Symbolic Resolution of Labeled Measurements
Contents
SymNmrMs
Problem setup
Used arguments
'-t' 'example/ALA_mapping.tsv' '-d' 'example/ALA_measurements.tsv'
Available measurements
|
HSQC_Ca |
HSQC_Cb |
HACO |
JRES_Ha |
JRES_Hb |
HACO-DIPSY |
GC-MS |
LC-MS |
000 |
|
|
|
e |
t |
|
o |
g |
001 |
|
k |
|
e |
u |
|
p |
h |
100 |
|
|
r |
e |
t |
|
o |
h |
101 |
|
k |
r |
e |
u |
|
p |
i |
010 |
a |
|
|
f |
t |
m |
p |
h |
011 |
b |
l |
|
f |
u |
m |
q |
i |
110 |
c |
|
s |
f |
t |
n |
p |
i |
111 |
d |
l |
s |
f |
u |
n |
q |
j |
Equation system
i000 + i001 + i100 + i101 + i010 + i011 + i110 + i111 = 1
a·(i010 + i011 + i110 + i111) - i010 = 0
b·(i010 + i011 + i110 + i111) - i011 = 0
c·(i010 + i011 + i110 + i111) - i110 = 0
d·(i010 + i011 + i110 + i111) - i111 = 0
-i001 - i101 + k·(i001 + i011 + i101 + i111) = 0
-i011 - i111 + l·(i001 + i011 + i101 + i111) = 0
-i100 - i101 + r·(i100 + i101 + i110 + i111) = 0
-i110 - i111 + s·(i100 + i101 + i110 + i111) = 0
e - i000 - i001 - i100 - i101 = 0
f - i010 - i011 - i110 - i111 = 0
-i000 - i010 - i100 - i110 + t = 0
-i001 - i011 - i101 - i111 + u = 0
-i010 - i011 + m·(i010 + i011 + i110 + i111) = 0
-i110 - i111 + n·(i010 + i011 + i110 + i111) = 0
-i000 - i100 + o = 0
-i001 - i010 - i101 - i110 + p = 0
-i011 - i111 + q = 0
g - i000 = 0
h - i001 - i010 - i100 = 0
i - i011 - i101 - i110 = 0
-i111 + j = 0
Solution
Isotopomers
variable |
formula |
000 |
g |
001 |
g + h - j·m - n·(-f + j) - t |
100 |
-g + o |
101 |
i + j·(m + 1) + n·(-f + j) - q |
010 |
j·m + n·(-f + j) - o + t |
011 |
-j + q |
110 |
-j·m - n·(-f + j) |
111 |
j |
EMU
variable |
Exx |
xEx |
xxE |
EEx |
ExE |
xEE |
EEE |
M+0 |
2·g + h - j - o + q |
e |
t |
2·g + h - j·m - n·(-f + j) - t |
g + j·m + n·(-f + j) - o + t |
o |
g |
M+1 |
-g + i + 2·j + o - q |
f |
u |
-g + i + 2·j·m + 2·n·(-f + j) + t |
h - j·(2·m + 1) - 2·n·(-f + j) - p + u |
p |
h |
M+2 |
|
|
|
f·n |
i + j·(m + 2) + n·(-f + j) - q |
q |
i |
M+3 |
|
|
|
|
|
|
j |
Cumomers
variable |
formula |
1xx |
-g + i + 2·j + o - q |
x1x |
f |
xx1 |
u |
11x |
f·n |
1x1 |
i + j·(m + 2) + n·(-f + j) - q |
x11 |
q |
111 |
j |
System Status
The system is over-determined.
The reason is that following measurements were not used: a, b, c, d, e, f, k, l, r, s.
Number of redundant measurements: 10.
Redundant measurements
Measurement |
Formula |
Methods |
a |
(j·m + n·(j + o - q - t) - o + t)/(-o + q + t) |
HSQC_Ca: GC-MS, HACO-DIPSY, JRES_Hb, LC-MS |
b |
(-j + q)/(-o + q + t) |
HSQC_Ca: GC-MS, JRES_Hb, LC-MS |
c |
(-j·m - n·(j + o - q - t))/(-o + q + t) |
HSQC_Ca: GC-MS, HACO-DIPSY, JRES_Hb, LC-MS |
d |
j/(-o + q + t) |
HSQC_Ca: GC-MS, JRES_Hb, LC-MS |
e |
o - q + u |
JRES_Ha: GC-MS, JRES_Hb |
f |
-o + q + t |
JRES_Ha: GC-MS, JRES_Hb |
k |
-(q - u)/u |
HSQC_Cb: GC-MS, JRES_Hb |
l |
q/u |
HSQC_Cb: GC-MS, JRES_Hb |
r |
(g - i - j·(m + 1) - n·(j + o - q - t) - o + q)/(g - i - 2·j - o + q) |
HACO: GC-MS, HACO-DIPSY, JRES_Hb, LC-MS |
s |
-n·(-o + q + t)/(g - i - 2·j - o + q) |
HACO: GC-MS, HACO-DIPSY, JRES_Hb, LC-MS |
Measurable elementary combinations
N° |
Combination |
Accumulated |
Formula |
Methods |
1 |
000 |
000 |
g |
LC-MS |
2 |
001 |
001 |
g + h - j·m - n·(-f + j) - t |
HACO-DIPSY, JRES_Ha, JRES_Hb, LC-MS |
3 |
100 |
100 |
-g + o |
GC-MS, LC-MS |
4 |
101 |
101 |
i + j·(m + 1) + n·(-f + j) - q |
GC-MS, HACO-DIPSY, JRES_Ha, LC-MS |
5 |
010 |
010 |
j·m + n·(-f + j) - o + t |
