1. Big Challenges with Big Data in Life Sciences Shankar Subramaniam UC San Diego

2. The Digital Human

3. A Super-Moore’s Law Adapted from Lincoln Stein 2012

4. The Phenotypic Readout

5. Data to Networks to Biology

6. NETWORK RECONSTRUCTION Data-driven network reconstruction of biological systems – Derive relationships between input/output data – Represent the relationships as a network Inverse Problem: Data-driven Network Reconstruction Experiments/Measurements

7. Network Reconstructions Reverse Engineering of biological networks Reverse engineering of biological networks: - Structural identification: to ascertain network structure or topology. - Identification of dynamics to determine interaction details. Main approaches: - Statistical methods - Simulation methods - Optimization methods - Regression techniques - Clustering

8. Network Reconstruction of Dynamic Biological Systems: Doubly Penalized LASSO Behrang Asadi *, Mano R. Maurya *, Daniel Tartakovsky, Shankar Subramaniam Department of Bioengineering University of California, San Diego NSF grants (STC-0939370, DBI-0641037 and DBI-0835541) NIH grants 5 R33 HL087375-02 * Equal effort

9. APPLICATION Phosphoprotein signaling and cytokine measurements in RAW 264.7 macrophage cells.

10. MOTIVATION FOR THE NOVEL METHOD Various methods – Regression-based approaches (least-squares) with statistical significance testing of coefficients – Dimensionality-reduction to handle correlation: PCR and PLS – Optimization/Shrinkage (penalty)-based approach: LASSO – Partial-correlation and probabilistic model/Bayesian-based Different methods have distinct advantages/disadvantages ‒ Can we benefit by combining the methods? ‒ Compensate for the disadvantages A novel method: Doubly Penalized Linear Absolute Shrinkage and Selection Operator (DPLASSO) ‒ Incorporate both “statistical significant testing” and “Shrinkage”

11. LINEAR REGRESSION Goal: Building a linear-relationship based model X: input data (m samples by n inputs), zero mean, unit standard deviation y: output data (m samples by 1 output column), zero-mean b: model coefficients: translates into the edges in the network e: normal random noise with zero mean Ordinary Least Squares solution: Formulation for dynamic systems:

12. Most coefficients non-zero, a mathematical artifact Perform statistical significance testing Compute the standard deviation on the coefficients Ratio Coefficient is significant (different from zero) if: Edges in the network graph represents the coefficients. STATISTICAL SIGNIFICANCE TESTING * Krämer, Nicole, and Masashi Sugiyama. "The degrees of freedom of partial least squares regression." Journal of the American Statistical Association106.494 (2011): 697-705.

13. Partial least squares finds direction in the X space that explains the maximum variance direction in the Y space PLS regression is used when the number of observations per variable is low and/or collinearity exists among X values Requires iterative algorithm: NIPALS, SIMPLS, etc Statistical significance testing is iterative CORRELATED INPUTS: PLS * H. WOLD, (1975), Soft modelling by latent variables; the non-linear iterative partial least squares approach, in Perspectives in Probability and Statistics, Papers in Honour of M. S. Bartlett, J. Gani, ed., Academic Press, London.

14. Derivative of the regression coefficients and degrees of freedom for PLS X: n x p y: n x 1 S: n x n M: Number of (latent) components

15. LASSO Shrinkage version of the Ordinary Least Squares, subject to L-1 penalty constraint (the sum of the absolute value of the coefficients should be less than a threshold) Where represents the full least square estimates 0 < t < 1: causes the shrinkage The LASSO estimator is then defined as: * Tibshirani, R.: ‘Regression shrinkage and selection via the Lasso’, J. Roy. Stat. Soc. B Met., 1996, 58, (1), pp. 267–288 Cost Function L-1 Constraint

16. Noise and Missing Data – More systematic comparison needed with respect to: 1.Noise: Level, Type 2.Size (dimension) 3.Level of missing data 4.Collinearity or dependency among input channels 5.Missing data 6.Nonlinearity between inputs/outputs and nonlinear dependency 7.Time-series inputs(/outputs) and dynamic structure

