6. Gene Regulatory Networks EECS 600: Systems Biology & Bioinformatics Instructor: Mehmet Koyuturk 1

Regulation of Gene Expression 6. Gene Regulatory Networks Regulation of Gene Expression Transcriptional Regulation of telomerase protein component gene hTERT 2 EECS 600: Systems Biology & Bioinformatics

Genetic Regulation & Cellular Signaling 6. Gene Regulatory Networks Genetic Regulation & Cellular Signaling 3 EECS 600: Systems Biology & Bioinformatics

Organization of Genetic Regulation 6. Gene Regulatory Networks Organization of Genetic Regulation Negative ligand-independent repression at chromatin level Up-regulation Gene Genetic network that controls flowering time in A. thaliana (Blazquez et al, EMBO Reports, 2001) Down-regulation 4 EECS 600: Systems Biology & Bioinformatics

Gene Regulatory Networks Transcriptional Regulatory Networks Nodes with outgoing edges are limited to transcription factors Can be reconstructed by identifying regulatory motifs (through clustering of gene expression & sequence analysis) and finding transcription factors that bind to the corresponding promoters (through structural/sequence analysis) 5 EECS 600: Systems Biology & Bioinformatics

Gene Regulatory Networks Gene expression networks General model of genetic regulation Identify the regulatory effects of genes on each other, independent of the underlying regulatory mechanism Can be inferred from correlations in gene expression data, time-series gene expression data, and/or gene knock-out experiments Observation Inference 6 EECS 600: Systems Biology & Bioinformatics

Boolean Network Model Binary model, a gene has only two states 6. Gene Regulatory Networks Boolean Network Model Binary model, a gene has only two states ON (1): The gene is expressed OFF (0): The gene is not expressed Each gene’s next state is determined by a boolean function of the current states of a subset of other genes A boolean network is specified by two sets Set of nodes (genes) State of a gene: Collection of boolean functions 7 EECS 600: Systems Biology & Bioinformatics

Logic Diagram Cell cycle regulation 6. Gene Regulatory Networks Logic Diagram Cell cycle regulation Retinoblastma (Rb) inhibits DNA synthesis Cyclin Dependent Kinase 2 (cdk2) & cyclin E inactivate Rb to release cell into S phase Up-regulated by CAK complex and down- regulated by p21/WAF1 p53 8 EECS 600: Systems Biology & Bioinformatics

Wiring Diagram 6. Gene Regulatory Networks 9 EECS 600: Systems Biology & Bioinformatics

Dynamics of Boolean Networks 6. Gene Regulatory Networks Dynamics of Boolean Networks Gene activity profile (GAP) Collection of the states of individual genes in the genome (network) The number of possible GAPs is 2n The system ultimately transitions into attractor states Steady state (point) attractors Dynamic attractors: state cycle Each transient state is associated with an attractor (basins of attraction) In practice, only a small number of GAPs correspond to attractors What is the biological meaning of an attractor? 10 EECS 600: Systems Biology & Bioinformatics

State Space of Boolean Networks 6. Gene Regulatory Networks State Space of Boolean Networks Equate cellular with attractors Attractor states are stable under small perturbations Most perturbations cause the network to flow back to the attractor Some genes are more important and changing their activation can cause the system to transition to a different attractor This slide is taken from the presentation by I. Shmulevich 11 EECS 600: Systems Biology & Bioinformatics

Identification of Boolean Networks 6. Gene Regulatory Networks Identification of Boolean Networks We have the “truth table” available Binarize time-series gene expression data REVEAL Use mutual information to derive logical rules that determine each variable If the mutual information between a set of variables and the target variable is equal to the entropy of that variable, then that set of variables completely determines the target variable For each variable, consider functions consisting of 1 variable, then 2, then 3, …, then i…, until one is found Once the minimum set of variables that determine a variable is found, we can infer the function from the truth table In general, the indegrees of genes in the network is small 12 EECS 600: Systems Biology & Bioinformatics

REVEAL 6. Gene Regulatory Networks 13 EECS 600: Systems Biology & Bioinformatics

Limitations of Boolean Networks 6. Gene Regulatory Networks Limitations of Boolean Networks The effect of intermediate gene expression levels is ignored It is assumed that the transitions between states are synchronous A model incorporates only a partial description of a physical system Noise Effects of other factors One may wish to model an open system A particular external condition may alter the parameters of the system Boolean networks are inherently deterministic 14 EECS 600: Systems Biology & Bioinformatics

