Abstract
Cell size is thought to play an important role in choosing between temporal and spatial sensing in chemotaxis. Large cells are thought to use spatial sensing due to large chemical difference at its ends whereas small cells are incapable of spatial sensing due to rapid homogenization of proteins within the cell. However, small cells have been found to polarize and large cells like sperm cells undergo temporal sensing. Thus, it remains an open question what exactly governs spatial versus temporal sensing. Here, we identify the factors that determines sensing choices through mathematical modeling of chemotactic circuits. Comprehensive computational search of three-node signaling circuits has identified the negative integral feedback (NFB) and incoherent feedforward (IFF) circuits as capable of adaptation, an important property for chemotaxis. Cells are modeled as one-dimensional circular system consisting of diffusible activator, inactivator and output proteins, traveling across a chemical gradient. From our simulations, we find that sensing outcomes are similar for NFB or IFF circuits. Rather than cell size, the relevant parameters are the 1) ratio of cell speed to the product of cell diameter and rate of signaling, 2) diffusivity of the output protein and 3) ratio of the diffusivities of the activator to inactivator protein. Spatial sensing is favored when all three parameters are low. This corresponds to a cell moving slower than the time it takes for signaling to propagate across the cell diameter, has an output protein that is polarizable and has a local-excitation global-inhibition system to amplify the chemical gradient. Temporal sensing is favored otherwise. We also find that temporal sensing is more robust to noise. By performing extensive literature search, we find that our prediction agrees with observation in a wide range of species and cell types ranging from E. coli to human Fibroblast cells and propose that our result is universally applicable.
Highlights
Chemotaxis is the process whereby cells move towards a region of higher chemical stimulus concentration
There are two ways for a cell to sense these external chemicals: temporal sensing, where the cell senses the external chemical at two different time points after it has moved through a certain
We find that the choice between temporal and spatial sensing is determined by the ratio of cell velocity to the product of cell diameter and rate of signaling, as well as the diffusivities of the signaling proteins
Summary
Chemotaxis is the process whereby cells move towards a region of higher chemical stimulus concentration. Information about the external chemical gradient is transduced into the cell by binding of chemoattractant and chemorepellant molecules to specific receptors at the cell surface. These binding events trigger downstream intracellular signaling to modulate the cell’s motility. In temporal or sequential sensing, cells compare the intensity of receptor stimulation at different times (Fig 1, left) and modulate their probability of moving in the same direction or switching directions. Binding of chemoattractant decreases the switching probability from counter-clockwise to clockwise rotation, reducing tumbling and increasing the run length when the cell is moving in the favorable direction. Cells simultaneously measure the intensity of receptor stimulation at its two ends (Fig 1, right). Binding of chemoattractant results in activation of signaling pathways involving small Rho guanosine triphosphatases (Rho GTPases) and phosphoinositide 3 kinases (PI3Ks) and asymmetric polymerization of actin at the up-gradient edge of the cell, facilitating motion up the gradient [3]
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