Multi-bit Boolean model for chemotactic drift of Escherichiacoli
- Author(s): Anuj Deshpande 1 ; Sibendu Samanta 1 ; Sutharsan Govindarajan 2 ; Ritwik Kumar Layek 3
-
-
View affiliations
-
Affiliations:
1:
Department of Electronics and CommunicationEngineering , SRM University – AP , AndhraPradesh , India ;
2: Department of Biology , SRMUniversity – AP , Andhra Pradesh , India ;
3: Department of Electronics and Electrical CommunicationEngineering , Indian Institute of Technology - Kharagpur , West Bengal , India
-
Affiliations:
1:
Department of Electronics and CommunicationEngineering , SRM University – AP , AndhraPradesh , India ;
- Source:
Volume 14, Issue 6,
December
2020,
p.
343 – 349
DOI: 10.1049/iet-syb.2020.0060 , Print ISSN 1751-8849, Online ISSN 1751-8857
Dynamic biological systems can be modelled to an equivalent modular structure using Booleannetworks (BNs) due to their simple construction and relative ease of integration. The chemotaxisnetwork of the bacterium Escherichia coli (E. coli) is one of themost investigated biological systems. In this study, the authors developed a multi-bit Booleanapproach to model the drifting behaviour of the E. coli chemotaxis system. Theirapproach, which is slightly different than the conventional BNs, is designed to provide finerresolution to mimic high-level functional behaviour. Using this approach, they simulated thetransient and steady-state responses of the chemoreceptor sensory module. Furthermore, theyestimated the drift velocity under conditions of the exponential nutrient gradient. Theirpredictions on chemotactic drifting are in good agreement with the experimental measurements undersimilar input conditions. Taken together, by simulating chemotactic drifting, they propose thatmulti-bit Boolean methodology can be used for modelling complex biological networks. Application ofthe method towards designing bio-inspired systems such as nano-bots is discussed.
Inspec keywords: cell motility; Boolean functions; microorganisms
Other keywords: drift velocity; multibit Boolean model; Boolean networks; bacterium Escherichia coli; biological systems; complex biological networks; chemoreceptor sensory module; conventional BNs; dynamic biological systems; steady-state responses; bio-inspired systems; high-level functional behaviour; chemotactic drifting; equivalent modular structure; chemotactic drift; simple construction; multibit Boolean methodology; multibit Boolean approach; chemotaxis network
Subjects: Function theory, analysis; Biological transport; cellular and subcellular transmembrane physics
References
-
-
1)
-
24. Tu, Y., Berg, H.C.: ‘Tandem adaptation with a common design in Escherichia coli chemotaxis’, J. Mol. Biol., 2012, 423, (5), pp. 782–788.
-
-
2)
-
38. Tu, Y.: ‘Quantitative modeling of bacterial chemotaxis: signal amplification and accurate adaptation’, Annu. Rev. Biophys., 2013, 42, pp. 337–359.
-
-
3)
-
10. Bren, A., Eisenbach, M.: ‘How signals are heard during bacterial chemotaxis: protein-protein interactions in sensory signal propagation’, J. Bacteriol., 2000, 182, (24), pp. 6865–6873.
-
-
4)
-
13. Sen, S.: ‘Transient response characteristics in a biomolecular integral controller’, IET Syst. Biol., 2016, 10, (2), pp. 57–63.
-
-
5)
-
41. Ali, J., Cheang, U.K., Martindale, J.D., et al: ‘Bacteria-inspired nanorobots with flagellar polymorphic transformations and bundling’, Nat. Sci. Rep., 2017, 7, (14098), pp. 1–10.
-
-
6)
-
14. Shimizu, T.S., Tu, Y., Berg, H.C.: ‘A modular gradient-sensing network for chemotaxis in Escherichia coli revealed by responses to time-varying stimuli’, Mol. Syst. Biol., 2010, 6, (382), pp. 1–14.
-
-
7)
-
9. Clausznitzer, D., Micali, G., Neumann, S., et al: ‘Predicting chemical environments of bacteria from receptor signaling’, PLoS Comput. Biol., 2014, 10, (10), p. e1003870.