Probabilistic Models Stochasticity can account for 6. Gene Regulatory Networks Probabilistic Models Stochasticity can account for Noise Variability in the biological system Aspects of the system that are not captured by the model Random variables include Observed attributes Expression level of a particular gene in a particular sample Hidden attributes The boolean function assigned to a gene? 15 EECS 600: Systems Biology & Bioinformatics

Probabilistic Boolean Networks 6. Gene Regulatory Networks Probabilistic Boolean Networks Each gene is associated with multiple boolean functions Each function is associated with a probility Can characterize the stochastic behavior of the system 16 EECS 600: Systems Biology & Bioinformatics

6. Gene Regulatory Networks Bayesian Networks A Bayesian network is a representation of a joint probability distribution A Bayesian network B=(G, ) is specified by two components A directed acyclic graph G, in which directed edges represent the conditional dependence between expression levels of genes (represented by nodes of the graph) A function  that specifies the conditional distribution of the expression level of each gene, given the expression levels of its parents Gene A is gene B’s parent if there is a directed edge from A to B P(B | Pa(B)) = (B, Pa(B)) 17 EECS 600: Systems Biology & Bioinformatics

Conditional Independence 6. Gene Regulatory Networks Conditional Independence In a Bayesian network, if no direct between two genes, then these genes are said to be conditionally independent The probability of observing a cellular state (configuration of expression levels) can be decomposed into product form 18 EECS 600: Systems Biology & Bioinformatics

Variables in Bayesian Network 6. Gene Regulatory Networks Variables in Bayesian Network Discrete variables Again, genes’ expression levels are modeled as ON and OFF (or more discrete levels) If a gene has k parents in the network, then the conditional distribution is characterized by rk parameters (r is the number of discrete levels) Continuous variables Real valued expression levels We have to specify multivariate continuous distribution functions Linear Gaussian distribution: Hybrid networks 19 EECS 600: Systems Biology & Bioinformatics

Equivalence Classes of Bayesian Nets 6. Gene Regulatory Networks Equivalence Classes of Bayesian Nets Observe that each network structure implies a set of independence assumptions Given its parents, each variable is independent of its non- descendants More than one graph can imply exactly the same set of independencies (e.g., X->Y and Y->X) Such graphs are said to be equivalent By looking at observations of a distribution, we cannot distinguish between equivalent graphs An equivalence class can be uniquely represented by a partially directed graph (some edges are undirected) 20 EECS 600: Systems Biology & Bioinformatics

Learning Bayesian Networks 6. Gene Regulatory Networks Learning Bayesian Networks Given a training set D = {x1, x2, …, xn} of m independent instances of the n random variables, find an equivalence class of networks B=(G, ) that best matches D x’s are the gene expression profiles Based on Bayes’ formula, the posterior probability of a network given the data can be evaluated as where C is a constant (independent of G) and is the marginal likelihood that averages the probability of data over all possible parameter assignments to G 21 EECS 600: Systems Biology & Bioinformatics

6. Gene Regulatory Networks Learning Algorithms The Bayes score S(G : D) depends on the particular choice of priors P(G) and P( | G) The priors can be chosen to be structure equivalent, so that equivalent networks will have the same score decomposable, so that the score can be represented as the superposition of contributions of each gene The problem becomes finding the optimal structure (G) We can estimate the gain associated with addition, removal, and reversal of an edge Then, we can use greedy-like heuristics (e.g., hill climbing) 22 EECS 600: Systems Biology & Bioinformatics

6. Gene Regulatory Networks Causal Patterns Bayesian networks model dependencies between multiple measurements How about the mechanism that generated these measurements? Causal network model: Flow of causality Model not only the distribution of observations, but also the effect of observations If gene X codes for a transcription factor of gene Y, manupilating X will affect Y, but not vice versa But in Bayesian networks, X->Y and Y->X are equivalent Intervention experiments (as compared to passive observation): Knock X out, then measure Y 23 EECS 600: Systems Biology & Bioinformatics

Dynamic Bayesian Networks 6. Gene Regulatory Networks Dynamic Bayesian Networks Dependencies do not uncover temporal relationships Gene expression varies over time Dynamic Bayesian Networks model the dependency between a gene’s expression level at time t and expression levels of parent genes at time t-1 24 EECS 600: Systems Biology & Bioinformatics

Linear Additive Regulation Model 6. Gene Regulatory Networks Linear Additive Regulation Model The expression level of a gene at a certain time point can be calculated by the weighted sum of the expression levels of all genes in the network at a previous time point ei : expression level of gene i wij : effect of gene j on gene i uk: kth external variable ik: effect of kth external variable on gene j i : gene-specific bias Can be fitted using linear regression 25 EECS 600: Systems Biology & Bioinformatics