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1 Title Trancription factor activity etimation baed on particle warm optimization and fat networ component analyi Author() Chen, W; Chang, C; Hung, YS Citation 00 Annual International Conference Of The Ieee Engineering In Medicine And Biology Society, Embc'0, 00, p Iued Date 00 URL Right IEEE Engineering in Medicine and Biology Society Conference Proceeding Copyright IEEE

2 3nd Annual International Conference of the IEEE EMBS Bueno Aire, Argentina, Augut 3 - September 4, 00 Trancription factor activity etimation baed on particle warm optimization and fat networ component analyi Wei Chen, Chunqi Chang, Member, IEEE, and YS Hung, Senior Member, IEEE Abtract Trancription factor (TF) play an important role in regulating the expreion of gene The accurate meaurement of trancription factor activitie (TFA) depend on a erie of experimental technologie of molecular biology and i intractable in mot practical ituation Some ignal proceing method for blind ource eparation have been applied in the prediction of TFA from gene expreion data Mot of uch method mae ue of tatitical propertie of the gene expreion data only, leading to the inaccurate detection of TFA In contrat, networ component analyi (NCA) can provide much improved reult through utilizing the tructural information of the gene regulatory networ However, the tructure of the gene regulatory networ, required by NCA, i not available in mot practical cae o that NCA i not directly applicable In thi paper, we propoe to ue particle warm optimization (PSO) to find the mot plauible networ tructure iteratively from the gene expreion data, with the aitance of recently developed fat algorithm for networ component analyi (FatNCA) Thi novel approach to TFA inference can thu tae advantage of NCA, even when the required networ tructure i unnown The effectivene of our novel approach ha been demontrated by application to both imulated data and real gene expreion microarray data, in the ene that TFA can be inferred with high accuracy T I INTRODUCTION RANSCRIPTION factor (TF) are protein molecule that regulate the trancription of gene through binding to the promoter region of the gene [-] Trancription i an important biological proce which prepare for the generation of protein (final product of gene expreion) The quantitative regulation of gene trancription depend on the trancription factor activitie (TFA) [3] Therefore, obtaining accurate TFA i very important in undertanding how the gene expreion i regulated Currently, meaurement of TFA i mainly performed in an in vivo ytem on the interaction among TF and ciregulatory element [4], which i difficult and of high expene, intractable in mot practical ituation Since in mot cae it i not applicable to meaure TFA directly, we mut mae inference about TFA indirectly from gene expreion data which can be obtained through high throughput microarray technology or more recently next generation equencing (NGS) With high throughput microarray gene expreion data, ome ignal proceing Manucript received April, 00 Thi wor i upported by Hong Kong RGC GRF grant (HKU 70709E) and Univerity of Hong Kong Seed Funding Program for Baic Reearch ( ) W Chen, CQ Chang, and YS Hung are with Department of Electrical and Electronic Engineering, The Univerity of Hong Kong, Pofulam Road, Hong Kong ( {chenwei,cqchang,yhung}@eeehuh) /0/$ IEEE 06 method for blind ource eparation, uch a principal component analyi (PCA) [5] and independent component analyi (ICA) [6], can be adopted to deduce TFA However, TFA inferred from thee method could be o inaccurate that they are not acceptable for meaningful biological interpretation Thi i becaue the effectivene of uch method depend on mathematical aumption (eg ICA require tatitical independence of ource ignal) which are unliely to be atified by the microarray gene expreion data Contrary to blind ource eparation approache which aume unrealitic model of trancriptional gene regulation, networ component analyi (NCA) [7] i an alternative approach that doe not mae unrealitic aumption on the independence of TFA Intead, NCA mae ue of the tructural information of the gene regulatory networ, which i available for ome pecie uch a yeat through genomewide location analyi uing ChIP-chip technology Since NCA mae ue of relevant biological information and i not dependent on unrealitic tatitical aumption, the TFA inferred by NCA are much more accurate [7] However, the original NCA algorithm could be computationally untable and time conuming and may have multiple local olution To overcome thee diadvantage, an improved algorithm called FatNCA wa developed recently [] A critical requirement for inferring TFA uing NCA i that the TF-gene connectivity tructure of the gene regulatory networ mut be nown However, it i quite difficult and expenive to get thi required networ tructure by ChIP-chip experiment In fact, uch tructure o far i only available for yeat and E Coli [9] In mot other ituation, we have to wor without prior nowledge on the networ tructure and thu NCA cannot be applied directly In order to deal with uch difficulty, we propoe to apply NCA on all poible networ tructure and chooe the reult of the mot plauible one Though thi approach i in general too time conuming to be applicable, we can apply heuritic optimization technique uch a particle warm optimization (PSO) to deduce a nearly optimal networ tructure without exhautive earching With the help of the fat NCA algorithm FatNCA, uch procedure become computationally feaible A a recently developed and fatdeveloping heuritic optimization technology, PSO ha been hown to be effective in variou application In PSO, the olution of the optimization problem i earched by a warm of particle with inter-particle communication [0] It ha the advantage of imple operation and fat convergence []

