Natural rf oscillations

In the following sections we shall give a brief survey of the microdielectrophoresis and the spinning studies to date, and show how they demonstrate the existence of natural rf oscillations in cells. Next, we shall indicate the line of future research and make some suggestions as to the applications. 

The frequency of the natural rf oscillations term of cell can be estimated from the salt effect. It will be recalled that the a term of K contains the frequency o). Using this fact, and the known conductivity, (x, required to repress the ju-DEP, we estimate a minimum frequency / = Inco as 5 kHz. Later experiments using observations of cell-spin-resonance give a result of 1-30 kHz for the actual frequency, and confirm the ju-DEP result. 

In summary, the presence of natural rf oscillations by cells is confirmed (a) by the preference of (dividing) cells for accumulating particles of high DK over that for ones of low DK (b) by the predicted suppression of this by salt effect (c) by the predicted increase of this by poling (d) as we shall see, by cellular spin resonance " and (e) by direct detection. " ... 

If these natural rf oscillations are necessary and linked to cellular reproduction, what new control might we then have over cellular division At the moment we judge these natural rf fields to be of very short range (microns) and to be linked more to intracellular rather than intercellular processes such as communication. This conservative view may be too cautious and needs examination. There are a number of critical questions which suggest themselves as ways to test the hypothesis that such natural rf oscillations are necessary in reproduction. Some of these are the following ... 

To the extent that favorable answers are found to the questions posed above, our knowledge of the origins, meaning, and control of the natural rf oscillations connected with cell growth could mean better insights into disease control and somatic repair. 

To observe such rf oscillations, we have used two very different techniques, each needing only relatively simple apparatus. The first technique is called micro-DEP and essentially requires only a microscope. > Here one observes the collection of various highly polarizable particles by a cell so as to examine the radio frequency (if) field emitted from it. In the second technique, direct observation is made of the spinning of cells evoked by external rf fields. Both methods yields similar conclusions as to the nature, frequency, strength, and occurrence of the rf electrical oscillations of cells. We believe, therefore, that the presence of the postulated rf oscillations has been established beyond reasonable doubt. It now remains to study their meaning. Are they cause or effect, necessity or frill, in the life of cells Where and how do they operate What causes them What controls, intracellular or intercellular, do they evoke or reflect With what processes are they associated in the cellular life cycle ... 

Whatever the origin(s) of the natural rf cellular oscillations, it will be of much interest to learn if they are necessary or incidental, of cause or effect, in the living state. 

During cell divisions from fertilized egg to blastula, is there evident dipole interaction due to the postulated natural electrical rf oscillations Or is there overall organization of the ac fields about cells ... 

We now have a total of six parameters four from the autonomous system (p, r0, and the desorption rate constants k, and k2) and two from the forcing (rf and co). The main point of interest here is the influence of the imposed forcing on the natural oscillations. Thus, we will take just one set of the autonomous parameters and then vary rf and co. Specifically, we take p = 0.019, r0 = 0.028, fq = 0.001, and k2 = 0.002. For these values the unforced model has a unique unstable stationary state surrounded by a stable limit cycle. The natural oscillation of the system has a period t0 = 911.98, corresponding to a natural frequency of co0 = 0.006 889 6. 

Fig. 13.9. The forced Takoudis-Schmidt-Aris model with a forcing frequency twice that of the natural oscillation (a) zero-amplitude forcing (autonomous oscillation and limit cycle) (b) r, = 0.002 (c) r, = 0.003 (d) r, = 0.004 (e) r, = 0.005 (f) rr = 0.006 (g) rf = 0.007 (h) rf = 0.01. Traces show the time series 0p(t) over 10 natural periods (or 20 forcing periods) and the associated limit cycle in the 0 -6, plane.

Figure 13.10 shows a representation of the phase plane behaviour appropriate to small-amplitude forcing. There are two basic cycles which make up the full motion first, there is the natural limit cycle, corresponding for example to Fig. 13.9(a) around which the unforced system moves secondly, there is a small cycle, perpendicular to the limit cycle, corresponding to the periodic forcing term. The overall motion, obtained as the small cycle is swept around the large one, gives a torus and the buckled limit cycle oscillations at low rf in Fig. 13.9 draw out a path over the surface of such a torus. 

As before o is the cross section in the absence of a microwave field. Naturally <70(0) = o. This expression is the origin of the lines drawn in Fig. 9, which evidently match the experimental cross sections. Similar results have also been observed with the K system of Eq. (10) using velocity selected beams to obtain narrower collisional linewidths allowing, the use of rf frequencies of 4 MHz, instead of 15 GHz [Thomson 1992], Since the collisions last longer, the rf fields can be very weak, < 0.1 V/cm. An interesting aspect of both the 15 GHz and the 4 MHz measurements is that the Bessel function oscillation of the cross section with microwave or rf field amplitude is observed indicating that the coherence of the colliding atoms is maintained over multiple field cycles. 

However, there is an important distinction between the kind of transitions caused by RF pulses and those which lead to relaxation. When an RF pulse is applied all of the spins experience the same oscillating field. The kind of transitions which lead to relaxation are different in that the transverse fields are local, meaning that they only affect a few spins and not the whole sample. In addition, these fields vary randomly in direction and amplitude. In fact, it is precisely their random nature which drives the sample to equilibrium. 

The rf experiment also provides some information about the nature bf CR effects in molecular crystals. When the oscillator frequency was tuned... 

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