## Sunday, April 10, 2005

### Constructing the Phase Response Curve

This is the third post in a series about mechanism of entrainment. In order to understand the content of this post, you need to read the first two installments. The first one is here, and the second one here.

After months of applying light pulses to your animals you are ready to analyze and plot your data. You will print out the actographs (see how in the post "On Methodology" in the "Clock Tutorials" category) and you will see many instances of phase-shifts, somewhat like the very last figure in this po st.

For each light pulse you applied to each animal, you measure the direction of the phase-shift (i.e., if it was a delay or an advance) and the size of the shift (e.g., 10 minutes or 10 hours, or whatever may be the case). In order to plot these values, you also need to know the phase of the circadian rhythm at which you have applied the pulse. Usually the onset of the light pulse is used, so if you used a 14-hour long pulse, you mark the time that the light came on, not off. You need to know at which circadian phase did the light come on.

Here comes the hitch. You cannot just start counting hours since the onset of animal's activity. Each individual is going to have a different freerunning period (tau), thus its subjecti ve perception of one hour is going to be different from its neighbor's and likely different from real 60 minutes. You need to know at which point in the motion of the circadian oscillation is the animal at the time of the pulse because, if you just use r eal hours, you will calculate different phases for different individuals. Thus, you have to normalize the phase to reflect this.

If an individual has a freerunning period of, let's say, 22 hours, each of its subjective hours will be shorter tha n the real hour. How much shorter? You calculate 22/24 = 0.92h. Each of its hours is 0.92h long. If you have applied a light pulse 2.76 real hours after the activity onset in a diurnal animal (or 14.76 hours after the activity onset in a nocturnal an imal), you have hit exactly the Circadian Time 3 (CT3).

Another individual has a freerunning period of 26 hours. Each of its subjective hours will be a little longer than the real hour, i.e., it will be 26/24 = 1.08h. Thus, if it is a diurnal an imal, and you find that the pulse started 6.48 hours after the onset of activity, you have hit exactly CT6. If it is a nocturnal animal, you add another 12 hours, i.e., 12 + 6 = CT18.

Now that you have determined the circadian phase of each pulse, direc tion of each phase-shift, and size of each phase-shift, you can start plotting the PRC.

On the X-axis, you use Circadian Time, expressed in circadian hours, thus the axis will go from 0 to 24 and will cover the duration of one circadian cyc le.

On the Y-axis you plot size of phase-shifts (in hours or minutes). Phase-advances are positive numbers and will be plotted above the X-axis. Phase-delays are negative numbers and you will plot them below the X-axis (some of the very earliest PRCs i n the early 1960s have been plotted in reverse - delays positive, advances negative - so be careful when you read the classical literature).

When each phase-shift is represented by a little dot on your graph, draw a best fit line through the data. You h ave just plotted a Phase Response Curve.

What you will see, in most cases, is that there is little or no effect of light pulses administered during the subjective day (CT0 - CT12). This portion of the curve is called the dead zone. As you follow the curve into the early subjective night you will see gradually greater and greater phase-delays (the curve shows a negative slope), followed by a reversal (positive slope): smaller and smaller delays, no effect about mid-night, then greater and greater phase-advances in the late night. Finally, just before "morning", the curve slopes down again and hits zero (joins the X-axis) at about CT24 (=CT0 of the next cycle).

You can see a schematic PRC here.

In the next post, I will try to explain how a Phase Response Curve helps us understand the principles of entrainment.

Part 1:Entrainment,
Part 2:Phase-Shifting Effects of Light..