Michael A. Idowu

Engineering simulations for cancer systems biology

Computer simulation can be used to inform in vivo and in vitro experimentation, enabling rapid, low-cost hypothesis generation and directing experimental design in order to test those hypotheses. In this way, in silico models become a scientific instrument for investigation, and so should be developed to high standards, be carefully calibrated and their findings presented in such that they may be reproduced. Here, we outline a framework that supports developing simulations as scientific instruments, and we select cancer systems biology as an exemplar domain, with a particular focus on cellular signalling models. We consider the challenges of lack of data, incomplete knowledge and modelling in the context of a rapidly changing knowledge base. Our framework comprises a process to clearly separate scientific and engineering concerns in model and simulation development, and an argumentation approach to documenting models for rigorous way of recording assumptions and knowledge gaps. We propose interactive, dynamic visualisation tools to enable the biological community to interact with cellular signalling models directly for experimental design. There is a mismatch in scale between these cellular models and tissue structures that are affected by tumours, and bridging this gap requires substantial computational resource. We present concurrent programming as a technology to link scales without losing important details through model simplification. We discuss the value of combining this technology, interactive visualisation, argumentation and model separation to support development of multi-scale models that represent biologically plausible cells arranged in biologically plausible structures that model cell behaviour, interactions and response to therapeutic interventions.

Matrix Operations for the Simulation and Immediate Reverse-Engineering of Time Series Data

We present a new method for constructing and decomposing square matrices. This method, based on the computed parameterisation of their implied determinants and minors, operates on the product of factors of a new form of matrix decomposition. This method may be employed to build new matrices with fixed determinant(s). We demonstrate that this new approach is fundamentally well-connected to the Cholesky decomposition if applied on symmetric matrices. We also demonstrate that it is related to the LU decomposition method via a diagonal matrix multiplier. Also through this new method a direct relation between Cholesky decomposition and LU factorisation is shown. This method, presented for the first time, is useful for (re)constructing matrices with a predefined determinant and simulating inverse problems. The inference method introduced here also is based on new matrix manipulation techniques that we have developed for the identification of systems from reproducible time series data.

A Novel Theoretical Framework Formulated for Information Discovery from Number System and Collatz Conjecture Data

Abstract 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.

Matrix-Based Analytical Methods for Recasting Jacobian Models to Power-Law Models

New methods for inferring data-consistent, self-reconfigurable power-law models from time series data are required and developed. These novel methods may be categorised into two broad groups, namely: straightforward (or direct) inference methods based on power-law models; and a jacobian based indirect inference method. The direct method involves applying direct means to infer a power-law model from time series data. The indirect method, however, uses a new system identification method to first infer a jacobian model as instant and temporal solution to the inverse problem before recasting the inferred jacobian model to corresponding power-law model using our newly developed recast technique. The recast method, in addition to normal behaviour, also provides a novel analytical technique for integrating power-law and jacobian models together. The modelling approach we have developed extends previous work on matrix-based network inference to model interoperability and multiple model transformation in terms of finding two distinct models (solutions) to an inverse problem.

Cyclin-Dependent Kinases as Drug Targets for Cell Growth and Proliferation Disorders. A Role for Systems Biology Approach in Drug Development. Part I—Cyclin-Dependent Kinases as Drug Targets in Cancer

ABSTRACT Cyclin-dependent kinases (CDKs) are key regulators of cell growth and proliferation. Impaired regulation of their activity leads to various diseases such as cancer, heart hypertrophy and chronic inflammation. 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.

Instantaneous Modelling and Reverse Engineering of Data-Consistent Prime Models in Seconds!

Abstract 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.

Abstract 4921: A new method for identifying a data-consistent self-reconfigurable predictive bio-network model of the cell cycle based on time series data and its application in cancer systems biology

A new method for (re)constructing interaction networks using a limited number of time series data has been developed. This method may provide better opportunities for immediate identification of data-consistent models of biological systems. It may serve as an alternative or complementary approach to other existing data-driven strategies for modeling or mining time-evolutionary properties of complex biological processes based on the analysis of their time series data. We present some practically useful data-mining techniques for constructing self-reconfigurable predictive models of complex biological systems, which approximate their underlying processes. These parametric models, if well reverse-engineered, may help capture key features of data relevant for the purpose of interest. To demonstrate our network inference method, we focus on analyzing time series data of cdk2, cyclinA1, cyclinD1, cycinD2, cyclinD3, E2F1, p16 and p27 obtained from real experiments. The constructed predictive model of the cell-cycle is found to be data-consistent. This model approximates the underlying biological processes hidden in the data, and may help reveal or identify key processes that may govern G1-S phase progression. Given multiple sets of time series data from a cell line, where some sets represent control conditions and other intervention conditions, the method introduced here can help construct interaction networks for each of these data sets. To investigate areas of the signaling network most affected by the intervention, critical areas that have been identified in those networks could be compared to the effects of real perturbations. This may help inform future experimental design by targeting sensitive areas in the signaling network or avoiding resistant pathways. Citation Format: {Authors}. {Abstract title} [abstract]. In: Proceedings of the 103rd Annual Meeting of the American Association for Cancer Research; 2012 Mar 31-Apr 4; Chicago, IL. Philadelphia (PA): AACR; Cancer Res 2012;72(8 Suppl):Abstract nr 4921. doi:1538-7445.AM2012-4921

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

ABSTRACT 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.