17. METHODS Linear Matrix Inequalities (LMI) * – Converts a nonlinear optimization problem into a linear optimization problem. – Congruence transformation: – Pre-existing knowledge of the system (e.g. ) can be added in the form of LMI constraints: – Threshold the coefficients: * [Cosentino, C., et al., IET Systems Biology, 2007. 1(3): p. 164-173]

18. METRICS Metrics for comparing the methods o Reconstruction from 80% of datasets and 20% for validation o RMSE on the test set, and the number and the identity of the significant predictors as the basic metric to evaluate the performance of each method 1.Fractional error in the estimating the parameters 2.Sensitivity, specificity, G, accuracy parameters smaller than 10% of the standard deviation of all parameter values were set to 0 when generating the synthetic data TP : True Positive FP : False Positive TN : True Negative FN : False Negative

19. RESULTS: DATA SETS Data sets for benchmarking: Two data sets 1.First set: experimental data measured on macrophage cells (Phosphoprotein (PP) vs Cytokine) * 2.Second sets consist of synthetic data generated in Matlab. We build the model using 80% of the data-set (called training set) and use the rest of data-set to validate the model (called test set). * [Pradervand, S., M.R. Maurya, and S. Subramaniam, Genome Biology, 2006. 7(2): p. R11].

20. RESULTS: PP-Cytokine Data Set Schematic representation of Phosphoprotein (PP) vs Cytokine -Signals were transmitted through 22 recorded signaling proteins and other pathways (unmeasured pathways). -Only measured pathways contributed to the analysis Schematic graphs from: [Pradervand, S., M.R. Maurya, and S. Subramaniam, Genome Biology, 2006. 7(2): p. R11].

21. PP-CYTOKINE DATASET Measurements of phosphoproteins in response to LPS Courtesy: AfCS

22. Measurements of cytokines in response to LPS ~ 250 such datasets

23. RESULTS: COMPARISON Comparison on synthetic noisy data The methods are applied on synthetic data with 22 inputs and 1 output. The true coefficients for the inputs (about 1/3rd) are made zero to test the methods if they identify them as insignificant. Effect of noise level Four outputs with 5, 10, 20 and 40% noise levels, respectively, are generated from the noise-free (true) output. Effect of noise type Three outputs with White, t-distributed, and uniform noise types, respectively are generated from the noise-free (true) output

24. RESULTS: COMPARISON Variability between realizations of data with white noise PCR, LASSO, and LMI—are used to identify significant predictors for 1000 input-output pairs. Histograms of the coefficients in the three significant predictors common to the three methods: MethodPredictor #11011 True value-3.405.82-6.95 PCRMean-3.814.73-6.06 Std.0.330.32 Frac. Err. in mean0.120.190.13 LASSOMean-2.824.48-5.62 Std.0.340.320.33 Frac. Err. in mean0.170.230.19 LMIMean-3.704.74-6.34 Std.0.340.320.34 Frac. Err. in mean0.090.180.09 Mean and standard deviation in the histograms of the coefficients computed with PCR, LASSO, and LMI.

25. RESULTS: COMPARISON Comparison of outcome of different methods on the real data  Different methods identified unique sets of common and distinct predictors for each output Graphical illustration of methods PCR, LASSO, and LMI in detection of significant predictors for output IL-6 in PP/cytokine experimental dataset Only the PCR method detects the true input cAMP zone I provides validation and it highlights the common output of all the methods

26. RESULTS: SUMMARY Comparison with respect to different noise types: – LASSO is the most robust methods for different noise types. Missing data RMSE: – LASSO less deviation, more robust. Collinearity: – PCR less deviation against noise level, better accuracy and G with increasing noise level.

