CN108021787B - Method for constructing dynamic metabolic network according to primitive reaction topological structure - Google Patents

Method for constructing dynamic metabolic network according to primitive reaction topological structure Download PDF

Info

Publication number
CN108021787B
CN108021787B CN201711294057.7A CN201711294057A CN108021787B CN 108021787 B CN108021787 B CN 108021787B CN 201711294057 A CN201711294057 A CN 201711294057A CN 108021787 B CN108021787 B CN 108021787B
Authority
CN
China
Prior art keywords
reaction
reaction rate
elementary
rate constants
michaelis
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201711294057.7A
Other languages
Chinese (zh)
Other versions
CN108021787A (en
Inventor
赵阔
潘天宇
魏冰洁
陈楚赟
仇隽
张丽梅
关岳
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
East China University of Science and Technology
Original Assignee
East China University of Science and Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by East China University of Science and Technology filed Critical East China University of Science and Technology
Priority to CN201711294057.7A priority Critical patent/CN108021787B/en
Publication of CN108021787A publication Critical patent/CN108021787A/en
Application granted granted Critical
Publication of CN108021787B publication Critical patent/CN108021787B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Classifications

    • G—PHYSICS
    • G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
    • G16B—BIOINFORMATICS, i.e. INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR GENETIC OR PROTEIN-RELATED DATA PROCESSING IN COMPUTATIONAL MOLECULAR BIOLOGY
    • G16B5/00—ICT specially adapted for modelling or simulations in systems biology, e.g. gene-regulatory networks, protein interaction networks or metabolic networks

Abstract

The invention discloses a dynamic metabolic network construction method, which comprises the steps of (a) finding out all isolated reactions and regulation and control reactions for a dynamic metabolic network to be constructed, and determining the number of redundant elementary reaction rate constants in each isolated reaction; (b) obtaining michaelis kinetic parameters of all isolated reactions and regulated reactions by in vitro experimental determination or from existing enzymology databases; (c/d) in each isolated reaction and regulation reaction, calculating the absolute value and/or relative value of all the other elementary reaction rate constants; (e) and (d) establishing a primitive reaction topological structure type dynamic metabolic network by using the primitive reaction rate constants obtained in the steps (c) and (d) through a computer. The method does not need to deduce the analytical formula of the michaelis dynamics rate equation one by one, obtains the elementary reaction rate constant related to the regulation and control reaction on the premise of thermodynamic equilibrium constant, is simple, and is suitable for a computer to construct a large-scale metabolic network.

