Biological Network Reconstruction and Equation Inference with Hidden Nodes

点击翻译按钮获取中文摘要

Biological systems are highly complex and usually involve components which cannot be directly measured. These systems can be modelled using networks, with nodes representing variables and edges their interactions. This project will start from methodology developed by the Isambert group at Institut Curie, Paris called temporal multivariate information-based inductive causation (tMIIC) which takes time series data and constructs a causal network. A key feature of tMIIC is its ability to identify latent causal factors, what we will call 'hidden nodes'. This project can be split into three main subsections. Firstly, tMIIC will be benchmarked on its ability to reconstruct hidden nodes. Here, toy models with known network structures are used to generate trajectories. These are given to tMIIC which should be able to reconstruct the network. A trajectory corresponding to a variable will then be omitted, and tMIIC will be expected to identify the presence of the hidden node. Its performance will be assessed and can be used as a benchmark.Once tMIIC has been used to infer a network to uncover the interactions of the system, we plan to use a generative modelling approach to infer the equations which describe them. This involves the use of two machine learning models: a generator and a discriminator. The objective of the generator is to generate trajectories of the model which are indistinguishable from the true data. The discriminator is a classifier and is trained simultaneously, with the objective of distinguishing true trajectories from those produced by the generator. Initially, the dynamic form of the equations will be assumed as Langevin type stochastic equations which couple the observed and hidden dynamics. A starting point would be to use linear equations where the interaction matrix is determined by the adjacency matrix of the learned network structure. Depending on the system being modelled, different functional forms for terms in the equations (such as mass-action and Michaelis-Menten type kinetics) can be adapted and used. An extension to this part of the project is to use neural ODEs to learn appropriate functions for the equations. Neural ODEs are models which use neural networks trained on observational data to specify the dynamics of the system of interest.Once this methodology has been developed, we plan to apply the techniques to a dataset of live cell imaging microscopy from an ex-vivo tumour ecosystem. This is a technology which allows cancer cells to grow in the presence of components found where they normally grow (what is known as the tumour microenvironment). Specifically, the data that we will be looking at considers the effect of immune cells and cancer associated fibroblasts (CAFs). This data comes from experimental collaborators in the Parrini group at Institut Curie, Paris. A preliminary literature search found a gap in published models for this system, so novel model design will be required here.This project falls within the EPSRC biological informatics and mathematical biology research themes.