A modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions by which a real world problem can be described by a mathematical formulation. It has become indispensable tools for integrating and interpreting heterogeneous biological data, validating hypothesis and identifying potential diagnostic markers. The modern molecular biology that is characterized by experiments that reveal the behaviours of entire molecular systems is called systems biology. A fundamental step in synthetic biology and systems biology is to derive appropriate mathematical model for the purposes of analysis and design. This manuscript has been engaged in the use of mathematical modeling in the Gene Regulatory System (GRN). Different mathematical models that are inspired in gene regulatory network such as Central dogma, Hill function, Gillespie algorithm, Oscillating gene network and Deterministic vs Stochastic modelings are discussed along with their codes that are programmed in Python using different modules. Here, we underlined that the model should describes the continuous nature of the biochemical processes and reflect the non-linearity. It is also found that the stochastic model is far better than deterministic model to calculate future event exactly with low chance of error.

The artificial neural network (ANN) has had remarkable success in pattern recognition in recent years. It stands for a new learning paradigm in artificial intelligence (AI) and machine learning and has been applied to problems ranging from speech recognition to the prediction of protein secondary structure, cancers, and gene prediction. Recent breakthrough results in image analysis and speech recognition have generated massive interest in this field. However, the mathematical and computational methodology underlying deep learning models is very challenging, especially for interdisciplinary scientists. In this manuscript, a Neural Network model is used to classify whether a given mushroom is edible or poisonous using Tensorflow in Python based on the attributes present in the dataset. The dataset includes descriptions of hypothetical samples corresponding to 23 species of gilled mushrooms in the Agaricus and Lepiota Family Mushroom, drawn from The Audubon Society Field Guide to North American Mushrooms (1981).

Biological systems, at all scales of organization from nucleic acids to ecosystems, are inherently complex and variable. Therefore mathematical models have become an essential tool in systems biology, linking the behavior of a system to the interaction between its components. Parameters in empirical mathematical models for biology must be determined using experimental data, a process called regression because the experimental data are noisy and incomplete. The term "regression" dates back to Galton's studies in the 1890s. Considering all this, biologists, therefore, use statistical analysis to detect signals from the system noise. Statistical analysis is at the core of most modern biology and many biological hypotheses, even deceptively. Regression analysis is used to demonstrate association among the variables believed to be biologically related and fit the model to give the best model. There are two types of regression, linear and nonlinear regression to determine the best fit of the model. In this manuscript, we perform a least squares error fit to different models and select the best fit model using the chi-test, and determine the p-value of the selected model to data that was collected when various doses of a drug were injected into three animals, and the change in blood pressure for each animal was recorded.