-
-
8)
-
39. Mano, M.M., Ciletti, M.D.: ‘Digital design: with an introduction to the Verilog HDL’ (Pearson Education, New Jersey, USA., 2013, 5th edn.).
-
-
9)
-
4. Park, M.J., Dahlquist, F., Doyle, F.: ‘Simultaneous high gain and wide dynamic range in a model of bacterial chemotaxis’, IET Syst. Biol., 2007, 1, (4), pp. 222–229.
-
-
10)
-
30. Cucchi, A., Etchegaray, C., Meunier, N., et al: ‘Cell migration in complex environments: chemotaxis and topographical obstacles’, ESAIM Proc. Surv., 2020, 67, pp. 191–209.
-
-
11)
-
17. Ji, T., Li, M., Wu, Q., et al: ‘Optimal estimation of harmonics in a dynamic environment using an adaptive bacterial swarming algorithm’, IET Gener. Transm. Distrib., 2011, 5, (6), pp. 609–620.
-
-
12)
-
32. Arif, M.S., Raza, A., Rafiq, M., et al: ‘A reliable numerical analysis for stochastic hepatitis B virus epidemic model with the migration effect’, Iran. J. Sci. Technol. Trans. A, Sci., 2019, 43, (5), pp. 2477–2492.
-
-
13)
-
28. Negreanu, M., Tello, J.I.: ‘Asymptotic stability of a two species chemotaxis system with non-diffusive chemoattractant’, J. Differ. Equ., 2015, 258, (5), pp. 1592–1617.
-
-
14)
-
31. Arif, M.S., Raza, A., Rafiq, M., et al:‘A reliable stochastic numerical analysis for typhoid fever incorporating withprotection against infection’, Comput. Mater. Continua, 2019, 59, (3), pp. 787–804.
-
-
15)
-
43. Bhuyan, T., Bhattacharjee, M., Singh, A.K., et al:‘Boolean-chemotaxis of logibots deciphering the motions of self-propellingmicroorganisms’, Soft Matter, 2018, 14, (16), pp. 3182–3191.
-
-
16)
-
13. Sen, S.:‘Transient response characteristics in a biomolecular integralcontroller’, IET Syst. Biol., 2016, 10, (2), pp. 57–63.
-
-
17)
-
25. Kauffman, S.A.:‘Metabolic stability and epigenesis in randomly constructed geneticnets’, J. Theor. Biol., 1969, 22,(3), pp. 437–467.
-
-
18)
-
36. Stötzel, C., Röblitz, S., Siebert, H.:‘Complementing ODE-based system analysis using Boolean networks derived from anEuler-like transformation’, PLoS ONE, 2015, 10, (10), pp. 1–20.
-
-
19)
-
23. Sourjik, V., Berg, H.C.:‘Receptor sensitivity in bacterial chemotaxis’, Proc. Natl.Acad. Sci., 2002, 99, (1), pp. 123–127.
-
-
20)
-
27. Zheng, J.:‘Boundedness of the solution of a higher-dimensional parabolic–ODE–parabolicchemotaxis–haptotaxis model with generalized logistic source’, Nonlinearity, 2017, 30, (5), p. 1987.
-
-
21)
-
16. Berg, H.C.: ‘E.coli in motion’ (Springer Science & Business Media, New York, USA., 2008).
-
-
22)
-
28. Negreanu, M., Tello, J.I.:‘Asymptotic stability of a two species chemotaxis system with non-diffusivechemoattractant’, J. Differ. Equ., 2015, 258, (5), pp. 1592–1617.
-
-
23)
-
34. Deshpande, A., Samanta, S., Das, H., et al:‘A boolean approach to bacterial chemotaxis’. IEEE 38thAnnual Int. Conf. of the Engineering in Medicine and Biology Society (EMBC), Orlando, Florida, USA., 2016, pp. 6125–6129.
-
-
24)
-
41. Ali, J., Cheang, U.K., Martindale, J.D., et al:‘Bacteria-inspired nanorobots with flagellar polymorphic transformations andbundling’, Nat. Sci. Rep., 2017, 7,(14098), pp. 1–10.
-
-
25)
-
1. Alon, U.: ‘AnIntroduction to systems biology: design principles of biological circuits’(CRC Press, Boca Raton, FL, USA., 2006).
