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The Modeling Techniques to Simulate Cellular Networks and Systems

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Biotechnology is the use of living organisms for the welfare of mankind. Biotechnology refers to the understanding the metabolism of cells, also considers the characteristics of individual bio-molecules and their job in interaction networks. Mathematical modeling has become an important element to understand the complexity of biology. Mathematical fields such as calculus, statistics, algebra, various types of equations are now used in the field of biotechnology.

Mathematics plays a key role in many disciplines of science, as a mathematical modeling tool. Mathematical models describe us the past performance and predict the future performance of biotechnological processes. Mathematics provides logic rather than faith and helps in quantification. Without math biology would never have been a modern science and biotechnology never had taken the first step. Mathematics is use to do routine lab activities like cloning or to run a gel or PCR or to operate an HPLC. We also want to scale up the recombinant product or to do a genomic analysis of an isolate gene or to understand a reaction we must need a lot of mathematics for calculations or estimations.There is a field of Mathematics known as ‘Biostatistics and Probability’ which have application in the field of biotechnology. Basic statistics are also involved in subjects like Genetics, Bioinformatics and Research Methodology. There are many fields of mathematics now in biology like biomathematics.

Application Of Mathematics In Biotechnology

Mathematics plays an important role in the field of biotechnology. Mathematics is the strong indicator of success in the field of biotech in the field of industry or academia. The whole world of science and technology talks about the language of mathematics at some level. Mathematics most definitely refers to the areas of biotechnology like bioinformatics, biochemical engineering, systems biology, biostatistics, instrumentations etc.Mathematics is also so helpful for deeper understanding of biotechnology itself. Because there is a lot of connection between every field like a layer below biology is chemistry, than after chemistry there is physics and to understand physics there is must to understand the concepts of mathematics.

There is a use of “TECHNOLOGY” in biotechnology that directly show that there is a use of math, physics, chemistry and all:

Mathematics Used In Biotechnology, On The Base Of Physical Manner:

  1. For finding the exact quantity of DNA, there is a use of mathematics for calculation.
  2. For calculating the composition of any culture medium.
  3. Finding the morality, molality and the normality of the solution.

In industrial company there is a lot of use of mathematics for estimating the percentage and pH of any solution.

There is a big role of math in bioinformatics, matching or deleting the arrangements of DNAduring the process, biostatics are used in respect to math like finding the old data of any research we find mean , median.

Mathematical modeling is most preferable in the field of biotechnology. Mathematical modeling becomes an important tool, not only for theories that biology needs the most but also for application of the acquired knowledge on the genetic and molecular basis of life. There are followings models that play an important role in the field of biotechnology:

  • Metabolic Network Models and Flux Balance Analysis (FBA).
  • Reverse Engineering of Gene Regulatory Networks (GRNs).
  • Continuous ordinary differential equation based dynamic models.
  • Single cell models and stochastic simulations.
  • Qualitative models; fuzzy and Petri nets.

Metabolic Network Models and Flux Balance Analysis (FBA)

Stoichiometric and flux balance analysis (FBA) are the tools for modeling interaction networks. These models emerge as most powerful tools that combine outside cell process like uptake, production rates, growth rate, yields etc with inside cellular carbon and energy flux distribution. FBA and stoichiometric models have been used to calculate genomic-scale. Dynamic flux balance analysis first proposed by Doyle and co-workers , uses extracellular concentration information to calculate the maximum yield. Limitations of FBA include the loss of dynamic metabolic information, inability of model dynamic transient etc. FBA simulations have also been used to inform the concept of underlying biology. Flux distributions estimated by FBA are calculated by solving the mass balance equations at steady rate.

Reverse Engineering of Gene Regulatory Networks (GRNs)

FBA while successful in many ways but has limited power because it does not include the regulation of gene expression or protein activity. At cell level the activity of enzymes and other proteins are slightly regulated. A powerful use of gene regulatory networks is in the combination with FBA. Covert and Palsson demonstrated the effects of gene regulation in the central metabolism of E. coli .In this study gene regulation was represented as a logical Boolean network using the logical operators AND OR NOT. These include linear weight modeling, linear and nonlinear ordinary differential equations etc. In Boolean approach, genes are assumed to be either ON or OFF and the input-output relationships between them are express through logical functions (such as AND, OR, NOT, etc).

Continuous Ordinary Differential Equation Based Dynamic Models

Continuous dynamic models have become famous tools to model the time evolution of complex protein-protein and protein-DNA interaction networks. The most common formulations as mass action which considers the rate of reaction are proportional to the product of reactants and Michaelis-Menten. The stoichiometric matrix and rate formulations are combine to form a network of ordinary differential equations (ODEs) , which describes the evolution of each species in the network. These such systems are non-linear , thus , must be solved numerically. There are also exists software packages produced specifically for modeling biochemical reaction networks.

Single Cell Models And Stochastic Simulations

Deterministic models depend on continuum mathematics and ignore discrete events. However molecular reactions occur discretely between individual molecules. In SSA we again have a system of species, which can be described by a state vector. These species interact with one another through reaction channels characterized by propensity functions. Because SSA considers the occurrence of every reaction event in the system, the algorithm is inefficient for large systems. Many methods have been developed to improve the performance of SSA. Although simple cases where stochastic effects are important have been identified , many industrial relevant systems are considerably larger.

Qualitative Models: Fuzzy Logic And Petri nets

The dimensionality and non-linearity of biologically same interaction networks makes it difficult to predict many features using intuition. As model sizes increase towards the genome-scale , structural difference makes models hard to identify even with complex computational methods. Fuzzy logic is one method of incorporating qualitative rules into biochemical models. Petri Nets are another way of modeling a distribution of states for a system of interacting elements . The membership function determined a variable’s degree of membership. Therefore, it was possible to have a variable at few degree of ‘on’ as opposed to on/off TRUE/FALSE value.


In this we study the modeling techniques to simulate cellular networks and systems. However the choice of method depends upon both the system in question and the goal of the analysis. With networks increasing in size and complexity, the most powerful models may be hybridmodelsthat is the mixture of the benefits of different simulations techniques.


  1. A. Arkin, J. Ross, H. H. McAdams. Stochastic kinetic analysis of developmental pathway bifurcation in phage lambda-infected Escherichia coli cells. Genetics, 149:1633-1648, 1998.
  2. M. B Elowitz, A. J Levine, E. D Siggia, and P. S Swain. Stochastic gene expression in a single cell. Science, 297:1183-1186, 2002.
  3. M. Heiner, I. Koch, and J. Will. Model validation of biological pathways using petri nets-demonstrated for apoptosis. Biosystems, 75:15-28, 2004.
  4. M.L. Shuler. Single-cell models: promise and limitations. J. Biotechnol., 71:225

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