Showing papers by "Don Kulasiri published in 2013"

Novel recurrent neural network for modelling biological networks: Oscillatory p53 interaction dynamics

Abstract: Understanding the control of cellular networks consisting of gene and protein interactions and their emergent properties is a central activity of Systems Biology research. For this, continuous, discrete, hybrid, and stochastic methods have been proposed. Currently, the most common approach to modelling accurate temporal dynamics of networks is ordinary differential equations (ODE). However, critical limitations of ODE models are difficulty in kinetic parameter estimation and numerical solution of a large number of equations, making them more suited to smaller systems. In this article, we introduce a novel recurrent artificial neural network (RNN) that addresses above limitations and produces a continuous model that easily estimates parameters from data, can handle a large number of molecular interactions and quantifies temporal dynamics and emergent systems properties. This RNN is based on a system of ODEs representing molecular interactions in a signalling network. Each neuron represents concentration change of one molecule represented by an ODE. Weights of the RNN correspond to kinetic parameters in the system and can be adjusted incrementally during network training. The method is applied to the p53-Mdm2 oscillation system - a crucial component of the DNA damage response pathways activated by a damage signal. Simulation results indicate that the proposed RNN can successfully represent the behaviour of the p53-Mdm2 oscillation system and solve the parameter estimation problem with high accuracy. Furthermore, we presented a modified form of the RNN that estimates parameters and captures systems dynamics from sparse data collected over relatively large time steps. We also investigate the robustness of the p53-Mdm2 system using the trained RNN under various levels of parameter perturbation to gain a greater understanding of the control of the p53-Mdm2 system. Its outcomes on robustness are consistent with the current biological knowledge of this system. As more quantitative data become available on individual proteins, the RNN would be able to refine parameter estimation and mapping of temporal dynamics of individual signalling molecules as well as signalling networks as a system. Moreover, RNN can be used to modularise large signalling networks.

Computational experiments reveal the efficacy of targeting CDK2 and CKIs for significantly lowering cellular senescence bar for potential cancer treatment

Abstract: Lowering the threshold of cellular senescence, the process employed by cells to thwart abnormal cell proliferation, though inhibition of CDK2 or Skp2 (regulator of CDK inhibitors) has been recently suggested as a potential avenue for cancer treatment. In this study, we employ a published mathematical model of G1/S transition involving the DNA-damage signal transduction pathway to conduct carefully constructed computational experiments to highlight the effectiveness of manipulating cellular senescence in inhibiting damaged cell proliferation. We first demonstrate the suitability of the mathematical model to explore senescence by highlighting the overlap between senescence pathways and those involved in G1/S transition and DNA damage signal transduction. We then investigate the effect of CDK2 deficiency on senescence in healthy cells, followed by effectiveness of CDK2 deficiency in triggering senescence in DNA damaged cells. For this, we focus on the behaviour of CycE, whose peak response indicates G1/S transition, for several reduced CDK2 levels in healthy as well as two DNA-damage conditions to calculate the probability ( β ) or the percentage of CDK2 deficient cells passing G1/S checkpoint ((1 - β ) indicates level of senescence). Results show that 50% CDK2 deficiency can cause senescence in all healthy cells in a fairly uniform cell population; whereas, most healthy cells (≈67%) in a heterogeneous population escape senescence. This finding is novel to our study. Under both low- and high-DNA damaged conditions, 50% CDK deficiency can cause 65% increase in senescence in a heterogeneous cell population. Furthermore, the model analyses the relationship between CDK2 and its CKIs (p21, p27) to help search for other effective ways to bring forward cellular senescence. Results show that the degradation rate of p21 and initial concentration of p27 are effective in lowering CDK2 levels to lower the senescence threshold. Specifically, CDK2 and p27 are the most effective in triggering senescence while p21 having a smaller influence. While receiving experimental support, these findings specify in detail the inhibitory effects of CKIs. However, simultaneous variation of CDK2 and CKIs produces a dramatic reduction of damage cells passing the G1/S with CDK2&p27 combination causing senescence in almost all damaged cells. This combined effect of CDK2&CKIs on senescence is a novel contribution in this study. A review of the crucial protein complexes revealed that the concentration of active CycE/CDK2-p that controls cell cycle arrest provides support for the above findings with CycE/CDK2-p undergoing the largest reduction (over 100%) under the combined CDK2&CKI conditions leading to the arrest of most of the damaged cells. Our study thus provides quantitative assessments for the previously published qualitative findings on senescence and highlights new avenues for bringing forward senescence bar.

