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# 713 Class Note for PHYS 597A with Professor Albert at PSU

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This 22 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Pennsylvania State University taught by a professor in Fall. Since its upload, it has received 15 views.

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Date Created: 02/06/15

Inference methods Prepare cDNA Probe Prepare Microarray Probabilistic methods Clustering analysis Data mining Bayesian networks Deterministic methods Continuous Differential equations Discrete Boolean Four steps in clustering analysis Pairwise correlation analysis Timeseries data spatial data Gene coexpression network Clustering of genes Predicting proteinprotein interaction Drawback No insight into the causal relationship Pairwise similarities between expression profiles Pearson correlation Squared Pearson correlation coefficient Spearman rank correlation Jacknife correlation coefficient Euclidean distance Clustering algorithms Bottomup approach hierarchical clustering Topdown approach Selforganizing maps and K means clustering Expmsslnn ratlo Loca clustering algorithm Relationships between expression pro les Expression ralio N a N m b Exprcsmon ratio r N A a A N u a U Z 3 4 5 5 7 6 0 1 2 3 4 a l 7 8 9 U 1 2 3 4 D 7 0 time Time Time SiT39 tlltaneOUS Timedelayed Inverted Predict proteinprotein interactions m quot Qian et al 2001 JMB 314 10531066 Network view Height 05 08 Height 0 4 07 10 Oncogenic signaling network Glioblastoma data set 1 n55 Construction of weighted j i a gene coexpression network I l I based on painNise Pearson Glioblastoma data set 2 n65 COlTe39ations Hierarchical clustering to Illllll lllllll Illlllllllllllllllll llllllll quotMl detect groups or modules lllllllll lllllllllwllllllyllllIllllllll ll llllll llllllllIlllllllllll lllll Keyforatm I Neurogerlesis 143 genes I MitosisCell Cycle 135 genes I immune Response 608 genes I Metabolism 143 genes I oympiasm 1112genes Horvath S 613 2006 103 174027 Elucidation of directionality Geue A 4 6202 E Guhe C AGcne D 5 wow ituxmm 5 1 Time V min IIYXL be 5R bVX bw regression slopes rnu39 nquot i XYi J eg bw 1004 and bw 0976 Directionality is assigned to those edges forwhich SR a 0 1 v 1w 1 2 yeX 1139 SR 1 quot 3X42 SRW097 hmquot hYXi ll39 SR i Gupta A et al 2006 22 209214 Data mining Extract information based on the statistical co occurrence Algorithm searched for the cooccurrence of pair of genes resulting in the edge generation according to the user defined m threshold Network retrieved by the query IE1 IE DNA repair 39 52 IE IE1 W hm Bayesian networks These protocols are used for sparse datasets Probabilistic approach which is capable of handling noise The approach is based on the statistical properties of dependence and conditional independence in the data Estimate the confidence in the different features of the network Insight into the causal influence Bayesian analysis Bayes theorem PAB PBAPAPB or LABPA PB normalizing constant NC Posterior Prior Likelihood NC Steps in Bayesian analysis Define state of the system random variable known information Find conditional probability of each node Directed acyclic graph representation of possible causal relationships Conditional independencies 393 o IAE IBD l AE 393 3 ICADE l B D B CE l A o DAG IEAD Continued Find joint distribution A set of local joint probability distributions that statistically convey these relationships The distribution yielding highest Bayesian score is chosen as the best fit to the data Benchmarks for weighting are typically obtained from likelihood G 0 HA B C D E PAPB A EPC BPD APE o o l l l 0 DAG Bayesian analysis produces multiple candidate networks 0 The links can be established randomly or heuristically lterative search algorithms are employed eg genetic algorithm Local map for the gene SVS1 Edge width confidence CLN2 and SVS1 are conditionally i w lnependent given the expression level of CLN2 Friedman N etal 2000 J comp biol 7 601620 Deterministic Methods for Network Inference A deterministic inference correlates the rate of change in expression level of each gene With the levels of other genes by nding the functional or logical forms of these interdependence relationships Loosely Two classes of deterministic inference methods 1 Continuous 2 Discrete Continuous Methods Identified as systems of linear or nonlinear