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hjcdemo-ACh.txt
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Program HJCFIT Windows Version (Beta)
Copyright D. Colquhoun, I. Vais, University College London 2004
All rights reserved.(Intel Visual Fortran/Gino version)
Please cite: http://www.ucl.ac.uk/Pharmacology/dc.html
HJCFIT: Fit of model to open-shut times with missed events
(Uses HJC distributions, exact for 1st 2 deadtimes then
asymptotic, to calculate likelihood of record
DATE of analysis = 15-AUG-2012
Initialisation file = AChdemo.ini
DEFINE FILE FOR EXPERIMENTAL DATA (.scn)
Ex 0: Simulated run, model 29, 'true' rates=45, 50 nM, res=10 us imposed
Analysis DATEW 25-Feb-2003: 13948 transitions. Simulated data; res = 10.0, 10.0 microsec (open, shut)
Filter (-3dB) -1.0 Hz : Full amp (app) 6.00pA: RMS noise 0.000pA
Calibration (amplitude to pA) = 1.00000
Total number of transitions = 13948, in 1 sets.
Filtering and rise-time not defined for set 1
Set 1
set :Channel open at end of file # 1: number of intervals reduced to 13947
SET 1: Critical gap length to define end of group = 3.5 milliseconds
(defined so that all openings in a group prob come from same channel)
Initial and final vectors for bursts calculated as in C.,
Hawkes & Srodzinski, (1996, eqs 5.8, 5.11).
A bad gap ends a group, but does not eliminate the whole group
Set 1: Conversion to open periods
Input: 13947 transitions ( 0 bad openings, 1 bad gaps)
Output: 13946 transitions ( 0 bad open periods, 0 bad gaps)
------------------------------------------------------------
Set 1
Concentration of (micromolar) = 0.500000E-01
DEFINE THE REACTION MECHANISM
Mechanisms file: C:\dcwinprogs\qmechdem.mec
contains 6 records of rate constants +model
Record number 3 (starts at byte # 23272)
Two unequal bindings (C&Sakl 1985)
Model number = 2
Number of channels = 1
Number of open states = 3
conductance of state 1 (A2R*) (pS) = 60.0000
conductance of state 2 (AR*(a)) (pS) = 60.0000
conductance of state 3 (AR*(b)) (pS) = 60.0000
conductance of state 4 (A2R) (pS) = 0.00000
conductance of state 5 (AR(a)) (pS) = 0.00000
conductance of state 6 (AR(b)) (pS) = 0.00000
conductance of state 7 (R) (pS) = 0.00000
Number of ligands = 1
Concentration-dependent elements:
i j ligand # Ligand name
6 4 1 ACh
5 4 1 ACh
7 5 1 ACh
7 6 1 ACh
Number of ligands bound
State ACh
1: A2R* 2
2: AR*(a) 1
3: AR*(b) 1
4: A2R 2
5: AR(a) 1
6: AR(b) 1
7: R 0
Values of rate constants
1:q(1 ,4 ) = alpha2 * 1500.00 none
2:q(4 ,1 ) = beta2 * 50000.0 none
3:q(2 ,5 ) = alpha1a * 2000.00 none
4:q(5 ,2 ) = beta1a * 20.0000 none
5:q(3 ,6 ) = alpha1b * 80000.0 none
6:q(6 ,3 ) = beta1b * 300.000 none
7:q(4 ,6 ) = k(-2)a * 1000.00 none
8:q(6 ,4 ) = k(+2)a * 0.100000E+09ACh
9:q(4 ,5 ) = k(-2)b * 20000.0 none
10:q(5 ,4 ) = k(+2)b * 0.100000E+09ACh
11:q(5 ,7 ) = k(-1)a * 1000.00 none
12:q(7 ,5 ) = k(+1)a * 0.100000E+09ACh
13:q(6 ,7 ) = k(-1)b * 20000.0 none
14:q(7 ,6 ) = k(+1)b * 0.100000E+09ACh
Microscopic reversibility
cycle= 1 ,number of states= 4, states: 7; 5; 4; 6;
rate 7 q(4 ,6 ) k(-2)a is constrained to be
1.00000 times rate 11 q(5 ,7 ) k(-1)a
