Genetic programming-based approach to elucidate biochemical interaction networks from data

Abstract

Biochemical systems are characterised by cyclic/reversible reciprocal actions, non-linear interactions and a mixed relationship structures (linear and non-linear; static and dynamic). Deciphering the architecture of such systems using measured data to provide quantitative information regarding the nature of relationships that exist between the measured variables is a challenging proposition. Causality detection is one of the methodologies that are applied to elucidate biochemical networks from such data. Autoregressive-based modelling approach such as granger causality, partial directed coherence, directed transfer function and canonical variate analysis have been applied on different systems for deciphering such interactions, but with limited success. In this study, the authors propose a genetic programming-based causality detection (GPCD) methodology which blends evolutionary computation-based procedures along with parameter estimation methods to derive a mathematical model of the system. Application of the GPCD methodology on five data sets that contained the different challenges mentioned above indicated that GPCD performs better than the other methods in uncovering the exact structure with less false positives. On a glycolysis data set, GPCD was able to fill the 'interaction gaps' which were missed by other methods.

Fig. 1

Flowchart of GPCD methodology

Fig. 2

Network representation for case 1 a Original structure, PDC and GPCD b DTF

Fig. 3

Network representation for case 2 a Original structure b GPCD c PDC d CVA e Granger causality GPCD predicted the correct network. CVA and PDC gave too many additional interactions. Although GC also identified many pseudo‐relationships (indicated by grey lines), these were very weak and may be neglected in comparison with the strong interactions (indicated by bold lines) which depict the actual network

Fig. 4

Network structure for Case 3 a Original b GPCD c Granger causality Bold lines indicates actual interactions; dashed line shows extra connections identified and grey lines represent wrongly identified interactions

Fig. 5

Network interactions for Case 4 a Original b Granger causality (solid lines represent the network obtained for significance level of 0.95 while dashed lines represent the network obtained significance level of 0.90) c GPCD

Fig. 6

Glycolytic pathway a Original b Voit et al. c Srividhya et al. d GPCD