27. A COMPARISON (Asadi, et al., 2012) Methods / CriteriaPCRLASSOLMI Increasing Noise RMSE Score= (average RMSE across different noise levels for LS)/(average RMSE across different noise levels for the chosen method) / 0.68 degrades gradually with level of noise / 0.56 / 0.94 Standard deviation and error in mean of Coefficients. Score = 1 – average (fractional error in mean(10,12,20) + (std(10,12,20)/ |true associated coefficients|) ) / 0.53 / 0.47 / 0.55 Acc./G Score = average accuracy across different noise levels for chosen method (white noise) / 0.70 / 0.87 / 0.91 at high noise all similar Fractional Error in estimating the parameters Score = 1- average fractional error in estimating the coefficients across different noise levels for chosen method (white noise) / 0.81 /.55 / 0.78 Types of noise Fractional Error in estimating the parameters Score = 1- average fractional error in estimating the coefficients across different noise levels and different noise types (20% noise level) / 0.80 / 0.56 / 0.79 Accuracy and G Score = average accuracy across different noise levels and different noise types / 0.71 / 0.87 / 0.91 Dimension ratio / Size Fractional Error in estimating the parameters Score = 1- average fractional error in estimating the coefficients across different noise levels and different ratios (m/n = 100/25, 100/50, 400/100) / 0.77 / 0.53 / 0.75 Accuracy and G Score = average accuracy across different white noise levels and different ratios (m/n = 100/25, 100/50, 400/100) / 0.66 / 0.83 / 0.90

28. DPLASSO Doubly Penalized Least Absolute Shrinkage and Selection Operator

29. OUR APPROACH: DPLASSO Reconstructed Network Statistical Significant Testing PLS Statistical Significant Testing PLS LASSO Model

30. Our approach: DPLASSO includes two parameter selection layers: Layer 1 (supervisory layer): – Partial Least Squares (PLS) – Statistical significance testing Layer 2 (lower layer): – LASSO with extra weights on less informative model parameters derived in layer 1 – Retain significant predictors and set the remaining small coefficients to zero DPLASSO WORK FLOW

31. DPLASSO: EXTENDED VERSION Smooth weights: Layer 1 : –Continuous significance score η (versus binary): –Mapping function (logistic significance score): Layer 2: –Continuous weight vector (versus fuzzy weight vector) Tuning parameter

32. APPLICATIONS 1.Synthetic (random) networks: Datasets generated in Matlab 2.Biological dataset: Saccharomyces cerevisiae - cell cycle model

33. SYNTHETIC (RANDOM) NETWORKS Datasets generated in Matlab using: Linear dynamic system Dominant poles/Eigen values (λ) ranges [-2,0] Lyapunov stable –Informal definition from wikipedia: if all solutions of the dynamical system that start out near an equilibrium point x e stay near x e forever, then the system is “Lyapunov stable”. Zero-input/Excited-state release condition 5% measurement (white) noise.

34. Two metrics to evaluate the performance of DPLASSO 1.Sensitivity, Specificity, G (Geometric mean of Sensitivity and Specificity), Accuracy 2.The root-mean-squared error (RMSE) of prediction METRICS TP : True Positive FP : False Positive TN : True Negative FN : False Negative

35. TUNING Tuning shrinkage parameter for DPLASSO The shrinkage parameters in LASSO level (threshold t) via k-fold cross-validation (k = 10) on associated dataset Validation error versus selection threshold t for DPLASSO on synthetic data set Rule of thumb after cross validations: Example: Optimal value of the tuning parameter for a network with 65% connectivity roughly equal to 0.65

36. PERFORMANCE COMPARISON: ACCURACY PLS Better performance DPLASSO provides good compromise between LASSO and PLS in terms of accuracy for different network densities

37. PERFORMANCE COMPARISON: PRECISION DPLASSO provides good compromise between LASSO and PLS in terms of precision for different network densities.

38. PERFORMANCE COMPARISON: SENSITIVITY LASSO has better performance DPLASSO provides good compromise between LASSO and PLS in terms of Sensitivity for different network densities

39. PERFORMANCE COMPARISON: SPECIFICITY DPLASSO provides good compromise between LASSO and PLS in terms of specificity for different network densities.