3 II METHODOLOGY A NCA and FatNCA From nowledge of ytem biology, we oberve that microarray gene expreion data can be conidered a the integration of TF-gene networ and TFA Thi i the foundation of networ component analyi (NCA) NCA aume the following model: X= AS () where X i the microarray data, A i the matrix of TF-gene networ, and S i the TFA matrix When noie, denoted a Γ, i included in microarray data, the model of NCA will be changed to: Y = X+Γ = AS +Γ () According to biological nowledge, the connectivity matrix A i very pare with mot element being 0, which mean that each gene i regulated by only a mall number of TF Such a pare tructure of A, if nown, can be utilized by the NCA algorithm to deduce the TFA ( S ) from the microarray gene expreion data ( Y) uing alternating leat quare (ALS) method [] With the biological ignificance of ource ignal being conidered, NCA i a ignal eparation method uitable for trancription factor activity inference from microarray gene expreion data However, the original ALS-baed NCA algorithm ha ome drawbac uch a intability and multiple local olution An improved algorithm for NCA, called FatNCA, wa then developed to overcome thee drawbac [] By uing matrix factorization intead of ALS iteration, FatNCA i much fater and more robut B Objective Function In thi paper, FatNCA i applied to the microarray data for etimating the connectivity matrix A and the TFA matrix S, auming a pare connectivity tructure Z, a binary matrix with repreenting a connection and 0 for no connection To find the mot plauible unnown connectivity tructure, we minimize the objective function defined a below: Given Z, uppoe A and S are determined uing FatNCA ubject to A conformal with the tructure Z, o that A and S can be regarded a function of Z through the FatNCA procedure, ie A = A ( Z) and S = S ( Z) Hence, N i ( ( Z) ( Z)) Y A S Y i= i F f( Z) = N i F (3) where Y i i the i th row of Y, ( A( Z) S ( Z)) i i the i th row of A( Z) S ( Z), i Frobeniu norm, and N i the number F of row of Y (number of gene) The objective function f ( Z ) decribe the level of deviation between the deduced data ( A( Z) S ( Z) ) and the real data ( Y ) Therefore, a maller f ( Z ) implie a better etimate of the connectivity matrix ( A ) and TFA matrix ( S ) C Particle Swarm Optimization (PSO) PSO will be applied to find an optimal connectivity tructure Z that minimize the objective function f ( Z ) a tated in (3) Thi i decribed a follow: Initialize Z and it velocity v for each of the M particle, and et both the optimal connectivity tructure of each pecific particle, pbet, and the optimal connectivity tructure of the whole warm, gbet, a Z In the th iteration, update Z and v for each particle a v v ( pbet Z ) ( gbet Z ) (4) = + ϕ + + ϕ Z = Z + v (5) + + where ϕ and ϕ are cognitive confidence coefficient determining the particle tracing tendency on the local and global optimum, repectively, choen a random number with uniform ditribution over the interval [0, ] Such etting for ϕ and ϕ guarantee convergence [] The tructure matrix i then tranformed to a binary matrix by applying a threhold that eep only a certain pre-defined percentage, denoted a, of all poible connection 3 For each particle, apply FatNCA baed on the connectivity tructure Z + to etimate A and S, update pbet+ = Z + if f ( Z+ ) < f( pbet ), and update gbet+ = pbet + if f ( pbet+ ) < f ( gbet ) 4 Iterate Procedure and Procedure 3 until convergence The procedure i illutrated in the following example I Initialize 5 particle and their related matrice A an example, the firt particle i initialized a: Z0 = 0 0, v0 = , and pbet0 = Z0 Set gbet0 = Z0 II t iteration baed on (4) and (5): Z = ;

4 Auming the pare ratio to be 035, Z i further tranformed to the binary connectivity tructure 0 0 Z = III Apply FatNCA baed on Z to get the etimate of A and S, and then update pbet and gbet baed on the value of the objective function IV Iterate Procedure II and Procedure III until convergence Note that the prerequiite of calculating f ( A( Z), S ( Z)) i to now the particular value of A ( Z) and S ( Z), which are deduced by a NCA algorithm Becaue the number of particle and iteration i large, the fat execution and precie prediction of the algorithm i important The low algorithm complexity, high accuracy of deduction and the fat peed of FatNCA mae it poible to adopt heuritic optimization (iepso) to find out a uitable TF-gene networ tructure D Framewor of the algorithm The whole execution procedure i illutrated in Fig Initialize particle Obtain the tructure related to every particle Execute FatNCA and calculate the objective function related to every tructure Apply PSO to all particle Calculate the objective function