TIBS 22 - SEPTEMBER 1997 COMPUTER CORNER

Biochemistry by rmmbers: simulation of biochemical pathways with Gepasi 3

Many biochemistry laboratories are decorated with large posters depicting a complex r~etwork of biochemical reac- tions. The complexity of these posters creates a false sense of completeness, as we are now sure that a considerable part of the detail is missing: (1) we do not know the function of nearly half the genes in the genomes that have been fully sequenced~; (2) of those we do know, it is becoming apparent that there are fewer metabolic enzymes than regulatory ones; and (3) as enzymes a~e never tested against the effect of ell metabolites on the rate of reaction, there could be many unknown regulatory interactions.

Although we are still far from being able to carry out detailed computer simu- lations of cellular behaviour, computer simulation of kinetic models has an im- portant role in the biochemical sci- ences 2. It serves to check the consistency of our theories with observed behav- iour; it allows one to ask 'what-if' ques- tions that can reveal non-intuitive prop- erties of metabolism; it can be used to find estimates for kinetic: parameters and for genetic functional analysis; and it is an educational tool.

However, computer simulation of bio- chemical kinetics is not yet a routine technique in biochemical laboratories even though most biochemists use com- puters routinely. Here, ! discuss the pro- gram Gepasi version 3, a 32-bit package for Microsoft Windows (95 or NT 3.51 and above), and describe how it could be used to simulate an example pathway (Fig. 1). I have also included a listing of other free software for the simulation of biochemical kinetics, all of which are available through the Internet.

Gepasi first appeared in 1989 (Ref. 3), followed by a more modern version 2 in 1992 (Ref. 4). The new Gepasi 3 can now handle systems with a large numbez of metabolites and reactions (limited only by the available memory); the metab- olites can be distributed among several compartments; metabolic control analy- sis (MCA, see Refs 5, 6 for reviews) is used to characterize the simulation re- sults; steady states are also characterized with linear stability analysisT; simulations can be followed interactively, allowing

for the addition of perturbations of any kinetic parameter or metabolite concen- tration during a time-course simulation.

Building a metabolic pathway model Figure ] depicts a branched metabolic

pathway controlled by a signal metab- olite through an enzyme cascade. The external signal metabolite inhibits the phosphatase and activates the kinase of the first enzyme cycle. Although not rep- resenting any system in particular, read- ers will find some similarities with actual signaling cascades recently discussed in the pages of Ti~$ (e.g. Ref. 8).

As with Gepasi 2 (Ref. 4) and other similar programs (Table l), before simu- lating a pathway one has to: (1) define its structure and kinetics; (2) assign nu- merical values to the kinetic constants and initial concentrations; and (3) select output options.

Deiining the reactions and ki- netics. The first step in creating the model with Gepasi is to define and name the chemical reactions, entered in standard chemical notation. Next, one has to define the kinetics of all reactions. After pressing the 'Kinetics' button, a dialog box appears with the list of all re- actions in the model and a list of possible kinetic types for each reaction (those that match it in terms of the num- ber of reactants). Gepasi has a set of predefined kinetic types: the common Henri-Michaelis- Menten 9J°, several inhibition or activation mechanisms, Hill kinetics ~ and its equiva- lent for reversible reactions v-, and several allosteric and multi-reactant mechanisms. The user can also enter extra kinetic types, which are then kept in a database. In the example, reaction 1 follows 'catalytic activation' (a pre- defined type) where the obli- gatory activator affects the apparent limiting rate; reac- tion 5 follows a user-defined kinetic type, governed by an

equation like that of the Hend-Michae!is- Menten type save that the enzyme con- centration and the kc,,t are represented explicitly (rather than their product, V). Once a kinetic type is selected for a re- action, one has to assign values to its kinetic constants, and the metabolites that act as modifiers, by selecting them from a list On the case of reaction 1, Signal is the activator).

Compartments and mtabolite properties. Gepasi 3 allows for an unlimited num- ber of compartments to be defined, each with its own volume. The differences in volumes are taken into account in the calculations. This feature makes the pro- gram useful for pharmacoldnetic simu- lations as well.

Each metabolite has a set of proper- ties that need to be set. This includes its initial concentration, the compartment that it occupies and if its concentration is allowed to vary throughout the reac- tion or is otherwise fixed (buffered by some other process not made explicit in the model).

The user is allowed to define arbitrary functions of the parameters and/or vari- ables that are consequently calculated by the program. In the example, a function

Copyright © 1997, Elsevier Science Ltd. All rights reserved. 0968-0004/97/$17.00

/ Signal ~

~(/~ Kinasel 2~,~ j

, 1 K i n a s e l - ; /

f Enzyme-i

Kinase2 Kinase2-O( 5 6) ~, Enzyme-a j

~- M / / ~ . - - - - - - ~ P1

S 7 ~ ~ P2

Rgme 1 A signalling enzyme cascade. The external metabolite Signal activates the production of Kinasel-P, which phosphorylates Kinase2. Kinase2 then converts an enzyme from an inactive to an active form. The latter catalyses the metabolic step of conversion of M to PI. Signal also inhibits a phosphatase that dephos2horyl- ates the Kinasel-P back to an inactive form. Reaction 1 follows uncompetitive inhibition kinetics, reaction 2 compulsory catalytic activation, reactions 3-6 follow irreversible and reae, tions 7-9 reversible Michaelis- Menten kinetics. [S], IP1] and [P2] are kept constant at values that favour the flux in the direction of the ar rows. The nucleot.'gs and inorganic phosphate are assumed to be constant and are incorporated into the kinetic constants. Numerical values of the parameters and other details are available at http://gepasi.dbs. aber.ac.uk/metab/signal/signal.html