-
-
26)
-
14. Shimizu, T.S., Tu, Y., Berg, H.C.:‘A modular gradient-sensing network for chemotaxis in Escherichiacoli revealed by responses to time-varying stimuli’, Mol. Syst.Biol., 2010, 6, (382), pp. 1–14.
-
-
27)
-
38. Tu, Y.:‘Quantitative modeling of bacterial chemotaxis: signal amplification and accurateadaptation’, Annu. Rev. Biophys., 2013, 42, pp. 337–359.
-
-
28)
-
10. Bren, A., Eisenbach, M.:‘How signals are heard during bacterial chemotaxis: protein-protein interactions insensory signal propagation’, J. Bacteriol., 2000, 182, (24), pp. 6865–6873.
-
-
29)
-
18. Waite, A.J., Frankel, N.W., Emonet, T.:‘Behavioral variability and phenotypic diversity in bacterialchemotaxis’, Annu. Rev. Biophys., 2018, 47, pp. 595–616.
-
-
30)
-
8. Iglesias, P.A., Shi, C.:‘Comparison of adaptation motifs: temporal, stochastic and spatialresponses’, IET Syst. Biol., 2014, 8,(6), pp. 268–281.
-
-
31)
-
17. Ji, T., Li, M., Wu, Q., et al:‘Optimal estimation of harmonics in a dynamic environment using an adaptive bacterialswarming algorithm’, IET Gener. Transm. Distrib., 2011, 5, (6), pp. 609–620.
-
-
32)
-
35. Wittmann, D.M., Krumsiek, J., Saez.Rodriguez, J., et al:‘Transforming Boolean models to continuous models: methodology and application toT-cell receptor signaling’, BMC Syst. Biol., 2009, 3, (1), p. 98.
-
-
33)
-
40. Vladimirov, N., Løvdok, L., Lebiedz, D., et al:‘Dependence of bacterial chemotaxis on gradient shape and adaptationrate’, PLoS Comput. Biol., 2008, 4,(12), p. e1000242.
-
-
34)
-
42. Gutierrez, B., Bermúdez, C.V., Ureña, Y.R.C., et al:‘Nanobots: development and future’, Int. J. Biosens.Bioelectron., 2017, 2, (5), pp. 146–151.
-
-
35)
-
21. Samanta, S., Layek, R., Kar, S., et al:‘Predicting Escherichia coli's chemotactic drift under exponentialgradient’, Phys. Rev. E, 2017, 96,(3), p. 032409.
-
-
36)
-
2. Tashiro, Y., Furubayashi, M., Morijiri, T., et al:‘Escherichia coli robots that freeze, smell, swell, andtime-keep’, IET Synth. Biol., 2007, 1, (1), pp. 41–43.
-
-
37)
-
3. Lebiedz, D., Maurer, H.:‘External optimal control of self-organisation dynamics in a chemotaxis reactiondiffusion system’, IET Syst. Biol., 2004, 1, (2), pp. 222–229.
-
-
38)
-
33. Baleanu, D., Raza, A., Rafiq, M., et al:‘Competitive analysis for stochastic influenza model with constant vaccinationstrategy’, IET Syst. Biol., 2019, 13,(6), pp. 316–326.
-
-
39)
-
29. Buttenschön, A., Hillen, T., Gerisch, A., et al:‘A space-jump derivation for non-local models of cell–cell adhesion and non-localchemotaxis’, J. Math. Biol., 2018, 76, (1–2), pp. 429–456.
-
-
40)
-
32. Arif, M.S., Raza, A., Rafiq, M., et al:‘A reliable numerical analysis for stochastic hepatitis B virus epidemic model withthe migration effect’, Iran. J. Sci. Technol. Trans. A, Sci., 2019, 43, (5), pp. 2477–2492.
-
-
41)
-
26. Layek, R.K., Datta, A., Dougherty, E.R.:‘From biological pathways to regulatory networks’, Mol.Biosyst., 2011, 7, (3), pp. 843–851.
-
-
42)
-
4. Park, M.J., Dahlquist, F., Doyle, F.:‘Simultaneous high gain and wide dynamic range in a model of bacterialchemotaxis’, IET Syst. Biol., 2007, 1, (4), pp. 222–229.