40. PERFORMANCE COMPARISON: NETWORK-SIZE DPLASSO provides good compromise between LASSO and PLS in terms of accuracy for different network sizes DPLASSO provides good compromise between LASSO and PLS in terms of sensitivity (not shown) for different network sizes Network Size: 10 * 100 potential connections Network Size: 20 * 400 potential connections Network Size: 50 * 2500 potential connections Accuracy

41. ROC CURVE vs. DYNAMICS AND WEIGHTINGS DPLASSO exhibits better performance for networks with slow dynamics. The parameter γ in DPLASSO can be adjusted to improve performance for fast dynamic networks

42. ROC CURVE vs. DYNAMICS AND WEIGHTINGS DPLASSO exhibits better performance for networks with slow dynamics. The parameter γ in DPLASSO can be adjusted to improve performance for fast dynamic networks

43. YEAST CELL DIVISION Experimental dataset generated via well-known nonlinear model of a cell division cycle of fission yeast. The model is dynamic with 9 state variables. * Novak, Bela, et al. "Mathematical model of the cell division cycle of fission yeast." Chaos: An Interdisciplinary Journal of Nonlinear Science 11.1 (2001): 277-286.

44. CELL DIVISION CYCLE True Network (Cell Division Cycle) PLS DPLASSO LASSO Missing in DPLASSO!

45. RECONSTRUCTION PERFORMANCE Method Metric AccuracySensitivitySpecificitySD RMSE/Mean LASSO 0.310.920.160.14 DPLASSO0.560.730.520.08 PLS0.600.670.630.09 Case Study II: Cell Division Cycle, Average over γ value Case Study I: 10 Monte Carlo Simulations, Size 20, Average over different γ, λ, network density, and Monte Carlo sample datasets Method Metric AccuracySensitivitySpecificitySD RMSE/Mean LASSO 0.390.900.050.06 DPLASSO0.520.900.340.07 PLS0.590.800.200.07

46. RECONSTRUCTION PERFORMANCE Method Metric AccuracySensitivitySpecificityLiftSD RMSE/Mean LASSO 0.310.920.167.530.14 DPLASSO0.560.730.526.120.08 PLS0.600.670.636.050.09 Case Study II: Cell Division Cycle, Average over γ value Case Study I: 10 Monte Carlo Simulations, Size 20, Average over different γ, λ, network density, and Monte Carlo sample datasets Method Metric AccuracySensitivitySpecificityLiftSD RMSE/Mean LASSO 0.390.900.052.30.06 DPLASSO0.520.900.342.20.07 PLS0.590.800.202.10.07

47. CONCLUSION Novel method, Doubly Penalized Linear Absolute Shrinkage and Selection Operator (DPLASSO), to reconstruct dynamic biological networks –Based on integration of significance testing of coefficients and optimization –Smoothening function to trade off between PLS and LASSO Simulation results on synthetic datasets –DPLASSO provides good compromise between PLS and LASSO in terms of accuracy and sensitivity for Different network densities Different network sizes For biological dataset –DPLASSO best in terms of sensitivity –DPLASSO good compromise between LASSO and PLS in terms of accuracy, specificity and lift

48. Information Theory Methods Farzaneh Farangmehr

49. Mutual Information It gives us a metric that is indicative of how much information from a variable can be obtained to predict the behavior of the other variable. The higher the mutual information, the more similar are the two profiles. For two discrete random variables of X={x 1,..,x n } and Y={y 1,…y m }: p(x i,y j ) is the joint probability of x i and y j P(x i ) and p(y j ) are marginal probability of x i and y j

50. Information theoretical approach Shannon theory Hartley’s conceptual framework of information relates the information of a random variable with its probability. Shannon defined “entropy”, H, of a random variable X given a random sample in terms of its probability distribution: Entropy is a good measure of randomness or uncertainty. Shannon defines “mutual information” as the amount of information about a random variable X that can be obtained by observing another random variable Y:

51. Mutual information networks X={x 1, …,x i } Y={y 1, …,y j } The ultimate goal is to find the best model that maps X  Y - The general definition: Y= f(X)+U. In linear cases: Y=[A]X+U where [A] is a matrix defines the linear dependency of inputs and outputs Information theory maps inputs to outputs (both linear and non-linear models) by using the mutual information:

52. Mutual information networks The entire framework of network reconstruction using information theory has two stages: 1-Mutual information measurements 2- The selection of a proper threshold. Mutual information networks rely on the measurement of the mutual information matrix (MIM). MIM is a square matrix whose elements (MIM ij = I(X i ;Y j )) are the mutual information between X i and Y j. Choosing a proper threshold is a non-trivial problem. The usual way is to perform permutations of expression of measurements many times and recalculate a distribution of the mutual information for each permutation. Then distributions are averaged and the good choice for the threshold is the largest mutual information value in the averaged permuted distribution.

