Cyclin-dependent kinases as drug targets for cell growth and proliferation disorders. A role for systems biology approach in drug development. Part II - CDKs as drug targets in hypertrophic cell growth. Modelling of drugs targeting CDKs

Cyclin-dependent kinases (CDKs) are key regulators of cell growth and proliferation. Impaired regulation of their activity leads to various diseases such as cancer and heart hypertrophy. Consequently, a number of CDKs are considered as targets for drug discovery. We review the development of inhibitors of CDK2 as anti-cancer drugs in the first part of the paper and in the second part, respectively, the development of inhibitors of CDK9 as potential therapeutics for heart hypertrophy. We argue that the above diseases are systems biology, or network diseases. In order to fully understand the complexity of the cell growth and proliferation disorders, in addition to experimental sciences, a systems biology approach, involving mathematical and computational modelling ought to be employed

Fundamental relations between the Dirichlet beta function, euler numbers, and Riemann zeta function for positive integers

A new definition for the Dirichlet beta function for positive integer arguments is discovered and presented for the first time. This redefinition of the Dirichlet beta function, based on the polygamma function for some special values, provides a general method for obtaining all special constants associated with Dirichlet beta function. We also show various new and fundamental relations between the polygamma function, Riemann zeta, the even-indexed euler numbers, the Dirichlet beta functions in a way never seen or imagined before

A novel theoretical framework formulated for information discovery from number system and Collatz conjecture data

Newly discovered fundamental theories (metamathematics) of integer numbers may be used to formalise and formulate a new theoretical number system from which other formal analytical frameworks may be discovered, primed and developed. The proposed number system, as well as its most general framework which is based on the modelling results derived from an investigation of the Collatz conjecture (i.e., the 3x+1 problem), has emerged as an effective exploratory tool for visualising, mining and extracting new knowledge about quite a number of mathematical theorems and conjectures, including the Collatz conjecture. Here, we introduce and demonstrate many known applications of this prime framework and show the subsequent results of further analyses as new evidences to justify the claimed fascinating capabilities of the proposed framework in computational mathematics, including number theory and discrete mathematics

Instantaneous modelling and reverse engineering of data-consistent prime models in seconds!

A theoretical framework that supports automated construction of dynamic prime models purely from experimental time series data has been invented and developed, which can automatically generate (construct) data-driven models of any time series data in seconds. This has resulted in the formulation and formalisation of new reverse engineering and dynamic methods for automated systems modelling of complex systems, including complex biological, financial, control, and artificial neural network systems. The systems/model theory behind the invention has been formalised as a new, effective and robust system identification strategy complementary to process-based modelling. The proposed dynamic modelling and network inference solutions often involve tackling extremely difficult parameter estimation challenges, inferring unknown underlying network structures, and unsupervised formulation and construction of smart and intelligent ODE models of complex systems. In underdetermined conditions, i.e., cases of dealing with how best to instantaneously and rapidly construct data-consistent prime models of unknown (or well-studied) complex system from small-sized time series data, inference of unknown underlying network of interaction is more challenging. This article reports a robust step-by-step mathematical and computational analysis of the entire prime model construction process that determines a model from data in less than a minute