-
-
43)
-
31. Arif, M.S., Raza, A., Rafiq, M., et al: ‘A reliable stochastic numerical analysis for typhoid fever incorporating with protection against infection’, Comput. Mater. Continua, 2019, 59, (3), pp. 787–804.
-
-
44)
-
22. Samanta, S., Layek, R., Kar, S., et al: ‘Transient drift of Escherichia coli under a diffusing step nutrient profile’, Phys. Rev. E, 2018, 98, (5), p. 052413.
-
-
45)
-
2. Tashiro, Y., Furubayashi, M., Morijiri, T., et al: ‘Escherichia coli robots that freeze, smell, swell, and time-keep’, IET Synth. Biol., 2007, 1, (1), pp. 41–43.
-
-
46)
-
34. Deshpande, A., Samanta, S., Das, H., et al: ‘A boolean approach to bacterial chemotaxis’. IEEE 38th Annual Int. Conf. of the Engineering in Medicine and Biology Society (EMBC), Orlando, Florida, USA., 2016, pp. 6125–6129.
-
-
47)
-
36. Stötzel, C., Röblitz, S., Siebert, H.: ‘Complementing ODE-based system analysis using Boolean networks derived from an Euler-like transformation’, PLoS ONE, 2015, 10, (10), pp. 1–20.
-
-
48)
-
5. Sourjik, V., Wingreen, N.S.: ‘Responding to chemical gradients: bacterial chemotaxis’, Curr. Opin. Cell Biol., 2012, 24, (2), pp. 262–268.
-
-
49)
-
8. Iglesias, P.A., Shi, C.: ‘Comparison of adaptation motifs: temporal, stochastic and spatial responses’, IET Syst. Biol., 2014, 8, (6), pp. 268–281.
-
-
50)
-
35. Wittmann, D.M., Krumsiek, J., Saez.Rodriguez, J., et al: ‘Transforming Boolean models to continuous models: methodology and application to T-cell receptor signaling’, BMC Syst. Biol., 2009, 3, (1), p. 98.
-
-
51)
-
25. Kauffman, S.A.: ‘Metabolic stability and epigenesis in randomly constructed genetic nets’, J. Theor. Biol., 1969, 22, (3), pp. 437–467.
-
-
52)
-
42. Gutierrez, B., Bermúdez, C.V., Ureña, Y.R.C., et al: ‘Nanobots: development and future’, Int. J. Biosens. Bioelectron., 2017, 2, (5), pp. 146–151.
-
-
53)
-
26. Layek, R.K., Datta, A., Dougherty, E.R.: ‘From biological pathways to regulatory networks’, Mol. Biosyst., 2011, 7, (3), pp. 843–851.
-
-
54)
-
1. Alon, U.: ‘An Introduction to systems biology: design principles of biological circuits’ (CRC Press, Boca Raton, FL, USA., 2006).
-
-
55)
-
20. Sneddon, M.W., Pontius, W., Emonet, T.: ‘Stochastic coordination of multiple actuators reduces latency and improves chemotactic response in bacteria’, Proc. Natl. Acad. Sci., 2012, 109, (3), pp. 805–810.
-
-
56)
-
29. Buttenschön, A., Hillen, T., Gerisch, A., et al: ‘A space-jump derivation for non-local models of cell–cell adhesion and non-local chemotaxis’, J. Math. Biol., 2018, 76, (1–2), pp. 429–456.
-
-
57)
-
37. Valverde, J.C., Mortveit, H.S., Gershenson, C., et al: ‘Boolean networks and their applications in science and engineering’, Complexity, 2020, 2020, pp. 1–3.
-
-
58)
-
16. Berg, H.C.: ‘E. coli in motion’ (Springer Science & Business Media, New York, USA., 2008).
-
-
59)
-
12. Inouye, M., Dutta, R.: ‘Histidine kinases in signal transduction’ (Academic Press, London, UK., 2003).
-
-
60)
-
18. Waite, A.J., Frankel, N.W., Emonet, T.: ‘Behavioral variability and phenotypic diversity in bacterial chemotaxis’, Annu. Rev. Biophys., 2018, 47, pp. 595–616.
