ItemComputational techniques in mathematical modelling of biological switches(MSSANZ, 2015-12) Chong, KH; Samarasinghe, Sandhya; Kulasiri, Don; Zheng, J; Weber, T; McPhee, MJ; Anderssen, RSMathematical models of biological switches have been proposed as a means to study the mechanism of decision making in biological systems. These conceptual models are abstract representations of the key components involved in the crucial cell fate decision underlying the biological system. In this paper, the methods of phase plane analysis and bifurcation analysis are explored and demonstrated using an example from the literature, namely the synthetic genetic circuit proposed by Gardner et al. (2000) which involved two negative loops (from two mutually inhibiting genes). Figure 1 shows a schematic diagram of the synthetic genetic circuit constructed by Gardner et al. (2000). Particularly, a saddle-node bifurcation is used as a signal response curve to capture the bistability of the system. The notion of bistability is obscure to most novice researchers or biologists because it is difficult to understand the existence of two stable steady states and how to flip from one stable steady state to another and vice versa. Thus, the main purpose of this paper is to unlock the computational techniques (bifurcation analysis implemented in a software tool called XPPAUT) in mathematical modelling of bistability through a simple example from Gardner et al. (2000). In addition, time course simulations are provided to illustrate: 1) the notion of bistability where the existence of two stable steady states and we demonstrated that for two different initial conditions one of the genes is ‘ON’ and the other gene is ‘OFF’; 2) hysteresis behaviour where the saddle-node bifurcation points as two critical points in which to turn ‘ON’ one gene happens at a larger parameter value than to turn ‘OFF’ this gene (at a lower parameter value). The hysteresis behaviour is important for irreversible decision made by cell to commit to turn ‘ON’. In conclusion, the understanding of the computational techniques in modelling biological switch is important for elucidating genetic switch that has potential for gene therapy and can provide explanation for experimental findings of bistable systems. ItemModelling calmodulin dependent calcium signalling involved with synaptic plasticity : A thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy at Lincoln University(Lincoln University, 2018) Stevens-Bullmore, Hamish EdwardNeurotransmission of synapses is plastic in that they get modulated to increase or decrease conductivity (this is known as synaptic plasticity). Synaptic plasticity consists of two opposing forces: long term potentiation (LTP) which strengthens synapses; and long term depression (LTD) which weakens synapses. LTP and LTD are associated with memory formation and loss respectively. Synaptic plasticity is controlled at a molecular by Ca²⁺-mediated protein signalling. Here, Ca²⁺ binds the protein, calmodulin (CaM) which modulates synaptic plasticity in both directions. This is because Ca²⁺- bound CaM activates both LTD- and LTP- inducing proteins. Understanding how CaM responds to Ca²⁺ signalling, and how this translates into synaptic plasticity is therefore important to understand synaptic plasticity induction. In this thesis, CaM activation by Ca²⁺ and calmodulin binding to downstream proteins was mathematically modelled using differential equations. CaM was first modelled in isolation to determine its kinetic binding properties with Ca²⁺. By performing local and global sensitivity analyses of Ca²⁺ binding/unbinding parameters, distinct binding properties between the two Ca²⁺ binding lobes were found. The difference between the binding lobes was exacerbated as intracellular Ca²⁺ stimulation rose. A full model of the two opposing pathways of synaptic plasticity was then employed. Simulations were monitored, and global sensitivity analyses were performed to determine how Ca²⁺/CaM signalling occured at various Ca²⁺ signals. At elevated stimulations, the total CaM pool rapidly bound to its protein binding targets which regulate both LTP and LTD. This was followed by CaM getting redistributed from low affinity to high affinity binding targets. Specifically, CaM was redistributed away from LTD- inducing proteins to bind the high affinity LTP-inducing protein, calmodulin dependent kinase II (CaMKII). In this way, CaMKII acted as a dominant affecter and repressed activation of opposing CaM binding protein targets. This model thereby showed a novel form of CaM signalling by which the two opposing pathways can crosstalk indirectly. The model also investigated how cAMP is regulated by CaM. It was found that CaMKII can repress cAMP production by repressing CaM-regulated proteins which catalyse cAMP production. The model also found that at low Ca²⁺ stimulation levels typical of LTD- induction, CaM-signalling was unstable and is therefore unlikely to alone be sufficient to induce synaptic depression. Overall, this thesis showed how limiting levels of CaM may be a fundamental aspect of Ca²⁺ regulated signalling which allows crosstalk among proteins without requiring to interact directly. Understanding synaptic plasticity can help understand neurodegenerative disease and although the current study is focused on synaptic plasticity, understanding CaM regulation has implications in numerous other cell types. ItemContouring and earthwork estimation for bordered strip irrigation(Lincoln College, University