[Mathematical model: a tool for systems biology and systems biomedicine]

Systems biology is an approach by which biological questions are addressed through integrating experiments with computational modeling and theory in a reinforcing cycle. Systems biology can be described as a discipline that seeks to quantify and annotate complexity in biological systems in order to construct models with which we can predict outcomes from inputs. Systems biomedicine is an extension of these strategies into the study of biomedical problems. In the last decade, some significant changes occurred in different biomedical areas with the introduction of systems biology. Whereas at the present systems biology aims at modeling exhaustive networks [genetic networks, signal transduction pathways and metabolic network] of interactions, systems biomedicine emphasizes the multilevel hierarchical nature [cell, tissue, organ, organism and population] of the models. Examples are given to show how the problems are tackled in systems biomedicine. Analysis with mathematical models provides insight into complex diseases such as cancer, Alzheimer's, Aids etc. Multilayered complexity at different levels [cell, organ, organism and population] challenges mathematical solutions, and computational software tools and database provisions. It is likely that in future new mathematics and computational tools will be required to deal with these complexities

[Mathematical modelling of the growth and wafer therapy of glioblastoma]

Glioblastomas are the most malignant and most common gliomas in adults. Mathematical modeling is a powerful tool for analyzing problems of tumor formation and growth. It allows one to develop and test hypotheses which can lead to a better understanding of this malignancy. To construct a mathematical model to describe the effects of genetic mutations on the growth of glioblastoma tumor cells in the absence and presence of anticancer drug carmustine released locally from polymer implants. A modified logistic equation [in both algeobraic and differential forms] is proposed to describe the effect of genetic mutations on the growth of glioblatoma tumor cells in the absence and presence of anticancer drug carmustine released locally from polymer implants. A modified logistic equation [in both algebraic and differential forms] is proposed to describe the effect of genetic mutations on the growth of glioblatoma. The model predictions are adapted to available experimental and clinical findings. A semi-empirical equation similar to the probability density function of gamma distribution is used to describe the diffusion of carmustine from a polymer - implant [wafer] into the brain. Parameters of this equation are estimated from available experimental data for monkey brain. This equation is combined with the differential form of the above - mentioned modified logistic equation to describe the wafer therapy of glioblastoma in human brain. The prediction of this combined model is compared with the pattern of recurrence of glioblastoma reported in literatures. In all cases good agreements between models prediction and experimental and clinical findings are observed. Application of the model is discussed. The model describes the effect of genetic mutations on the growth of glioblastoma in the absence and presence of carmustine properly. A combination of the present model with that of Swanson and co-workers can lead to a better understanding of glioblastoma invasivenss. It is possible to use the model prospectively, optimizing the design of new experiments

[ hydrophobicity scale for the amino acids]

Abstract Introduction: The hydrophobic interaction is a major driving force behind many effects and phenomena in biological systems many hydrophobicity scales have already been proposed and have been used to predict the topography of proteins

Objective: In the present work based on some theoretical considerations a new hydrophobic scale for the amino acids is proposed

Materials and Methods: From the empirically justified assumptions that hydrophobicity of the amino acid residues as part of a polypeptide chain is dependent on the surface area and the electronegativity content of the residues, an equation which relates the hydrophobicity to the surface area and the number, and electro negativity of oxygen and nitrogen of the residue is proposed. From this equation a new hyrophobicity scale for the amino acids is obtained. Using this scale and a sliding window averaging method hrdrophobicity plots for the human melatonin receptor and prion protein [the cause of mad cow disease] are drawn and the intramembrane structure of melatonin mel1a receptor and hydrophobic core of the second half of the prion protein are determined and compared with those from literatures

Results: the proposed hydrophobicity scale in this work is in good agreement with that of Engelmann and coworkers. The intramembrane structure of melatonin receptor and the structure of the hydrophobic core of the prion protein predicted in this article are in good agreement with those proposed in the literatures

Conclusion: the proposed hydrophobicity scale in this work is suitable for predicting the topography of the tran membrane and globular proteins