Welcome to Tianhai Tian's homepage

Projects for Postgraduate Research Students

My research interests concentrate on mathematical modelling and simulation of biological systems. I used different types mathematical methods to study a wide range of complex networks in biological sciences. This website gives a number of my key research topics in recent years. Contact me at any time if you would like study computational biology and bioinformatics at Monash University.

Each year Monash University has various types of Monash Postgraduate Research Scholarships for excellent candidates, including international students scholarship. The Faculty of Science also provides the Dean's Postgraduate Research Scholarship. Externally-funded or self-funded candidates are always welcome to apply. Please see this page first for the application details at Monash University.

Project 1. Stochastic modelling of genetic regulatory networks

Recent advances in experimental genetics have shown that gene expression is governed by stochastic process. The fact that DNA is present in just one or few copies per cell means that the expression of a gene involves the discrete and inherently random biochemical reactions. Randomness in transcription and translation leads to cell-to-cell variations at message RNA (mRNA) and protein levels. In recent years a number of exciting experimental works have been published in the top international journals to study the mechanisms for generating and controlling the noise in gene expression. These experimental discoveries have stimulated an increasing number of mathematical modelling studies to discover the origin and consequences of stochasticity in gene expression. Mathematical modelling of regulatory networks is a broad research area, which covers a number of research topics in my research works. A research project may include the modelling method design and gene network(s) listed below for the PhD studies of three years.

Development of novel modelling methodologies. The stochastic simulation algorithm (SSA) represents an essentially exact procedure for modelling reaction systems in which the molecular population of some critical reactants is relatively small. This modelling framework is based on the assumption that all biochemical reactions are instantaneous events. However, biological systems are complex; thus this assumption is not adequate for describing the complex dynamics by using the simplified mathematical models. For example, when time delays in slow reactions are of the order of other processes, taking the delays into account will be crucial for the description of transient processes. Therefore we proposed the delay stochastic simulation algorithm (DSSA) to incorporate time delay and discreteness associated with chemical kinetic systems. In addition, recent biological studies showed that gene expression occurs as bursting events. More sophisticated mathematical tools are needed to represent the bursting events in gene expression properly. This project will develop novel modelling methodologies to address these issues. The developed strategy will be used to model the gene networks in the topics below.

The lactose operon.The lactose operon of Escherichia coli is a set of genes that are responsible for the metabolism of lactose in some bacterial cells. It served as the testable paradigm to establish most of the major concepts of genetic regulation as well as lay down the foundation of modern molecular biology. The inducible lactose operon is the classic example of bistability, and the bistable behaviour has been the subject of a number of studies ranging from experiments to mathematical modelling. Recently, a set of ingenious experiments demonstrated burst process in gene expression and raised questions regarding the origin of bistability in the lactose operon. However, current modelling approaches failed to illustrate the experimental results observed in single cells. This project will develop stochastic models to achieve deeper insights into the machinery that regulates gene expression.

The p53 gene network.The point mutation within the tumour suppressor gene p53 occurs in over half of all human tumours, there is clear consensus that elucidating the regulatory mechanisms of the p53 gene will contribute tremendously to the development of therapeutic strategies for cancers. Although extensive research in the last thirty years have produced massive amount of knowledge of p53 regulation, experimental discoveries are continually complicating the role of p53 in tumour suppression. A fundamental yet challenging question regarding p53 regulation is how human cells generate damped oscillations in a population of cells while simultaneously maintain sustained oscillations in single cells. This project will develop realistic stochastic models to explore the fundamental regulatory mechanisms of gene expression and to discover the origin of bistability and oscillation that have been observed in single-cell experiments.

Other gene networks.You may also study other gene networks that were not listed here in detail. These gene networks include the NF-kappaB network that plays a central role in cardiovascular growth, stress response, and inflammation; the GATA-PU.1 gene network that control differentiation of stem cells; and the Sox2-Oct4-Nanog gene network for maintaining pluripotency of embryonic stem cells.

