Modelling the effects of cell-to-cell variability on the output of interconnected gene networks in bacterial populations

Nicolò Politi, Lorenzo Pasotti, Susanna Zucca, Paolo Magni

The interconnection of quantitatively characterized biological devices may lead to composite systems with apparently unpredictable behaviour. Context-dependent variability of biological parts has been investigated in several studies, measuring its entity and identifying the factors contributing to variability. Such studies rely on the experimental analysis of model systems, by quantifying reporter genes via population or single-cell approaches. However, cell-to-cell variability is not commonly included in predictability analyses, thus relying on predictive models trained and tested on central tendency values. This work aims to study in silico the effects of cell-to-cell variability on the population-averaged output of interconnected biological circuits. The steady-state deterministic transfer function of individual devices was described by Hill equations and lognormal synthetic noise was applied to their output. Two- and three-module networks were studied, where individual devices implemented inducible/repressible functions. The single-cell output of such networks was simulated as a function of noise entity; their population-averaged output was computed and used to investigate the expected variability in transfer function identification. The study was extended by testing different noise models, module logic, intrinsic/extrinsic noise proportions and network configurations. First, the transfer function of an individual module was identified from simulated data of a two-module network. The estimated parameter variability among different noise entities was limited (14%), while a larger difference was observed (up to 62%) when estimated and true parameters were compared. Thus, low-variability parameter estimates can be obtained for different noise entities, although deviating from the true parameters, whose measurement requires noise knowledge. Second, the black-box input-output function of a two/three-module network was predicted from the knowledge of the transfer function of individual modules, identified in the presence of noise. Estimates variability was low (16%); however, differences up to 68% were observed by simulating a typical experimental study where the predictions obtained above were compared to network outputs generated in the presence of noise. Network predictions can, thus, deviate from real outputs when modules are characterized and re-used in different noise contexts. The adopted approach can support predictability studies in synthetic biology by distinguishing between actual unpredictability and contribution of noise and by guiding researchers in the design of suitable experimental measurement for gene networks.