Hi Tim - the results from this paper have had big impact on quite
complicated problems of physiology so I thought I might like to
understand how they came by, calculating them myself. Writing up the
statements from which the inferences in the paper were generated using
Mathematica were meant to inspire clever friends to suggest probably
quite simple ways to handle the problem in R.
All best wishes
Troels
Den 19-01-2023 kl. 15:28 skrev Ebert,Timothy Aaron:
This is a poster child for why we like open source software. "I dump numbers into a
black box and get numbers out but I cannot verify how the numbers out were calculated so
they must be correct" approach to analysis does not really work for me.
Tim
-----Original Message-----
From: R-help <r-help-boun...@r-project.org> On Behalf Of Troels Ring
Sent: Thursday, January 19, 2023 9:18 AM
To: Valentin Petzel <valen...@petzel.at>; r-help mailing list
<r-help@r-project.org>
Subject: Re: [R] R emulation of FindRoot in Mathematica
[External Email]
Thanks, Valentin for the suggestion. I'm not sure I can go that way. I
include below the statements from the paper containing the knowledge on the
basis of which I would like to know at specified [H] the concentration of each
of the many metabolites given the constraints. I have tried to contact the
author to get the full code but it seems difficult.
BW Troels
hatp <- 10^6.494*H*atp
hhatp <- 10^3.944*H*hatp
hhhatp <- 10^1.9*H*hhatp
hhhhatp <- 10*H*hhhatp
mgatp <- 10^4.363*atp*mg
mghatp <- 10^2.299*hatp*mg
mg2atp <- 10^1-7*mg*mgatp
katp <- 10^0.959*atp*k
hadp <- 10^6.349*adp*H
hhadp <- 10^3.819*hadp*H
hhhadp <- 10*H*hhadp
mgadp <- 10^3.294*mg*adp
mghadp <- 10^1.61*mg*hadp
mg2adp <- 10*mg*mgadp
kadp <- 10^0.82*k*adp
hpi <- 10^11.616*H*pi
hhpi <- 10^6.7*h*hpi
hhhpi <- 10^1.962*h*hhpi
mgpi <- 10^3.4*mg*pi
mghpi <- 10^1.946*mg*hpi
mghhpi <- 10^1.19*mg*hhpi
kpi <- 10^0.6*k*pi
khpi <- 10^1.218*k*hpi
khhpi <- 10^-0.2*k*hhpi
hpcr <- 10^14.3*h*pcr
hhpcr <- 10^4.5*h*hpcr
hhhpcr <- 10^2.7*h*hhpcr
hhhhpcr <- 100*h*hhhpcr
mghpcr <- 10^1.6*mg*hpcr
kpcr <- 10^0.74*k*pcr
khpcr <- 10^0.31*k*hpcr
khhpcr <- 10^-0.13*k*hhpcr
hcr <- 10^14.3*h*cr
hhcr <- 10^2.512*h*hcr
hlactate <- 10^3.66*h*lactate
mglactate <- 10^0.93*mg*lactate
tatp <- atp + hatp + hhatp + hhhatp + mgatp + mghatp + mg2atp + katp
tadp <- adp + hadp + hhadp + hhhadp + mghadp + mgadp + mg2adp + kadp
tpi <- pi + hpi + hhpi + hhhpi + mgpi + mghpi + mghhpi + kpi + khpi + khhpi
tpcr <- pcr + hpcr + hhpcr + hhhpcr + hhhhpcr + mghpcr + kpcr + khpcr + khhpcr
tcr <- cr + hcr + hhcr
tmg <- mg + mgatp + mghatp + mg2atp + mgadp + mghadp + mg2adp + mgpi + kghpi +
mghhpi +
mghpcr + mglactate
tk <- k + katp + kadp + kpi + khpi + khhpi + kpcr + khpcr + khhpcr
tlactate <- lactate + hlactate + mglactate
# conditions
tatp <- 0.008
tpcr <- 0.042
tcr <- 0.004
tadp <- 0.00001
tpi <- 0.003
tlactate <- 0.005
# free K and Mg constrained to be fixed
#
mg <- 0.0006
k <- 0.12
Den 19-01-2023 kl. 12:11 skrev Valentin Petzel:
Hello Troels,
As fair as I understand you attempt to numerically solve a system of
non linear equations in multiple variables in R. R does not provide
this functionality natively, but have you tried multiroot from the
rootSolve package:
https://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fcran
.r-project.org%2Fweb%2Fpackages%2FrootSolve%2FrootSolve.pdf&data=05%7C
01%7Ctebert%40ufl.edu%7C7cb98cd926b34284cd5f08dafa28026c%7C0d4da0f84a3
14d76ace60a62331e1b84%7C0%7C0%7C638097347110882622%7CUnknown%7CTWFpbGZ
sb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3
D%7C3000%7C%7C%7C&sdata=D9A3fwJ5x7GbEV4A01wncLUil7szTdSPul5vd0lsSBw%3D
&reserved=0
multiroot is called like
multiroot(f, start, ...)
where f is a function of one argument which is a vector of n values
(representing the n variables) and returning a vector of d values
(symbolising the d equations) and start is a vector of length n.
E.g. if we want so solve
x^2 + y^2 + z^2 = 1
x^3-y^3 = 0
x - z = 0
(which is of course equivalent to x = y = z, x^2 + y^2 + z^2 = 1, so x
= y = z = ±sqrt(1/3) ~ 0.577)
we'd enter
f <- function(x) c(x[1]**2 + x[2]**2 + x[3]**2 - 1, x[1]**3 - x[2]**3,
x[1] - x[3])
multiroot(f, c(0,0,0))
which yields
$root
[1] 0.5773502 0.5773505 0.5773502
$f.root
[1] 1.412261e-07 -2.197939e-07 0.000000e+00
$iter
[1] 31
$estim.precis
[1] 1.2034e-07
Best regards,
Valentin
Am Donnerstag, 19. Jänner 2023, 10:41:22 CET schrieb Troels Ring:
Hi friends - I hope this is not a misplaced question. From the
literature (Kushmerick AJP 1997;272:C1739-C1747) I have a series of
Mathematica equations which are solved together to yield over
different
pH values the concentrations of metabolites in skeletal muscle using
the
Mathematica function FindRoot((E1,E2...),(V2,V2..)] where E is a
list of
equations and V list of variables. Most of the equations are
individual
binding reactions of the form 10^6.494*atp*h == hatp and next
10^9.944*hatp*h ==hhatp describing binding of singe protons or Mg or
K
to ATP or creatin for example, but we also have constraints giving
total
concentrations of say ATP i.e. ATP + ATPH, ATPH2..ATP.Mg
I have, without success, tried to find ways to do this in R - I have
36
equations on 36 variables and 8 equations on total concentrations.
As
far as I can see from the definition of FindRoot in Wolfram, Newton
search or secant search is employed.
I'm on Windows R 4.2.2
Best wishes
Troels Ring, MD
Aalborg, Denmark
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