Description

Method for constructing dynamic metabolic network according to primitive reaction topological structure
Technical Field
The invention belongs to the field of enzyme reaction kinetics, and particularly relates to a method for constructing a dynamic metabolic network according to a primitive reaction topological structure.
Background
Existing models for describing metabolic networks are largely divided into two categories: 1) a model of stoichiometry based on network topology (O' Brien, e.j.et., Cell,2015:161, 971-; schuster et al, Nature Biotechnology,2000:18, 326-); 2) a dynamic Metabolic network model of metabolite concentration, enzyme amount, and Metabolic regulation was introduced (Khodayari, a.et al, Metabolic engineering 2014,25: 50-62). The former involves only metabolic flow (i.e., reaction rate), the method is simple, but the information is limited; the latter is relatively comprehensive, but obtaining model parameters is a huge challenge.
With respect to dynamic metabolic network models, only the michaelis-kinetic-like rate equations are theoretical kinetic forms, as opposed to empirical or semi-empirical rate equations. The method comprises the steps of (a) performing steady-state assumption on an enzyme intermediate complex or performing rapid equilibrium assumption on a certain elementary reaction, (b) integrating the elementary reaction parameters by utilizing the mass action law of the elementary reaction to obtain an analytic expression of metabolite concentration and parameters, and further obtaining a series of rate equations, wherein a classical michaelis equation is a typical example. Parameters of the Michaelis kinetic class (e.g. k)cat,KmS,KmpEtc.) can be determined by in vitro experimental reaction rates, and the primitive reaction rate constant (k)i) It is generally not possible. Some professional enzymological data (e.g., BRENDA, SABIO-RK, etc.) are also compiled and included in the Michaelis-Menten parameters experimentally determined for decades. Such processing is not very difficult for single enzyme reactions using the mie kinetics-like rate equations, but reactions in metabolic networks often introduce interactions between effectors and enzymes (e.g., regulatory reactions), which are increasingly complex (sometimes no analytical expressions exist at all), and are not easily amenable to computer automation.
Disclosure of Invention
The invention aims to provide a novel method for constructing a metabolic network according to a primitive reaction topological structure, which can determine primitive reaction rate constants related to all enzyme reactions in the metabolic network through a single in-vitro reaction (namely isolated reaction) rate experiment so as to solve the problems that the primitive reaction rate constants are too much and cannot be completely determined through experiments.
The primitive reaction topological structure only has one form of mass action law, and as long as the network structure and the internal regulation function are proper and have kinetic parameters, the whole network construction process can be completely completed by a machine, so that a new method is provided for constructing a large dynamic metabolic network.
The dynamic metabolism network construction method comprises the following steps:
(a) for a dynamic metabolic network to be constructed, finding out all isolated reactions and regulation reactions, involved Michaelis kinetic parameters and elementary reaction rate constants, determining the number of independent kinetic parameters of each isolated reaction and regulation reaction, and further determining the number of redundant elementary reaction rate constants in each isolated reaction; wherein, the number of redundant elementary reaction rate constants in each isolated reaction and regulation reaction is the difference between the total number of the elementary reaction rate constants involved and the number of independent kinetic parameters;
(b) obtaining michaelis kinetic parameters of all isolated reactions and regulated reactions by in vitro experimental determination or from existing enzymology databases;
(c) in each isolated reaction, assigning values to redundant elementary reaction rate constants or determining the redundant elementary reaction rate constants as fixed constants by using the Michaelis kinetic parameters obtained in the step (b), and calculating absolute values or relative values of all other elementary reaction rate constants involved in the isolated reaction by combining the Michaelis kinetic parameters and the elementary reaction rate constants;
(d) in each regulation reaction, assigning values to redundant elementary reaction rate constants or determining the redundant elementary reaction rate constants as fixed constants by using the Michaelis kinetic parameters obtained in the step (b), and calculating the relative values of all the other elementary reaction rate constants involved in the regulation reaction by combining the Michaelis kinetic parameters and the elementary reaction rate constants;
(e) and (d) establishing a primitive reaction topological structure type dynamic metabolic network by using the primitive reaction rate constants obtained in the steps (c) and (d) through a computer.
In the step (e), the dynamic metabolic network of the motif reaction topology type includes a motif reaction rate formula of each complex of the metabolite and the enzyme and an enzyme amount constraint condition. As a general method, the construction of a metabolic network by using the topological dynamics of a motif reaction requires writing a motif reaction rate formula for a complex of each metabolite (including substrates and products) and an enzyme, eliminating all free enzyme concentrations by using enzyme quantity constraints, and then obtaining a dynamic curve of all metabolite concentrations by using software (such as the odefun function of MATLAB).
