Physical Constraints in Sensory Ecology
9
4 Consequences For Small Plankton
For microscopic organisms that live in water free of any constraint on movement
but viscosity (i.e., not attached to any surface and not containing magnets),
Brownian motion causes continual random translation and rotation. The rates at
which these occur set limits on the time available for obtaining information useful
for guiding locomotion.
Such small organisms live in a world where viscous effects are far stronger than
inertial effects. The Reynolds number is well below unity, and flow is laminar,
never turbulent. In this situation, hydrodynamic drag can be rigorously calculated
for simple shapes, and it is possible to relate speed to energy consumption. Using
Stokes Jaw for spherical shapes (Rouse 1961, pp. 212-216) and observing that
specific metabolic rates (power per unit volume) are relatively uniform for all
kinds of organisms, it can be demonstrated that speed of swimming should be
proportional to size (Dusenbery and Snell 1995). With the best estimates of
efficiency, the typical speed is estimated to be in the vicinity of 10 diameters per
second, consistent with many observations (Dusenbery 1996, p. 45; Mann and
Lazier 1991).
4.1 Size and Motility
In addition, the rates of translation and rotation caused by Brownian motion can be
rigorously calculated (Berg 1993). Taking advantage of these relations, formulas
have been derived for estimating the signal-to-noise ratio for detecting gradients of
light, chemicals, and heat (Table 1).
These results lead to the surprising conclusion that there exists a sharp size
limit (about half a micrometer diameter) below which free bacteria have no use
for motility. A review of published literature (Fig. 2) indicated that the prediction
is supported, and about 20% of free, nonmotile genera are below this size limit
but the smallest of 97 motile genera was about 0.8 J.lm in length (Dusenbery
1997).
4.2 Consequences of Shape
Perrin (1934, 1936) derived expressions for the motion of ellipsoids subject to
Brownian motion. Unfortunately, they involve defmite integrals that have no
solution in common functions, but approximations for high axial ratios are
available, and have been much used to estimate the shapes of molecules (Tanford
1963; van Holde 1985). With computers it is now easy to evaluate these integrals,
and these relations have been used to quantitatively evaluate the effects of
constant-volume changes in shape (including small axial ratios) on several possible
functions (Dusenbery 1998a).
9
4 Consequences For Small Plankton
For microscopic organisms that live in water free of any constraint on movement
but viscosity (i.e., not attached to any surface and not containing magnets),
Brownian motion causes continual random translation and rotation. The rates at
which these occur set limits on the time available for obtaining information useful
for guiding locomotion.
Such small organisms live in a world where viscous effects are far stronger than
inertial effects. The Reynolds number is well below unity, and flow is laminar,
never turbulent. In this situation, hydrodynamic drag can be rigorously calculated
for simple shapes, and it is possible to relate speed to energy consumption. Using
Stokes Jaw for spherical shapes (Rouse 1961, pp. 212-216) and observing that
specific metabolic rates (power per unit volume) are relatively uniform for all
kinds of organisms, it can be demonstrated that speed of swimming should be
proportional to size (Dusenbery and Snell 1995). With the best estimates of
efficiency, the typical speed is estimated to be in the vicinity of 10 diameters per
second, consistent with many observations (Dusenbery 1996, p. 45; Mann and
Lazier 1991).
4.1 Size and Motility
In addition, the rates of translation and rotation caused by Brownian motion can be
rigorously calculated (Berg 1993). Taking advantage of these relations, formulas
have been derived for estimating the signal-to-noise ratio for detecting gradients of
light, chemicals, and heat (Table 1).
These results lead to the surprising conclusion that there exists a sharp size
limit (about half a micrometer diameter) below which free bacteria have no use
for motility. A review of published literature (Fig. 2) indicated that the prediction
is supported, and about 20% of free, nonmotile genera are below this size limit
but the smallest of 97 motile genera was about 0.8 J.lm in length (Dusenbery
1997).
4.2 Consequences of Shape
Perrin (1934, 1936) derived expressions for the motion of ellipsoids subject to
Brownian motion. Unfortunately, they involve defmite integrals that have no
solution in common functions, but approximations for high axial ratios are
available, and have been much used to estimate the shapes of molecules (Tanford
1963; van Holde 1985). With computers it is now easy to evaluate these integrals,
and these relations have been used to quantitatively evaluate the effects of
constant-volume changes in shape (including small axial ratios) on several possible
functions (Dusenbery 1998a).