rate 9 q(4 ,5 ) k(-2)b is constrained to be
1.00000 times rate 13 q(6 ,7 ) k(-1)b
rate 10 q(5 ,4 ) k(+2)b is constrained to be
1.00000 times rate 14 q(7 ,6 ) k(+1)b
rate 12 q(7 ,5 ) k(+1)a calculated by MR
Equilibrium conc-response curve for ligand # 1 = ACh
At zero concentration of ACh , P(open) = -0.28124E-22
Equilibrium response-concentration curve is monotonic
Maximum Popen = 0.970874
EC50 = Conc of ACh for 50% of this maximum (muM) = 0.31623E+08
_____________________________________________________
Impose resolution
Number of resolved intervals= 9703
0 intervals with dubious amplitudes in output
0 shut intervals with fixed amplitudes in output
0 open intervals with fixed amplitudes in output
0 intervals with constrained amplitudes in output
0 bad intervals (undefined durations) in output
Resolution (microsec) for openings = 0.250000E-01
Resolution (microsec) for shuttings = 0.250000E-01
For sublevels take:
full amplitude (pA)= 6.00; pA for real difference= 0.000
EC50 FOR INITIAL GUESSES:
SET 1: Critical gap length to define end of group = 3.5 milliseconds
(defined so that all openings in a group prob come from same channel)
Initial and final vectors for bursts calculated as in C.,
Hawkes & Srodzinski, (1996, eqs 5.8, 5.11).
A bad gap ends a group, but does not eliminate the whole group
Set 1: Conversion to open periods
Input: 9703 transitions ( 0 bad openings, 1 bad gaps)
Output: 9464 transitions ( 0 bad open periods, 0 bad gaps)
Total number of rates = 14
Number that are fixed = 1
Number that are constrained = 3
Number set by micro rev = 1
Number set by fixed EC50 = 0
Number of free rates to be estimated = 9
For initial guesses:
Set 1: Initial CHS vector for burst = 0.147824 0.768518 0.836571E-01
et 1: End CHS vector for burst =
0.297370 0.978416 0.997492 0.999686
EQUILIBRIUM CALCULATIONS FOR INITIAL GUESSES
Equilibrium conc-response curve for ligand # 1 = ACh
At zero concentration of ACh , P(open) = -0.28124E-22
Equilibrium response-concentration curve is monotonic
Maximum Popen = 0.970874
EC50 = Conc of ACh for 50% of this maximum (muM) = 0.31623E+08
_____________________________________________________
log(likelihood) = 38617.91
Set 1: likelihood = 38617.91
3727 groups: mean no of openings/group = 1.26965
(likelihood scaled down 2 times by 1.e-100)
Note: if a particular set of parameter values causes the
likelihood for a group to appear <0, the log(lik) for this
group is taken as zero, thus penalising these parameters
Fit 9 parameters: initial theta() =
alpha2 1500.00 beta2 50000.0 alpha1a
2000.00 beta1a 20.0000 alpha1b 80000.0
beta1b 300.000 k(-1)a 1000.00 k(-1)b
20000.0 k(+1)b 0.100000E+09
Initial step size factor= 1.609437943
Simplex contraction factor (0-1)= 0.500000
Restart step size=resfac*critstep: resfac= 10.000000000
Limit number of restarts= 3
Print every Nth estimate= 10
Relative error= 0.001000
Simplex started at:12:15:53
Set 1: Initial CHS vector for burst = 0.147824 0.768518 0.836571E-01
et 1: End CHS vector for burst =
0.297370 0.978416 0.997492 0.999686