The construction of the dynamic metabolic network with the primitive reaction topological structure of the invention is illustrated by the following demonstration type metabolic network (the network cannot spontaneously reach the metabolic steady state, so the network is unreal) shown in the formula A, and the step-by-step primitive reaction of the demonstration type metabolic network is shown in the formula B.
Figure BDA0001499915240000021
In which 2 enzymes are involved (enzyme amounts and concentrations e respectively)0，1And e0，2) Involving 2 isolated reactions (i.e.single substrate single product reversible reactions v)1And double substrate double product irreversible reaction v2) And 2 regulatory reactions (i.e., v)3And v4). This network has a total of 6 "metabolites" (i.e., S)1，S2，S3，P1，P2，P3) 6 enzymes complex (i.e.E)1S1，E1P2，E2S2，E2P1，E2P3And E2S2S3) And 2 free enzymes (i.e., E)1And E2). Amount of enzyme e0，1And e0，2As a constraint, it is possible to eliminate 2 free enzyme concentrations (E)1) And (E)2)。
For the above-described demonstration-type metabolic network, the topological dynamics of the elementary reactions (equation (1)) consist of the following 12 ordinary differential equations (the number of ordinary differential equations is the sum of the number of metabolites and enzyme complexes):
Figure BDA0001499915240000031
Figure BDA0001499915240000032
Figure BDA0001499915240000033
Figure BDA0001499915240000034
Figure BDA0001499915240000035
Figure BDA0001499915240000036
Figure BDA0001499915240000037
Figure BDA0001499915240000038
Figure BDA0001499915240000039
Figure BDA00014999152400000310
Figure BDA00014999152400000311
Figure BDA00014999152400000312
the following 2 constraints can be used to eliminate the free enzyme concentration (E) in equation (1)1) And (E)2)：
e0，1＝(E1)+(E1S1)+(E1P2) (2-1)
e0，2＝(E2)+(E2S2)+(E2P3)+(E2P1)+(E2S2S3) (2-2)
In constructing the above metabolic network, it is necessary to determine each of the primitive reaction rate constants, and in the present invention, the primitive reaction rate constants are determined by the steps (a) to (d).
Comparing the topological structure of elementary reaction and the analytic formula of the Michaelis dynamic rate equation with the Michaelis dynamic parameters and the elementary reaction rate constants as parameters, the elementary reaction rate constants are completely the same. Independent Michaelis kinetic parameters of all isolated reactions and regulation reactions can be obtained through in vitro experimental determination or from the existing enzymology database, redundant elementary reaction rate constants are assigned or set as fixed constants, and absolute values or relative values of all elementary reaction rate constants related to the isolated reactions and relative values of all elementary reaction rate constants related to the regulation reactions can be calculated according to the relationship between the elementary reaction rate constants and the independent Michaelis kinetic parameters; and then combining the primitive reaction topological kinetic equation and the mass conservation constraint relation to construct a primitive reaction topological structure type dynamic metabolic network.
In step (a), each isolated reaction and the control reaction has its corresponding elementary reaction rate constant and number, for example, 3 elementary reaction rate constants for the enzyme-catalyzed single-substrate single-product irreversible reaction, 4 elementary reaction rate constants for the enzyme-catalyzed single-substrate single-product reversible reaction, 6 elementary reaction rate constants for the enzyme-catalyzed double-substrate double-product irreversible reaction, 8 elementary reaction rate constants for the enzyme-catalyzed double-substrate double-product reversible reaction, and two elementary reaction rate constants for the control reaction.
Although all of the elementary reaction rate constants are independent of each other for each isolated reaction and the control reaction, the fact that some or individual parameters can be regarded as constants when solving the equation of rate of michaelis dynamics with all of the elementary reaction rate constants as parameters indicates that some or individual parameters are redundant. This is a very specific type of parameter redundancy, which we call Redundant kinetic parameters (abbreviated RKP), hereinafter referred to as Redundant parameters. The remaining specific number of elementary reaction rate constants are Independent of each other in the solution, and the Independent elementary reaction rate constants are also called Independent Kinetic Parameters (IKP).
Similarly, the above independent kinetic parameters and redundant parameters are also present in the analytic formula of the michaelis equation with michaelis kinetic parameters as parameters. And no matter the independent kinetic parameters are the michaelis kinetic parameters or the michaelis kinetic rate equation analytic expression taking the elementary reaction rate constant as the parameter, the number of the independent kinetic parameters is not changed and is not changed along with the change of the used parameter types.
