A Multiscale Model of Escherichia coli Chemotaxis in a Stokes Flow
Abstract
I. Introduction
A trait common to all life is the ability to sense the conditions of the surrounding environment and to elicit appropriate responses based on sensory inputs. It has been known since at least the late 19 th century that populations of motile bacteria sense the chemical composition of their surroundings and respond by moving through their fluid environment toward chemical attractants and away from chemical repellants (Pfeffer 1883), a phenomenon known as chemotaxis. Bacteria such as
Escherichia coli sense attractant and repellant chemicals through binding interactions with clustered arrays of receptor proteins (methyl-accepting chemotaxis proteins or MCPs) that traverse the bacterial cell membrane (Falke 2001). Within the cell, chemical sensory inputs are processed through a series of phosphoryl group transfers among the Che proteins that influence MCP ligand binding activity and cell motility responses (Wadhams 2004). In fluid environments containing gradients of chemoattractants or repellants, cells use a random biased walk to move toward attractants or away from repellants (Berg and Brown 1972; Macnab and Koshland, 1972).
A comprehensive understanding of bacterial chemotaxis is important for a variety of reasons.
For example, the establishment of infection sites in host tissue or colonization of other surfaces (such as pipes used for transport of water, oil or other fluids) by motile bacteria requires the bacterium to swim in order to locate sites for colonization, and the colonization process requires a transition from a motile state to a stationary state. An understanding of the principles of chemotactic motility may also prove useful in the design and engineering of biologically-inspired nanomachines and devices
(biomimetics). Understanding chemotaxis is also important in characterizing the behavior of natural populations of, e.g., aquatic bacteria. Additionally, bacterial chemotaxis represents a valuable model system for the understanding of biological signaling circuitry and networks. Thus, the goal of the present study is to produce a multiscale model of bacterial chemotaxis that encompasses phenomena occurring over angstrom-scale (e.g., atomic/molecular interactions among chemotaxis proteins) to the micron/millimeter scale (e.g., at the level of intact cells eliciting responses in fluid environments).
We begin this paper with a description of the components and mechanism of bacterial chemotaxis and proceed from there to the development of our multiscale chemotaxis model.
An overview of the components and signal flow involved in chemotaxis in E. coli is shown in
Figure 1. Chemotactic behavior is initiated through binding of attractant or repellant molecules to receptor sites within clusters of cognate membrane-spanning MCPs (Hazelbauer 1990). Five such
MCPs have been characterized in E. coli : Tar (recognizes aspartate, glutamate and maltose); Tsr
(recognizes serine); Trg (recognizes ribose and galactose) Tap (recognizes dipeptides), and Aer
(responds to oxygen) (Adler 1975). Following the binding of chemical molecules, the MCP undergoes conformational changes, and in this way environmental chemical stimulus inputs are transduced to the chemotaxis machinery within the cell (Mise, 2014).
On the cytoplasmic side of the cell membrane, MCP conformational changes are transmitted to the chemotaxis protein CheW (Gegner 1992, Liu, 1972, Liu, 1991). CheW functions as an adaptor protein through which chemical sensory input is transduced to the sensor kinase protein CheA (Liu
1989, Liu 1991). CheA belongs to the two-component sensor family and comprises the histidine sensor kinase component of a two-component sensor system (Hoch 2000). Sensor kinases of this type possess conserved histidine residues that serve as sites of autophosphorylation activity of the protein. The phosphoryl group on CheA-P is transferred to either CheY or CheB. CheY constitutes the response regulator component of the two-component system; upon transfer of the phosphoryl

group from CheA-P to a conserved aspartic acid residue on CheY, CheY-P interacts with the flagellar switch to change the direction of flagellar rotation from the default counterclockwise direction (running) to clockwise rotation (tumbling) (Stock 1989). Alternatively, phosphoryl transfer can occur from CheA-P to CheB: CheB-P is a methyl esterase that removes methyl groups from
MCPs (Djordjevic 1998; Li 1995; Lupas 1989). The substrates for CheB-P are MCP glutamic acid residues within the MCPs; MCPs become methylated by the methyl group donor CheR (Springer and
Koshland 1977).
In response to attractants (for example the amino acid aspartic acid interacting with the Tar
MCP), CheA autophosphorylation activity is drastically reduced. As a consequence, the levels of
CheY-P remain low (since CheA-P is the phosphoryl donor for CheY), and the cell will preferentially continue to swim “up the gradient”, towards increasing attractant levels in the environment. This is because CheY-P is required to switch the direction of flagellar motor rotation to the clockwise tumbling mode. At the same time, the levels of CheB-P also will remain low, since the CheA-P is also the phosphoryl donor for CheB. And since CheB-P acts as the MCP methylesterase for removal of methyl groups from the MCP, MCP methylation levels become elevated. As MCP methylation levels increase, the autophosphorylation activity of CheA in response to attractants increases; thereby allowing the return of CheA activity to pre-stimulus levels.
Modeling and analysis of chemotactic signaling and flagellar motility in bacteria can be considered from several scales. Firstly, motility can be considered at the
ngstrom scale of biochemical interactions among ligands and protein interactions that participate in transducing sensory inputs to flagellar output behavior, for example at the level of MCP methylation and phosphorylation state of
CheA or CheY. In this regard, discuss here the MCP and CheY models, e.g,. Monod Chagaux or?
