, may be a bridge for closer cooperation between them and engineers in the future.

Genetic Alterations in the INK4a/ARF Locus: Effects on Melanoma Development and Progression

Genetic alterations in the INK4a/ARF (or CDKN2A) locus have been reported in many cancer types, including melanoma; head and neck squamous cell carcinomas; lung, breast, and pancreatic cancers. In melanoma, loss of function CDKN2A alterations have been identified in approximately 50% of primary melanomas, in over 75% of metastatic melanomas, and in the germline of 40% of families with a predisposition to cutaneous melanoma. The CDKN2A locus encodes two critical tumor suppressor proteins, the cyclin-dependent kinase inhibitor p16^INK4a and the p53 regulator p14^ARF. The majority of CDKN2A alterations in melanoma selectively target p16^INK4a or affect the coding sequence of both p16^INK4a and p14^ARF. There is also a subset of less common somatic and germline INK4a/ARF alterations that affect p14^ARF, while not altering the syntenic p16^INK4a coding regions. In this review, we describe the frequency and types of somatic alterations affecting the CDKN2A locus in melanoma and germline CDKN2A alterations in familial melanoma, and their functional consequences in melanoma development. We discuss the clinical implications of CDKN2A inactivating alterations and their influence on treatment response and resistance.

Model-based optimization of combination protocols for irradiation-insensitive cancers

Alternations in the p53 regulatory network may render cancer cells resistant to the radiation-induced apoptosis. In this theoretical study we search for the best protocols combining targeted therapy with radiation to treat cancers with wild-type p53, but having downregulated expression of PTEN or overexpression of Wip1 resulting in resistance to radiation monotherapy. Instead of using the maximum tolerated dose paradigm, we exploit stochastic computational model of the p53 regulatory network to calculate apoptotic fractions for both normal and cancer cells. We consider combination protocols, with irradiations repeated every 12, 18, 24, or 36 h to find that timing between Mdm2 inhibitor delivery and irradiation significantly influences the apoptotic cell fractions. We assume that uptake of the inhibitor is higher by cancer than by normal cells and that cancer cells receive higher irradiation doses from intersecting beams. These two assumptions were found necessary for the existence of protocols inducing massive apoptosis in cancer cells without killing large fraction of normal cells neighboring tumor. The best found protocols have irradiations repeated every 24 or 36 h with two inhibitor doses per irradiation cycle, and allow to induce apoptosis in more than 95% of cancer cells, killing less than 10% of normal cells.

Phenotypic selection through cell death: stochastic modelling of O-6-methylguanine-DNA methyltransferase dynamics

Glioblastoma (GBM) is the most aggressive malignant primary brain tumour with a median overall survival of 15 months. To treat GBM, patients currently undergo a surgical resection followed by exposure to radiotherapy and concurrent and adjuvant temozolomide (TMZ) chemotherapy. However, this protocol often leads to treatment failure, with drug resistance being the main reason behind this. To date, many studies highlight the role of O-6-methylguanine-DNA methyltransferase (MGMT) in conferring drug resistance. The mechanism through which MGMT confers resistance is not well studied-particularly in terms of computational models. With only a few reasonable biological assumptions, we were able to show that even a minimal model of MGMT expression could robustly explain TMZ-mediated drug resistance. In particular, we showed that for a wide range of parameter values constrained by novel cell growth and viability assays, a model accounting for only stochastic gene expression of MGMT coupled with cell growth, division, partitioning and death was able to exhibit phenotypic selection of GBM cells expressing MGMT in response to TMZ. Furthermore, we found this selection allowed the cells to pass their acquired phenotypic resistance onto daughter cells in a stable manner (as long as TMZ is provided). This suggests that stochastic gene expression alone is enough to explain the development of chemotherapeutic resistance.

