Figure 2.1 Electromagnetic spectrum showing extremely low frequency and other bands Error!
Figure 2.2 Field-particle interactions: "classical" forces, torques, and energies 56
Figure 2.3 Illustration of "cross-product" (equations (a), (C) and (c) in Figure 2.2: The resulting vector c = ab is in a direction perpendicular to the plane defined by a and b and its magnitude is equal to the product of their mutually perpendicular components: c = ab sin ). 57
Figure 4.1 Equivalent circuit for an array of N membrane channels with conductive media on each side of the membrane (A discrete resistance value is associated with each channel (RG) and with each of the access resistances (RA and RB) near the channel mouths. All resistors in the circuit produce voltage noise, and these sources (VGi, VAi, and VBi) are completely independent and uncorrelated. When circuit analysis techniques with the proper methods are used for summing incoherent signals, the net noise voltage across an arbitrary channel (V1 in this figure) can be calculated. Note that the noise voltage of interest (V1) is that occurring across the channel, and not across the series combination of the channel and access resistances. The model assumes that any voltage gating mechanism is inside the channel or at the channel mouth. From Gailey (Gailey, 1996). 385
Figure 4.2 Normalized correlation coefficients for thermal electrical noise occurring across an ion channel as a function of the number of channels in the membrane (Electrical parameters used in this calculation apply to gap-junction channels with a channel resistance of 6.5 G and an access resistance of 0.33 G.). The coherence or correlation between noise signals occurring in different channels decreases by a factor of 10 per decade with increasing number of channels. From Gailey (Gailey, 1996). 386
Figure 4.3 Improvement in signal-to-(thermal) voltage noise ratio due to lack of correlation between noise signals occurring in different open channels in the membrane (The x axis is the absolute value of the slope of the closing rate constant divided by the slope of the opening rate constant. The solid line was generated from equation 4.15 with equal opening and closing rate constants and assuming no effect of thermal voltage noise on the closing rate constants ( = 0, No .)). When the slight correlation between voltage noise in the open channels and the effect of the uncorrelated noise in these channels is included, the dashed line is obtained for a membrane with 50,000 open channels. From Gailey (Gailey, 1996). 387
Figure 4.4 Voltage noise spectra of a frog node of Ranvier at various membrane potentials. From Verveen and DeFelice (Verveen & DeFelice, 1974); reproduced by Barnes (Barnes, 1986). 388
Figure 4.5 Effect of magnetic fields on radical-pair energy levels (Electron spins in the three sub-levels of the triplet state: T+1 spins parallel in the direction of the magnetic field, T-1 spins parallel in the direction opposite to the magnetic field, T0 spins antiparallel but in phase in the field direction.). S, singlet state From Polk (Polk, 1992a). 389
Figure 4.6 Maximum change in escape probability and maximum relative change are shown as a function of cage retainment time for an increment of 5 µT to an external field of 50 µT (The recombination probability for electrons in a relative singlet state is taken as twice the escape probability and the internal field magnitudes and directions are selected from Monte Carlo procedures, as is the direction of the external field. The variation of escape probability with cage time of radicals with fields chosen so as to maximize the escape at a cage time of 10 ns, is also shown.) From Adair (Adair, 1997). 390