differential equations in which for example rate of change of expression oint is a linear combination of concentrations of all other Xt dX z N w X l dz 0 Pros and cons can be quite accurate accuracy increases as number of experimental time points increases computational intractability quickly becomes an issue Have been used to infer generegulatory networks in B SUbtiiS Gupta A Varner J D and Maranas C D 39Largesale inference of the transcriptional regulation of Bacillus subtilis39 Computers and Chemical Engineering 2005 29 pp 565576 Rat Chen T He H L and Church G M 39Modeling gene expression with differential equations39 Pac Symp Biocomput 1999 pp 2940 An Example Inferring generegulatory networks in B subtilis A Linear Model of Network Inference Microarray data dXirr N m Microarray data w gt 0 gt activation of i by j w lt 0 gt inhibition of i by j Gupta A Varner J D and Maranas C D 39Largesale inference of the transcriptional regulation of Bacillus subtilis39 Computers and Chemical Engineering 2005 29 pp 565576 Optimization minimize W i Maximizing ka wifwquotf ij Sparseness subject to N T1 Wij 2ch Vki Wij wl j VI J 1 2 N k1 Post Opti mization Dense network Sparse network Discrete Methods Identified as Boolean and other logicbased methods that predict discrete regulatory relationships as for example Boolean A set of nodes V x1x and a list of Boolean functions F f1fn where a Boolean function with k specified input nodes is assigned to node x f xi1xik Example to follow in next slide Pros and cons More computationalIytractable than continuous methods Less accurate than continuous methods Much practical application is currently focused on developing and implementing algorithms for largescale inference eg REVEAL REVerse Engineering ALgorithm Liang S Fuhrman S and Somogyi R 39Reveal a general reverse engineering algorithm for inference of genetic network architectures39 Pac Symp Biocomput 1998 pp 1829 An Example Boolean protocol for network inference Boolean network basics A Boolean network GF consists of a set of nodes Vv1v representing genes and a list of Boolean functions Ff f A Boolean function fv1vk with inputs from specified nodes v1vk is assigned to each node v and this function gives the logical rules AND OR AND NOT etc for the ways in which nodes v1vk will affect the expression of node V The nodes of a Boolean network can take one of two states 0 not expressed or 1 expressed Thus the state of each node V at time t1 is determined by the states of its input nodes at time tand the Boolean function that dictates how these input nodes affect the expression of V A picture no inference yet GVF V1 V2 V3 RULES 11 v2 12 v1 ANDv3 v NOT v1 INPUT OUTPUT v1 v2 v3 V1 V2 V3 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 1 0 1 An algorithm for inferring a Boolean network Akutsu T and Miyano 8 Pac Symp on Biocomputing 4 1728 1999 1 For each node v e V execute STEP 2 2 If there is a triplet flWWW satisfying 01m fi1jvk1jvh for all j1m where OJ and I are state outputs and inputs take 2 as a Boolean function assigned to v and take vk vh as input nodes to v 2 Enumerate all triplets flvkvh satisfying Ojv f1jvk1jvh for alj1m What do STEPS 2 and 2 actually mean Not consistent Genes at An algorithmcontinued 5 we d reject it time 1 Genes at A time t1 Kkv 1 CD 2 39 39 g vl v3 v1 v3 I 1 0 0 0 0 1 0 39 39 g 1 1 v2 v2 AND NOTv3 v2 v2 XORV3 LIJ 12 0 1 0 0 1 1 02 V3 N0TV3 v v1 0R v3 a a 1 0 1 1 1 0 1 0 1 39 Conduct an exhaustive search to find these vkvh triplets All possible combinations of the 16 Boolean functions x AND y x OR y etc for the three node pairs v1v2 v1v3 v2v3 must be checked for each node This assumes that only two or less nodes determine the next state of each node Hybrid Methods Inference methods that bridge the gap between probabilistic and deterministic approaches usually by incorporating some type of stochastic process variability uncertainty into the inference algorithm Pros and cons Arguably most accurate and realistic network inference methods Amount of training data and computational time make methods prohibitive for large networks For Example Probabilistic Boolean Inference N Boolean functions are assigned to each node each with some probability of being selected to advance the state of the node a machinelearning algorithm must be used to update the state of each node at each time point

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