Fine-grained mathematical modeling for cost-effectiveness evaluation of public health policies for cervical cancer, with application to a Colombian case study.

BACKGROUND: Cervical cancer (CC) is globally ranked fourth in terms of incidence and mortality among women. Vaccination against Human Papillomavirus (HPV) and screening programs can significantly reduce CC mortality rates. Hence, executing cost-effective public health policies for prevention and surveillance is crucial. However, defining policies that make the best use of the available resources is not easy, as it requires predicting the long-term costs and results of interventions on a changing population. Since the simpler task of predicting the results of public health policies is difficult, devising those that make the best usage of available resources is an arduous challenge for decision-makers. METHODS: This paper proposes a fine-grained epidemiological simulation model based on differential equations, to effectively predict the costs and effectiveness of CC public health policies that include vaccination and screening. The model represents population dynamics, HPV transmission within the population, likelihood of infection clearance, virus-induced appearance of precancerous lesions and eventually CC, as well as immunity gained with vaccination and early detection with screening. RESULTS: We offer a compartmentalized modeling approach that separates population, epidemics, and intervention concerns. We instantiate models with actual data from a Colombian case study and analyze their results to show how our modeling approach can support CEA studies. Moreover, we implement models in an open-source software tool to simultaneously define and evaluate multiple policies. With the support of the tool, we analyze 54 policies within a 30-year time horizon and use as a comparator the CC policy that has been used until recently. We identify 8 dominant policies, the best one with an ICER of 6.3 million COP (Colombian Pesos) per averted DALY. We also validate the modeling approach against the available population and HPV epidemic data. The effects of uncertainty in the values of key parameters (discount rate, sensitivity of screening tests) is evaluated through one-way sensitivity analysis. CONCLUSIONS: Our modeling approach can provide valuable support for healthcare decision-makers. The implementation into an automated tool allows customizing the analysis with country-specific data, flexibly defining public health policies to be evaluated, and conducting disaggregate analyses of their cost and effectiveness.

An Integrative Approach to Computational Modelling of the Gene Regulatory Network Controlling Clostridium botulinum Type A1 Toxin Production.

Clostridium botulinum produces botulinum neurotoxins (BoNTs), highly potent substances responsible for botulism. Currently, mathematical models of C. botulinum growth and toxigenesis are largely aimed at risk assessment and do not include explicit genetic information beyond group level but integrate many component processes, such as signalling, membrane permeability and metabolic activity. In this paper we present a scheme for modelling neurotoxin production in C. botulinum Group I type A1, based on the integration of diverse information coming from experimental results available in the literature. Experiments show that production of BoNTs depends on the growth-phase and is under the control of positive and negative regulatory elements at the intracellular level. Toxins are released as large protein complexes and are associated with non-toxic components. Here, we systematically review and integrate those regulatory elements previously described in the literature for C. botulinum Group I type A1 into a population dynamics model, to build the very first computational model of toxin production at the molecular level. We conduct a validation of our model against several items of published experimental data for different wild type and mutant strains of C. botulinum Group I type A1. The result of this process underscores the potential of mathematical modelling at the cellular level, as a means of creating opportunities in developing new strategies that could be used to prevent botulism; and potentially contribute to improved methods for the production of toxin that is used for therapeutics.

Time Series Analysis of the Bacillus subtilis Sporulation Network Reveals Low Dimensional Chaotic Dynamics.

Chaotic behavior refers to a behavior which, albeit irregular, is generated by an underlying deterministic process. Therefore, a chaotic behavior is potentially controllable. This possibility becomes practically amenable especially when chaos is shown to be low-dimensional, i.e., to be attributable to a small fraction of the total systems components. In this case, indeed, including the major drivers of chaos in a system into the modeling approach allows us to improve predictability of the systems dynamics. Here, we analyzed the numerical simulations of an accurate ordinary differential equation model of the gene network regulating sporulation initiation in Bacillus subtilis to explore whether the non-linearity underlying time series data is due to low-dimensional chaos. Low-dimensional chaos is expectedly common in systems with few degrees of freedom, but rare in systems with many degrees of freedom such as the B. subtilis sporulation network. The estimation of a number of indices, which reflect the chaotic nature of a system, indicates that the dynamics of this network is affected by deterministic chaos. The neat separation between the indices obtained from the time series simulated from the model and those obtained from time series generated by Gaussian white and colored noise confirmed that the B. subtilis sporulation network dynamics is affected by low dimensional chaos rather than by noise. Furthermore, our analysis identifies the principal driver of the networks chaotic dynamics to be sporulation initiation phosphotransferase B (Spo0B). We then analyzed the parameters and the phase space of the system to characterize the instability points of the network dynamics, and, in turn, to identify the ranges of values of Spo0B and of the other drivers of the chaotic dynamics, for which the whole system is highly sensitive to minimal perturbation. In summary, we described an unappreciated source of complexity in the B. subtilis sporulation network by gathering evidence for the chaotic behavior of the system, and by suggesting candidate molecules driving chaos in the system. The results of our chaos analysis can increase our understanding of the intricacies of the regulatory network under analysis, and suggest experimental work to refine our behavior of the mechanisms underlying B. subtilis sporulation initiation control.