nresmax = 3istart = 0 resfac = 10.0000 crtstp = 0.100000E-02 0.100000E-02 0.100000E-02 0.100000E-02 0.100000E-02 0.100000E-02 0.100000E-02 0.100000E-02 0.100000E-02
Simplex finished at:12:16:21
Duration of fit: 0 days 0 hours 0 min 28 sec
number of evaluations = 642 theta =
2127.05 52245.3 5952.94 56.6902 56176.3
89.0061 1520.60 9465.47 0.414488E+09
Number of evaluations = 642 Max log(likelihood) = 39823.81
Press any key to continue
(Fit 'very stable' at time of convergence)
FINAL VALUES OF RATE CONSTANTS
Set 1
0.500000E-01 micromolar of ACh
Analysed in bursts, tcrit (ms) = 3.50000
CHS vector used for start and end of bursts
Resolution (microsec) = 25.0000
A bad gap ends a group, but does not eliminate the whole group
Simplex used log(rate constant) for searching
initial final
1 q( 1, 4) = alpha2 1500.00 2127.05
2 q( 4, 1) = beta2 50000.0 52245.3
3 q( 2, 5) = alpha1a 2000.00 5952.94
4 q( 5, 2) = beta1a 20.0000 56.6902
5 q( 3, 6) = alpha1b 80000.0 56176.3
6 q( 6, 3) = beta1b 300.000 89.0061
7 q( 4, 6) = k(-2)a 1000.00 1520.60
(constrained)
8 q( 6, 4) = k(+2)a 0.100000E+09 0.100000E+09
(fixed)
9 q( 4, 5) = k(-2)b 20000.0 9465.47
(constrained)
10 q( 5, 4) = k(+2)b 0.100000E+09 0.414488E+09
(constrained)
11 q( 5, 7) = k(-1)a 1000.00 1520.60
12 q( 7, 5) = k(+1)a 0.100000E+09 0.100000E+09
(micro-rev)
13 q( 6, 7) = k(-1)b 20000.0 9465.47
14 q( 7, 6) = k(+1)b 0.100000E+09 0.414488E+09
Equilibrium constants calculated for fitted rate constants
E = q( 4, 1)/q( 1, 4) = beta2 /alpha2 = 24.5623
E = q( 5, 2)/q( 2, 5) = beta1a /alpha1a = 0.952305E-02
E = q( 6, 3)/q( 3, 6) = beta1b /alpha1b = 0.158441E-02
K (uM) = q( 4, 6)/q( 6, 4) = k(-2)a /k(+2)a = 15.2060
K (uM) = q( 4, 5)/q( 5, 4) = k(-2)b /k(+2)b = 22.8365
K (uM) = q( 5, 7)/q( 7, 5) = k(-1)a /k(+1)a = 15.2060
K (uM) = q( 6, 7)/q( 7, 6) = k(-1)b /k(+1)b = 22.8365
EC50 calculations for final parameter values
Equilibrium conc-response curve for ligand #
------------------------------------------------------------
VALUES CALCULATED FROM FINAL FIT
Equilibrium values for set number 1:
concentration(s) =
0.500000E-01 micromolar of ACh
------------------------------------------------------------
Subset Open Equilibrium Mean life Mean latency (ms)
state occupancy (ms) to next shutting
(#i) given start in i
A 0.210418E-03 0.279392
1 0.175832E-03 0.470135 0.470135
2 0.311362E-04 0.167984 0.167984
3 0.344937E-05 0.178011E-01 0.178011E-01
Subset Shut Equilibrium Mean life Mean latency (ms)
state occupancy (ms) to next opening
(#i) given start in i
B 0.545379E-02 0.207118
4 0.715862E-05 0.158149E-01 386.497
5 0.326956E-02 0.625778 2212.77
6 0.217707E-02 0.104608 2297.00
C 0.994336 38.8736
7 0.994336 38.8736 2319.50
Distributions for set number 1
------------------------------------------------------------
Concentration of ligand 1 (micromolar) = 0.500000E-01
HJC Initial vector for open times =
0.378648 0.478658 0.142694
HJC Initial vector for shut times =
0.226904 0.588437 0.130775 0.538839E-01
ASYMPTOTIC OPEN TIME DISTRIBUTION
f(t) =
term coeff (W) rate const (1/sec) area tau (ms)
1 7971.77 55940.4 0.142505 0.178762E-01
2 2844.35 5944.03 0.478522 0.168236
3 273.389 721.794 0.378763 1.38544