53. Mutual information networks Data Processing Inequality (DPI) The DPI for biological networks states that if genes g 1 and g 3 interact only through a third gene, g 2, then: Checking against the DPI may identify those gene pairs which are not directly dependent even if

54. ARACNe algorithm ARACNE flowchart [Califano and coworkers] ARACNE stands for “Algorithm for the Reconstruction of Accurate Cellular NEtworks” [25]. ARACNE identifies candidate interactions by estimating pairwise gene expression profile mutual information, I(g i, g j ) and then filter MIs using an appropriate threshold, I 0, computed for a specific p-value, p 0. In the second step, ARACNe removes the vast majority of indirect connections using the Data Processing Inequality (DPI).

55. Protein- Cytokine Network in Macrophage Activation

56. Application to Protein-Cytokine Network Reconstruction Release of immune-regulatory Cytokines during inflammatory response is medicated by a complex signaling network [45]. Current knowledge does not provide a complete picture of these signaling components. 22 Signaling proteins responsible for cytokine releases: cAMP, AKT, ERK1, ERK2, Ezr/Rdx, GSK3A, GSK3B, JNK lg, JNK sh, MSN, p38, p40Phox, NFkB p65, PKCd, PKCmu2,RSK, Rps6, SMAD2, STAT1a, STAT1b, STAT3, STAT5 7 released cytokines (as signal receivers): G-CSF, IL-1a, IL-6, IL-10, MIP-1a, RANTES, TNFa we developed an information theoretic-based model that derives the responses of seven Cytokines from the activation of twenty two signaling Phosphoproteins in RAW 264.7 macrophages. This model captured most of known signaling components involved in Cytokine releases and was able to reasonably predict potentially important novel signaling components.

57. Protein-Cytokine Network Reconstruction MI Estimation using KDE - Given a random sample for a univariate random variable X with an unknown density a kernel density estimator (KDE) estimates the shape of this function as: assuming Gaussian kernels: - Bivariate kernel density function of two random variables X and Y given two random samples and : - Mutual information of X and Y using Kernel Density Estimation: n =sample size; h=kernel width

58. Protein-Cytokine Network Reconstruction Kernel bandwidth selection There is not a universal way of choosing h and however the ranking of the MI’s depends only weakly on them. The most common criterion used to select the optimal kernel width is to minimize expected risk function, also known as the mean integrated squared error (MISE): Loss function (Integrated Squared Error) : Unbiased Cross-validation approach select the kernel width that minimizes the lost function by minimizing: where f (-i),h (x i ) is the kernel density estimator using the bandwidth h at x i obtained after removing i th observation.

59. Protein-Cytokine Network Reconstruction Threshold Selection Based on large deviation theory (extended to biological networks by ARACNE), the probability that an empirical value of mutual information I is greater than I 0, provided that its true value, is: Where the bar denotes the true MI, N is the sample size and c is a constant. After taking the logarithm of both sides of the above equation: Therefore, lnP can be fitted as a linear function of I 0 and the slope of b, where b is proportional to the sample size N. Using these results, for any given dataset with sample size N and a desired p-value, the corresponding threshold can be obtained.

60. Protein-Cytokine Network Reconstruction Kernel density estimation of cytokines Figure 3: The probability distribution of seven released cytokines in macrophage 246.7 using on Kernel density estimation (KDE) Mutual information for all 22x7 pairs of phosphoprotein-cytokine from toll data (the upper bar) and non-toll data (the lower bar).

