Biological Network Reconstruction and Equation Inference with Hidden Nodes

生物系统是高度复杂的，通常涉及无法直接测量的成分。这些系统可以用网络来建模，节点代表变量，边代表变量的交互作用。这个项目将从巴黎居里夫人研究所的Isambert小组开发的称为基于时间多变量信息的归纳因果关系(TMIIC)的方法开始，该方法获取时间序列数据并构建因果网络。TMIIC的一个关键特征是它能够识别潜在的因果因素，我们将其称为“隐藏节点”。这个项目可以分成三个主要部分。首先，tMIIC将根据其重建隐藏节点的能力进行基准测试。这里，具有已知网络结构的玩具模型被用来生成轨迹。这些都被提供给tMIIC，tMIIC应该能够重建网络。然后，将省略对应于变量的轨迹，并且将期望tMIIC识别隐藏节点的存在。它的性能将被评估并可以用作基准。一旦tMIIC被用于推断网络以揭示系统的交互作用，我们计划使用生成建模方法来推断描述它们的方程。这涉及到两种机器学习模型的使用：生成器和鉴别器。生成器的目标是生成与真实数据难以区分的模型轨迹。鉴别器是一个分类器，同时被训练，目的是区分真实的轨迹和由生成器产生的轨迹。首先，方程的动力学形式将被假定为朗之万型随机方程，它耦合了观测到的动力学和隐藏的动力学。起始点将是使用线性方程，其中交互矩阵由学习的网络结构的邻接矩阵确定。根据所模拟的系统的不同，方程中项的不同函数形式(如质量作用力和米氏动力学)可以被采用和使用。该项目这一部分的扩展是使用神经常导函数来学习方程的适当函数。神经ODE是使用根据观察数据训练的神经网络来指定感兴趣系统的动力学的模型。一旦开发出这种方法，我们计划将这些技术应用于来自体外肿瘤生态系统的活细胞成像显微镜的数据集。这是一项允许癌细胞在正常生长的成分(即所谓的肿瘤微环境)存在的情况下生长的技术。具体地说，我们将看到的数据考虑了免疫细胞和癌症相关成纤维细胞(CAF)的影响。这些数据来自巴黎居里研究所帕里尼小组的实验合作者。初步的文献检索发现，已发表的该系统模型存在差距，因此需要进行新的模型设计。该项目属于EPSRC生物信息学和数学生物学研究主题。

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.