Total area (for non-zero eigenvalues) = 0.999790
Mean (ms) = 0.607805 SD= 1.05441 SD/mean = 1.73478
Areas for asymptotic pdf renormalised for t=0 to infinity (and sum=1)
(so areas can be compared with ideal pdf)
1 0.380154
2 0.365766
3 0.254080
ASYMPTOTIC SHUT TIME DISTRIBUTION
f(t) =
term coeff (W) rate const (1/sec) area tau (ms)
1 10286.0 57252.8 0.179660 0.174664E-01
2 3.67571 9506.24 0.386663E-03 0.105194
3 41.2093 1591.47 0.258938E-01 0.628350
4 0.207084 0.262716 0.788242 3806.39
Total area (for non-zero eigenvalues) = 0.994182
Mean (ms) = 3000.38 SD= 3720.06 SD/mean = 1.23986
Areas for asymptotic pdf renormalised for t=0 to infinity (and sum=1)
(so areas can be compared with ideal pdf)
1 0.479601
2 0.312868E-03
3 0.171906E-01
4 0.502896
Set 1: Initial CHS vector for burst = 0.236289 0.583053 0.180658
et 1: End CHS vector for burst =
0.174873 0.958106 0.996516 0.999223
Open time roots (1/sec) = -55940.4 -5944.03 -721.794
shut time roots (1/sec) = -57252.8 -9506.24 -1591.47 -0.262716
EXACT SOLUTIONS FOR OPEN TIMES
****** In HJCEXACT, eigen(1) of Q reset from -0.584987E-10 to 0
eigen = 0.00000 355.047 1528.30 6029.09 9473.07 56283.4
65002.0
g00(m) = 0.506965 279.346 34.4368 2800.11 17.8937 7981.83
7.30495
g10(m) = 0.862889 4.97104 34.2469 -41.2517 13.9927 -14.2173
1.39546
g11(m) = 0.257013 99708.4 2358.70 -201450. 1500.53 -671073.
-2584.30
EXACT SOLUTIONS FOR SHUT TIMES
g00(m) = 0.561931 323.864 22.5570 0.629645 3.44754 0.190697E-01
10921.3
g10(m) = 2.25722 258.250 6.47323 0.469287 -0.130204 0.146514E-02
-267.321
g11(m) = 0.315766 527152. 1496.59 -40.6231 90.1319 -0.499906
0.178019E+08
Shut time pdf with zero resolution
f(t) =
term coeff (W) rate const (1/sec) area (%) tau (ms)
1 25932.5 63234.7 41.009888 0.158141E-01
2 25.4409 9579.87 0.265567 0.104386
3 23.7223 1599.59 1.483023 0.625161
4 0.246824 0.431198 57.241524 2319.12
Total area= 1.00000
Mean (ms) = 1327.51 SD= 2096.42 SD/mean = 1.57920
Open time pdf with zero resolution
f(t) =
term coeff (W) rate const (1/sec) area (%) tau (ms)
1 14453.6 56176.3 25.729046 0.178011E-01
2 1465.07 5952.94 24.610918 0.167984
3 1056.29 2127.05 49.660034 0.470135
Total area= 1.00000
Mean (ms) = 0.279392 SD= 0.394356 SD/mean = 1.41148
Shut time pdf with zero resolution
f(t) =
term coeff (W) rate const (1/sec) area (%) tau (ms)
1 25932.5 63234.7 41.009888 0.158141E-01
2 25.4409 9579.87 0.265567 0.104386
3 23.7223 1599.59 1.483023 0.625161
4 0.246824 0.431198 57.241524 2319.12
Total area= 1.00000
Mean (ms) = 1327.51 SD= 2096.42 SD/mean = 1.57920
Ideal (zero resolution)
Mean open time (ms) = 0.279392 Mean shut time (ms) = 1327.51
P(open) (ideal) = 0.00021
HJC distributions (exact)
Mean open time (ms) = 0.632806 Mean shut time (ms) = 3000.40
P(open) (HJC) = 0.00021
Plot for set number= 1
concentration of ACh = 0.500000E-01
Distributions for set number 1
------------------------------------------------------------
Concentration of ligand 1 (micromolar) = 0.500000E-01
HJC Initial vector for open times =
0.378648 0.478658 0.142694
HJC Initial vector for shut times =
0.226904 0.588437 0.130775 0.538839E-01
ASYMPTOTIC OPEN TIME DISTRIBUTION