61. Protein-Cytokine Network Reconstruction Protein-Cytokine signaling networks + = The topology of signaling protein-released cytokines obtained from the non-Toll (A) and Toll (B) data. A B

62. Protein-cytokine Network Reconstruction Summary This model successfully captures all known signaling components involved in cytokine releases It predicts two potentially new signaling components involved in releases of cytokines including: Ribosomal S6 kinase on Tumor Necrosis Factor and Ribosomal Protein S6 on Interleukin-10. For MIP-1α and IL-10 with low coefficient of determination data that lead to less precise linear the information theoretical model shows advantage over linear methods such as PCR minimal model [Pradervand et al.] in capturing all known regulatory components involved in cytokine releases.

63. Network reconstruction from time-course data Background: Time-delayed gene networks Comes from the consideration that the expression of a gene at a certain time could depend by the expression level of another gene at previous time point or at very few time points before. The time-delayed gene regulation pattern in organisms is a common phenomenon since: If effect of gene g 1 on gene g 2 depends on an inducer,g 3, that has to be bound first in order to be able to bind to the inhibition site on g 2, there can be a significant delay between the expression of gene g 1 and its observed effect, i.e., the inhibition of gene g 2. Not all the genes that influence the expression level of a gene are necessarily observable in one microarray experiment. It is quite possible that there are not among the genes that are being monitored in the experiment, or its function is currently unknown.

64. Network reconstruction from time-course data The Algorithm

65. Network reconstruction from time-course data Algorithm

66. Network reconstruction from time-course data The flow diagram The flow diagram of the information theoretic approach for biological network reconstruction from time-course microarray data by identifying the topology of functional sub-networks

67. Network reconstruction from time-course data Case study: the yeast cell-cycle The cell cycle consists of four distinct phases: G 0 (Gap 0) :A resting phase where the cell has left the cycle and has stopped dividing. G1 (Gap 1) : Cells increase in size in Gap 1. The G 1 checkpoint control mechanism ensures that everything is ready for DNA synthesis. S1 (Synthesis): DNA replication occurs during this phase. G2 (Gap 2): During the gap between DNA synthesis and mitosis, the cell will continue to grow. The G 2 checkpoint control mechanism ensures that everything is ready to enter the M (mitosis) phase and divide. M (Mitosis) : Cell growth stops at this stage and cellular energy is focused on the orderly division into two daughter cells. A checkpoint in the middle of mitosis (Metaphase Checkpoint) ensures that the cell is ready to complete cell division.

68. Network reconstruction from time-course data Case study: the yeast cell-cycle Data from Gene Expression Omnibus (GEO) Culture synchronized by alpha factor arrest. samples taken every 7 minutes as cells went through cell cycle. Value type: Log ratio 5,981 genes, 7728 probes and 14 time points 94 Pathways from KEGG Pathways

69. Network reconstruction from time-course data Case study: the yeast cell-cycle The reconstructed functional network of yeast cell cycle obtained from time-course microarray data

70. Mutual information networks Advantages and Limits A major advantage of information theory is its nonparametric nature. Entropy does not require any assumptions about the distribution of variables [43]. It does not make any assumption about the linearity of the model for the ease of computation. It is applicable for time series data. A high mutual information does not tell us anything about the direction of the relationship.

71. Time Varying Networks Causality Maryam Masnardi-Shirazi

72. Causal Inference of Time-Varying Biological Networks

73. Definition of Causality

74. Beyond Correlation: Causation Idea: map a set of K time series to a directed graph with K nodes where an edge is placed from a to b if the past of a has an impact on the future of b How do we quantitatively do this in a general purpose manner?

75. Granger’s Notion of Causality It is said that process X Granger Causes Process Y, if future values of Y can be better predicted using the past values of X and Y than only using past values of Y.