Project 2: Effective numerical methods for simulating chemical reaction systems

When cellular processes are governed by key molecules with small copy numbers, the standard chemical kinetics framework described by systems of differential equations breaks down. In recent years, the stochastic simulation algorithm (SSA) has been successfully applied for simulating genetic/enzymatic reactions in which the molecular population of a critical reactant species is relatively small. Since the bottleneck in the application of the SSA arises from the huge amount of computing time, this has stimulated the development of effective methods for simulating large-scale stochastic systems, including our designed binomial tau-leap methods and multi-scale simulation methods. Although substantial achievement has been obtained in this research area, recent advances in experimental biology have increases imposed new challenges. For example, we have proposed the first method to model and simulate chemical systems with time delay. However, it is still a challenge to represent multistep chemical reactions in the form of a delayed reaction. In addition, the huge computing time is an obstacle to develop stochastic models with time delay for complex biological systems. This project will address these challenges by designing efficient multi-scale simulation methods and high performance computer programs.

This project may be an independent project for a PhD or Master Research student. It may also serve as the first step of the other PhD research projects. This may be helpful for candidates from mathematical sciences since they may not have adequate background of biological sciences.

Project 3. Mathematical modelling of cell signalling pathways

Cell signalling pathways regulate a large number of cellular processes by transmitting extracellular signals into intracellular targets via a network of interacting proteins. One of the most prominent signalling pathways, the mitogen-activated protein (MAP) kinase cascade, communicates signal from the growth factor receptors on the surface of the cell to effector molecules located in the cytoplasm and the nucleus of the cell. A number of mathematical models have been designed to study the MAP kinase module and the growth factor regulated signalling pathway. More recently, mathematical models have been proposed to investigate the cross talk between different signalling pathways including Raf/MEK/ERK pathway, p38 MAPK pathway and PI3K/Akt pathway. A major challenge in the modelling of signalling pathways is the lack of experimental data for determining the rate constants in mathematical models. The advances in high-throughout technologies such as microarray and proteomics have produced an unprecedented amount of genome-scale data from many organisms. These datasets not only provided a unique opportunity to study complex signalling networks but also raised significant challenges in mathematical modelling. This project will develop mathematical models for the cell signalling pathways based on both omics datasets and traditional experimental data such as western-blot assays.

Project 4. Mathematical modelling of cancer robustness and cancer therapy

Cancer has become the leading cause of death for people under the age of 85. Despite over 50 years of research, cancer mortality rates have remained static. This is because cancer is an inherently robust biological system, with tumour cells able to survive and proliferate despite a wide range of aggressive therapeutic interventions. However, the fundamental mechanisms underpinning tumour robustness are largely unknown. In addition, therapy resistance appears to be inevitable in aggressive solid tumours such as brain cancer. Resistance can be either present prior to starting treatment, or evolve during the course of therapy. The complexity of tumour response to therapy is a significant challenge for the design of therapies that delay or overcome therapy resistance that are required to increase progression-free survival of patients. In recent years, different types of mathematical methods, including stochastic models, dynamic systems and partial differential equations, have been used to study different aspects of cancer systems and cancer therapy. Based on the collaborations with biologists at the University of Queensland, this proposal will develop novel stochastic models to provide deep insights into the role of noise during tumour formation, tumour robustness and the evolution of therapy resistance. This project will also design mathematical models to study tumour reproduction and drug resistance.

Project 5: Mathematical modelling of telomere length regulation in ageing research

A long-standing proposition in ageing study is the "telomere length hypothesis" because in experimental studies the telomere lengths correlate with cellular life span. Telomeres are repeated DNA sequences located at the ends of linear chromosomes, and shorten with every cell division until a cell is no longer able to divide. Telomeres with shortened length are related to various age- and inactivity-related diseases including cancer. An understanding of the role of telomeres in disease has important implications for diagnosis, genetic counselling, clinical management, and therapy. Extensive experimental studies have been carried out since the discovery of telomere in the 1970s, leading to the Nobel Prize in Physiology/Medicine for 2009 being award to this area of research. In addition, experimental studies in recent years have suggested a number of potential noise sources contribute to the heterogeneity of telomere length. However, this research topic is still at its infancy and sophisticated mathematical models need to be developed to identify the roles of regulatory mechanisms at the systems levels. This project will develop new mathematical models to explore the molecular mechanisms governing telomere length regulation and elucidate the function of telomere in determining cell fate.