Sliding mode controller-observer pair for p53 pathway

A significant loss of p53 protein, an anti-tumour agent, is observed in early cancerous cells. Induction of small molecules based drug is by far the most prominent technique to revive and maintain wild-type p53 to the desired level. In this study, a sliding mode control (SMC) based robust non-linear technique is presented for the drug design of a control-oriented p53 model. The control input generated by conventional SMC is discontinuous; however, depending on the physical nature of the system, drug infusion needs to be continuous. Therefore, to obtain a smooth control signal, a dynamic SMC (DSMC) is designed. Moreover, the boundedness of the zero-dynamics is also proved. To make the model-based control design possible, the unknown states of the system are estimated using an equivalent control based, reduced-order sliding mode observer. The robustness of the proposed technique is assessed by introducing input disturbance and parametric uncertainty in the system. The effectiveness of the proposed control scheme is witnessed by performing in-silico trials, revealing that the sustained level of p53 can be achieved by controlled drug administration. Moreover, a comparative quantitative analysis shows that both controllers yield similar performance. However, DSMC consumes less control energy.

System-based strategies for p53 recovery

The authors have proposed a systems theory-based novel drug design approach for the p53 pathway. The pathway is taken as a dynamic system represented by ordinary differential equations-based mathematical model. Using control engineering practices, the system analysis and subsequent controller design is performed for the re-activation of wild-type p53. p53 revival is discussed for both modes of operation, i.e. the sustained and oscillatory. To define the problem in control system paradigm, modification in the existing mathematical model is performed to incorporate the effect of Nutlin. Attractor point analysis is carried out to select the suitable domain of attraction. A two-loop negative feedback control strategy is devised to drag the system trajectories to the attractor point and to regulate cellular concentration of Nutlin, respectively. An integrated framework is constituted to incorporate the pharmacokinetic effects of Nutlin in the cancerous cells. Bifurcation analysis is also performed on the p53 model to see the conditions for p53 oscillation.

Promoter Hypermethylation of the ATM Gene as a Novel Biomarker for Breast Cancer

Background: Breast cancer may be induced by activation of protooncogenes to oncogenes and in many cases inactivation of tumor suppressor genes. Ataxia telangiectasia mutated (ATM) is an important tumor suppressor gene which plays central roles in the maintenance of genomic integrity by activating cell cycle checkpoints and promoting repair of double-strand breaks of DNA. In breast cancer, decrease ATM expression correlates with a poor outcome; however, the molecular mechanisms underlying downregulation are still unclear. Promoter hypermethylation may contribute in downregulation. Hence the present investigation was designed to evaluate promoter methylation and expression of the ATM gene in breast cancer cases, and to determine links with clinical and demographic manifestations, in a South Indian population. Methods: Tumor biopsy samples were collected from 50 pathologically confirmed sporadic breast cancer cases. DNA was isolated from tumor and adjacent non-tumorous regions, and sodium bisulfite conversion and methylation-specific PCR were performed using MS-PCR primers for the ATM promoter region. In addition, ATM mRNA expression was also analyzed for all samples using real-time PCR. Results: Fifty eight percent (58%) of cancer tissue samples showed promoter hypermethylation for the ATM gene, in contrast to only 4.44% of normal tissues (p= 0.0001). Furthermore, ATM promoter methylation was positively associated with age (p = 0.01), tumor size (p=0.045) and advanced stage of disease i.e. stages III and IV (p =0.019). An association between promoter hypermethylation and lower expression of ATM mRNA was also found (p=0.035). Conclusion: We report for the first time that promoter hypermethylation of ATM gene may be useful as a potential new biomarker for breast cancer, especially in the relatively young patients.

Influence of parameter perturbations on the reachability of therapeutic target in systems with switchings

Background

Examination of physiological processes and the influences of the drugs on them can be efficiently supported by mathematical modeling. One of the biggest problems is related to the exact fitting of the parameters of a model. Conditions inside the organism change dynamically, so the rates of processes are very difficult to estimate. Perturbations in the model parameters influence the steady state so a desired therapeutic goal may not be reached. Here we investigate the effect of parameter deviation on the steady state in three simple models of the influence of a therapeutic drug on its target protein. Two types of changes in the model parameters are taken into account: small perturbations in the system parameter values, and changes in the switching time of a specific parameter. Additionally, we examine the systems response in case of a drug concentration decreasing with time.