-
-
61)
-
6. Meacci, G., Lan, G., Tu, Y.: ‘Dynamics of the bacterial flagellar motor: the effects of stator compliance, back steps, temperature, and rotational asymmetry’, Biophys. J., 2011, 100, (8), pp. 1986–1995.
-
-
62)
-
43. Bhuyan, T., Bhattacharjee, M., Singh, A.K., et al: ‘Boolean-chemotaxis of logibots deciphering the motions of self-propelling microorganisms’, Soft Matter, 2018, 14, (16), pp. 3182–3191.
-
-
63)
-
23. Sourjik, V., Berg, H.C.: ‘Receptor sensitivity in bacterial chemotaxis’, Proc. Natl. Acad. Sci., 2002, 99, (1), pp. 123–127.
-
-
64)
-
40. Vladimirov, N., Løvdok, L., Lebiedz, D., et al: ‘Dependence of bacterial chemotaxis on gradient shape and adaptation rate’, PLoS Comput. Biol., 2008, 4, (12), p. e1000242.
-
-
65)
-
21. Samanta, S., Layek, R., Kar, S., et al: ‘Predicting Escherichia coli's chemotactic drift under exponential gradient’, Phys. Rev. E, 2017, 96, (3), p. 032409.
-
-
66)
-
11. Spiro, P.A., Parkinson, J.S., Othmer, H.G.: ‘A model of excitation and adaptation in bacterial chemotaxis’, Proc. Natl. Acad. Sci., 1997, 94, (14), pp. 7263–7268.
-
-
67)
-
19. Tu, Y., Shimizu, T.S., Berg, H.C.: ‘Modeling the chemotactic response of Escherichia coli to time-varying stimuli’, Proc. Natl. Acad. Sci., 2008, 105, (39), pp. 14855–14860.
-
-
68)
-
15. Adler, J.: ‘Chemoreceptors in bacteria’, Science, 1969, 166, (3913), pp. 1588–1597.
-
-
69)
-
3. Lebiedz, D., Maurer, H.: ‘External optimal control of self-organisation dynamics in a chemotaxis reaction diffusion system’, IET Syst. Biol., 2004, 1, (2), pp. 222–229.
-
-
70)
-
33. Baleanu, D., Raza, A., Rafiq, M., et al: ‘Competitive analysis for stochastic influenza model with constant vaccination strategy’, IET Syst. Biol., 2019, 13, (6), pp. 316–326.
-
-
71)
-
7. Dufour, Y.S., Fu, X., Hernandez.Nunez, L., et al:‘Limits of feedback control in bacterial chemotaxis’, PLoSComput. Biol., 2014, 10, (6), p. e1003694.
-
-
72)
-
6. Meacci, G., Lan, G., Tu, Y.:‘Dynamics of the bacterial flagellar motor: the effects of stator compliance, backsteps, temperature, and rotational asymmetry’, Biophys. J., 2011, 100, (8), pp. 1986–1995.
-
-
73)
-
30. Cucchi, A., Etchegaray, C., Meunier, N., et al:‘Cell migration in complex environments: chemotaxis and topographicalobstacles’, ESAIM Proc. Surv., 2020, 67, pp. 191–209.
-
-
74)
-
9. Clausznitzer, D., Micali, G., Neumann, S., et al:‘Predicting chemical environments of bacteria from receptorsignaling’, PLoS Comput. Biol., 2014, 10, (10), p. e1003870.
-
-
75)
-
20. Sneddon, M.W., Pontius, W., Emonet, T.:‘Stochastic coordination of multiple actuators reduces latency and improveschemotactic response in bacteria’, Proc. Natl. Acad. Sci., 2012, 109, (3), pp. 805–810.
-
-
76)
-
7. Dufour, Y.S., Fu, X., Hernandez.Nunez, L., et al: ‘Limits of feedback control in bacterial chemotaxis’, PLoS Comput. Biol., 2014, 10, (6), p. e1003694.
-
-
77)
-
27. Zheng, J.: ‘Boundedness of the solution of a higher-dimensional parabolic–ODE–parabolic chemotaxis–haptotaxis model with generalized logistic source’, Nonlinearity, 2017, 30, (5), p. 1987.
-
-
1)