related to all tructure of particle, update local and global optimum Not Satified Chec convergence criterion Output global optimum Satified Fig Execution flow graph of the whole algorithm III EXPERIMENTS AND RESULTS A Data Decription In our experiment, we ue both imulated microarray data and real microarray data The ize of the two type of microarray data are both 00 5 Hence, the microarray data have 00 gene and 5 ample point The number of TF related to the two microarray data are both 6 B Reult on Simulated Data Baed on our tet of the optimization performance of PSO, 300 particle and 00 iteration are adopted in our experiment The imulated microarray data do not include noie The pare ratio of the imulated TF-gene networ i = 0075 After convergence of the PSO, we get the etimate of both the connectivity matrix A and the TFA matrix S, denoted a Â and Ŝ, repectively Becaue the order of the row of Ŝ and that of S may be different, we need to determine which row of Ŝ i the etimate of a particular original TFA It can be done by finding the row of Ŝ that i motly correlated to thi pecific TFA Mathematically, the etimate of the th original TFA can be determined a g = {,,, M } arg max corr(, ) (6) where ˆ j i the j th etimated TFA, M i the number of TFA, and corr (, ˆ ) i the correlation coefficient between ˆ j j and Replace corr (, ˆ ) j with rho The reult i hown in Table I TABLE I CORRELATION RESULTS FOR SIMULATED DATA g From Table I, we ee that there exit repetition for two etimated TFA and, each of which hould be aigned to the etimate of only one of the original TFA After eliminating repetition, we get etimate for 4 TFA, with high correlation with their original TFA (abolute correlation coefficient above 0) The detection ratio i rho 063

5 75% (4/6) C Reult on Real Microarray Data The real microarray data i from a microarray experiment of E Coli [3] The biological bacground i that E Coli carbon ource tranmit from glucoe to acetate The pare ratio of TF-gene connectivity matrix i 003 The noie ratio i 0303 We run PSO 4 time The reult i hown in Table II We oberve that there alway exit TFA which are not detected in each experiment However, only TFA5 i not detected in all experiment Through integrating the reult of 4 experiment, we detect other TFA So the detection ratio of original TFA i 9375% (5/6) The detected TFA (circle) are compared with their correponding original TFA (tar) in Fig TABLE II PSO PREDICTION FROM E COLI MICROARRAY DATA Experiment No 3 4 Number of TFA not detected Lit of not detected TFA TFA, TFA4 TFA5, TFA6 TFA3, TFA4, TFA, TFA9, TFA5 TFA, TFA, TFA5 TFA7, TFA9, TFA, TFA4, TFA5 From Fig, we can ee that the predicted normalized TFA almot overlap with the real normalized TFA IV CONCLUSION In thi paper, we conider the problem of etimating trancription factor activitie (TFA) from microarray gene expreion data by integrating FatNCA (a recently developed fat networ component analyi algorithm) and particle warm optimization (PSO) to earch for the optimal TF-gene networ and etimate TFA imultaneouly Experiment on both imulated data and real microarray data demontrate that our method can etimate the unnown TFA accurately Our future wor i to improve the method in order to mae it wor robutly for more complicated biological networ REFERENCES [] D S Latchman, Trancription factor: an overview, Int J Biochem Cell Biol, vol 9, pp 305-3, Dec 997 [] M Karin, Too many trancription factor poitive and negative interaction, New Biol, vol, pp 6-3, Feb 990 [3] P Jorgenen and M Tyer, The for ed path to mitoi, Genome Biol, vol, pp 0-04, Sep 000 [4] J Locer, Trancription Factor (chapter ) San Diego: Academic Pre, 00 [5] O Alter, PO Brown and D Bottein, Singular value decompoition for genome-wide expreion data proceing and modeling, Proc Natl Acad Sci, vol 97, pp , Augut 000 [6] SI Lee and S Batzoglou, Application of independent component analyi to microarray, Genome Biology, vol 4, pp R76-R96, Oct 003 [7] J Liao, R Bocolo, YL Yang, LM Tran, C Sabatti and VP Roychowdhury, Networ component analyi: Recontruction of regulatory ignal in biological ytem, Proc Natl Acad Sci, vol 00, pp , Dec 003 [] CQ Chang, Z Ding, YS Hung and PCW Fung, Fat networ component analyi (FatNCA) for gene regulatory networ recontruction from microarray data, Bioinformatic, vol 4, pp , April 00 [9] M Zheng, LO Barrera, B Ren and YN Wu, Chip-chip: data, model, and analyi, Biometric, vol 63, pp , Sep 007 [0] J Kennedy and R Eberhart, Particle warm optimization, In Proceeding of nd IEEE International Conference on Neural Networ, pp 94-94, Hawaii, 995 [] M Clerc and J Kennedy, The particle warm exploion, tability, and convergence in a multidimenional complex pace, Evolutionary Computation, IEEE Tranaction on, vol 6, pp 5-73, Feb 00 [] L M Tran, MP Brynilden, KC Kao, JK Suen and JC Liao, gnca: A framewor for determining trancription factor activity baed on trancriptome: identifiability and numerical implementation, Metabolic Engineering, vol 7, pp -4, March 005 [3] KC Kao, YL Yang, R Bocolo, C Sabatti, V Roychowdhury and JC Liao, Trancriptome-baed determination of multiple trancription regulator activitie in Echerichia coli by uing networ component analyi, Proc Natl Acad Sci, vol 0, pp , Dec 003 Fig Comparion of detected TFA with real TFA 064