Preferably, therefore, the specific steps in step (a) for determining the number of independent kinetic parameters for each isolated reaction and for the regulatory reaction are: firstly, determining the number of independent kinetic parameters in each isolated reaction and regulation reaction through mathematical simulation according to two forms of analytical expressions of the Michaelis dynamics rate equation which respectively take Michaelis dynamics parameters and elementary reaction rate constants as parameters and the limiting conditions that the analytical expressions of the Michaelis dynamics rate equation have finite solutions.
Regarding how to determine the number of independent kinetic parameters, or how to determine the redundant elementary reaction rate constants and the number thereof, the following description will be made by taking an enzyme-catalyzed two-substrate two-product reversible reaction (i.e., Bi-Bi Ping Pong reversible reaction) and an enzyme-catalyzed single-substrate single-product irreversible reaction (i.e., Uni-Uni irreversible reaction) as examples, and further explaining how to solve the elementary reaction rate constants by using the michaelis kinetic parameters.
1. Bi-Bi Ping Pong reversible reaction
Can be composed of the following set of elementary reactions (or topologies),
Figure BDA0001499915240000041
wherein S1And S2As a substrate, P1And P2For the product, E and E' are free enzymes, ES1And E' S2Is 2 complexes of enzymes, k1～k4And k-1～k-4Is 8 elementary reaction rate constants.
The reaction has a total of 10 mie kinetic parameters, collectively referred to as M-M parameters, and a total of 2 classes. The first type of parameter is the catalytic constant kcat(if the reaction is reversible, then there are
Figure BDA0001499915240000043
And
Figure BDA0001499915240000047
) And the Michaelis constant Km(for the two-substrate two-product reversible reaction, there are
Figure BDA0001499915240000044
). A second type of parameter is proposed by Cleland (Cleland, W.W., Biochimica et Biophysica Acta 1963:67,104-137), which is generally the inhibition constant K of the enzymei(for a two-substrate two-product reversible reaction, this is possible
Figure BDA0001499915240000045
). In the analytical formula of the Michaelis dynamics rate equation, the first type of parameters must be used completely, and the second type of parameters can be used only when the first type of parameters are insufficient; there may be non-independent parameters in the second class of parameters. The Bi-Bi Ping Pong reversible reaction has 6 first type M-M parameters (namely
Figure BDA0001499915240000046
Figure BDA00014999152400000512
Figure BDA0001499915240000051
Figure BDA0001499915240000052
A second class of 4 (usually the suppression constants) is,
Figure BDA0001499915240000053
as an isolated reaction, the rate equation analytic formula v of the Bi-Bi Ping Pong reversible reaction can be expressed as,
Figure BDA0001499915240000054
alternatively, the first and second electrodes may be,
Figure BDA0001499915240000055
both equation (4-1) and equation (4-2) may be referred to as the Michaelis kinetic rate equation, but equation (4-1) uses a parameter that is the elementary reaction rate constant ki(i.e., all 8 ki) While the parameter used in equation (4-2) is the M-M parameter [ i.e., of the first type
Figure BDA0001499915240000056
Figure BDA0001499915240000058
And in the second class
Figure BDA0001499915240000059
And
Figure BDA00014999152400000510
(total 8)]。
This reaction involves only 8 independent elementary reaction rate constants (i.e., k)1，k2，k3，k4，k5，k6，k7，k8And) so the number of independent parameters IKPN is less than or equal to 8. However, equations (3-1) and (3-2) together define 10M-M parameters (redefined and reduced to M)1，M2，M3，M4，M5，M6，M7，M8，M9，M10) Therefore, there must be at least two constraint relations between the 10M-M parameters, i.e. at least twoThe M-M parameters are not independent. Since the 6M-M parameters in equation (3-1) must be compulsorily used as independent M-M parameters, IKPN ≧ 6. Accordingly, 6 ≦ IKPN ≦ 8, there are 3 possibilities (i.e., IKPN 6, 7, and 8).
As an axiom of algebra, to solve a set of n unknowns requires n independent and compatible equations. If at least one of the n equations is not independent, then an array-less solution exists for the system of equations. If at least one of the n equations is incompatible, then the system of equations is unsolved. If all of the equations in the system are linear, their solutions must be unique if they exist. Even if the equation set has a non-linear equation, a finite set of solutions with physical significance may exist on the premise of no unique solution.
As a first step to demonstrate the determination of IKPN, we first assume IKPN to be 8. Thus there should be 8 kiCan be divided into 8 independent MiAnd (5) resolving. For example by M1，M2，M3，M4，M5，M6，M7And M8Form a system of equations (5.1), i.e.
Figure BDA00014999152400000511
Thus, M does not enter the system of equations9And M10Then certainly not the independent M-M parameter, which is associated with kiThe relation of (A) is as follows,
M9＝f9(k1，k2，k3，k4，k5，k6，k7，k8)，M10＝f10(k1，k2，k3，k4，k5，k6，k7，k8) (5-2)
due to 6M in equation (3-1)iMust be taken as an independent M-M parameter, thus selecting any 2M in equation (5-2)iThere are 6 possibilities (i.e. there are no more than
Figure BDA0001499915240000061
). Considering 8M-M parameters as known quantities, 8 kiFor unknown quantities, the resulting solution (if present) must have the following form,
Figure BDA0001499915240000062
using equation (5.1), 2 independent Mie parameters M9And M10Can be characterized in the form of,
Figure BDA0001499915240000063
solving with the solve function of MATLAB, when n is 8, the above 8 equations cannot obtain a unique solution or a finite solution. From this, IKPN ≠ 8.
