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PRC Atlas

Comments on the Standardized Format

Contents in this page:

  Definition of stimulus time
  Circadian time
  Definition of circadian time zero
  Number of cycles between stimulus and assayed phase shift
  Direction of Phase shift

The PRC Atlas is an attempt to compile all of the PRCs which have ever been published in one volume where the PRCs are plotted in a standardized format. I believe the Atlas includes nearly all PRCs published prior to 1984 (with the exception of some Drosophila PRCs) and it includes the PRCs published since 1984 that were submitted voluntarily by the authors themselves.

What good is a Phase Response Curve Atlas, anyway? The most obvious answer is that an Atlas of standardized PRCs facilitates comparison of the entire spectrum of published PRCs. For example, light and/or temperature PRCs can be easily juxtaposed so that hypotheses concerning the entrainment of circadian pacemakers to environmental cycles can be tested.

A more subtle consequence of compiling previously published PRCs into a standard format is that PRCS which are now only gleams in researchers' eyes might be published in the same format henceforth. Hopefully, the existence of the Atlas will (1) make future PRCs from different labs easier to compare, (2) encourage phase response experiments to be done properly, and (3) ensure that all the important information concerning the experiment is included in the report a common problem with many early PRCs.

Because the format of PRCs has not been standardized hitherto, the form of PRCs as they have been published varies considerably. Consequently, the form of many PRCs in the Atlas is quite different from the form in which they were published. The following comments define the way in which PRCs have been converted to the standardized format herein.

Definition of stimulus time : Irrespective of the type of stimulus, be it a light, temperature, or chemical pulse, the onset of the stimulus pulse has been selected as the stimulus time for the Atlas. Many authors originally plotted their PRCs using other conventions for stimulus time--often the midpoint was used, and sometimes even the end of the pulse. The beginning of the pulse, however, is intuitively a better marker for "stimulus time," because the phase-shifting response of an oscillator is likely to be a characteristic of the phase when the stimulus begins, that is, of the first unperturbed phase to be presented with a stimulus. If one uses the midpoint or end of the stimulus as the marker, then one is choosing a phase which has already been perturbed. Depending upon the direction and magnitude of phase shift and the duration of the stimulus pulse, it may even be a phase which the oscillation never reaches during the stimulus. For those readers who do not wish to use the stimulus onset as the marker, however, the tabulation of the raw data in the Atlas facilitates replotting the data in any other form.

Circadian time : Because circadian pacemakers have different endogenous frequencies under different conditions (e.g., DD vs.LL) and in different organisms, PRCs cannot be directly compared unless their time scales are standardized to "circadian time." This means that the scales for both the circadian time of stimulus and the magnitude of phase shift are expressed in "circadian hours." A circadian hour is equal to 1/24 of the endogenous period, t(therefore, a circadian hour = t/24 hours). The PRCs in this Atlas are scaled in circadian hours (with only a few exceptions which are individually explained in the comments section of those specific PRCs). To convert "real" hours to "circadian" hours, the number of real hours was multiplied by a constant, 24/t.

Definition of circadian time zero: A PRC must be plotted along its abscissa relative to some defined time, i.e., circadian time zero (ct 0). In general, deciding how to define ct O for different PRCs has been the most perilous judgment of all and it is absolutely crucial for being able to compare the phase-shifting responses among organisms.

The standard definition of ct O is the time in the freerun which extrapolates by modulo-t intervals back to "dawn" (i.e., "lights-on") of the last-seen LD 12:12 cycle prior to release into constant conditions (DD or LL). This definition was used whenever possible.

In many cases, however, alternative definitions are necessary. For example, some PRCs which were measured in LL used the beginning of LL as the extrapolated "dawn" rather than "lights-on" of the final light cycle. Another prevalent definition of circadian time specifies ct 12 as the extrapolated "dusk" (e.g., nocturnal rodents). Therefore, ct O becomes that time which is twelve circadian hours before or after ct 12.

In addition, many PRCs are measured from organisms which have been in constant conditions for a long time so that it is inaccurate or inconvenient to extrapolate to the final lights-on signal. For these PRCs, a circadian time is usually defined for the phase reference point (f r) of the rhythm on the basis of its phase angle in LD 12:12, and thereby ct O becomes a certain number of circadian hours before or after f r in the freerun.

Number of cycles between stimulus and assayed phase shift : In many measurements of phase resetting--especially early studies--phase shifts have been computed as the difference between phase reference points (f r) of the control(s) and that of the experimental culture(s) on a given cycle after the stimulus. If there is no effect of the perturbation on t, then this method of calculation is valid. Frequently, however, t is changed as a consequence of the stimulus. In these cases, it is necessary to extrapolate phase reference points (f r) before and after the stimulus and calculate the phase shift as the difference on the day of the stimulus between the two extrapolations. Both modes of calculating phase shifts have beenused in the PRCs included in the Atlas.

Direction of Phase shift (i.e., delay vs. advance): In general, the direction of the phase shift in the Atlas is as assigned by the authors. For Type 1 resetting, authors usually decided between delays and advances on the basis of whether the reset phase was closest to control phase when calculated as advance or delay. For Type 0 resetting, the distinction between advance and delay shifts is messy. Most authors have chosen arbitrary definitions (e.g., see Dharmanda's and Feldman's Neurospora PRCs). Another approach is to plot the PRCs with all-delay shifts, as in the case of many of the Drosophila pseudoobscura PRCs in the Atlas. On the basis of limit-cycle models of the pacemaker, there is in fact no difference between delays and advances for either Type 0 or 1 resetting. It is therefore unfortunate that the PRC Atlas does not also include Phase Transition Curves (PTCs) for the resetting data, as PTCs do not distinguish between advances and delays. The decision to exclude PTC plots was made early in the development of the Atlas, and it was not feasible to reverse that decision later. The computer disk form of the Atlas, however, has plotting programs which allow the data to be seen as either PRCs or PTCs. And, of course, the reader of the printed Atlas can replot the data from the table into a PTC format.

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