0README

batch-calorimeter
|-- 0README               obvious
|-- calorimeter.data      data: time series calorimeter voltages
|-- commands.s            R commands for analysis of data
|-- results.fit           text generated by analsysis
`-- results.fit.ps        plots generated by analsysis


FIT OF BATCH CALORIMETER DATA

The data in the file "calorimeter.data" are from a batch calorimetric
experiment.  The 912 data points, taken at 1 second intervals, are
for the calorimeter voltage signal (given in nanovolts).  The voltage
from the thermopiles is proportional to the heat flow across the
thermopiles, between the bath and the calorimeter vessel.  Time is
given in seconds.  The initial flat baseline is the near-zero voltage
found when both calorimeter vessel and bath have been equilibrated
to the same temperature.  At about 120 seconds, the vessel contents
are mixed.  The heat content and temperature of the vessel change
instantaneously, on this time scale, according to the heat change
for the reaction initiated by the mixing.  The fast iniyial increase in the
size of the signal represents the establishment of a new instrument
state (most particularly, temperature equilibrium within the reaction
vessel, which is after mixing is at a different temperature than
the surrounding bath).  The slower decay reflects the change in
heat content of the calorimeter vessel owing to exchange of heat
between vessel and bath: the heat change per second (heat flow)
decreases to zero as temperatures of the vessel and bath become the
same.  The final flat baseline is the near-zero voltage found when
both vessel and bath are again at thermal equilibrium; it may differ
slightly from the initial baseline.

The data are fit to the following model, in which 
both the fast and slow processes are assumed to be first order
and separated in time:

for t <  t_mixing:
	V  =  B-i	

for t >= t_mixing:
	V  =  B-f + A * (exp( - k_d * (t - t_mix)) - exp( - k_i * (t - t_mix)))

V is the voltage, t is the time, t-mix is the time of mixing of the
vessel contents, A is the amplitude of the signal from the fast
process, k-i and $k-d are the first-order rate constants of the two
processes, fast initial change to new internal state and slow decay,
and B-i and B-f are the initial and final baselines.


RESULTS

Fit of the data to the above model, by use of the R-language function
nls (file "commands.s") gives the following results (file "results.fit"):

	Formula: voltage ~ (time < tzero) * (base1 - base2) + base2 + 
	    amp * 
		(exp(-kinit * (time >= tzero) * (time - tzero)) - 
		exp(-kdecay * (time >= tzero) * (time - tzero)))

	Parameters:
		Estimate Std. Error  t value Pr(>|t|)    
	tzero  1.191e+02  2.494e-02 4774.470   <2e-16 ***
	base1  2.475e+01  1.323e+01    1.870   0.0618 .  
	base2  1.519e+00  8.463e+00    0.179   0.8576    
	amp    4.191e+04  5.068e+01  826.893   <2e-16 ***
	kinit  1.188e-01  5.726e-04  207.471   <2e-16 ***
	kdecay 8.319e-03  1.314e-05  633.344   <2e-16 ***
	---
	Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 

	Residual standard error: 144.3 on 906 degrees of freedom

	Correlation of Parameter Estimates:
	       t b1 b2 a kn
	base1    1         
	base2       1      
	amp    .       1   
	kinit  ,       , 1 
	kdecay      ,  , . 
	attr(,"legend")
	[1] 0 ` ' 0.3 `.' 0.6 `,' 0.8 `+' 0.9 `*' 0.95 `B' 1



The file "results.fit.ps" has a plot of the data, the fitted values, and the
residuals at 10-fold expanded scale.


The fit is good - the largest deviation is 3 percent near the signal
extremum.  Estimates for the two rate constants, the amplitude, and the time
of mixing have small relative standard error (< 1%).  The baseline values are
less significant.


John Rupley
 rupley@u.arizona.edu -or- jar@rupley.com
 30 Calle Belleza, Tucson AZ 85716 - (520) 325-4533; fax - (520) 325-4991
 Dept. Biochemistry & Molecular Biophysics, Univ. Arizona, Tucson AZ 85721