Do you want to lay out equations within each of these levels as we build up the model in fluid?
One can also approach chemotactic models from the standpoint of flagellar motor activity and the consequent effects of rotational directional on the behavior of individual cells. Cell behavior can be described as either running (flagellar motor rotating counterclockwise, as viewed down the longitudinal axis of a flagellar filament on the outside of the cell) or tumbling (motor rotating clockwise) Briefly describe models that look at run/tumble behavior.
As motile flagellate cells naturally swim and exhibit chemotactic behavionr in fluid environments, we wished to produce an algorithm model to explore chemotaxis in such a fluid environment. To approach this we applied and here start talking about and introducing our layer onto the model
References
Adler, J. 1975 Chemotaxis in bacteria. Ann. Rev. Biochem. 44, 341-356.
Berg, H.C., Brown, D.A. 1972 Chemotaxis in Escherichia coli analysed by three-dimensional tracking. Nature. 239,
500-504.
Bilwes, A.M., Alex, L.A., Crane, B.R., Simon, M.L. 1999. Structure of CheA, a signal-transducing histidine kinase.
Cell 96, 131-141.
Gegner, J.A., Graham, D.R., Roth, A.F., Dahlquist, F.W. 1992. Assembly of an MCP receptor, CheW, and kinase
CheA complex in the bacterial chemotaxis signal transduction pathway. Cell 70, 975-982.
Falke, J.J., Hazebauer, G.L. 2001. Transmembrane signaling in bacterial chemoreceptors. Trends Biochem. Sci. 26,
257-265.
Hazelbauer, G.L., Yaghmai, R., Burrows, G.G., Baumgartner, J.W., Dutton, D.P., Morgan, D.G. 1990. Transducers:
Transmembrane receptor proteins involved in bacterial chemotaxis. In Biology of the chemotactic response.
Cambridge, Cambridge University Press 107-134.

Djordjevic, S., Goudreau, P.N., Xu, Q., Stock, A.M., West, A.H. 198. Structural basis for methylesterase CheB regulation by a phosphorylation activation domain. Proc. Natl. Acad. Sci 95, 1381-1386
Hoch, J.A. 2000. Two-component and phosphorelay signal transduction. Curr. Op. Microbiol. 3, 165-170.
Kort, E.N., Goy, M.F., Larsen, S.H., Adler, J. 1975. Methylation of a membrane protein involved in bacterial chemotaxis. Proc. Natl. Acad. Sci. 72, 3939-3943.
Larsen, S.H., Adler J., Gargus, J.J., Hogg, R.W., 1974. Chemochemical coupling without ATP: the source of energy for motility and chemotaxis in bacteria. Proc. Natl. Acad. Sci. 71, 1239-1243.
Larsen S.H., Reader R.W., Kort E.N., Tso W.W., Adler J. 1974. Change of direction of flagellar rotation is the basis of the chemotactic response in Escherichia coli . 249, 74-77.
Li, J., Swanson, R.V., Simon, M.I., Weis, R.M.1995 The response regulators CheB and CheY exhibit competitive binding to the kinase CheA. Biochem. 34, 14626-14636
Liu J, Parkinson J.S. 1989. Role of CheW protein in coupling membrane receptors to the intracellular signaling system of bacterial chemotaxis. Proc. Natl. Acad. Sci. 86, 8703-8707.
Liu, J., Parkinson, J.S., 1991. Genetic evidence for interaction between the CheW and Tsr proteins during chemorecptor signaling by Escherichia coli . J. Bact. 173, 4941-4951.
Lupas, A., Stock, J. 1989. Phosphorylation of an N-terminal regulatory domain activates the CheB methylesterase in bacterial chemotaxis. J. Biol. Chem. 264, 17337-17342.
Macnab, R.M., Koshland, D.E., 1972. The gradient-sensing mechanism in bacterial chemotaxis. Proc. Natl. Acad.
Sci. 69, 2509-2512.
Mise, T., Matsunami, H., Samatey, F.A., Maruyama, I.N. 2014. Crystallization and preliminary X-ray diffraction analysis of the periplasmic domain of the Escherichia coli aspartate receptor Tar and its complex with aspartate.
Acta Cryst. Sec. F, 1219-1223.
Pfeffer W. 1884. Locomotorische Richtungsbewegungen durch chemische Reize. Unters Bot Inst Tübingen 1, 363-
382.
Springer, W.R., Koshland, D.E. 1977. Identification of a protein methyltransferase as the cheR gene product in the bacterial sensing system. Proc. Natl. Acad. Sci. 74, 533-537.
Stock, A.M., Mottonen, J.M., Stock, J.B., Schutt, C.E. 1989. Three-dimensional structure of CheY, the response regulator of bacterial chemotaxis. Nature 337, 745-749.
Wadhams, G.W., Armitage, J.P. 2004. Making sense of it all: bacterial chemotaxis. Nat. Rev. Mol. Cell Biol. 5,
1024-1037.