New Elements To Consider When Modeling the Hazards Associated with Botulinum Neurotoxin in Food.

Botulinum neurotoxins (BoNTs) produced by the anaerobic bacterium Clostridium botulinum are the most potent biological substances known to mankind. BoNTs are the agents responsible for botulism, a rare condition affecting the neuromuscular junction and causing a spectrum of diseases ranging from mild cranial nerve palsies to acute respiratory failure and death. BoNTs are a potential biowarfare threat and a public health hazard, since outbreaks of foodborne botulism are caused by the ingestion of preformed BoNTs in food. Currently, mathematical models relating to the hazards associated with C. botulinum, which are largely empirical, make major contributions to botulinum risk assessment. Evaluated using statistical techniques, these models simulate the response of the bacterium to environmental conditions. Though empirical models have been successfully incorporated into risk assessments to support food safety decision making, this process includes significant uncertainties so that relevant decision making is frequently conservative and inflexible. Progression involves encoding into the models cellular processes at a molecular level, especially the details of the genetic and molecular machinery. This addition drives the connection between biological mechanisms and botulism risk assessment and hazard management strategies. This review brings together elements currently described in the literature that will be useful in building quantitative models of C. botulinum neurotoxin production. Subsequently, it outlines how the established form of modeling could be extended to include these new elements. Ultimately, this can offer further contributions to risk assessments to support food safety decision making.

Role of Computational Modeling in Understanding Cell Cycle Oscillators.

The periodic oscillations in the activity of the cell cycle regulatory program, drives the timely activation of key cell cycle events. Interesting dynamical systems, such as oscillators, have been investigated by various theoretical and computational modeling methods. Thanks to the insights achieved by these modeling efforts we have gained considerable insights about the underlying molecular regulatory networks that can drive cell cycle oscillations. Here we review the basic features and characteristics of biological oscillators, discussing from a computational modeling point of view their specific architectures and the current knowledge about the dynamics that the life evolution selected to drive cell cycle oscillations.

The pattern of growth observed for Clostridium botulinum type A1 strain ATCC 19397 is influenced by nutritional status and quorum sensing: a modelling perspective.

Botulinum neurotoxins (BoNTs) produced by the anaerobic bacterium Clostridium botulinum are the most poisonous substances known to mankind. However, toxin regulation and signals triggering synthesis as well as the regulatory network and actors controlling toxin production are unknown. Experiments show that the neurotoxin gene is growth phase dependent for C. botulinum type A1 strain ATCC 19397, and toxin production is influenced both by culture conditions and nutritional status of the medium. Building mathematical models to describe the genetic and molecular machinery that drives the synthesis and release of BoNT requires a simultaneous description of the growth of the bacterium in culture. Here, we show four plausible modelling options which could be considered when constructing models describing the pattern of growth observed in a botulinum growth medium. Commonly used bacterial growth models are unsuitable to fit the pattern of growth observed, since they only include monotonic growth behaviour. We find that a model that includes both the nutritional status and the ability of the cells to sense their surroundings in a quorum-sensing manner is most successful at explaining the pattern of growth obtained for C. botulinum type A1 strain ATCC 19397.

Computational modelling and analysis of the molecular network regulating sporulation initiation in Bacillus subtilis.

BACKGROUND: Bacterial spores are important contaminants in food, and the spore forming bacteria are often implicated in food safety and food quality considerations. Spore formation is a complex developmental process involving the expression of more than 500 genes over the course of 6 to 8 hrs. The process culminates in the formation of resting cells capable of resisting environmental extremes and remaining dormant for long periods of time, germinating when conditions promote further vegetative growth. Experimental observations of sporulation and germination are problematic and time consuming so that reliable models are an invaluable asset in terms of prediction and risk assessment. In this report we develop a model which assists in the interpretation of sporulation dynamics. RESULTS: This paper defines and analyses a mathematical model for the network regulating Bacillus subtilis sporulation initiation, from sensing of sporulation signals down to the activation of the early genes under control of the master regulator Spo0A. Our model summarises and extends other published modelling studies, by allowing the user to execute sporulation initiation in a scenario where Isopropyl ß-D-1-thiogalactopyranoside (IPTG) is used as an artificial sporulation initiator as well as in modelling the induction of sporulation in wild-type cells. The analysis of the model results and the comparison with experimental data indicate that the model is good at predicting inducible responses to sporulation signals. However, the model is unable to reproduce experimentally observed accumulation of phosphorelay sporulation proteins in wild type B. subtilis. This model also highlights that the phosphorelay sub-component, which relays the signals detected by the sensor kinases to the master regulator Spo0A, is crucial in determining the response dynamics of the system. CONCLUSION: We show that there is a complex connectivity between the phosphorelay features and the master regulatory Spo0A. Additional we discovered that the experimentally observed regulation of the phosphotransferase Spo0B for wild-type B. subtilis may be playing an important role in the network which suggests that modelling of sporulation initiation may require additional experimental support.