GC-MS, HACO-DIPSY, JRES_Ha, JRES_Hb, LC-MS |
6 |
011 |
011 |
-j + q |
GC-MS, LC-MS |
7 |
110 |
110 |
-j·m - n·(-f + j) |
HACO-DIPSY, JRES_Ha, LC-MS |
8 |
111 |
111 |
j |
LC-MS |
Least Squares
Problem summary
Item |
Value |
Comment |
number of measurements |
21 |
m |
system rank (number of statistically defined parameters) |
7 |
p |
degree of freedom |
14 |
dof=m - p |
χ²(14) |
3.179 |
Σ((estimated-measured)/sd)² 95% confidence interval is [0; 24] |
χ²(14)/14 |
0.227 |
Reduced χ², χ²(dof)/dof: if ≫ 1 then poor fitting, ~ 1 means ‘good’ fitting and ≪ 1 means over-fitting or overestimating sd |
p-value of one-tail χ² test, i.e. P(χ²(14) > 3.179) |
0.999 |
Value close to 0 (e.g. under 0.05) means poor fitting. Value close to 1 can be an evidence for over-fitting or that sd are overestimated. It can be NaN (not a number) for dof=0 |
Measured values
name |
sd |
value |
estimated |
(estimated - value)/sd |
a |
0.02004 |
0.254 |
0.249 |
-0.25475 |
b |
0.02004 |
0.254 |
0.244 |
-0.49063 |
c |
0.02004 |
0.248 |
0.248 |
-0.0216 |
d |
0.02004 |
0.244 |
0.26 |
0.76697 |
k |
0.02 |
0.497 |
0.496 |
-0.04218 |
l |
0.02 |
0.503 |
0.504 |
0.04218 |
r |
0.03 |
0.502 |
0.511 |
0.29765 |
s |
0.03 |
0.498 |
0.489 |
-0.29765 |
e |
0.03 |
0.51 |
0.497 |
-0.42222 |
f |
0.03 |
0.49 |
0.503 |
0.42222 |
t |
0.03 |
0.496 |
0.497 |
0.02311 |
u |
0.03 |
0.504 |
0.503 |
-0.02311 |
m |
0.03 |
0.496 |
0.493 |
-0.11238 |
n |
0.03 |
0.504 |
0.507 |
0.11238 |
o |
0.01 |
0.25 |
0.247 |
-0.29363 |
p |
0.01 |
0.5 |
0.499 |
-0.05006 |
q |
0.01 |
0.25 |
0.253 |
0.34369 |
g |
0.01 |
0.117 |
0.122 |
0.533 |
h |
0.01 |
0.355 |
0.358 |
0.34705 |
i |
0.01 |
0.387 |
0.389 |
0.16109 |
j |
0.01 |
0.141 |
0.131 |
-1.04114 |
Redundant measurements
Measurement |
Measured Value |
Formula Applied |
Δ=FA-MV |
a |
0.254 |
0.276 |
0.023 |
b |
0.254 |
0.220 |
-0.034 |
c |
0.248 |
0.219 |
-0.028 |
d |
0.244 |
0.285 |
0.040 |
e |
0.51 |
0.504 |
-0.006 |
f |
0.49 |
0.496 |
0.006 |
k |
0.497 |
0.504 |
0.007 |
l |
0.503 |
0.496 |
-0.007 |
r |
0.502 |
0.548 |
0.046 |
s |
0.498 |
0.452 |
-0.046 |
Isotopomers
variable |
value |
sd |
000 |
0.122 |
0.00844 |
001 |
0.108 |
0.01277 |
100 |
0.125 |
0.01008 |
101 |
0.142 |
0.01054 |
010 |
0.125 |
0.00867 |
011 |
0.123 |
0.00673 |
110 |
0.125 |
0.00745 |
111 |
0.131 |
0.00584 |
Cumomers
variable |
value |
sd |
1xx |
0.522 |
0.01784 |
x1x |
0.503 |
0.01021 |
xx1 |
0.503 |
0.0122 |
11x |
0.255 |
0.00822 |
1x1 |
0.272 |
0.01368 |
x11 |
0.253 |
0.00607 |
111 |
0.131 |
0.00584 |
EMU values
variable |
Exx |
xEx |
xxE |
EEx |
ExE |
xEE |
EEE |
M+0 |
0.478 |
0.497 |
0.497 |
0.23 |
0.247 |
0.247 |
0.122 |
M+1 |
0.522 |
0.503 |
0.503 |
0.514 |
0.48 |
0.499 |
0.358 |
M+2 |
|
|
|
0.255 |
0.272 |
0.253 |
0.389 |
M+3 |
|
|
|
|
|
|
0.131 |
EMU standard deviations
variable |
Exx |
xEx |
xxE |
EEx |
ExE |
xEE |
EEE |
M+0 |
0.01784 |
0.01021 |
0.0122 |
0.01673 |
0.01214 |
0.00748 |
0.00844 |
M+1 |
0.01784 |
0.01021 |
0.0122 |
0.0163 |
0.01818 |
0.00733 |
0.00903 |
M+2 |
|
|
|
0.00822 |
0.01368 |
0.00607 |
0.00844 |
M+3 |
|
|
|
|
|
|
0.00584 |
Measurable combinations
Combination |
Accumulated |
value |
sd |
000 |
000 |
0.122 |
0.00844 |
001 |
001 |
0.108 |
0.01277 |
100 |
100 |
0.125 |
0.01008 |
101 |
101 |
0.142 |
0.01054 |
010 |
010 |
0.125 |
0.00867 |
011 |
011 |
0.123 |
0.00673 |
110 |
110 |
0.125 |
0.00745 |
111 |
111 |
0.131 |
0.00584 |