Mathematical and Statistical Techniques for Systems Medicine: The Wnt Signaling Pathway as a Case Study

The last decade has seen an explosion in models that describe phenomena in systems medicine. Such models are especially useful for studying signaling pathways, such as the Wnt pathway. In this chapter we use the Wnt pathway to showcase current mathematical and statistical techniques that enable modelers to gain insight into (models of) gene regulation, and generate testable predictions. We introduce a range of modeling frameworks, but focus on ordinary differential equation (ODE) models since they remain the most widely used approach in systems biology and medicine and continue to offer great potential. We present methods for the analysis of a single model, comprising applications of standard dynamical systems approaches such as nondimensionalization, steady state, asymptotic and sensitivity analysis, and more recent statistical and algebraic approaches to compare models with data. We present parameter estimation and model comparison techniques, focusing on Bayesian analysis and coplanarity via algebraic geometry. Our intention is that this (non exhaustive) review may serve as a useful starting point for the analysis of models in systems medicine.Comment: Submitted to 'Systems Medicine' as a book chapte

Elective high-frequency oscillatory ventilation in preterm infants with respiratory distress syndrome: an individual patient data meta-analysis

<p>Abstract</p> <p>Background</p> <p>Despite the considerable amount of evidence from randomized controlled trials and meta-analyses, uncertainty remains regarding the efficacy and safety of high-frequency oscillatory ventilation as compared to conventional ventilation in the early treatment of respiratory distress syndrome in preterm infants. This results in a wide variation in the clinical use of high-frequency oscillatory ventilation for this indication throughout the world. The reasons are an unexplained heterogeneity between trial results and a number of unanswered, clinically important questions. Do infants with different risk profiles respond differently to high-frequency oscillatory ventilation? How does the ventilation strategy affect outcomes? Does the delay – either from birth or from the moment of intubation – to the start of high-frequency oscillation modify the effect of the intervention? Instead of doing new trials, those questions can be addressed by re-analyzing the individual patient data from the existing randomized controlled trials.</p> <p>Methods/Design</p> <p>A systematic review with meta-analysis based on individual patient data. This involves the central collection, validation and re-analysis of the original individual data from each infant included in each randomized controlled trial addressing this question.</p> <p>The study objective is to estimate the effect of high-frequency oscillatory ventilation on the risk for the combined outcome of death or bronchopulmonary dysplasia or a severe adverse neurological event. In addition, it will explore whether the effect of high-frequency oscillatory ventilation differs by the infant's risk profile, defined by gestational age, intrauterine growth restriction, severity of lung disease at birth and whether or not corticosteroids were given to the mother prior to delivery. Finally, it will explore the importance of effect modifying factors such as the ventilator device, ventilation strategy and the delay to the start of high-frequency ventilation.</p> <p>Discussion</p> <p>An international collaborative group, the PreVILIG Collaboration (Prevention of Ventilator Induced Lung Injury Group), has been formed with the investigators of the original randomized trials to conduct this systematic review. In the field of neonatology, individual patient data meta-analysis has not been used previously. Final results are expected to be available by the end of 2009.</p

3-D Ultrastructure of O. tauri: Electron Cryotomography of an Entire Eukaryotic Cell

The hallmark of eukaryotic cells is their segregation of key biological functions into discrete, membrane-bound organelles. Creating accurate models of their ultrastructural complexity has been difficult in part because of the limited resolution of light microscopy and the artifact-prone nature of conventional electron microscopy. Here we explored the potential of the emerging technology electron cryotomography to produce three-dimensional images of an entire eukaryotic cell in a near-native state. Ostreococcus tauri was chosen as the specimen because as a unicellular picoplankton with just one copy of each organelle, it is the smallest known eukaryote and was therefore likely to yield the highest resolution images. Whole cells were imaged at various stages of the cell cycle, yielding 3-D reconstructions of complete chloroplasts, mitochondria, endoplasmic reticula, Golgi bodies, peroxisomes, microtubules, and putative ribosome distributions in-situ. Surprisingly, the nucleus was seen to open long before mitosis, and while one microtubule (or two in some predivisional cells) was consistently present, no mitotic spindle was ever observed, prompting speculation that a single microtubule might be sufficient to segregate multiple chromosomes

Frozen and Invariant Quantum Discord under Local Dephasing Noise

In this chapter, we intend to explore and review some remarkable dynamical properties of quantum discord under various different open quantum system models. Specifically, our discussion will include several concepts connected to the phenomena of time invariant and frozen quantum discord. Furthermore, we will elaborate on the relation of these two phenomena to the non-Markovian features of the open system dynamics and to the usage of dynamical decoupling protocols.Comment: 29 pages, 8 figure