Results

The models which we analyze are simplified, because we want to avoid influences of complex dynamics on the results. A system with a negative feedback loop is the most robust and the most rapid, so it requires the largest drug dose but the effects are observed very quickly. On the other hand a system with positive feedback is very sensitive to changes, so small drug doses are sufficient to reach a therapeutic target. In systems without feedback or with positive feedback, perturbations in the model parameters have a bigger influence on the reachability of the therapeutic target than in systems with negative feedback. Drug degradation or inactivation in biological systems enforces multiple drug applications to maintain the level of a drug’s target under the desired threshold. The frequency of drug application should be fitted to the system dynamics, because the response velocity is tightly related to the therapeutic effectiveness and the time for achieving the goal.

Conclusions

Systems with different types of regulation vary in their dynamics and characteristic features. Depending on the feedback loop, different types of therapy may be the most appropriate, and deviations in the model parameters have different influences on the reachability of the therapeutic target.

Control of apoptosis by SMAR1

The nuclear matrix associated protein SMAR1 is sensitive to p53 and acts as a stress inducer as well as a regulator in the p53 regulatory network. Depending on the amount of stress SMAR1 stimulates, it can drive the p53 dynamics in the system to various dynamical states which correspond to various cellular states. The behavior of p53 in these dynamical states is found to be multifractal, due to the mostly long range correlations and large scale fluctuations imparted by stress. This fractal behavior is exhibited in the topological properties of the networks constructed from these dynamical states, and is a signature of self-organization to optimize information flow in the dynamics. The assortativity found in these networks is due to perturbation induced by stress, and indicates that the hubs in the time series play a significant role in stress management. SMAR1 can also regulate apoptosis in the presence of HDAC1, depending on the stress induced by it.

On p53 revival using system oriented drug dosage design

We propose a new paradigm in the drug design for the revival of the p53 pathway in cancer cells. It is shown that the current strategy of using small molecule based Mdm2 inhibitors is not enough to adequately revive p53 in cancerous cells, especially when it comes to the extracting pulsating behavior of p53. This fact has come to notice when a novel method for the drug dosage design is introduced using system oriented concepts. As a test case, small molecule drug Mdm2 repressor Nutlin 3a is considered. The proposed method determines the dose of Nutlin to revive p53 pathway functionality. For this purpose, PBK dynamics of Nutlin have also been integrated with p53 pathway model. The p53 pathway is the focus of researchers for the last thirty years for its pivotal role as a frontline cancer suppressant protein due to its effect on cell cycle checkpoints and cell apoptosis in response to a DNA strand break. That is the reason for finding p53 being absent in more than 50% of tumor cancers. Various drugs have been proposed to revive p53 in cancer cells. Small molecule based drugs are at the foremost and are the subject of advanced clinical trials. The dosage design of these drugs is an important issue. We use control systems concepts to develop the drug dosage so that the cancer cells can be treated in appropriate time. We investigate by using a computational model how p53 protein responds to drug Nutlin 3a, an agent that interferes with the MDM2-mediated p53 regulation. The proposed integrated model describes in some detail the regulation network of p53 including the negative feedback loop mediated by MDM2 and the positive feedback loop mediated by Mdm2 mRNA as well as the reversible represses of MDM2 caused by Nutlin. The reported PBK dynamics of Nutlin 3a are also incorporated to see the full effect. It has been reported that p53 response to stresses in two ways. Either it has a sustained (constant) p53 response, or there are oscillations in p53 concentration. The claimed dosage strategy achieves the p53 response in the first case. However, for the induction of oscillations, it is shown through bifurcation analysis that to achieve oscillating behavior of p53 inhibition of Mdm2 is not enough, rather antirepression of the p53-Mdm2 complex is also needed which leads to the need of a new drug design paradigm.