f(t) =
term coeff (W) rate const (1/sec) area tau (ms)
1 7971.77 55940.4 0.142505 0.178762E-01
2 2844.35 5944.03 0.478522 0.168236
3 273.389 721.794 0.378763 1.38544
Total area (for non-zero eigenvalues) = 0.999790
Mean (ms) = 0.607805 SD= 1.05441 SD/mean = 1.73478
Areas for asymptotic pdf renormalised for t=0 to infinity (and sum=1)
(so areas can be compared with ideal pdf)
1 0.380154
2 0.365766
3 0.254080
ASYMPTOTIC SHUT TIME DISTRIBUTION
f(t) =
term coeff (W) rate const (1/sec) area tau (ms)
1 10286.0 57252.8 0.179660 0.174664E-01
2 3.67571 9506.24 0.386663E-03 0.105194
3 41.2093 1591.47 0.258938E-01 0.628350
4 0.207084 0.262716 0.788242 3806.39
Total area (for non-zero eigenvalues) = 0.994182
Mean (ms) = 3000.38 SD= 3720.06 SD/mean = 1.23986
Areas for asymptotic pdf renormalised for t=0 to infinity (and sum=1)
(so areas can be compared with ideal pdf)
1 0.479601
2 0.312868E-03
3 0.171906E-01
4 0.502896
Set 1: Initial CHS vector for burst = 0.236289 0.583053 0.180658
et 1: End CHS vector for burst =
0.174873 0.958106 0.996516 0.999223
Open time roots (1/sec) = -55940.4 -5944.03 -721.794
shut time roots (1/sec) = -57252.8 -9506.24 -1591.47 -0.262716
EXACT SOLUTIONS FOR OPEN TIMES
****** In HJCEXACT, eigen(1) of Q reset from -0.584987E-10 to 0
eigen = 0.00000 355.047 1528.30 6029.09 9473.07 56283.4
65002.0
g00(m) = 0.506965 279.346 34.4368 2800.11 17.8937 7981.83
7.30495
g10(m) = 0.862889 4.97104 34.2469 -41.2517 13.9927 -14.2173
1.39546
g11(m) = 0.257013 99708.4 2358.70 -201450. 1500.53 -671073.
-2584.30
EXACT SOLUTIONS FOR SHUT TIMES
g00(m) = 0.561931 323.864 22.5570 0.629645 3.44754 0.190697E-01
10921.3
g10(m) = 2.25722 258.250 6.47323 0.469287 -0.130204 0.146514E-02
-267.321
g11(m) = 0.315766 527152. 1496.59 -40.6231 90.1319 -0.499906
0.178019E+08
Shut time pdf with zero resolution
f(t) =
term coeff (W) rate const (1/sec) area (%) tau (ms)
1 25932.5 63234.7 41.009888 0.158141E-01
2 25.4409 9579.87 0.265567 0.104386
3 23.7223 1599.59 1.483023 0.625161
4 0.246824 0.431198 57.241524 2319.12
Total area= 1.00000
Mean (ms) = 1327.51 SD= 2096.42 SD/mean = 1.57920
Open time pdf with zero resolution
f(t) =
term coeff (W) rate const (1/sec) area (%) tau (ms)
1 14453.6 56176.3 25.729046 0.178011E-01
2 1465.07 5952.94 24.610918 0.167984
3 1056.29 2127.05 49.660034 0.470135
Total area= 1.00000
Mean (ms) = 0.279392 SD= 0.394356 SD/mean = 1.41148
Shut time pdf with zero resolution
f(t) =
term coeff (W) rate const (1/sec) area (%) tau (ms)
1 25932.5 63234.7 41.009888 0.158141E-01
2 25.4409 9579.87 0.265567 0.104386
3 23.7223 1599.59 1.483023 0.625161
4 0.246824 0.431198 57.241524 2319.12
Total area= 1.00000
Mean (ms) = 1327.51 SD= 2096.42 SD/mean = 1.57920
Ideal (zero resolution)
Mean open time (ms) = 0.279392 Mean shut time (ms) = 1327.51
P(open) (ideal) = 0.00021
HJC distributions (exact)
Mean open time (ms) = 0.632806 Mean shut time (ms) = 3000.40
P(open) (HJC) = 0.00021
Mean and SD of 4732 values= 0.632506 +/- 1.05923
Range from 0.00000 to 12.2463
Distribution of log(t) displayed- 33 bins, factor= 1.212
No of values below Xlow= 0 No of values above Xhigh= 0