Pll: S0968-0004(97)01103-1 361

COMPUTER TIBS 22 - SEPTEMBER 1997

L tl - ' ~ ' " T

Program Systems '~ I rl I II I

Gepasi 3 MS.Windows 95/NT 1997

r

Table i. Free biochemical hinet[cs simulators available on the lnlLemet L I ' r l l I I f f ~

Last update User-interface Limitations b URL Ref(s) i i IIII

KINSIM 4.0 ~ MS-DOS 1997

MetaModel 3 MS-DOS 1993

MIST 2.5 MS-Windows 3.1 1994

SCAMP 2.5g MS-DOS and Atari ST 1995

Entirely based on menus and dialog boxes

Menu-based, but reactions are entered in a separate text file

Entirely based on menus and dialog boxes

Entirely based on menus and dialog boxes

Model and simulation tasks are described in a text file following a specific syntax

r'rr

Unlimited c

100 reactions, 100 metabolites

30 metabolites, 20 reactions Unlimited c

Unlimited c

http://gepasi.dbs.aber.ac.uk/softw/ gepasi.html

http://www.L;ochem.wust;.cdu/cflab/ message.html

ftp://bmsdarwin.brookes.ac.uk/pub/software/ 20 ibmpc/metamod3/

http://chemengl.kat.lth.se/staff/Magnus_E/ 21 magnus_e.htm

http://www.fssc.demon.co.uk/Scamp/ 22 scamp.htm

18, 19

aAIl the MS-DOS and MS.Windows 3.1 programs run under MS.Windows 95 and, with exception of MIST, also under MS-Windows NT. ~Reactions and metabolites. CLimited only by the available computer memory - probably in the thousands for typical PC configurations. OKINSIM only allows for mass action kinetics steps, i.e. enzyme mechanisms need to be in terms of their elementary steps.

I

was defined to calculate the ratio of the fluxes towards P1 and P2. Also, some parameters can be linked to each other so that when one is changed the other is automatically varied according to a function defined by the user.

Running the simulations One powerful feature of Gepasi is the

ability to explore the behaviour of the model over a wide range of parameter values. This is an automatic process that varies the values of the required param-

eters and runs one simulation for each numerical combi- nation. For this 'parameter

Flux scan' the

(R908) ~ ~ ~ ~ par, ~0 ; varii

60 valu 50 40 resu 3o latic 20 , havi

,, ~r ~,~'~,b ~ ' ~ - ~ " " ' ~ ' ~ 1 ~ R4(Kr.) the nail

{[Signal]- ~'- ~,,,-o,a . . . . ues, that

Figure 2 Influence of the Signal and Krn of reaction 4 [R4(Km) ], a phosphatase, on the production flux of P2 (the pro- duction flux of Pl is complementary to that of P2). [Signal] was varied linearly between 0.3-0.7 in 20 steps and the R4(Km) logarithmically between 0.01=1.0 in ten steps; a steady state was calculated for each combination in a total of 200 simulations; all other parameters were held constant. For concen- trations of Signal smaller than 0.5, .most of the meta- bolic flux goes towards P2; for higher concentrations, the metabolic flux switches mostly to Pl. At low val- ues of R4(Km), the transition is steeper before the in- flexion point ([Signal] = 0.5) than after it; at higher val- ues of R4(Y~), the transition is steeper after the inflexion point, Values of R4(Km) - 0.1 cause the tran- sition to be equally steep on each side of the inflexion point, with a Hill coefficient exceeding 300. This switch- like behaviour of the enzyme cascade is a systemic property that requires the total concentration of target enzymes to be much larger than the /~ for their converting enzymes, and the inhibition/activation ef- fects of Signal on the first enzyme to be exerted on V~rather than on a~ K m . These characteristics are also present in the model.

