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Noise suppression in stochastic genetic circuits using PID controllers

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  • Saurabh Modi
  • Supravat Dey
  • Abhyudai Singh

Abstract

Inside individual cells, protein population counts are subject to molecular noise due to low copy numbers and the inherent probabilistic nature of biochemical processes. We investigate the effectiveness of proportional, integral and derivative (PID) based feedback controllers to suppress protein count fluctuations originating from two noise sources: bursty expression of the protein, and external disturbance in protein synthesis. Designs of biochemical reactions that function as PID controllers are discussed, with particular focus on individual controllers separately, and the corresponding closed-loop system is analyzed for stochastic controller realizations. Our results show that proportional controllers are effective in buffering protein copy number fluctuations from both noise sources, but this noise suppression comes at the cost of reduced static sensitivity of the output to the input signal. In contrast, integral feedback has no effect on the protein noise level from stochastic expression, but significantly minimizes the impact of external disturbances, particularly when the disturbance comes at low frequencies. Counter-intuitively, integral feedback is found to amplify external disturbances at intermediate frequencies. Next, we discuss the design of a coupled feedforward-feedback biochemical circuit that approximately functions as a derivate controller. Analysis using both analytical methods and Monte Carlo simulations reveals that this derivative controller effectively buffers output fluctuations from bursty stochastic expression, while maintaining the static input-output sensitivity of the open-loop system. In summary, this study provides a systematic stochastic analysis of biochemical controllers, and paves the way for their synthetic design and implementation to minimize deleterious fluctuations in gene product levels.Author summary: In the noisy cellular environment, biochemical species such as genes, RNAs and proteins that often occur at low molecular counts, are subject to considerable stochastic fluctuations in copy numbers over time. How cellular biochemical processes function reliably in the face of such randomness is an intriguing fundamental problem. Increasing evidence suggests that random fluctuations (noise) in protein copy numbers play important functional roles, such as driving genetically identical cells to different cell fates. Moreover, many disease states have been attributed to elevated noise levels in specific proteins. Here we systematically investigate design of biochemical systems that function as proportional, integral and derivative-based feedback controllers to suppress protein count fluctuations arising from bursty expression of the protein and external disturbance in protein synthesis. Our results show that different controllers are effective in buffering different noise components, and identify ranges of feedback gain for minimizing deleterious fluctuations in protein levels.

Suggested Citation

  • Saurabh Modi & Supravat Dey & Abhyudai Singh, 2021. "Noise suppression in stochastic genetic circuits using PID controllers," PLOS Computational Biology, Public Library of Science, vol. 17(7), pages 1-25, July.
  • Handle: RePEc:plo:pcbi00:1009249
    DOI: 10.1371/journal.pcbi.1009249
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    References listed on IDEAS

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    1. William J. Blake & Mads KÆrn & Charles R. Cantor & J. J. Collins, 2003. "Noise in eukaryotic gene expression," Nature, Nature, vol. 422(6932), pages 633-637, April.
    2. John R. S. Newman & Sina Ghaemmaghami & Jan Ihmels & David K. Breslow & Matthew Noble & Joseph L. DeRisi & Jonathan S. Weissman, 2006. "Single-cell proteomic analysis of S. cerevisiae reveals the architecture of biological noise," Nature, Nature, vol. 441(7095), pages 840-846, June.
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    1. Maurice Filo & Sant Kumar & Mustafa Khammash, 2022. "A hierarchy of biomolecular proportional-integral-derivative feedback controllers for robust perfect adaptation and dynamic performance," Nature Communications, Nature, vol. 13(1), pages 1-19, December.

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