Role of mRNA Gestation and Senescence in Noise Reduction during the Cell Cycle.

Recent innovations in experimental techniques on single molecule detection resulted in advances in the quantification of molecular noise in several systems, and provide suitable data for defining stochastic computational models of biological processes. Some of the latest stochastic models of cell cycle regulation analyzed the effect of noise on cell cycle variability. In their study, Kar et al. (Proc. Natl. Acad. Sci. USA 106, 6471-6476, 2009) found that the observed variances of cell cycle time and cell division size distributions cannot be matched with the measured long half-lives of mRNAs. Here, we investigate through modeling and simulation how the noise created by the transcription and degradation processes of a key cell cycle controller mRNA affect the statistics of cell cycle time and cell size at division. Our model consists of an encoding of the model of Kar et al. into a stochastic Petri net, with the extensions necessary to represent multiple synthesis (gestation) and degradation (senescence) steps in the regulation of mRNAs. We found that few steps of gestation and senescence of mRNA are enough to give a good match for both the measured half-lives and variability of cell cycle-statistics. This result suggests that the complex process of transcription can be more accurately approximated by multi-step linear processes.

Role of mRNA gestation and senescence in noise reduction during the cell cycle.

Recent innovations in experimental techniques on single molecule detection resulted in advances in the quantification of molecular noise in several systems, and provide suitable data for defining stochastic computational models of biological processes. Some of the latest stochastic models of cell cycle regulation analyzed the effect of noise on cell cycle variability. In their study, Kar et al. (Proc. Natl. Acad. Sci. USA 106, 6471-6476, 2009) found that the observed variances of cell cycle time and cell division size distributions cannot be matched with the measured long half-lives of mRNAs. Here, we investigate through modeling and simulation how the noise created by the transcription and degradation processes of a key cell cycle controller mRNA affect the statistics of cell cycle time and cell size at division. Our model consists of an encoding of the model of Kar et al. into a stochastic Petri net, with the extensions necessary to represent multiple synthesis (gestation) and degradation (senescence) steps in the regulation of mRNAs. We found that few steps of gestation and senescence of mRNA are enough to give a good match for both the measured half-lives and variability of cell cycle-statistics. This result suggests that the complex process of transcription can be more accurately approximated by multi-step linear processes.

An efficient and exact stochastic simulation method to analyze rare events in biochemical systems.

In robust biological systems, wide deviations from highly controlled normal behavior may be rare, yet they may result in catastrophic complications. While in silico analysis has gained an appreciation as a tool to offer insights into system-level properties of biological systems, analysis of such rare events provides a particularly challenging computational problem. This paper proposes an efficient stochastic simulation method to analyze rare events in biochemical systems. Our new approach can substantially increase the frequency of the rare events of interest by appropriately manipulating the underlying probability measure of the system, allowing high-precision results to be obtained with substantially fewer simulation runs than the conventional direct Monte Carlo simulation. Here, we show the algorithm of our new approach, and we apply it to the analysis of rare deviant transitions of two systems, resulting in several orders of magnitude speedup in generating high-precision estimates compared with the conventional Monte Carlo simulation.

Stochastic Petri Net extension of a yeast cell cycle model.

This paper presents the definition, solution and validation of a stochastic model of the budding yeast cell cycle, based on Stochastic Petri Nets (SPN). A specific family of SPNs is selected for building a stochastic version of a well-established deterministic model. We describe the procedure followed in defining the SPN model from the deterministic ODE model, a procedure that can be largely automated. The validation of the SPN model is conducted with respect to both the results provided by the deterministic one and the experimental results available from literature. The SPN model catches the behavior of the wild type budding yeast cells and a variety of mutants. We show that the stochastic model matches some characteristics of budding yeast cells that cannot be found with the deterministic model. The SPN model fine-tunes the simulation results, enriching the breadth and the quality of its outcome.