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

6. Gene Regulatory Networks

EECS 600: Systems Biology & BioinformaticsInstructor: Mehmet Koyuturk

Regulation of Gene Expression


EECS 600: Systems Biology & Bioinformatics

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Transcriptional Regulation of telomerase protein component gene hTERT

Genetic Regulation & Cellular Signaling



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Organization of Genetic Regulation



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GeneUp-regulation

Down-regulation

Negative ligand-independent repression at chromatin level

Genetic network that controls flowering time in A. thaliana(Blazquez et al, EMBO Reports, 2001)

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)



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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



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Observation Inference

Boolean Network Model



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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

Logic Diagram



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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

Wiring Diagram



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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?



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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



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This slide is taken from the presentation by I. Shmulevich

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



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REVEAL



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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



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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?



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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



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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))



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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



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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



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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)



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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



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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)



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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



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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



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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



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

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