As a second step in demonstrating the determination of IKPN, we assume that n is 7. Select 7MiAs a known quantity, 7 k are selected againiAs an unknown quantity [ k remainingi(here, k8 is demonstrated) as a constant]Using a nonlinear equation set of 7 equations [ i.e. using 6M of equation (3-1) ]iAnd 1M in equation (3-2)i]。
Figure BDA0001499915240000067
Unused 3Mi(i.e. the attempted 3 independent M-M parameters) and its KiThe relation is as follows,
Figure BDA0001499915240000068
in equation set (7-1), M1，...M7And k1，...k7Should be an independent model parameter, M8，M9And M10Should be the M-M parameter not be independent. If M is8，M9And M10Indeed, not independent, then the arbitrary constant k in equation (7-2)8≡CMust disappear (i.e. the following equation (7-4)]. And M8，M9And M10Different, k8Independent of k1，...k7Any one of k in (1)iSo a parameter dependent form like equation (7-4) is not possible. In the case where equation (7-1) has a unique or finite solution, it is clear that k8Is no longer a model parameter, but an arbitrary constant completely independent of the model. For the Bi-Bi Ping Pong reaction, there is a unique solution to the above equation set (7-1), indicating that IKPN is 7. Such a set of unique solutions has the form,
Figure BDA0001499915240000065
due to M1，M2，M3，M4，M5，M6，M7Can be taken as 7 independent kinetic parameters, 3 Mi's not appearing in the above equation set can be completely and independently represented by the 7MiIs expressed in the form of a solution of,
Figure BDA0001499915240000066
for the Bi-Bi Ping Pong reversible reaction equation, one particular form of equation (7-4) is,
Figure BDA0001499915240000071
although 8 kiAre independent of each other, but k is used to solve equation (7-1)8The fact that can be considered as a constant illustrates k8Is already redundant. This is a very specific type of parameter redundancy, which we call Redundant kinetic parameters (abbreviated RKP).
The processing method of equation (7-1) demonstrates that 8 kiOne of which is redundant (i.e., RKP is present). With k-4Is RKP namely (k)-4≡C1) Other kiCan be determined by independent Mie's parametersAnd (4) obtaining. For the Bi-Bi Ping Pong reaction, the remaining 7 kiIt can be determined that the determination is that,
Figure BDA0001499915240000074
Figure BDA0001499915240000075
Figure BDA0001499915240000076
Figure BDA0001499915240000077
Figure BDA0001499915240000078
Figure BDA0001499915240000079
Figure BDA00014999152400000710
such as artificially given k-4≡C1＝10-6The 7 independent mie parameters obtained were determined experimentally (i.e., using
Figure BDA00014999152400000712
Figure BDA00014999152400000721
) All 8 elementary reaction rate constants kiIt is thus determined that,
Figure BDA00014999152400000714
Figure BDA00014999152400000715
Figure BDA00014999152400000716
Figure BDA00014999152400000717
Figure BDA00014999152400000718
Figure BDA00014999152400000719
Figure BDA00014999152400000720
k-4＝10-6 (9-8)
2. Uni-Uni irreversible reaction
The elementary reaction formula is as follows:
Figure BDA0001499915240000081
wherein S is a substrate, E is an enzyme, ES is a complex of the enzyme, and P is a product; k is a radical of1、k2And k3Is a primitive reaction kinetic parameter; the Michaelis kinetic parameters include Michaelis constant KmAnd catalytic constant kcat；k1、k2、k3And Km、kcatThere is a correlation that,
Figure BDA0001499915240000082
the enzyme reaction rate is expressed as v, eoIndicates the total concentration of enzyme E, [ S ]]Represents the concentration of the substrate S; under the assumption of quasi-steady state, the following elementary reaction kinetic equation is obtained by calculation,
Figure BDA0001499915240000083
substitution into KmAnd kcatThe equation of mie kinetics is obtained as follows,
Figure BDA0001499915240000084
determining the number of independent mie kinetic parameters to be 2 through simulation calculation; then the number of independent primitive reaction rate constants is also 2, and it can be seen that the number of redundant primitive reaction rate constants is 1.
The Mie's constant K can be determined by in vitro experimentsmAnd catalytic constant kcat(ii) a From k to kcat＝k2Direct solution to independent elementary reaction kinetic parameters k2(ii) a And k is1And k—1One of which is dependent and the other of which is independent, if any of which is taken as dependent motif the reaction rate constant is given any positive value, which is then compared with k2And substituting the two parameters into a constraint equation and solving to obtain another elementary reaction kinetic parameter.
For the relationship between the michaelis kinetic parameters and the elementary reaction rate constants of other types of independent reactions, the number of the independent kinetic parameters, and how to solve the elementary reaction rate constants through the michaelis kinetic parameters, the method is the same, and details are not repeated herein.
For the regulation and control reactions, any one regulation and control reaction has a terminal product, under the condition of metabolic steady state, the reaction flux must be zero, namely thermodynamic equilibrium is achieved, the number of independent kinetic parameters of each regulation and control reaction is 1, and the thermodynamic equilibrium constant of the regulation and control reaction is the Michaelis kinetic parameter. The regulation reaction in the formula (B) is v3And v4For example, its elementary reactionThe formula is as follows:
Figure BDA0001499915240000085
Figure BDA0001499915240000086