Gene expression based computer aided diagnostic system for breast cancer: a novel biological filter for biomarker detection

Abstract: Cancer is a complex disease because it makes complex cellular changes. Therefore, microarrays have become a powerful way to analyse cancer and identify what changes are produced within a cell. Through DNA microarrays, it has become possible to look at the expression of thousands of genes in one sample and this is called gene expression profiling. Gene expression profiling is important to capture a set of expressed genes that determines a cell phenotype. However, analysing microarray data is challenged by the high-dimensionality of the data compared with the number of samples. The aim of this study was to enhance the diagnostic accuracy of Breast Cancer Computer Aided Diagnostic Systems (CADs) that use gene expression profiling of peripheral blood cells, by introducing a novel feature selection method called Bi-biological filter that was further refined by Best First Search with Support Vector Machines SVM (BFS-SVM) to select a small set of the most effective genes predictive of breast cancer. From each patient's gene expression profiles, a gene co-expression network was built and divided into functional groups or clusters using Topological Overlap Matrix (TOM) and Spectral Clustering (SC) in the design of the Bi-Biological filter to obtain the preliminary set of gene markers. BFS- SVM was used to further filter a smaller set of best gene markers, and Artificial Neural Networks (ANN), SVM and Linear Discriminant Analysis (LDA) were used to assess their classification performance. The study used 121 samples - 67 malignant and 54 benign cases as input to for the system. The Bi-biological filter selected 415 genes as mRNA biomarkers and BFS-SVM was able to select just 13 out of 415 genes for classification of breast cancer. ANN was found to be the superior classifier with 93.4% classification accuracy which was a 14% improvement over the past best CAD system developed by Aaroe et al. (2010).

Stochastic Differential Equations and Related Inverse Problems

Abstract: As we have discussed in Chap. 1, the deterministic mathematical formulation of solute transport through a porous medium introduces the dispersivity, which is a measure of the distance a solute tracer would travel when the mean velocity is normalized to be one. One would expect such a measure to be a mechanical property of the porous medium under consideration, but the evidence are there to show that dispersivity is dependent on the scale of the experiment for a given porous medium. One of the challenges in modelling the phenomena is to discard the Fickian assumptions, through which dispersivity is defined, and develop a mathematical description containing the fluctuations associated with the mean velocity of a physical ensemble of solute particles. To this end, we require a sophisticated mathematical framework, and the theory of stochastic processes and differential equations is a natural mathematical setting. In this chapter we review some essential concepts in stochastic processes and stochastic differential equations in order to understand the stochastic calculus in a more applied context.

Non-fickian Solute Transport

Abstract: This research monograph presents the modelling of solute transport in the saturated porous media using novel stochastic and computational approaches. Our previous book published in the North-Holland series of Applied Mathematics and Mechanics (Kulasiri and Verwoerd 2002) covers some of our research in an introductory manner; this book can be considered as a sequel to it, but we include most of the basic concepts succinctly here, suitably placed in the main body so that the reader who does not have the access to the previous book is not disadvantaged to follow the material presented.

A Generalized Mathematical Model in One-Dimension

Abstract: In the previous chapter we derived a stochastic solute transport model (Eq. 3.14); we developed the methods to estimate its parameters, and investigated its behaviour numerically. We see some promise to characterise the solute dispersion at different flow lengths, and there are some indications that Eq. (3.14) produce the behaviours that would be interpreted as capturing the scale-dependency of dispersivity.

Multiscale Dispersion in Two Dimensions

Abstract: In Chapter 7, we have developed the 2 dimensional solute transport model and estimated the dispersion coefficients in both longitudinal and transverse directions using the stochastic inverse method (SIM), which is based on the maximum likelihood method. We have seen that transverse dispersion coefficient relative to longitudinal dispersion coefficient increases as σ 2 increases when the flow length is confined to 1.0. In this chapter, we extend the SSTM2d into a partially dimensional form as we did for 1 dimension, so that we can explore the larger scale behaviours of the model. However, the experimental data on transverse dispersion is scarce in laboratory and field scales limiting our ability to validate the multiscale dispersion model. In this chapter, we briefly outline the dimensionless form of SSTM2d and illustrate the numerical solution for a particular value of flow length. We also estimate the dispersion coefficients using the SIM for the same flow length.

Theories of Fluctuations and Dissipation

Abstract: In the previous chapters, we see that the hydrodynamic dispersion is in fact a result of solute particles moving along a decreasing pressure gradient and encountering the solid surfaces of a porous medium. The pressure gradient provides the driving force which translates into kinetic energy, and the porous medium acts as the dissipater of the kinetic energy; any such energy dissipation associated with small molecules generates fluctuations among molecules.