The role of stochastic gene switching in determining the pharmacodynamics of certain drugs: basic mechanisms

In this paper we analyze the impact of the stochastic fluctuation of genes between their ON and OFF states on the pharmacodynamics of a potentially large class of drugs. We focus on basic mechanisms underlying the onset of in vitro experimental dose-response curves, by investigating two elementary molecular circuits. Both circuits consist in the transcription of a gene and in the successive translation into the corresponding protein. Whereas in the first the activation/deactivation rates of the single gene copy are constant, in the second the protein, now a transcription factor, amplifies the deactivation rate, so introducing a negative feedback. The drug is assumed to enhance the elimination of the protein, and in both cases the success of therapy is assured by keeping the level of the given protein under a threshold for a fixed time. Our numerical simulations suggests that the gene switching plays a primary role in determining the sigmoidal shape of dose-response curves. Moreover, the simulations show interesting phenomena related to the magnitude of the average gene switching time and to the drug concentration. In particular, for slow gene switching a significant fraction of cells can respond also in the absence of drug or with drug concentrations insufficient for the response in a deterministic setting. For higher drug concentrations, the non-responding fraction exhibits a maximum at intermediate values of the gene switching rates. For fast gene switching, instead, the stochastic prediction follows the prediction of the deterministic approximation, with all the cells responding or non-responding according to the drug dose.

Gene switching rate determines response to extrinsic perturbations in the self-activation transcriptional network motif

Gene switching dynamics is a major source of randomness in genetic networks, also in the case of large concentrations of the transcription factors. In this work, we consider a common network motif - the positive feedback of a transcription factor on its own synthesis - and assess its response to extrinsic noises perturbing gene deactivation in a variety of settings where the network might operate. These settings are representative of distinct cellular types, abundance of transcription factors and ratio between gene switching and protein synthesis rates. By investigating noise-induced transitions among the different network operative states, our results suggest that gene switching rates are key parameters to shape network response to external perturbations, and that such response depends on the particular biological setting, i.e. the characteristic time scales and protein abundance. These results might have implications on our understanding of irreversible transitions for noise-related phenomena such as cellular differentiation. In addition these evidences suggest to adopt the appropriate mathematical model of the network in order to analyze the system consistently to the reference biological setting.

Feedbacks, Bifurcations, and Cell Fate Decision-Making in the p53 System

The p53 transcription factor is a regulator of key cellular processes including DNA repair, cell cycle arrest, and apoptosis. In this theoretical study, we investigate how the complex circuitry of the p53 network allows for stochastic yet unambiguous cell fate decision-making. The proposed Markov chain model consists of the regulatory core and two subordinated bistable modules responsible for cell cycle arrest and apoptosis. The regulatory core is controlled by two negative feedback loops (regulated by Mdm2 and Wip1) responsible for oscillations, and two antagonistic positive feedback loops (regulated by phosphatases Wip1 and PTEN) responsible for bistability. By means of bifurcation analysis of the deterministic approximation we capture the recurrent solutions (i.e., steady states and limit cycles) that delineate temporal responses of the stochastic system. Direct switching from the limit-cycle oscillations to the “apoptotic” steady state is enabled by the existence of a subcritical Neimark—Sacker bifurcation in which the limit cycle loses its stability by merging with an unstable invariant torus. Our analysis provides an explanation why cancer cell lines known to have vastly diverse expression levels of Wip1 and PTEN exhibit a broad spectrum of responses to DNA damage: from a fast transition to a high level of p53 killer (a p53 phosphoform which promotes commitment to apoptosis) in cells characterized by high PTEN and low Wip1 levels to long-lasting p53 level oscillations in cells having PTEN promoter methylated (as in, e.g., MCF-7 cell line).

Cancers are diseases of signaling networks. Transcription factor p53 is a pivotal node of a network that integrates a variety of stress signals and governs critical processes of DNA repair, cell cycle arrest, and apoptosis. Somewhat paradoxically, despite the fact that carcinogenesis is prevalently caused by p53 network malfunction, most of our knowledge about p53 signaling is based on cancer or immortalized cell lines. In this paper, we construct a mathematical model of intact p53 network to understand dynamics of non-cancerous cells and then dynamics of cancerous cells by introducing perturbations to the regulatory system. Cell fate decisions are enabled by the presence of interlinked feedback loops which give rise to a rich repertoire of behaviors. We explain and analyze by means of numerical simulations how the dynamical structure of the regulatory system allows for generating unambiguous single-cell fate decisions, also in the case when the cell population splits into an apoptotic and a surviving subpopulation. Perturbation analysis provides an explanation why cancer cell lines known to have vastly diverse expression levels of p53 regulators can exhibit a broad spectrum of responses to DNA damage.