JPH04304553A - Method and device for simulating biological reaction - Google Patents

Abstract

PURPOSE:To obtain a simulation method and device having general applicability by which the reaction development of a reaction system including a nonlinear element can be easily and conveniently simulated. CONSTITUTION:A first arithmetic means 120 operates a data smoothing processing to experimental data, and prepares data base for simulation constituted of each variable and the specific speed. A second arithmetic means 310 successively searches a reaction rate equation parameter from the data by a method of least squares, so that the simulation can be operated. It is to be desired that an interpolation by a cubic spline function and the presumption of the specific speed are operated as the data smoothing processing, and that a primary regression type is used as the reaction rate equation.

Description

[Detailed description of the invention]

0001

[Field of Industrial Application] The present invention relates to a method and an apparatus for predicting the course of a reaction in a reaction system containing nonlinear elements, and more particularly, the present invention relates to a method and an apparatus for predicting the course of a reaction in a reaction system containing nonlinear elements, and more particularly, the present invention relates to a method and an apparatus for predicting the reaction progress of a reaction system containing nonlinear elements, and more particularly, to The present invention relates to a biological reaction simulation method and apparatus for predicting reaction progress.

0002

[Prior Art] Conventionally, when simulating the reaction progress of a reaction system including nonlinear elements such as a biological reaction, a mono (Mon) reaction rate equation (biological growth rate equation) has been used.
Deterministic unstructured models represented by od) equations or structured models that construct model equations by subdividing biological reactions based on in-vivo reactions are used, and appropriate reaction equation models are created for each organism. Biological reactions were predicted by determining the parameters of these reaction equation models from experimental data and solving them using numerical calculation methods.

[0003] Among the conventional techniques mentioned above, regarding the calculation of a deterministic unstructured model represented by the Monod equation as a reaction rate equation, for example, ``Biochemical Engineering (written by Shuichi Aiba and Shiro Nagai)
178 and 179 of ``Science and Technology Publishing Co., Ltd., published in 1975''. However, deterministic unstructured models greatly simplify complex biological reactions, resulting in large errors in prediction calculation results, and biological reactions that use a single reaction equation from the start to the end of the reaction. When carrying out batch culture or fed-batch culture, it was difficult to apply because the characteristics of the organism change as the reaction time progresses. On the other hand, regarding structured models, for example, "Biotechnology and Bioengineering (BIOTECHN)"
OLOGY AND BIOENGINEERING)
As stated on pages 160 to 184 of "Volume 35," we analyze in detail the reactions occurring within living organisms, determine each of these reactions one by one, and then analyze them. A model is constructed by synthesizing them. However, the more faithfully this structured model models in-vivo reactions, the more complicated it becomes, and the more difficult it becomes to determine parameters and calculate, the more it loses its practicality. In addition, all of the above models have the problem of not being able to accurately represent properties unique to biological reactions, such as changes in characteristics due to biological improvement and breeding, changes in properties over time, and nonlinearity of reactions. Furthermore, since the characteristics of each target microorganism must be taken into account, it is necessary to consider a model that fits each individual, which requires a great deal of effort and is a major obstacle to simulating biological reactions.

0004

[Problems to be Solved by the Invention] Therefore, it is an object of the present invention to develop a biological reaction system that can be applied to reaction systems in general that include nonlinear elements, without the need to form reaction equation models individually for each organism as in the past. An object of the present invention is to provide a method and a device for predicting progress.

Furthermore, an object of the present invention is to improve the ability to improve characteristics of living organisms through breeding, and to reduce changes over time that occur particularly in batch culture, fed-batch culture, etc., compared to cases that rely on conventional reaction equation models. It is an object of the present invention to provide a biological reaction simulation method and apparatus that can easily and accurately simulate nonlinear elements such as changes in characteristics, and therefore have smaller errors in predictive calculation results than conventional methods.

