Introduction to mathematical modelling – Part 2
Gathering of Dynamic/Kinetic information
In the previous section you might have noticed that modelling biochemical process requires calibrated set of fine parameters which fit into and across the set of chemical/reactant species (gene/protein/molecule) involved in the process.
Question arises, where do we collect data from? And what are the standard criteria for determining parameters? Basically, for a researcher, it is necessary to know the source of the data first and then how to manipulate to get relevant information for modelling. Source of the data can be chosen depending upon the requirement of experimental design. For modelling, data can be taken in the form of gene-gene interaction, Gene expression (micro-array) and gene-protein interaction. Basically, interaction and expression do not simply reveal the dynamic/kinetic values of the system and therefore need to be manipulated for further implication.
In order to obtain the parameter values for analysing the kinetic behaviour of biochemical processes, we simply investigate into expression data (gene/protein) at different transcriptional and translational level that enable us to frame-out the comprehensive structural biochemical pathway. This can be done by accounting the following methods:
- Genome (complete set of genes) analysis at transcription level through DNA sequencing & genotyping
- Transcriptome (all mRNA) analysis at translation level using microarrays
- Proteome (entire protein) analysis at cellular level (reaction between proteins and other molecule in cell) using Mass spectroscopy and 2D gel electrophoresis
- Metabolome (total metabolites and their intermediate) analysis at cell level, interaction metabolites and regulator using 13C labelling and NMR techniques
- Interactome (all interacting molecule) analysis by yeast-2 hybrid screen & TAP techniques
(Ligand: TAP- Tandem affinity purification, NMR- Nuclear magnetic resonance)
Above mentioned techniques are collectively referred to as Omics. They provide us structural and dynamic data that is used to generate mathematical formula representing observable reactions, followed by development of mathematical model and comprehensive pathway of biological system. These tentative models allow us (as mentioned in part-1) to observe the effect of a stimulus on specific signalling pathway, perturbation in cellular activities and gene expression level etc.
Omics are characterized by a number of features. First, they allow researcher for analyses on different molecular levels such as gene, protein and metabolites level. These different molecular levels sometimes show asynchronous behaviour—that is, although some metabolite such as glucose is higher in a cell and corresponding enzymes are lower than sugar to catalyse the reaction or vice versa. Asynchronous behaviour is an indication of complex regulatory mechanism. Therefore, it is crucially important to evaluate the degree of synchronization of all cellular level. Second, Omics are highly parallelized. This means all genes/mRNA (read-outs in sample) can be studied simultaneously rather than having to perform separate experiments focusing on individual genes. This parallelization also allows researcher to compare the degree of expression results for the same gene and to have an interaction between resultant proteins. Third, they are very standardized and therefore needs very high automation computing, providing scientist with a large number of samples at time. In the process, after collecting huge data, most relevant information is picked up and then processed further for final analyses.
Entireties of techniques in an Omics are very important in the sense that they generate numerical data based upon which we are able to develop structural pathway for mimicking the real picture of biological system and then to represent in the form of mathematical model.
( →Continue to part 3 )
Systems pharmacology and drug development
Systems pharmacology is an emerging area in the field of medicinal chemistry and pharmacology which utilizes systems network to understand drug action at the organ and organism level. It applies the computational and experimental systems biology approaches to pharmacology, which includes network analyzes at multiple biological organization levels facilitating the understanding of both therapeutic and adverse effects of the drugs. Nearly a decade ago, the term systems pharmacology was used to define the drug action in a specific organ system such as reproductive pharmacology , but to date, it has been expanded to different organ and organism levels . (more…)
MOTIF: Functional Unit of An Interaction Network
In a network, integration of elements and interacting components enables identification of conserved modules and
motifs. The topological analysis, however, reveals much about the nature and functions of a network and provides sufficient statistics for any further study. (more…)
Network Biology: Get Together of Macromolecules
A network is a group of two more than two interacting components. The complex biological systems can be represented as computable networks that provide a unique way of analyzing the complex underlying mechanisms. (more…)
Two Components System: Potential Drug Target in Mycobacterium tuberculosis
The genomic complexity and unknown functions of proteins/genes in Mycobacterium tuberculosis (Mt) has triggered an in-depth study of the entire genome to explore factors responsible for influencing Mt’s behaviour at molecular level. To set the stage of infection, to establish itself in the host’s defending environment, to cause the pathogenicity by overcoming the immune system and to escape out from any assailable host attack, this TB causing pathogen has developed a well-embodied system known as two-component system (TCS) that constitutes two proteins, universally designated as sensor protein and response regulator protein.
Explore Tuberculosis: A Systems Biology Approach
Systems biology is not sufficient to full fill the requirement of molecular understanding of any organism at any level. It seeks to contribute multiple approaches and fields to resolve a particular issue arisen from ongoing work. In this article you will find a combinatorial approach of systems biology i.e. molecular, cellular and network biology to understand how tuberculosis is developed and how pathogen succeeds in fighting with host immune systems. A well developed mathematical model, on PhoP-PhoR two component system, is also presented and explained to demonstrate the mode of molecular regulation by pathogen. (more…)
Introduction to Mathematical Modelling (Last Part)
In the previous section, mathematical modeling was exemplified by metabolic process and its biochemical regulation. It could also be done by signalling pathways and genetic regulatory process. At all cellular phase, one observe changing mode of a cell with effect from environmental factors. It is quite difficult to maintain cellular functions and reach to steady state. Thus, one needs to fix a range of parameters for all molecular reactions while going for mathematical modeling.
