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Register a new userMathematical and Statistical Techniques for Systems Medicine: The Wnt Signaling Pathway as a Case Study
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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.
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To support and guide an extensive experimental research into systems biology of signaling pathways, increasingly more mechanistic models are being developed with hopes of gaining further insight into biological processes. In order to analyse these models, computational and statistical techniques are needed to estimate the unknown kinetic parameters. This chapter reviews methods from frequentist and Bayesian statistics for estimation of parameters and for choosing which model is best for modeling the underlying system. Approximate Bayesian Computation (ABC) techniques are introduced and employed to explore different hypothesis about the JAK-STAT signaling pathway.
Two distinct mechanisms for filtering noise in an input signal are identified in a class of adaptive sensory networks. We find that the high frequency noise is filtered by the output degradation process through time-averaging; while the low frequency noise is damped by adaptation through negative feedback. Both filtering processes themselves introduce intrinsic noises, which are found to be unfiltered and can thus amount to a significant internal noise floor even without signaling. These results are applied to E. coli chemotaxis. We show unambiguously that the molecular mechanism for the Berg-Purcell time-averaging scheme is the dephosphorylation of the response regulator CheY-P, not the receptor adaptation process as previously suggested. The high frequency noise due to the stochastic ligand binding-unbinding events and the random ligand molecule diffusion is averaged by the CheY-P dephosphorylation process to a negligible level in E.coli. We identify a previously unstudied noise source caused by the random motion of the cell in a ligand gradient. We show that this random walk induced signal noise has a divergent low frequency component, which is only rendered finite by the receptor adaptation process. For gradients within the E. coli sensing range, this dominant external noise can be comparable to the significant intrinsic noise in the system. The dependence of the response and its fluctuations on the key time scales of the system are studied systematically. We show that the chemotaxis pathway may have evolved to optimize gradient sensing, strong response, and noise control in different time scales
In the last decades, the interest to understand the connection between brain and body has grown notably. For example, in psychoneuroimmunology many studies associate stress, arising from many different sources and situations, to changes in the immune system from the medical or immunological point of view as well as from the biochemical one. In this paper we identify important behaviours of this interplay between the immune system and stress from medical studies and seek to represent them qualitatively in a paradigmatic, yet simple, mathematical model. To that end we develop a differential equation model with two equations for infection level and immune system, which integrates the effects of stress as an additional parameter. We are able to reproduce a stable healthy state for little stress, an oscillatory state between healthy and infected states for high stress, and a burn-out or stable sick state for extremely high stress. The mechanism between the different dynamics is controlled by two saddle-node in cycle (SNIC) bifurcations. Furthermore, our model is able to capture an induced infection upon dropping from moderate to low stress, and it predicts increasing infection periods upon increasing before eventually reaching a burn-out state.
In machine learning applications, the reliability of predictions is significant for assisted decision and risk control. As an effective framework to quantify the prediction reliability, conformal prediction (CP) was developed with the CPKNN (CP with kNN). However, the conventional CPKNN suffers from high variance and bias and long computational time as the feature dimensionality increases. To address these limitations, a new CP framework-conformal prediction with shrunken centroids (CPSC) is proposed. It regularizes the class centroids to attenuate the irrelevant features and shrink the sample space for predictions and reliability quantification. To compare CPKNN and CPSC, we employed them in the classification of 12 categories of alternative herbal medicine with electronic nose as a case and assessed them in two tasks: 1) offline prediction: the training set was fixed and the accuracy on the testing set was evaluated; 2) online prediction with data augmentation: they filtered unlabeled data to augment the training data based on the prediction reliability and the final accuracy of testing set was compared. The result shows that CPSC significantly outperformed CPKNN in both two tasks: 1) CPSC reached a significantly higher accuracy with lower computation cost, and with the same credibility output, CPSC generally achieves a higher accuracy; 2) the data augmentation process with CPSC robustly manifested a statistically significant improvement in prediction accuracy with different reliability thresholds, and the augmented data were more balanced in classes. This novel CPSC provides higher prediction accuracy and better reliability quantification, which can be a reliable assistance in decision support.
Biomedical data are widely accepted in developing prediction models for identifying a specific tumor, drug discovery and classification of human cancers. However, previous studies usually focused on different classifiers, and overlook the class imbalance problem in real-world biomedical datasets. There are a lack of studies on evaluation of data pre-processing techniques, such as resampling and feature selection, on imbalanced biomedical data learning. The relationship between data pre-processing techniques and the data distributions has never been analysed in previous studies. This article mainly focuses on reviewing and evaluating some popular and recently developed resampling and feature selection methods for class imbalance learning. We analyse the effectiveness of each technique from data distribution perspective. Extensive experiments have been done based on five classifiers, four performance measures, eight learning techniques across twenty real-world datasets. Experimental results show that: (1) resampling and feature selection techniques exhibit better performance using support vector machine (SVM) classifier. However, resampling and Feature Selection techniques perform poorly when using C4.5 decision tree and Linear discriminant analysis classifiers; (2) for datasets with different distributions, techniques such as Random undersampling and Feature Selection perform better than other data pre-processing methods with T Location-Scale distribution when using SVM and KNN (K-nearest neighbours) classifiers. Random oversampling outperforms other methods on Negative Binomial distribution using Random Forest classifier with lower level of imbalance ratio; (3) Feature Selection outperforms other data pre-processing methods in most cases, thus, Feature Selection with SVM classifier is the best choice for imbalanced biomedical data learning.
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