Furthermore, it is an object of the present invention to develop a biological reaction model that does not require the creation of individual reaction equation models for each organism, and is easy to calculate, thus significantly reducing labor and costs. An object of the present invention is to provide a simulation method and apparatus.

[0007]

[Means for Solving the Problems] As a result of various studies in order to solve the above problems, the present inventors have developed a method and apparatus for universally simulating the reaction progress of a reaction system containing nonlinear elements. A simulation method and device that does not require the construction of a reaction equation model for each biological reaction, is faithful to experimental data as much as possible, is applicable to strongly nonlinear reaction systems, and can sufficiently counter changes in bacterial characteristics, etc. This is what made it possible.

That is, the present invention is a method for simulating the reaction progress of a reaction system containing nonlinear elements,
Smoothing processing is applied to the input experimental data of the reaction system, the results are stored as a database, and the period from the start to the end of the reaction system is divided into multiple simulation sections, and The method is characterized by comprising steps of performing regression processing on each of the simulation intervals based on initial conditions, a regression equation model selected in advance, and a plurality of data related to each simulation interval selected from the database. This provides a method to do this.

Furthermore, from another viewpoint of the present invention, there is provided a simulation apparatus for the reaction progress of a reaction system including nonlinear elements, which comprises an input means for inputting experimental data of the reaction system, and an input means for inputting experimental data of the reaction system; a first calculation means for performing smoothing processing on the experimental data; a storage means for storing the experimental data subjected to the smoothing processing as a database; Divide into a plurality of simulation intervals and perform regression processing for each simulation interval based on preset initial conditions, a preselected regression equation model, and a plurality of data related to each simulation interval selected from the database. and second calculation means for performing the calculation.

[0010] The present invention is directed to protozoa, bacteria, yeast,
Biological reactions that use microorganisms such as algae and fungi or animal, plant, and insect cells to produce target products or the microorganisms and animal, plant, and insect cells themselves by methods such as batch reactions, fed-batch culture, filtration culture, and continuous culture. This method is particularly suitable for reaction systems containing nonlinear elements.

When numerical values of experimental data are input based on the present invention, it is only necessary that the numerical values can be stored in the first arithmetic unit according to a predetermined input format. There are methods of inputting from an auxiliary storage device such as a disk, or online inputting from a data measuring device.

The smoothing process according to the present invention can be comprised of interpolation of experimental data by function approximation and estimation of specific speed based on the result. The function approximation in this case only needs to be able to smooth the data, and for example, calculation methods such as spline functions, least squares approximation, and Lagrange interpolation can be used, but function approximation using spline functions is more preferable. . The results of the function approximation are used to calculate specific rates of each experimental data, such as specific substrate consumption rate, specific growth rate, specific product production rate, etc.

The regression process based on the present invention is performed by dividing the reaction system from the start to the end into a plurality of simulation intervals, and is carried out for each interval, and the specific substrate consumption rate, specific growth rate, Rate equations such as specific product production rate are approximated by linear regression equations. The coefficients of the regression equation are calculated using statistical methods. In this case, the independent variables of the linear regression equation are selected from the initial conditions, the coefficients of the regression equation are determined by the least squares method using multiple data related to each simulation interval selected from the database, and the coefficients of the regression equation are determined from the equation. - The course of biological reactions can be predicted by obtaining solutions using numerical calculation methods such as the Kutta method.

Furthermore, according to the present invention, it is also possible to display numerically and graphically the calculation results of the smoothing process and the regression process. In this case, the calculation results can be displayed on a CRT, for example.
, and output to an auxiliary storage device such as a printer or floppy disk.

The present invention will be explained in more detail below with reference to the drawings.

FIG. 1 is a block diagram showing an overview of one embodiment of the present invention. Measured values such as the experiment number, measurement time, bacterial cell concentration, substrate concentration, and product concentration obtained from the experimental results of the target biological reaction are input from the experimental data input means 110. The input experimental data is sent to the first calculation means 12.
0, smoothing processing is performed, and the result is stored in a database in storage means 210. The second calculation means 310 uses the data stored in the storage means 210 to simulate the reaction progress of the target biological reaction by a statistical method, and the result is displayed on the display means 320.