for E1And E2So long as E is obtained from the database1And P2，E2And P1Equilibrium constant of binding
Figure BDA0001499915240000087
Figure BDA0001499915240000088
Each regulatory response increased by 1 IKP, where 2 regulatory responses increased by 2 IKP. Can see k7And k8Is 2 pieces of IKP, so that k is-7And k-8It becomes 2 RKPs (i.e. redundant parameters). For redundant k-7And k-8The arbitrary assignments are: k is a radical of-7＝C2，k-8＝C3From this we get k7And k8The values of (A) are: k is a radical of7＝C2Keq1，k8＝C3Keq2. For example, given k artificially-7≡C2＝10-6，k-8≡C3＝10-6Then all 4 elementary reaction rate constants k involved in the regulatory reactioniIt is thus determined that,
k7＝10-6Keq1 (10-1)k-7＝10-6 (10-2)k8＝10-6Keq2 (10-3)k-8＝10-6(10-4)
after the absolute value and/or the relative value of the elementary reaction rate constant of each independent reaction and regulation reaction obtained by the method is solved, the elementary reaction topological dynamic equation and the mass conservation constraint relation are combined to construct the elementary reaction topological structure type dynamic metabolic network.
The positive progress effects of the invention are as follows: after determining the redundant elementary reaction rate constants and the number thereof, the special elementary reaction rate constants can be assigned or determined as fixed constants, and the rest elementary reaction rate constants can be obtained according to the relation between the mie kinetic parameters and the elementary reaction rate constants by utilizing the mie kinetic parameters measured by experiments without deducing an analytic expression of the mie kinetic rate equation one by one, and the elementary reaction rate constants involved in the regulation and control reaction are simpler to obtain on the premise of thermodynamic equilibrium constants, so that the method is suitable for a computer to construct a large-scale metabolic network. The method can comprehensively calculate the elementary reaction kinetic parameters through the mie kinetic parameters measured by in vitro experiments or by utilizing the information of the existing database, not only can accurately and quantitatively describe the metabolic network, but also is convenient for computer automation operation, thereby enabling the construction of the large in silico metabolic network by using the elementary reaction to become possible.
Detailed Description
Example 1
Enzyme reaction: glucose 6 phosphate → fructose 6 phosphate, the enzyme is glucose phosphate isomerase with a molecular weight of 12000 Da.
The reaction is a single-substrate single-product irreversible reaction, and the elementary reaction formula is as follows,
Figure BDA0001499915240000092
wherein S represents glucose-6-phosphate, E represents glucose-phosphate isomerase, P represents fructose-6-phosphate, EP represents an enzyme complex, k1、k2And k3Is the elementary reaction rate constant.
Under the pseudo-steady state assumption, the elementary reaction kinetic equation is as follows:
Figure BDA0001499915240000093
whereas the classical mie equation for the substrate per product reaction is:
Figure BDA0001499915240000094
wherein the Michaelis kinetic parameters include the Michaelis constant KmAnd catalytic constant kcat。
k1、k2、k3And Km、kcatThere is a correlation that,
Figure BDA0001499915240000095
and the Mie constant K can be obtained through experimentsmAnd catalytic constant kcatThe method specifically comprises the following steps:
taking the double reciprocal of the Mie equation to obtain:
Figure BDA0001499915240000101
taking different substrate concentrations [ S]1，[S]2，…，[S]nThe reaction rate v can be determined1，v2…, and vnTo do so by
Figure BDA0001499915240000102
To pair
Figure BDA0001499915240000103
Plotting a line whose intercept with the transverse axis
Figure BDA0001499915240000104
Thereby obtaining Km(ii) a Intercept of longitudinal axis
Figure BDA0001499915240000105
Thereby obtaining Vmax. K was determined at 25 ℃ and pH 7 for 0.08g of pure enzymem＝60.25mM，Vmax＝10.60mMs-1，kcat＝1590s-1。
Further combining with
Figure BDA0001499915240000106
Therefore, the following steps are carried out:
k2＝kcat＝1590s-1and k is1And k-1One of which is a redundancy parameter, optionally one of which is, e.g., k1As a redundant parameter, then k is solved for1Can be regarded as a constant, and k can be obtained-1＝Km*k1-k2According to definition, k can be given1Given any positive value, k can be obtained-1. As a result, any k that satisfies the two constraint relationships described above1And k-1(which by definition should be greater than zero), i.e.a dynamic solution, will cause the same change in the rate of the enzymatic reaction. While the reaction rate characterized by the above 3 elementary reaction rate constants is exactly the same as the reaction rate expressed entirely in true values.
It can be seen that k obtained above2And k is1And k-1The dynamic solution of (a) can be used to characterize the enzymatic reaction: glucose 6 phosphate → fructose 6 phosphate. By the same method, other reactions of the same type or different types are solved one by one to obtain dynamic solutions capable of representing corresponding reactions, the dynamic solutions can be used for constructing a dynamic metabolic network, and the whole process does not need to deduce a michaelis dynamics type rate equation analytic expression one by one. And under the premise of thermodynamic equilibrium constant, the elementary reaction rate constant related to the obtained regulation reaction is relatively simple, and the method is suitable for constructing a large-scale metabolic network by a computer.

