The current approach to the treatment of MDR TB presents a particular challenge from an economic perspective. Several studies (Floyd and others 2012; Resch and others 2006; Suarez and others 2002; Tupasi and others 2006) have suggested that the treatment of MDR TB is cost-effective. A recent systematic review found that the cost per DALY averted was lower than gross domestic product per capita in all 14 of the WHO subregions considered (Fitzpatrick and Floyd 2012). However, the absolute price of second-line drug regimens, even for LICs, can run into the thousands of dollars, with a three- or fourfold burden on total costs of the health system. For example, in South Africa, treating MDR TB costs more than half of the total national budget for TB control (Schnippel and others 2013), with hospitalized treatment costing more than US$15,000 per person treated (Pooran and others 2013; Schnippel and others 2013). However, these costs may be substantially reduced given the efforts to decentralize MDR TB treatment and care. Also potentially cost-effective, the cost of drug-susceptibility testing required to confirm a diagnosis of MDR TB treatment can also be substantial (Acuna-Villaorduna and others 2008; Floyd and others 2012), and, as highlighted in previous sections, culture-based DST provides a substantial practical challenge in settings with limited laboratory capacity. Additionally, the economic burden of MDR TB on households may be substantially higher than the costs of first-line treatment and is likely to be catastrophic (Ramma and others 2015; survey of MDR TB patient costs in South Africa, unpublished data).
This special section of Physical Biology focuses on multiple aspects of signal transduction, broadly defined as the study of the mechanisms by which cells communicate with their environment. Mechanisms of cell communication involve detection of incoming signals, which can be chemical, mechanical or electromagnetic, relaying these signals to intracellular processes, such as cytoskeletal networks or gene expression systems, and, ultimately, converting these signals to responses such as cell differentiation or death. Given the multiscale nature of signal transduction systems, they must be studied at multiple levels, from the identities and structures of molecules comprising signal detection and interpretation networks, to the systems-level properties of these networks. The 11 papers in this special section illustrate some of the most exciting aspects of signal transduction research. The first two papers, by Marie-Anne Félix [1] and by Efrat Oron and Natalia Ivanova [2], focus on cell-cell interactions in developing tissues, using vulval patterning in worm and cell fate specification in mammalian embryos as prime examples of emergent cell behaviors. Next come two papers from the groups of Julio Saez-Rodriguez [3] and Kevin Janes [4]. These papers discuss how the causal relationships between multiple components of signaling systems can be inferred using multivariable statistical analysis of empirical data. An authoritative review by Zarnitsyna and Zhu [5] presents a detailed discussion of the sequence of signaling events involved in T-cell triggering. Once the structure and components of the signaling systems are determined, they can be modeled using approaches that have been successful in other physical sciences. As two examples of such approaches, reviews by Rubinstein [6] and Kholodenko [7], present reaction-diffusion models of cell polarization and thermodynamics-based models of gene regulation. An important class of models takes the form of enzymatic networks
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Signal transduction pathways are usually modelled using classical quantitative methods, which are based on ordinary differential equations (ODEs). However, some difficulties are inherent in this approach. On the one hand, the kinetic parameters involved are often unknown and have to be estimated. With increasing size and complexity of signal transduction pathways, the estimation of missing kinetic data is not possible. On the other hand, ODEs based models do not support any explicit insights into possible (signal-) flows within the network. Moreover, a huge amount of qualitative data is available due to high-throughput techniques. In order to get information on the systems behaviour, qualitative analysis techniques have been developed. Applications of the known qualitative analysis methods concern mainly metabolic networks. Petri net theory provides a variety of established analysis techniques, which are also applicable to signal transduction models. In this context special properties have to be considered and new dedicated techniques have to be designed. We apply Petri net theory to model and analyse signal transduction pathways first qualitatively before continuing with quantitative analyses. This paper demonstrates how to build systematically a discrete model, which reflects provably the qualitative biological behaviour without any knowledge of kinetic parameters. The mating pheromone response pathway in Saccharomyces cerevisiae serves as case study. We propose an approach for model validation of signal transduction pathways based on the network structure only. For this purpose, we introduce the new notion of feasible t-invariants, which represent minimal self-contained subnets being active under a given input situation. Each of these subnets stands for a signal flow in the system. We define maximal common transition sets (MCT-sets), which can be used for t-invariant examination and net decomposition into smallest biologically meaningful functional units. The