FIG. 2 shows the first calculation means 120 in the present invention.
2 is a flowchart showing details of. Experimental or operational data such as bacterial cell concentration, substrate concentration, and product concentration of the target biological reaction inputted by the input means 110 are smoothed by the first calculation means 120 . That is, the inputted experimental or operational data is subjected to function approximation by interpolation processing 122, and furthermore, the estimation 123 of specific speeds such as specific substrate consumption rate, specific growth rate, specific product production rate, etc. is performed using the results of this function approximation. These results are then stored in the storage means 210. The above series of processes is repeated under various experimental conditions, and is composed of various data such as substrate concentration, bacterial cell concentration, product concentration, specific substrate consumption rate, specific growth rate, specific product production rate, etc. at each predetermined time step. A database will be constructed. As a function approximation method using interpolation processing, it is sufficient if smoothing of data can be achieved, such as spline function,
Although calculation methods such as least squares approximation and Lagrange interpolation can be used, a successive division method using a spline function, particularly a cubic spline function, is suitable. Further, as methods for estimating the specific speed, there are two methods: calculating by taking a difference and calculating by first-order differentiation of a cubic spline function, but the method of calculating by calculating the difference is more suitable. By creating a database by smoothing the experimental data in this way, it is possible to reduce errors caused by variations and missing data that would otherwise occur when using raw data directly, and to calculate specific speeds with high precision and efficiency. It becomes possible to create a database.

FIG. 3 shows details of the database in the storage means 210 in the present invention. The database of each experiment created by the first calculation means includes substrate concentration, bacterial cell concentration, product concentration, specific substrate consumption rate, specific growth rate, Data such as specific product production rate, flow rate, experimental conditions, etc. are stored. These data are selected and used by the second calculation means as necessary.

FIG. 4 shows the second calculation means 310 in the present invention.
2 is a flowchart showing details of. In order to simulate the reaction progress of a reaction system including nonlinear elements in the second calculation means 310, the elapsed time from the start to the end of the experiment is divided into a plurality of simulation intervals, and a regression equation model is determined for each interval. However, it is necessary to perform simulations for each section based on the obtained reaction rate equation. First, in step 311, values such as substrate concentration and bacterial cell concentration at the time of culture initiation are input as initial conditions. Next, a simulation for the first simulation section is performed through 312 to 316. Furthermore, the simulation interval is incremented and the second
The same processing as the first simulation section is performed for the simulation section, and the reaction progress is estimated. A similar procedure is sequentially repeated from the start to the end of the experiment, and a simulation of the entire reaction process of the target reaction system is executed.

Next, the simulation method for each simulation section will be explained in detail. Basically, in 312, a predetermined regression equation model and 3
Simulation calculations are performed based on the initial conditions set in step 11 and the data smoothed by the first calculation means and stored in the storage means 210. 312
It is preferable to use a first-order regression equation as a reaction rate equation as the regression equation model selected in , and the independent variables include substrate concentration, bacterial cell concentration, and respiration rate depending on the characteristics of the target reaction. Select the appropriate one in advance. For example, if the independent variables of the reaction equation for the specific growth rate μ are the bacterial cell concentration X and the substrate concentration S, the format of the equation is:

[0021]

[Math 1]