Introduction to Mathematical Modelling Part-3
Derivation of Mathematical Equations for Understanding Systems Behaviour:
Depending upon the nature of biological process, it is essential to understand different modeling approach as numbers of methods have been used for different biological systems. Functionally, most of the cellular processes are dynamic that change with environmental change such that the signaling or regulation for specific genes when cell is exposed to an extraordinary medium. In order to describe such time-dependent phenomena it is necessary to choose mathematical equations that can capture these dynamic effects. In other biological systems where cellular products/molecules don’t change over time i.e., concentration remains same, it is not necessary to describe details of underlying dynamics. For modeling the systems behavior, suitable methods have been developed. Among them are two methods, commonly used in modeling of metabolic process, modeling of signaling and regulatory pathways.
Cancer: From the Eyes of Mathematical/Systems Biology
The month of November has just arrived with its generic glimpse of winter. We welcome this month with an evergreen and hot topic of cancer research. This time we intend to introduce you to an old research topic with a new vision…..
Cancer being an ailment with no remedy of full confidence has been pursued as a career by a lot of researchers. A cell biologist says it is an uncontrolled proliferation (increase in number by division and growth) of cells, molecular biologists call it a mutant variety of some biomolecules forcing a cell to commit such an uncontrolled cell division cycle. But, how does a Systems Biologist see such kind of a problem? Let us try to pursue it in a different way.
Proteins if are not assigned some name based on their function or structure, scientists mark them according to their molecular weight, e.g. p53, p200, p19 etc. Scientists have proven an abnormally high expression of p53 protein in Cancerous cells/tissues. p53 protein is actually the reason behind those other proteins which regulate the cell cycle and makes it to divide in to two as a normal scenario, p53 also helps in the manufacture of its inhibitor named Mdm2 protein. In any case of mutation in p53, that leads the failure of abnormality recognition by p53, doesn’t lead to increase in p53 and consequently Mdm2, p21 and other p53 regulated proteins. And thus, the division of abnormal cells continues indefinitely and causes Cancer.
From a Mathematical Biology perspective, systems biologists form some ordinary differential equations that look like a mathematical formula. These mathematical formulae are actually nothing else than the representative of chemical reactions and their combinations occurring inside a cell. As in our previous blogs (by Fozail Ahmad), we have mentioned about how to combine the chemical reactions in a shape of Ordinary Differential Equations (ODEs) and about how we follow Zero-Order chemical kinetics (reaction rate doesn’t depend on any participating chemical), First-Order chemical kinetics (reaction rate depends on only one participating chemical) and Second-Order chemical kinetics (reaction rate depends on two or more participating chemicals) to form the equations. In addition to that, I would like to mention that there are some reactions which occur with the help of some biomolecular machineries. These machines (enzymes) just help the reactions to occur, but do not take part in it themselves and thus affect the reaction in a different form of kinetics as described by the combined work of German Scientist of Biochemistry Leonor Michaelis and Canadian Scientist of Physics Maud Menten in 1913.
So, in a normal cell, when p53 senses the danger and signals the Cell by increasing p21 to combine with PCNA (Proliferating Cell Nuclear Antigen – An enzyme that helps in cell division) it stops the cell division. This type of cell cycle division has been shown in one of the diagrams mentioned below, while for the mutated case of p53 where it can not sense the cellular damage and thus divides normally is also shown in one of the images above.
We have also mentioned a combined picture, which shows a referral of how different stages of Mathematical Biology looks like. These figures are in special contrast to Cancer cells and normal cells.
Reference: Alam MJ, Kumar S, Singh V, Singh RKB (2015) Bifurcation in Cell Cycle Dynamics Regulated by p53. PLoS ONE 10(6): e0129620. doi:10.1371/journal.pone.0129620
Basics of Mathematical Modelling – Part 1
Biochemical processes are simply complex, and their apparent feature does not easily allow us to investigate what exactly system means. Moreover, most of the biochemical processes obey nonlinear reaction kinetics. That is, amount of reactant (Protein/RNA/DNA/) is not directly proportional to its product. (more…)
BioMiner & Personalized Medicine: A new perspective
Personalized medicines have become a very important part of the medicine world now a days. They are also known as ‘Individualized Medicines’. Personalized medicines allow a doctor to prescribe more specific and efficient medicines to a particular patient. This concept has created many more opportunities and aspects in the medicine world. (more…)
Tumor progression prediction by variability based expression signatures
Cancer has become a very common disease now a days, but the main reason of causing this is unknown up till now. Various reasons have been given and recent research says that improper sleeping patterns may also lead to cancer. Like cause of cancer is difficult to predict, similarly, its progression and prognosis is also very difficult. Despite of many advances in cancer treatment, early detection is still very difficult. (more…)
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