Background Signal transduction pathways are usually modelled using classical quantitative methods, which are based on ordinary differential equations (ODEs). However, some difficulties are inherent in this approach. On the one hand, the kinetic parameters involved are often unknown and have to be estimated. With increasing size and complexity of signal transduction pathways, the estimation of missing kinetic data is not possible. On the other hand, ODEs based models do not support any explicit insights into possible (signal-) flows within the network. Moreover, a huge amount of qualitative data is available due to high-throughput techniques. In order to get information on the systems behaviour, qualitative analysis techniques have been developed. Applications of the known qualitative analysis methods concern mainly metabolic networks. Petri net theory provides a variety of established analysis techniques, which are also applicable to signal transduction models. In this context special properties have to be considered and new dedicated techniques have to be designed. Methods We apply Petri net theory to model and analyse signal transduction pathways first qualitatively before continuing with quantitative analyses. This paper demonstrates how to build systematically a discrete model, which reflects provably the qualitative biological behaviour without any knowledge of kinetic parameters. The mating pheromone response pathway in Saccharomyces cerevisiae serves as case study. Results We propose an approach for model validation of signal transduction pathways based on the network structure only. For this purpose, we introduce the new notion of feasible t-invariants, which represent minimal self-contained subnets being active under a given input situation. Each of these subnets stands for a signal flow in the system. We define maximal common transition sets (MCT-sets), which can be used for t-invariant examination and net decomposition into smallest biologically
Background Combinatorial complexity is a challenging problem in detailed and mechanistic mathematical modeling of signal transduction. This subject has been discussed intensively and a lot of progress has been made within the last few years. A software tool (BioNetGen) was developed which allows an automatic rule-based set-up of mechanistic model equations. In many cases these models can be reduced by an exact domain-oriented lumping technique. However, the resulting models can still consist of a very large number of differential equations. Results We introduce a new reduction technique, which allows building modularized and highly reduced models. Compared to existing approaches further reduction of signal transduction networks is possible. The method also provides a new modularization criterion, which allows to dissect the model into smaller modules that are called layers and can be modeled independently. Hallmarks of the approach are conservation relations within each layer and connection of layers by signal flows instead of mass flows. The reduced model can be formulated directly without previous generation of detailed model equations. It can be understood and interpreted intuitively, as model variables are macroscopic quantities that are converted by rates following simple kinetics. The proposed technique is applicable without using complex mathematical tools and even without detailed knowledge of the mathematical background. However, we provide a detailed mathematical analysis to show performance and limitations of the method. For physiologically relevant parameter domains the transient as well as the stationary errors caused by the reduction are negligible. Conclusion The new layer based reduced modeling method allows building modularized and strongly reduced models of signal transduction networks. Reduced model equations can be directly formulated and are intuitively interpretable. Additionally, the method provides very good approximations especially for
Mathematical models of biological processes become more and more important in biology. The aim is a holistic understanding of how processes such as cellular communication, cell division, regulation, homeostasis, or adaptation work, how they are regulated, and how they react to perturbations. The great complexity of most of these processes necessitates the generation of mathematical models in order to address these questions. In this chapter we provide an introduction to basic principles of dynamic modeling and highlight both problems and chances of dynamic modeling in biology. The main focus will be on modeling of s transduction pathways, which requires the application of a special modeling approach. A common pattern, especially in eukaryotic signaling systems, is the formation of multi protein signaling complexes. Even for a small number of interacting proteins the number of distinguishable molecular species can be extremely high. This combinatorial complexity is due to the great number of distinct binding domains of many receptors and scaffold proteins involved in signal transduction. However, these problems can be overcome using a new domain-oriented modeling approach, which makes it possible to handle complex and branched signaling pathways. 2ff7e9595c
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