of Canterbury, 1977) Harrington, G. J.Computer programmes were developed for processing data from grid, direct, and random stadia field contouring systems. The three systems were evaluated for their use in providing contour plans for bordered strip irrigation design. A computer method of calculating the earthwork volumes associated with bordered strip irrigation was developed which uses terrain data from the above surveying methods or any other convenient source. This method was compared with land grading to form plane or warped paddock surfaces onto which levees may be formed, thus creating bordered strips. With the aid of the bordered strip earthwork calculating programme, the effect of changes of bordered strip paddock layout and slope restraints was investigated. An attempt to correlate estimated earthworks with earthmoving machine times was made. ItemA nutrient dependant switch explains mutually exclusive existence of meiosis and mitosis initiation in budding yeast(Elsevier, 2014-01-21) Wannige, C; Kulasiri, Don; Samarasinghe, SandhyaNutrients from living environment are vital for the survival and growth of any organism. Budding yeast diploid cells decide to grow by mitosis type cell division or decide to create unique, stress resistant spores by meiosis type cell division depending on the available nutrient conditions. To gain a molecular systems level understanding of the nutrient dependant switching between meiosis and mitosis initiation in diploid cells of budding yeast, we develop a theoretical model based on ordinary differential equations (ODEs) including the mitosis initiator and its relations to budding yeast meiosis initiation network. Our model accurately and qualitatively predicts the experimentally revealed temporal variations of related proteins under different nutrient conditions as well as the diverse mutant studies related to meiosis and mitosis initiation. Using this model, we show how the meiosis and mitosis initiators form an all-or-none type bistable switch in response to available nutrient level (mainly nitrogen). The transitions to and from meiosis or mitosis initiation states occur via saddle node bifurcation. This bidirectional switch helps the optimal usage of available nutrients and explains the mutually exclusive existence of meiosis and mitosis pathways. ItemRemodelling circadian rhythm in Drosophila melanogaster: to investigate the role of a new clock component clockwork orange (CWO)(Lincoln University, 2015) Ranganathan, JeevabharathiThe ability of almost all organisms to change their behaviour on a daily basis is one of the remarkable features of life on earth. This phenomenon which is called circadian rhythm is observed in diverse organisms such as algae, fruit flies and humans and is a response arising due to the rotation of the earth around the axis resulting in an internal time-keeping system. Changes in myriad of biochemical and physiological processes take place in order for an organism to adapt for changes in physical environment. The period of this process is close to 24 hours in duration, hence the name “circadian rhythms”, from Latin circa diem meaning about a day. In the fruit fly Drosophila melanogaster, due to the increase in knowledge of genetics and molecular biology the molecular components such as genes and proteins involved in circadian rhythm and their roles are well understood. Due to the oscillatory properties of clock components they are an ideal candidate for mathematical models and many such models have been developed in the past. In this study, three new Drosophila circadian rhythm models were developed, each with three transcriptional regulatory feedback loops. Among which, two feedback loops (VRI/PDP1 and PER/TIM) are well known and have been included in earlier models. The main focus of this study is the newly discovered third feedback loops (CWO). The differences between the three models are defined by our conceptualization of three probable actions by which the newly discovered clock component CWO (Clockwork Orange) performs its dual role both as an activator and repressor of per, tim, vri, pdp1 genes, and cwo genes. We included existing in vitro understanding of molecular components and extended it to include probable molecular roles of the newly discovered clock component CWO. We based our hypothesis on discovered in vivo dynamics and by analysing the CWO protein sequence using basic bioinformatics servers. Detailed modelling in the form of probability based transcription factor binding and unbinding processes are used. All three models are expressed by a set of probability based mass action governed ordinary differential equations and the parameters were estimated using modelling tool COPASI. Due to the randomness and variation of different data sets generated for CWO activity by biologists, we made a choice to differ from a traditional approach in modelling, by not over-relaying on data generated from in vitro analysis. The reliance on wet-lab data was scaled down and we include them only to choose manageable mathematical inputs and validate a solved model. This approach gave us a relative degree of space to be innovative and permited us to test different hypothesis at conceptual level in three models. We proceeded to solve the models and validate the oscillations by testing with mutations. Outputs of our simulations will help broaden the research arguments in the field of cricadian biology. In particular our models hypothetically answers the molecular role of CWO protein.