1. Genetic network inference: from co-expression clustering to reverse engineering Patrik D’haeseleer,Shoudan Liang and Roland Somogyi

2. The goal of this review Principles of genetic network organization Computational methods for extracting network architectures from experimental data

3. Outline Introduction A conceptual approach to complex network dynamics Inference of regulation through clustering of gene expression data Modeling methodologies Gene network inference:reverse engineering Conclusions and Outlook

4. Genes encode proteins, some of which in turn regulate other genes  determine the structure of this intricate network of genetic regulatory interactions

5. Traditional approach: local Examining and collecting data on a single gene, a single protein or a single reaction at a time  functional genomics

6. Functional Genomics Specifically, functional genomics refers to the development and application of global experimental approaches to assess gene function by making use of the information and reagents provided by structural genomic. high throughput large scale experimental methodologies combined with statistical and computational analysis of the results.

7. Functional Genomics(Cont.) We need to define the mapping from sequence space to functional space.

8. Intermediate representation Focus at the level of single cells A biological system can be considered to be a state machine,where the change in internal state of the system depends on both its current internal state and any external inputs.

9. The goal Observe the state of a cell and how it changes under different circumstances, and from this to derive a model of how these state changes are generated The state of cell All those variables determining its behavior

10. Example A simple,6-node regulatory network

11. Outline Introduction A conceptual approach to complex network dynamics Inference of regulation through clustering of gene expression data Modeling methodologies Gene network inference:reverse engineering Conclusions and Outlook

12. The global gene expression pattern is the result of the collective behavior of individual regulatory pathways Gene function depends on its cellular context; thus understanding the network as a whole is essential.

13. Boolean Networks Each gene is considered as a binary variable—either ON or OFF—regulated by other genes through logical or Boolean functions. Even with this simplification,the network behavior is already extremely rich.

14. Boolean Networks(Cont.) Cell differentiation corresponds to transitions from one global gene expression pattern to another.

15. Outline Introduction A conceptual approach to complex network dynamics Inference of regulation through clustering of gene expression data Modeling methodologies Gene network inference:reverse engineering Conclusions and Outlook

16. Scoring methods Whether there has been a significant change at any one condition Whether there has been a significant aggregate change over all conditions Whether the fluctuation pattern shows high diversity according to Shannon entropy

17. Guilt By Association Select a gene Determine its nearest neighbors in expression space within a certain user- defined distance cut-off

18. Clustering extract groups of genes that are tightly co-expressed over a range of different experiments.

19. Caution Different clustering methods can have very different results It’s not yet clear which clustering methods are most useful for gene expression analysis.

20. Definition:Gene Expression Profile An expression profile e j of an ordered list of N samples(k=1 to N) for a particular gene j is a vector of scaled expression values v jk The expression profile is: e j =(v j1,v j2,v j3,…,v jN )

21. Definition:Gene Expression Profile( Cont.) A difference between two genes p and q may be estimated as N-dimensional metric “distance” between e p and e q. Euclidean distance: =

22. Clustering algorithms Non-hierarchical methods Cluster N objects into K groups in an iterative process until certain goodness criteria are optimized E.g. K-means

23. Clustering algorithms Hierarchical methods Return an hierarchy of nested clusters, where each cluster typically consists of the union of two or more smaller clusters. Agglomerative methods Start with single object clusters and recursively merge them into larger clusters Divisive methods Start with the cluster containing all objects and recursively divide it into smaller clusters

24. Other applications of co- expression clusters Extraction of regulatory motifs Genes in the same expression share biological funtions Inference of functional annotation Functions of unknown genes may be hypothesized from genes with know function within the same cluster As a molecular signature in distinguishing cell or tissue types mRNA expression

25. Which clustering method to use? There is no single best criterion for obtaining a partition because no precise and workable definition of ‘cluster’ exists. Clusters can be of any arbitrary shapes and sizes in a multidimensional pattern space.

26. Challenge in cluster analysis A gene could be a member of several clusters, each reflecting a particular aspect of its function and control Solutions clustering methods that partition genes into non-exclusive clusters Several clustering methods could be used simultaneously

27. Outline Introduction A conceptual approach to complex network dynamics Inference of regulation through clustering of gene expression data Modeling methodologies Gene network inference:reverse engineering Conclusions and Outlook

28. Level of biochemical detail abstract Boolean networks concrete Full biochemical interaction models with stochastic kinetics in Arkin et al.(1998)

29. Forward and inverse modeling Forward modeling approach Inverse modeling, or reverse engineering Given an amount of data, what can we deduce about the unknown underlying regulatory network? Requires the use of a parametric model, the parameters of which are then fit to the real-world data.

30. Outline Introduction A conceptual approach to complex network dynamics Inference of regulation through clustering of gene expression data Modeling methodologies Gene network inference:reverse engineering Conclusions and Outlook

31. Goal of network inference Construct a coarse-scale model of the network of regulatory interactions between the genes It’s possible to reverse engineer a network from its activity profiles

32. Data requirements We need to observe the expression of that gene under many different combinations of expression levels of its regulatory inputs Use data from different sources Deal with different data types

33. Estimates for network models a sparse network model of N genes, where each gene is only affected by K other genes on average.  a sparsely connected, directed graph with N nodes and NK edges.

34. Estimate for network models(Cont.) To specify the correct model, we need bits of information.

35. Correlation Metric Construction Adam Arkin and John Ross A method to reconstruct reaction networks from measured time series of the component chemical species. The system is driven using inputs for some of the chemical species and the concentration of all the species is monitored over time.

36. Correlation Metric Construction(Cont. ) The time-lagged correlation matrix is calculated From this a distance matrix is constructed based on the maximum correlation between any two chemical species This distance matrix is then fed into a simple clustering algorithm to generate a tree of connections between the species The results are mapped into a two- dimensional graph for visualization

37. Additive regulation models Property The regulatory inputs are combined using a weighted sum Can be used as a first-order approximation to the gene network

38. Additive regulation models The change in each variable over time is given by a weighted sum of all other variables is the level of the i-th varibale is a bias term indicating whether I is expressed of not in the absence of regulatory inputs represents the influence of j on the regulation of i

39. Use of such models We can infer regulatory interactions directly from the data, by fitting these simple network models to large scale gene expression data.

40. Outline Introduction A conceptual approach to complex network dynamics Inference of regulation through clustering of gene expression data Modeling methodologies Gene network inference:reverse engineering Conclusions

41. Conclusion Conceptual foundations for understanding complex biological networks Several practical methods for data analysis