76. Ganger Causality Formulation There are many ways to formulate the notion of granger causality, some of which are: - Information Theory and the concept of Directed Information - Learning Theory - Dynamic Bayesian Networks - Vector Autoregressive Models (VAR) - Hypothesis Tests, e.g. t-test and F tests

77. Vector Autoregressive Model (VAR)

78. Least Squares Estimation

79. Least Squares Estimation (Cont.)

80. Processing the data Phosphoprotein two-ligand screen assay: RAW 264.7 There are 327 experiments from western blots processed with mixtures of phosphospecific antibodies. In all experiments, the effects of single ligand and simultaneous ligand addition are measured Each experiment includes the fold change of Phosphoprotein at time points t=0, 1, 3, 10, 30 minutes Data at time=30 minute is omitted, and data from t=0:10 is interpolated by steps=1 min

81. Least Squares Estimation and Rank Deficiency of Transformation Matrix Exp.1 Exp.2 Exp. 327 All Y data Exp.1 Exp.2 Exp. 327 All X data

82. Normalizing the data

83. Statistical Significance Test (Confidence Interval)

84. The Reconstructed Phosphoproteins Signaling Network The network is reconstructed by estimating causal relationships between all nodes All the 21 phosphoproteins are present and interacting with one another There are 122 edges in this network

85. Correlation and Causation The conventional dictum that "correlation does not imply causation" means that correlation cannot be used to infer a causal relationship between the variablescorrelation does not imply causation This does not mean that correlations cannot indicate the potential existence of causal relations. However, the causes underlying the correlation, if any, may be indirect and unknown Consequently, establishing a correlation between two variables is not a sufficient condition to establish a causal relationship (in either direction).

86. Correlation and Causality comparison Heat-map of the correlation matrix between the input (X) and output (Y) The reconstructed network considering significant coefficients and their intersection with connections having correlations higher than 0.5 The conventional dictum that "correlation does not imply causation" means that correlation cannot be used to infer a causal relationship between the variables. This dictum should not be taken to mean that correlations cannot indicate the potential existence of causal relations. However, the causes underlying the correlation, if any, may be indirect and unknown. Consequently, establishing a correlation between two variables is not a sufficient condition to establish a causal relationship (in either direction).correlation does not imply causation

87. Correlation and Causality comparison (cont.) Heat-map of the correlation matrix between the input (X) and output (Y) The reconstructed network considering significant coefficients and their intersection with connections having correlations higher than 0.4

88. Validating our network Identification of Crosswalk between phosphoprotein Signaling Pathways in RAW 264.7 Macrophage Cells (Gupta et al., 2010)

89. The Reconstructed Phosphoproteins Signaling Network for t=0 to t=4 minutes Heat-map of the correlation matrix between the input (X) and output (Y) for t=0 to t=4 minutes Intersection of Causal Coefficients with connections with correlations higher than 0.4 for time t=0 to t=4 minutes 9 nodes 15 edges

90. The Reconstructed Phosphoproteins Signaling Network for t=3 to t=7 minutes Heat-map of the correlation matrix between the input (X) and output (Y) for t=3 to t=7 minutes Intersection of Causal Coefficients with connections with correlations higher than 0.4 for time t=3 to t=7 minutes 19 nodes 51 edges

91. The Reconstructed Phosphoproteins Signaling Network for t=6 to t=10 minutes Heat-map of the correlation matrix between the input (X) and output (Y) for t=6 to t=10 minutes Intersection of Causal Coefficients with connections with correlations higher than 0.4 for time t=6 to t=10 minutes 19 nodes 56 edges

92. Time-Varying reconstructed Network t=0 to 4 mint=3 to 7 mint=6 to 10 min

93. The Reconstructed Network for t=0 to t=4 minutes without the presence of LPS as a Ligand With LPS 15 Edges Without LPS 16 Edges

94. The Reconstructed Network for t=3 to t=7 minutes without the presence of LPS as a Ligand VS the presence of all ligands With all ligands including LPS (51 Edges) Without LPS (55 Edges)

95. The Reconstructed Network for t=6 to t=10 minutes without the presence of LPS as a Ligand VS the presence of all ligands With all ligands including LPS (56 Edges) Without LPS (66 Edges)

96. Time-Varying Network with LPS not present as a ligand t=0 to 4 min t=3 to 7 mint=6 to 10 min

97. Summary Information theory methods can help in determining causal and time- dependent networks from time series data. The granularity of the time course will be a factor in determining the causal connections. Such dynamical networks can be used to construct both linear and nonlinear models from data.