Biophotons and Diffusion in Biology - Inside the Photon: A Journey to Health - page 159

203ms − 1 ascalculatedpreviously.Suchasmalloffsetindicateshow
many collisions are required to move significant distances at the
molecular level. While the offset is tiny compared with the random
thermal step across these time intervals, we are now in a position
toestimatehowmuchtimeisneededbeforethenon-randomoffsets
accumulatetogiveanoveralloffsetsignificantwhencomparedwith
thethermaleffect.Theionwillbeoffsetonaverageby6.2 × 10 − 9 m
in0.1seconds.Thisdistanceisabout1,650timeslargerthanasingle
step,whichissignificant,andwemaythusassessthatanEfieldof1
Vm − 1 will produce an observable effect if we have a current probe
ofsu cientareatomeasureit.Similarly,anEfieldof1/1,650Vm − 1 ,
or 6.1 × 10 − 4 Vm − 1 will produce an offset as large as the thermal
step size after 0.1 seconds.
For elasmobranch electrosensitivity, in particular a sting-ray
pursuingprey(whotransmitsabiogenicEfieldbyfiringitsmuscles
in an attempt to evade capture), we assume a glide speed through
the water of 5-10 m s − 1 and a prey size of 0.5 m, so the averaging
time is no more than 0.1 seconds, perhaps 1 second, given that the
ion flow could spread out somewhat over a larger volume than the
original prey size. Using the estimate obtained above for t ave = 0.1
seconds,weobtainthelowestpossibleEfieldthatcouldbedetected
as 6.1 × 10 − 4 Vm − 1 .
ApplyingthetheoryderivedbyBarnesandSeyed-Madani(1987)
wemay writean expression for this same E field 'noisefloor' as
< E n > =

4k T f
σ Vol (4.12)
where σ is the conductivity, and Vol is a measuring volume. For
a calcium ion, we need to sense distances of 6.2 × 10 − 8 mper
unit E field, so Vol is dependent upon the E field. The area of
the probe volume is equal to that of the pore on the surface of
the elasmobranch's skin, about 1 mm 2 (Fishman, 1987). For a
conductivity of 0.5 S m − 1 , (Barnes and Seyed-Madani, 1987), and
f 10.0 s − 1 ,theEfieldis1.7 × 10 − 4 Vm − 1 , 35% of the random
walk estimate. Both estimates incorporate the Boltzmann constant,
itself a limiton noise,in verydifferent fashions.
To complete this analysis, an estimate of thermal diffusion will
enable another measure of the biological significance of the E field
offsets. The Fick's diffusion constant, D , and the associated particle