362

user selects the parameters that are to be varied, their boundaries and the number of intermediate values. Figure 2 shows the result of calculating 200 simu- lations o[ the steady-state be- haviour of the example path- way with varying amounts of the concentration of the Sig- nal metabolite at different val- ues of K m for the phosphatase

inactivates Kinase2.P. Clearly, this is a dramatic illustration of how a signal- ling enzyme cascade can gen- erate a switch-like behaviour (e.g. Refs 13, 14). This also illustrates how simulation is important to reveal unintui- tire behaviours, in this case the effect of the K m of reac- tion 4 on the shape of the re- sponse of the metabolic fluxes to [Signal]. Figure 3 shows the transient fluxes after [Sig- nal] had increased from 0.45 to 0.55. More details about this model can be found at http://gepasi.dbs.aber.ac.uk/ metab/signal/signal.html

Gepasi 3 can carry out both time-course and steady- state simulations, the results of each being written to a

different file. The user has control over the content and format of the output data files. These are ASCII columnar files, where the user can select the width of the columns, the separating character and whether titles are included. Two- or three-dimensional plots can be generated directly from within the program (using the freeware program gnuplot, also sup- plied with Gepasi). The data available [or output are all the kinetic constants, compartment volumes, concentrations, fluxes, MCA's elasticity and control coefficients° linear stability indicators, transition times zs, any user-defined [unc- tions (like the ratio of fluxes mentioned above) or technical indices of the nu- merical methods.

Oiscu~sion A free metabolic simulator such as

Gepasi is not just a research tool, it is also intended for educational use. Lec- tures are more effective if accompanied with examples and demonstrations, but often there is not enough time and money to carry out all the relevant experiments in the laboratory. Simulation can thus help in bridging this gap, and Gepasi 3 allows students to study the kinetics of biochemical pathways with little invest- ment in learning the use of the program itself and none on differential equations. The main advantage over textual descrip- tions is that the student can change any parameter of the pathway and 'immedi- ately' see its effect on the system's be- hay[our. This is likely to increase many students' interest, as it allows them to discover rather than just to learn.

Gepasi's Help file includes explanations of various basic concepts in metabolic simulation, and of all the predefined ki- netic mechanisms. As references to the

T~BS 22 - SEPTEMBER 1997

- /

[ ~ ' . , ~ . ~ o

L . / 7 I JHgJP2 t [10,$741~ 0

2

Figure The time-course page of Gepasi 3. The user has se- lected to follow the transient [Signal], the fluxes to- wards Pl and P2 and their ratio (a user-defined func- tion). Perturbations could be applied by pressing the 'Pause' button, altering any of the four items dis- played and pressing 'Continue'.

relevant literature are included in this Help file, it is a good starting point |or further bibliographic searches.

Metabolic simulators can also be useful to the experimental scientist as a planning tool, allowing one to study he possible outcomes of an experiment

without spending unneces- sary time and reagents in the laboratory (and possibly rul- ing out others that would not provide useful information). Of course, the theoretical bio- chemist will find plenty of other uses for a simu~a. ,r of biochemical kinetics.

A¢knowledgemonts I thank D. Kell for sugges-

tions on the functional specifi- cation of Gepasi and for proof- reading this manuscript, and the many colleagues, espe- cially J. Hofme~, who sug- gested improvements to Gepasi and helped in its testing stages. I am indebted to the Chemicals and Pharmaceuticals Directorate of the UK BBSRC for financial support and to the Portuguese JNICT for sup- porting the development of a previous version of Gepasi.

Re[emnces I Oliver, S. G. (1996) Nature 379, 597-600 2 Garfinkel, D. (1981) Trends Bioct,ern. Sci. 6,

69-71 3 Mendes, P. (1990)in Control of Metabolic

Processes (Cornish-Bowden, A. and C~rdenas, M L., eds), pp. 434-435,

COMPUTER CORNER Plenum Press

4 Mendes, P. (1993) Comput. Appl. BioscL 9, 563-571

5 Fe~L D. A. (1992) Biochern. J. 286, 313-330 6 Fell, D. A. (1996) Understanding the Control of

Metabolism, Port!and Press 7 Stucki, J. W. (11978) Prog. Biophys. Mol. Biol.

33, 99-187 8 Feig, L. A., Urano, T. and Cantor, S. (1996)

Trends Biochern. ScL 23., 438-443. 9 Henri, V. (1902) Compt. Rend. Hebd. Acad. $cL

Paris 135, 916-919 10 Michaelis, L. and Menten, M. L. (1913)

Biochem. Z. 49, 333-369 /1 Hill, A. V. (1910) J. Physiol. 40, iv-vii 12 Hofmeyr, J-H. S. and Cornish-Bowden, A.

Cornput. Appl. Biosci. (in press) / 3 Koshland, D. E. (1987) Trends Biochern. ScL

12, 225-229 14 Ferrell, J. E., Jr (1996) Trends Biochern. $ci. 21,

460-466 15 Easterby, J. S. (1981) Biochem. J. 199,

155-161 16 Barshop, B. A., Wrenn, R. F. and Frieden, C.

(1983) Anal. Biochem. 130, 135-145 17 Frieden, C. (1993) Trends Biochem. Sci. 18,

58-60 18 Cornish-Bowden, A. and Hofmeyr, J. H. (1991)

Comput. Appl. Biosci. 7, 89-93 19 Ehlde, M. and Zacchi, G. (1995) Comput. Appl.

Biosci. 11, 201-207 20 Sauro, H. M. (1993) Comput. Ap#I. Biosci. 9,

441-450

PEDRO MENDES

Institu~.. of Biological Sciences, Edward Llwyd Building, University of Wales, Aberystwyth, Ceredigion, UK SY23 3DA. Email: prm@aber.ac.uk

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