Modelling the effects of biological intervention in a dynamical gene network

TL;DR

The work develops two rigorous frameworks for modeling gene network alterations after perturbations, tailored to whether the base network is quantitative or mechanistic. It formally defines conditioning- and mechanistic-alt constructions that predict post-al alteration behavior from an initial model, and demonstrates their use in design of experiments and statistical validation or refitting of model parameters. The paper provides explicit derivations for Gaussian graphical models, dynamic Bayesian networks, and LiRE-style penalized regression, showing how alteration data can improve inference and prediction. Overall, the approach enables principled design and evaluation of gene perturbation experiments and improves estimation of baseline network parameters using alteration outcomes, with potential applications to CRISPR, RNAi, and related perturbation platforms.

Abstract

Cellular response to environmental and internal signals can be modeled by dynamical gene regulatory networks (GRN). In the literature, three main classes of gene network models can be distinguished: (i) non-quantitative (or data-based) models which do not describe the probability distribution of gene expressions; (ii) quantitative models which fully describe the probability distribution of all genes coexpression; and (iii) mechanistic models which allow for a causal interpretation of gene interactions. We propose two rigorous frameworks to model gene alteration in a dynamical GRN, depending on whether the network model is quantitative or mechanistic. We explain how these models can be used for design of experiment, or, if additional alteration data are available, for validation purposes or to improve the parameter estimation of the original model. We apply these methods to the Gaussian graphical model, which is quantitative but non-mechanistic, and to mechanistic models of Bayesian networks and penalized linear regression.

Figures (9)

• Figure 1: Schematic representation of a Gaussian graphical model and prediction of alteration (knock-out) of gene 1. Each node corresponds to a gene labeled from 1 to 4. (a) Without alteration: the mean expression of gene $i$ is $\mu_i$ and the covariance matrix of genes expression is $(\sigma_{ij})_{1\leq i,j\leq 4}$. (b) After knock-out of gene 1: $\mu_1$ and $\sigma_{11}$ were set to 0; the question of prediction amounts to determine the new values of the means and covariances $(\mu'_i)_{2\leq i\leq 4}$ and $(\sigma'_{ij})_{2\leq i,j\leq 4}$.
• Figure 2: Schematic representation of a mechanistic model and prediction of alteration (knock-out) of gene 1. Each node corresponds to a gene labeled from 1 to 4. (a) Without alteration: arrows represent direct influence of a gene on another; they encode a quantitative relation (not shown here). (b) After knock-out of gene 1: the problem of prediction consists in determining how the arrows and the quantitative relations they encode are modified.
• Figure 3: Prediction of gene alteration
• Figure 4: Dependency network between the expressions of genes 1, 2 and 3
• Figure 5: Bayesian dependency network of $(X_{ik})_{1\leq i\leq 3,\,1\leq k\leq 2}$ under $\mathbb{P}_\theta$.

Theorems & Definitions (7)

• Proposition 4.1
• Proposition 4.2
• Proposition 4.3
• Theorem 4.4
• Theorem 4.5
• Theorem A.1
• Proposition A.2