A formally verified compiler back-end

This article describes the development and formal verification (proof of semantic preservation) of a compiler back-end from Cminor (a simple imperative intermediate language) to PowerPC assembly code, using the Coq proof assistant both for programming the compiler and for proving its correctness. Such a verified compiler is useful in the context of formal methods applied to the certification of critical software: the verification of the compiler guarantees that the safety properties proved on the source code hold for the executable compiled code as well

Pedestrian, Crowd, and Evacuation Dynamics

This contribution describes efforts to model the behavior of individual pedestrians and their interactions in crowds, which generate certain kinds of self-organized patterns of motion. Moreover, this article focusses on the dynamics of crowds in panic or evacuation situations, methods to optimize building designs for egress, and factors potentially causing the breakdown of orderly motion.Comment: This is a review paper. For related work see http://www.soms.ethz.c

Nucleocytoplasmic transport: a thermodynamic mechanism

The nuclear pore supports molecular communication between cytoplasm and nucleus in eukaryotic cells. Selective transport of proteins is mediated by soluble receptors, whose regulation by the small GTPase Ran leads to cargo accumulation in, or depletion from the nucleus, i.e., nuclear import or nuclear export. We consider the operation of this transport system by a combined analytical and experimental approach. Provocative predictions of a simple model were tested using cell-free nuclei reconstituted in Xenopus egg extract, a system well suited to quantitative studies. We found that accumulation capacity is limited, so that introduction of one import cargo leads to egress of another. Clearly, the pore per se does not determine transport directionality. Moreover, different cargo reach a similar ratio of nuclear to cytoplasmic concentration in steady-state. The model shows that this ratio should in fact be independent of the receptor-cargo affinity, though kinetics may be strongly influenced. Numerical conservation of the system components highlights a conflict between the observations and the popular concept of transport cycles. We suggest that chemical partitioning provides a framework to understand the capacity to generate concentration gradients by equilibration of the receptor-cargo intermediary.Comment: in press at HFSP Journal, vol 3 16 text pages, 1 table, 4 figures, plus Supplementary Material include

Logistics of community smallpox control through contact tracing and ring vaccination: a stochastic network model

BACKGROUND: Previous smallpox ring vaccination models based on contact tracing over a network suggest that ring vaccination would be effective, but have not explicitly included response logistics and limited numbers of vaccinators. METHODS: We developed a continuous-time stochastic simulation of smallpox transmission, including network structure, post-exposure vaccination, vaccination of contacts of contacts, limited response capacity, heterogeneity in symptoms and infectiousness, vaccination prior to the discontinuation of routine vaccination, more rapid diagnosis due to public awareness, surveillance of asymptomatic contacts, and isolation of cases. RESULTS: We found that even in cases of very rapidly spreading smallpox, ring vaccination (when coupled with surveillance) is sufficient in most cases to eliminate smallpox quickly, assuming that 95% of household contacts are traced, 80% of workplace or social contacts are traced, and no casual contacts are traced, and that in most cases the ability to trace 1–5 individuals per day per index case is sufficient. If smallpox is assumed to be transmitted very quickly to contacts, it may at times escape containment by ring vaccination, but could be controlled in these circumstances by mass vaccination. CONCLUSIONS: Small introductions of smallpox are likely to be easily contained by ring vaccination, provided contact tracing is feasible. Uncertainties in the nature of bioterrorist smallpox (infectiousness, vaccine efficacy) support continued planning for ring vaccination as well as mass vaccination. If initiated, ring vaccination should be conducted without delays in vaccination, should include contacts of contacts (whenever there is sufficient capacity) and should be accompanied by increased public awareness and surveillance

18F-FDG PET during stereotactic body radiotherapy for stage I lung tumours cannot predict outcome: a pilot study

(18)F-Fluorodeoxyglucose positron emission tomography (FDG PET) has been used to assess metabolic response several months after stereotactic body radiotherapy (SBRT) for early-stage non-small cell lung cancer. However, whether a metabolic response can be observed already during treatment and thus can be used to predict treatment outcome is undetermined. Ten medically inoperable patients with FDG PET-positive lung tumours were included. SBRT consisted of three fractions of 20 Gy delivered at the 80% isodose at days 1, 6 and 11. FDG PET was performed before, on day 6 immediately prior to administration of the second fraction of SBRT and 12 weeks after completion of SBRT. Tumour metabolism was assessed semi-quantitatively using the maximum standardized uptake value (SUV(max)) and SUV(70%). After the first fraction, median SUV(max) increased from 6.7 to 8.1 (p = 0.07) and median SUV(70%) increased from 5.7 to 7.1 (p = 0.05). At 12 weeks, both median SUV(max) and median SUV(70%) decreased by 63% to 3.1 (p = 0.008) and to 2.5 (p = 0.008), respectively. SUV increased during treatment, possibly due to radiation-induced inflammation. Therefore, it is unlikely that (18)F-FDG PET during SBRT will predict treatment success