Table 2

Constraints on size

StimulusMechanismConstraint formulas2 r, μm
NoneDiffusion Embedded Image 0.64
ChemicalSpatial Embedded Image 0.58
ChemicalTemporal Embedded Image 0.65
LightSpatial Embedded Image 1.77
LightTemporal Embedded Image 1.05
LightDirection Embedded Image 1.24
TemperatureSpatial Embedded Image 0.74
TemperatureTemporal Embedded Image 0.69
  • In the constraint formulas, the parameters are grouped so that the term on the left is a performance factor (signal-to-noise ratio or ratio of diffusion coefficients with and without motility), the first term to the right of the equal sign involves hydrodynamics, the second term involves stimulus intensity, the third term involves gradient magnitude and/or relative speed, and the right-most term involves the size of the organism. The right-hand column gives the minimum diameter an organism can have and usefully employ the indicated mechanism, assuming the parameter values in Table 1 and S/N = (DmD0)/D0 ≥ 1 for useful function.