EECS 600: Systems Biology & Bioinformatics
Instructor: Mehmet Koyuturk

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

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

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

6. Gene Regulatory Networks


Transcriptional Regulatory Networks
Nodes with outgoing edges are limited to transcription factors
5

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)
EECS 600: Systems Biology & Bioinformatics

6. 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
6
Observation Inference
EECS 600: Systems Biology & Bioinformatics

6. Gene Regulatory Networks




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

6. Gene Regulatory Networks
8

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 downregulated by p21/WAF1 p53
EECS 600: Systems Biology & Bioinformatics

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

10
6. Gene Regulatory Networks




Gene activity profile (GAP)
Collection of the states of individual genes in the genome
(network)

The number of possible GAPs is 2 n




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?
EECS 600: Systems Biology & Bioinformatics

6. Gene Regulatory 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
11
This slide is taken from the presentation by I. Shmulevich
EECS 600: Systems Biology & Bioinformatics

6. Gene Regulatory 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

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

6. Gene Regulatory Networks





14
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
EECS 600: Systems Biology & Bioinformatics

6. Gene Regulatory Networks





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

6. Gene Regulatory 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




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

6. Gene Regulatory Networks

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

6. Gene Regulatory Networks





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 r k 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

6. Gene Regulatory Networks




Observe that each network structure implies a set of independence assumptions
Given its parents, each variable is independent of its nondescendants

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

6. Gene Regulatory Networks



Given a training set D = {x
1
, x
2
, …, x n
} 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
21 is the marginal likelihood that averages the probability of data over all possible parameter assignments to G
EECS 600: Systems Biology & Bioinformatics

6. Gene Regulatory Networks


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




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




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
6. Gene Regulatory Networks

6. Gene Regulatory Networks

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




 e i
: expression level of gene i w ij
: effect of gene j on gene i u k
: kth external variable n ik
: effect of kth external variable on gene j b i
: gene-specific bias

Can be fitted using linear regression
25 EECS 600: Systems Biology & Bioinformatics