It becomes as follows. Then at 313 3
As data for determining the coefficients of the 12 regression equations, neighborhood data of a predetermined simulation interval is stored in the storage means 21.
Selected from among the data stored in 0. The selection of neighboring data is performed by calculating the Euclidean distance from the start point of a predetermined simulation section to each data stored in the storage means 210, and selecting about 6 to 12 points from the shortest distance. conduct. Based on the selected neighborhood data, a multiple regression calculation is performed in 314 to determine the coefficients of the regression equation. The reaction rate equation determined in this way is substituted into the mass balance equation in 315,
Then, at 316, a numerical calculation method such as the Runge-Kutta method is used to solve the equation, completing the simulation for the simulation interval. The simulation interval is then incremented at 317 and the same procedure is repeated for the next simulation interval. When this procedure is repeated until the simulation interval reaches a predetermined experimental end point, the algorithm is terminated at 318. In this way, the simulation of the entire reaction course of the desired reaction system is completed. In addition, when performing fed-batch culture, by specifying the substrate feeding method as the initial condition, it is possible to obtain case studies for various fed-batch conditions. The simulation results are
The data is output to a display means such as a CRT, printer, or auxiliary storage device for later use.

[0023]

[Examples] The present invention will be specifically explained below with reference to Examples.

The target biological reaction was Bacillus subtilis.
The production of α-amylase by S. lus Amyloliquefacience. α-Amylase production by Bacillus subtilis is a highly nonlinear reaction in which α-amylase is produced rapidly as glucose is depleted, with almost no production during the lag phase and logarithmic growth phase when the substrate concentration is high because it is inhibited by catabolites.

[Example 1] Production of α-amylase was simulated using the simulation method and apparatus based on the present invention shown in FIG. The above-mentioned batch culture and fed-batch culture experiments were carried out 10 times using a conventional culture tank while changing conditions such as initial substrate concentration and substrate feeding method. Examples of experimental data are shown in Table 1.

[0026]

[Table 1]

The experimental results shown in Table 1 were input using an input device. These data were subjected to calculations by the first calculation means, and the results were stored in a database in the storage means. Table 2 shows an example of the database.

[0028]

[Table 2]

Next, a regression equation model of this reaction system in the second calculation means will be shown.

[0030]

[Math 2]

[0031] The coefficients of these regression equation models are determined hourly by multiple regression analysis using the database in the storage means, and a simulation is performed using the model equations.
This was repeated until the end of the culture, which was 24 hours. A batch culture experiment was conducted with an initial substrate concentration of 10 gr/l as the initial condition.
A simulation was performed based on the present invention. FIG. 5 shows an example in which the results are displayed on a display means.

[0032] Each plot shows the experimental results, and the solid line shows the results of the simulation based on the present invention. It can be seen that as glucose is depleted, catabolite suppression is released and α-amylase production begins, and that the bacterial cells peak out and decline can be well simulated.

[Example 2] Figure 6 shows the results of simulating the results of a fed-batch culture experiment using this bacterium based on the present invention.
Shown below. Substrate feeding time was 10 hours from 4th to 14th hour;
The flow rate is set to 1.0 (gr-glucose/L·HR). Note that the same database as in Example 1 was used. It has been shown that the present invention makes it possible to obtain good simulation results even when relatively complicated culture operations such as such fed-batch culture are performed.

[Comparative Example] This is a simulation of the same experiment as in Example 2, but unlike the present invention, the first calculation means was not used when creating the database (that is, the data smoothing process using the spline function was not performed). ), and the results of a simulation based on a manually created database are shown in Figure 7. Since there was a large error in estimating the specific speed, the curve of the simulation result in the second calculation means was not smooth, and it took a great deal of effort and time to create the database.

[0035]

EFFECT OF THE INVENTION As is clear from the above explanation, the present invention makes it possible to realize various functions that were previously impossible in predicting the state of biological reactions. That is, according to the simulation method and apparatus based on the present invention, (1)
Simulation is possible by solving a regression equation approximation model using a statistical method without requiring the creation of reaction model equations that take into account the characteristics of individual biological reactions. (2)
A simulation database can be easily and accurately created without errors due to variations in experimental data. (3) It is fully applicable to nonlinear reaction systems such as protein production. (4) It can also be applied to unsteady reactions such as batch culture and fed-batch culture. (5) Various case studies can be conducted by changing operating conditions, substrate feeding conditions, etc. It has many great advantages such as: Furthermore, while conventional simulations required about 10 days from obtaining experimental data to creating a database and performing simulations, the method and apparatus of the present invention can be used to complete the process in half a day or even one day.
Significant savings in time and effort can be achieved.

