[R] R emulation of FindRoot in Mathematica

Thu Jan 19 16:18:57 CET 2023

Hi Jeff - that is definitely not fair, this is a highly respected 
scientist but old me are probably not clever enough to explain problem 
which I think is not too difficult. Basically, it is a series of 
consecutive statements of H and Mg and K combining to ATP and ADP, 
creatin and creatinP under assumption og known total inorganic phosphate 
(pi), total ATP total ADP, creatin and creatinphosphate. It was written 
in 1997 when R was less mature - and if we know how to do it in R so not 
to depend on black box operations it would be fun. For the moment, I'm 
not even sure I understand why there is now focus on the problem being 
nonlinear, since I want to evaluate at given H or pH.  hatp <- 10^6.494 
* H * ATP ?

BW Troels

Den 19-01-2023 kl. 15:54 skrev Jeff Newmiller:
> But it is simultaneously an example of why some researchers like black box solvers... a system of dozens of nonlinear equations can potentially have many or even infinite solutions. If the researcher is weak in math, they may have no idea which solutions are possible and having a tool like FindRoot confidently return a solution lets them focus on other things. Sort of like ChatGPT.
>
> TL;DR the author may have no idea about how to resolve this without relying on the opaque FindRoot.
>
> On January 19, 2023 6:28:53 AM PST, "Ebert,Timothy Aaron" <tebert using ufl.edu> wrote:
>> 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-bounces using r-project.org> On Behalf Of Troels Ring
>> Sent: Thursday, January 19, 2023 9:18 AM
>> To: Valentin Petzel <valentin using petzel.at>; r-help mailing list <r-help using 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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