Mathematical Modelling Systems Biology

Mathematical Modelling- Systems Biology
Student’s Name
Institution
Mathematical Modelling- Systems Biology
Stochastic and deterministic mathematical modeling techniques are modeling approaches that are used for developing and studying multiscale biology models and systems. In this case, the use of stochastic numerical simulations and deterministic numerical simulations in understanding and evaluating biology systems has been of critical importance in the last few years. Naturally, biological processes and systems are multiscale, that is, they require the application of a series of models at varying scales to illustrate these systems effectively. To determine the most effective mathematical model to apply, it relatively important to consider the biological questions to be addressed and the data available for validating that particular model.
Stochastic and deterministic mathematical models combine the use of differential equations and analytic numerical methods to illustrate and explain the quantitative aspect of biological phenomena. Mathematical models: stochastic and deterministic approaches use denominational semantics to describe the relationship between quantities in biological systems through the use of equations. For stochastic mathematical models, they employ an indeterminacy approach in the evolution stage of the biological systems (Twycross et al., 2010).
The Auxin transports through a series of plant cells is a typical biology system that can be used to demonstrate the stochastic and deterministic mathematical modeling approaches in biological systems.

Plants growth and development is largely influenced by the presence of auxin hormone in the plant’s body. Auxin moves around the plant’s body in a polar manner as a result of spatial distributions of cell membranes’ efflux and influx carriers. The Auxin distributions in the plants affect several processes in the plants’ which include vein formation, organ initiation, and gravitropism. This represents a multiscale biology system that can be defined by both the stochastic and deterministic modeling approaches (Twycross et al., 2010).
In the Auxin hormone transport system, the stochastic mathematical model applies a multi-compartment stochastic p system framework to obtain stochastic solutions. Through this technique, small portions of the hormone molecules are designed as objects which transverse through compartments following the set rules set for each particular compartments. The applicability of each of these mathematical models depends on several factors which include but are not limited to, the researcher’s judgment concerning the time requirements for the model development and the resources for computations available. For instance, the stochastic computational mathematical model ought to be carried out several consecutive times to evaluate the common behavioral characteristics of the biological systems based on the preset parameters. As a result, it means that the cost of computing through the stochastic technique is relatively greater compared to the deterministic mathematical model. On the other hand, the multi-compartment stochastic P system framework is relatively instinctual. Therefore, it provides the best method for biological audience engagement. Additionally, application of the deterministic model through numerical computation provides the quickest method of formulating a solution. However, the stochastic model provides a better understanding of the solution through enhance data and information. It is important to note that both models are essential in the evaluation and study of biological systems (Twycross et al., 2010).
References
Twycross, J., Band, L. R., Bennett, M. J., King, J. R., & Krasnogor, N. (2010). Stochastic and deterministic multiscale models for systems biology: an auxin-transport case study. BMC systems biology, 4(1), 34.