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6. Gene Regulatory Networks
EECS 600: Systems Biology & BioinformaticsInstructor: Mehmet Koyuturk
Regulation of Gene Expression
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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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