Theoretical range over which bacteria and nematodes locate plant roots using carbon dioxide

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Abstract
A theory used to estimate the smallest relative chemical gradient that is potentially detectable is given approximately byG>(DCR ν 2t3)−1/2 whereD is the diffusion constant andC the concentration of the stimulus chemical,R is the effective radius of the receptor,ν the velocity of the organism, andt the time period within which the organism measures the concentration. Of these factors, time has the strongest influence. Combining this result with available information on gradients of carbon dioxide around roots and behavior of bacteria and nematodes leads to several conclusions. Bacteria can potentially detect carbon dioxide gradients in the layer of water in contact with the root but not further away. In contrast, plant-parasitic nematodes can potentially detect gradients one meter from a single long root fiber and over 2 m from a plant root mass using klinokinesis. A direct approach using klinotaxis can start a few centimeters from a single root fiber and half a meter from a root mass. These differences are due to differences in the time available to measure the concentrations. Increasing the length of a bacterium could increase its ability to detect gradients by reducing its rotational diffusion. Collimating stimuli that serve to maintain a straight path may provide a means of improving chemotaxis by permitting concentration to be measured for longer times during klinokinesis. More accurate predictions can be made when more precise data are available. The analysis is applicable to a wide variety of other organisms and stimuli.