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.
Identification of Model parameters:
Parameters for any equation in a model describe certain biochemical features of the components involved in reactions or pathways under study. For example, when modeling the dynamics of a metabolic network, the mathematical equations inferred from the processes must contain parameters that represent the kinetic features of the involved metabolic enzymes, as a number of reactions enzyme can perform within a given period of time (i.e., the rate constant). We must come across to these kinetic parameters prior to setting up well-defined systems of differential equations. Therefore, kinetic parameters for all the relevant reaction components can be experimentally determined. In practice, however, a number of kinetic parameters, even for otherwise well-investigated biological components (enzyme, proteins & hormones), still are not known, primarily because the reliable experimental data are lacking. It is very often that the kinetic parameters are measured but no experimental validation has been performed in wet lab (i.e. in vitro). In practice, enzymes behave similarly found in a cell. This creates a hurdle which is overcome by measuring the overall dynamics of the system being studied. Computational procedure have made them easier by providing appropriate estimation techniques to optimize parameter values by taking different multiple parameter set from the data set until they fit or get optimized for available experimental dataset. This method to is critically dependent on the quality of the dataset being validated, and therefore prediction made from such unreliable data will definitely lead to unreliable validated parameters and to a limited model of no use. In order to develop a simple network model for any biological process is awfully lagging behind mainly due to unavailability of high quality experimental data which is still a major focus in the field of systems biology.
It is important to mention that few biological process cannot be described using such simple models that are based on only concentration of molecules, ignoring the existence and importance of concerned components as the molecular movements adorns a significant impact on cellular mechanism. Due to the closely packing of the molecules in a cell, their thermal induction, and random movement from changing environmental conditions may cause the initiation of signal transmission that propagates across the cell and stops until reaches to its target. In order to account for such random effects, (i.e., stochastic) component must be incorporated into the equations of the model. For rare signaling molecules, of which lesser and fewer effect is observed, can be neglected. Whereas, molecules of which, rarest copies are existing in the cell must not be neglected and should be integrated into mathematical equations.
The next issue after optimization of parameter comes to be different time and distance scales of the components in integrated into a pathway. For example metabolism occurs in within seconds or minutes whereas genetic regulation takes longer (say it hours or even days) times to exert their effect or to express a particular gene induced by metabolic processes from a greater distance. It may be that signals (enzymes, protein, hormones) have to travel longer distance across the cell membrane via circulatory system of body fluids in between tissues. To overcome these different length and time scale, we can use multi-scale model to avoid complexity of the system.
Finally, it is important to assure that developed model is as good as assumption upon which it is based.
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 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
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.
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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