Claims (2)

1. A method for constructing a dynamic metabolic network based on a primitive reaction topology, the method comprising the steps of:
(a) for a dynamic metabolic network to be constructed, finding out all isolated reactions and regulation reactions, involved Michaelis kinetic parameters and elementary reaction rate constants, determining the number of independent kinetic parameters of each isolated reaction and regulation reaction, and further determining the number of redundant elementary reaction rate constants in each isolated reaction;
wherein, the number of redundant elementary reaction rate constants in each isolated reaction and regulation reaction is the difference between the total number of the elementary reaction rate constants involved and the number of independent kinetic parameters;
(b) obtaining michaelis kinetic parameters of all isolated reactions and regulated reactions by in vitro experimental determination or from existing enzymology databases;
(c) in each isolated reaction, assigning values to redundant elementary reaction rate constants or determining the redundant elementary reaction rate constants as fixed constants by using the Michaelis kinetic parameters obtained in the step (b), and calculating absolute values or relative values of all other elementary reaction rate constants involved in the isolated reaction by combining the Michaelis kinetic parameters and the elementary reaction rate constants;
(d) in each regulation reaction, assigning values to redundant elementary reaction rate constants or determining the redundant elementary reaction rate constants as fixed constants by using the Michaelis kinetic parameters obtained in the step (b), and calculating the relative values of all the other elementary reaction rate constants involved in the regulation reaction by combining the Michaelis kinetic parameters and the elementary reaction rate constants;
(e) building a primitive reaction topological structure type dynamic metabolic network by a computer by using the primitive reaction rate constants obtained in the steps (c) and (d);
wherein the specific steps of determining the number of independent kinetic parameters of each isolated reaction and regulation reaction in step (a) are as follows: firstly, determining the number of independent kinetic parameters in each isolated reaction and regulation reaction through mathematical simulation according to two forms of analytical expressions of the Michaelis dynamics rate equation which respectively take Michaelis dynamics parameters and elementary reaction rate constants as parameters and the limiting conditions that the analytical expressions of the Michaelis dynamics rate equation have finite solutions;
the enzyme-catalyzed double-substrate double-product reversible reaction is composed of the following elementary reaction groups:
Figure FDA0003201733290000021
wherein S1And S2As a substrate, P1And P2For the product, E and E' are free enzymes, ES1And E' S2Is 2 of enzymeCompound, k1～k4And k-1～k-4Is 8 elementary reaction rate constants;
the elementary reaction formula of the enzyme-catalyzed single-substrate single-product irreversible reaction is as follows:
Figure FDA0003201733290000022
wherein S is a substrate, E is free enzyme, ES is a complex of the enzyme, and P is a product; k is a radical of1、k2And k3Is the elementary reaction rate constant; the Michaelis kinetic parameters include Michaelis constant KmAnd catalytic constant kcat；k1、k2、k3And Km、kcatThere is a correlation that,
Figure FDA0003201733290000023
kcat＝k2
the enzyme reaction rate is expressed as v, eoIndicates the total concentration of enzyme E, [ S ]]Represents the concentration of the substrate S; under the assumption of quasi-steady state, the following elementary reaction kinetic equation is obtained by calculation,
Figure FDA0003201733290000024
substitution into KmAnd kcatThe equation of mie kinetics is obtained as follows,
Figure FDA0003201733290000025
the number of independent mie kinetic parameters is determined to be 2 through simulation calculation, so that the number of independent elementary reaction rate constants is also 2, and further, the number of redundant elementary reaction rate constants is known to be 1.
2. The method of claim 1, wherein in step (e), the motif reaction topology-based dynamic metabolic network comprises a motif reaction rate formula for each complex of a metabolite and an enzyme amount constraint.
CN201711294057.7A 2017-12-08 2017-12-08 Method for constructing dynamic metabolic network according to primitive reaction topological structure Active CN108021787B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201711294057.7A CN108021787B (en) 2017-12-08 2017-12-08 Method for constructing dynamic metabolic network according to primitive reaction topological structure