[Brief explanation of the drawing]

FIG. 1 is a block diagram schematically showing a simulation method and apparatus based on the present invention.

FIG. 2 is a flowchart showing an algorithm for smoothing processing executed in the first calculation means of FIG. 1;

FIG. 3 shows a database stored in the storage means of FIG. 1;

FIG. 4 is a flowchart showing an algorithm of a simulation procedure executed in the second calculation means of FIG. 1;

FIG. 5 is a graph showing the results of a simulation of α-amylase production by a batch culture method based on the present invention.

FIG. 6 is a graph showing simulation results when a fed-batch culture experiment was conducted based on the present invention.

FIG. 7 is a graph showing the simulation results of an experiment similar to FIG. 6, but in the case where the database was created manually without using the present invention.

[Explanation of symbols]

110...Input means 120...first calculation means 210...Storage means 310...Second calculation means 320...display means

Claims (12)

[Claims] 1. A method for simulating the reaction progress of a reaction system including nonlinear elements, wherein inputted experimental data of the reaction system is subjected to smoothing processing, and the results are stored as a database. Divide the reaction system from the start point to the end point into multiple simulation sections,
performing regression processing on each of the simulation intervals based on preset initial conditions, a preselected regression model, and a plurality of data related to each simulation interval selected from the database;
A method characterized in that it consists of each step. 2. The method according to claim 1, further comprising the step of outputting and displaying the results of regression processing for each of the simulation intervals. 3. The method according to claim 1, wherein the smoothing process consists of interpolating the experimental data by function approximation and estimating the specific speed based on the result. 4. Selection of a plurality of data associated with each of the simulation intervals from the database comprises: calculating a Euclidean distance from the start of a given simulation interval to each data stored in the database;
4. The method according to claim 1, wherein the method is carried out by selecting a predetermined number of shortest distances. 5. The regression process uses a linear regression equation as the regression equation model, selects an independent variable from the initial conditions, and is further based on a plurality of data related to each simulation interval selected from the database. 5. The method according to claim 1, wherein the method is carried out by determining coefficients and solutions of the regression equation. 6. The reaction system including the nonlinear element is a biological reaction that uses microorganisms or animal and plant cells to obtain a target product, or a reaction that obtains the microorganism or animal and plant cells themselves. 6. The method according to any one of 1 to 5. 7. A simulation device for the reaction progress of a reaction system including nonlinear elements, comprising an input means for inputting experimental data of the reaction system, and a smoothing process applied to the inputted experimental data. a first calculation means for storing the smoothed experimental data as a database; and a storage means for storing the experimental data subjected to the smoothing process as a database; a second step for performing regression processing on each simulation interval based on set initial conditions, a preselected regression equation model, and a plurality of data related to each simulation interval selected from the database;
A device characterized in that it consists of a calculation means. 8. The apparatus according to claim 7, further comprising display means for displaying the results of regression processing for each of the simulation sections. 9. The smoothing process in the first calculation means comprises interpolation of the experimental data by function approximation and estimation of specific speed based on the result. The method described in. 10. The second calculation means selects a plurality of data related to each simulation interval from the database based on the Euclidean distance from the start of a predetermined simulation interval to each data stored in the database. 10. The method according to claim 7, wherein the method is carried out by calculating a predetermined number of shortest distances. 11. The regression processing in the second calculation means uses a linear regression equation as the regression equation model, selects an independent variable from the initial condition, and further relates to each simulation interval selected from the database. Claims 7 to 1, characterized in that the regression equation is performed by determining coefficients and solutions of the regression equation based on a plurality of data.
0. The method according to any one of 0. 12. The reaction system including the nonlinear element is a biological reaction that uses microorganisms or animal or plant cells to obtain a target product, or a reaction that obtains the microorganism or animal or plant cell itself. 12. The method according to any one of 7 to 11.