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201711294057.7A CN108021787B (en) 2017-12-08 2017-12-08 Method for constructing dynamic metabolic network according to primitive reaction topological structure

Publications (2)

Publication Number Publication Date
CN108021787A CN108021787A (en) 2018-05-11
CN108021787B true CN108021787B (en) 2021-10-15

Family

ID=62079047

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201711294057.7A Active CN108021787B (en) 2017-12-08 2017-12-08 Method for constructing dynamic metabolic network according to primitive reaction topological structure

Country Status (1)

Country Link
CN (1) CN108021787B (en)

Families Citing this family (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111341382B (en) * 2020-02-20 2023-04-18 江南大学 Macroscopic dynamics and cell metabolism flux coupling modeling method in lysine biological manufacturing
US20220148684A1 (en) * 2020-11-09 2022-05-12 X Development Llc In silico enzymology

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP0647450A1 (en) * 1993-09-09 1995-04-12 BEHRINGWERKE Aktiengesellschaft Improved prodrugs for enzyme mediated activation
EP1102861A1 (en) * 1998-08-05 2001-05-30 University Of Pittsburgh Modelling organic compound reactivity in cytochrome p450 mediated reactions
CN103714432A (en) * 2013-12-30 2014-04-09 南京大学 Method for predicating biomass of submerged plant by establishing growth simulation model
CN105447337A (en) * 2015-11-13 2016-03-30 大连理工大学 Time sequence data processing method based on dynamic network diagram analysis
CN105574358A (en) * 2015-12-14 2016-05-11 华东理工大学 System for reproducing in vivo reaction in vitro

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP0647450A1 (en) * 1993-09-09 1995-04-12 BEHRINGWERKE Aktiengesellschaft Improved prodrugs for enzyme mediated activation
EP1102861A1 (en) * 1998-08-05 2001-05-30 University Of Pittsburgh Modelling organic compound reactivity in cytochrome p450 mediated reactions
CN103714432A (en) * 2013-12-30 2014-04-09 南京大学 Method for predicating biomass of submerged plant by establishing growth simulation model
CN105447337A (en) * 2015-11-13 2016-03-30 大连理工大学 Time sequence data processing method based on dynamic network diagram analysis
CN105574358A (en) * 2015-12-14 2016-05-11 华东理工大学 System for reproducing in vivo reaction in vitro

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
Dynamic Simulations on the Arachidonic Acid Metabolic Network;Kun yang等;《PLoS Computational Biology》;20070323;第3卷(第3期);第523-530页 *
核苷糖供体代谢网络建模及其在单克隆抗体生产中的应用探索;李玉书;《中国优秀硕士学位论文全文数据库 医药卫生科技辑》;20170315(第3期);第E059-195页 *

Also Published As

Publication number Publication date
CN108021787A (en) 2018-05-11

Similar Documents

Publication Publication Date Title
Österlund et al. Mapping condition-dependent regulation of metabolism in yeast through genome-scale modeling
Papp et al. Systems-biology approaches for predicting genomic evolution
Mukhopadhyay et al. Causality and pathway search in microarray time series experiment
Kim et al. The validity of quasi-steady-state approximations in discrete stochastic simulations
Polisetty et al. Identification of metabolic system parameters using global optimization methods
Latendresse et al. Accurate atom-mapping computation for biochemical reactions
Savoglidis et al. A method for analysis and design of metabolism using metabolomics data and kinetic models: Application on lipidomics using a novel kinetic model of sphingolipid metabolism
Qian Cooperativity and specificity in enzyme kinetics: a single-molecule time-based perspective
Costa et al. Kinetic modeling of cell metabolism for microbial production
CN108021787B (en) Method for constructing dynamic metabolic network according to primitive reaction topological structure
Goličnik Exact and approximate solutions for the decades‐old Michaelis‐Menten equation: Progress‐curve analysis through integrated rate equations
Xu et al. Mathematical exploration on control of bifurcation for a plankton–oxygen dynamical model owning delay
Fell et al. Building and analysing genome-scale metabolic models
Shuler et al. Modeling a minimal cell
Gudmundsson et al. Recent advances in model-assisted metabolic engineering
Zhang et al. Parallel isotope differential modeling for instationary 13C fluxomics at the genome scale
Maeda et al. Quasi-multiparameter sensitivity measure for robustness analysis of complex biochemical networks
CN108984925B (en) Parallel computing method for integrated simulation analysis of reliability of electronic product
Lin et al. Theoretical and computational studies of the glucose signaling pathways in yeast using global gene expression data
Gautam et al. Construction and validation of a genome-scale metabolic network of Thermotoga sp. strain RQ7
CN109801676B (en) Method and device for evaluating activation effect of compound on gene pathway
Clement et al. On a queueing theory method to simulate in-silico metabolic networks
Xu et al. Modeling the temporal dynamics of master regulators and CtrA proteolysis in Caulobacter crescentus cell cycle
Chis et al. Methods for checking structural identifiability of nonlinear biosystems: A critical comparison.
CN108945526A (en) A kind of Racemization control method and system of inert satellite

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant