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Organizers |
Hungry? Go ballistic! Or what should you do to find your dinner?
by
Richard Brown
University of Canterbury
Coauthors: Alex James, Mike Plank
An important question in foraging theory is "What is the optimal search strategy for a predator to maximise its efficiency in finding its prey?" Going hand in hand is the question of whether real-life predators search in an optimal way.
These question have been the focus of a significant amount of research over the last decade with many articles published, both theoretical and based on field work. In particular, there is a significant body of research pointing to certain heavy-tailed Levy random walks as being optimal predator search strategies in a variety of scenarios.
This talk will address certain recent advances in the area, focusing on the case of search for moving targets.
Date received: October 30, 2008
Passive dynamics of animal locomotion
by
Te-yuan Chyou
Department of Mathematics and Statistics, University of Otago
Coauthors: Gerrard Liddell, Mike Paulin
For decades biologists believed that animals walk because the brains calculates the motion trajectories for the limbs. More recently, there is a new hypothesis about animal locomotion that suggests the contrary. Animal framework is built for walking in the first place. It has the correct dynamics so that they can work without relying on controls. Instead, the walking gait is generated simply by interaction of gravity and inertia, in a stable, naturally emerged limit-cycle, known as passive dynamic walking. The feasibility of passive dynamic walking had been demonstrated for biped system that consists of only a pair of legs. In this talk we will look into full-body passive dynamic walking models, by showing that some simple and animal-like mechanical linkages can generate walking gait by using only gravity, and can recover from small perturbation without the need of controller input. The contribution of a torso on the stability and efficiency of passive biped walking will also be addressed.
Date received: October 24, 2008
A multiscale, spatially-distributed model of airway hyper-responsiveness
by
Graham Donovan
Auckland Bioengineering Institute
Coauthors: Antonio Politi, James Sneyd, Merryn Tawhai
Airway hyper-responsiveness (AHR), along with airway hyper-sensitivity, is a defining feature of asthma, and greater understanding of this emergent phenomenon may lead to better insight into and treatment of the condition. Our model couples together the organ scale with the tissue scale in the lung in a multiscale approach to the problem. At the organ level, parenchymal tissue is modeled as a compressible Blatz-Ko material in three dimensions, with expansion and recoil of lung tissue due to tidal breathing. The governing equations of finite elasticity deformation are solved using a finite element method. An airway tree is embedded in this tissue, with airway smooth muscle behavior described by a modified Hai-Murphy cross-bridge model (Wang et al., Biophys. J. 94:2008). Each airway segment is initially assumed to be radially symmetric and longitudinally stiff, and thus the embedded airway tree is essentially 1D. Preliminary results from the integrated model indicate potential use in the study of many phenomena associated with asthmatic AHR, including spatial distribution of ventilation defects, patchiness, and effects of deep inspirations.
Date received: October 28, 2008
Mathematical modeling of the HER2-receptor overexpression in breast cancer
by
Amina Eladdadi
Mathematical Sciences Department, Rensselaer Polytechnic Institute, New York
Coauthors: David Isaacson
Overexpression of the HER2 receptor due to the neu gene amplification contributes to the development of human breast cancers. The carcinogenic effects of HER2 protein overexpression on cell growth and cell proliferation have been observed in a variety of experimental systems. These observations suggest that HER2 overexpression provides tumor cells with a growth advantage leading to a more aggressive phenotype. To investigate the effects of HER2 receptor overexpression on cell proliferation, we have developed two mathematical models that describe the proliferative behavior of HER2-overexpressing cells.
We address by means of mathematical models and numerical simulation the following major questions:
1. How does the cell proliferation rate depend on the number (expression level of the HER2 receptor?
2. How do changes in the number of HER2 and EGFR receptors during the cell-cycle affects the cell proliferation rate?
The cell proliferation models enable us to simulate the proliferative behavior of the HER2-overexpressing cells with various HER2 and EGFR expression levels at various ligand concentrations. Both mathematical models predict a growth advantage associated with excess in cell surface HER2 receptors.
Date received: September 25, 2008
The countercurrent mechanism
by
Scott Graybill
Department of Mathematics and Statistics, University of Canterbury
Coauthors: Alex James, Mike Plank, Tim David, Zoltan Endre
A concentration gradient exists in the kidney, with the higest concentration deep within the medulla. This gradient can be explained by the countercurrent mechanism, where a modest gradient is increased by the interaction of two parallel tubules.
This talk will discuss how the water and solute transport properties of the two parallel tubules can establish and maintain this concentraion gradient and present some results.
Date received: October 29, 2008
Understanding complicated oscillations in intracellular calcium dynamics
by
Emily Harvey
University of Auckland
Coauthors: Vivien Kirk, James Sneyd
Calcium controls a huge range of crucial cellular processes. It is thought that oscillations in intracellular calcium act as signals, with the message being encoded in the frequency and form of the oscillations. However, the mechanisms underlying these oscillations are not well known. In this talk I will show how the analysis of mathematical models of intracellular calcium can give us insight into these underlying mechanisms, particularly for the complicated oscillations known as mixed mode oscillations.
Date received: November 2, 2008
Existence of solutions in a model of chondrogenesis
by
Bogdan Kazmierczak
Institute of Fundamental Technological Research, Poland
Coauthors: M.Alber, St.Newman, G. Hentschel
The paper considers conditions sufficient for the existence of global classical solutions to a new model of chondrogenesis during the vertebrate limb formation. We assume that the diffusion coefficient of the fibronectin is positive and that the function describing the interaction between the fibronectin and cells satisfies some additional properties.
Date received: September 1, 2008
Modeling autoregulation in the rat kidney
by
Nicole Kleinstreuer
Centre for Bioengineering, University of Canterbury
Coauthors: Tim David, Mike Plank, Zoltan Endre
A transient mathematical model of whole-organ renal autoregulation in the rat is presented, incorporating the myogenic response throughout the renal vasculature and the tubuloglomerular feedback response at the level of the nephrons. The myogenic response to a change in circumferential wall tension is modeled with vessel size-specific parameters, including effects of in-vivo viscosity variation and flow-induced dilation. This myogenic model is coupled with a system representing change in concentration of the tubular filtrate and corresponding resistance changes of the afferent arteriole via the TGF mechanism. Computer simulation results of the steady state and transient autoregulatory response to pressure perturbations are examined, as well as the modulatory influences of metabolic and hemodynamic factors. A comprehensive model of autoregulation allows for the examination of both normal and pathological states, such as the altered NO production in chronic kidney disease or the inhibited tubular reabsorption of water seen in diabetes.
Date received: October 20, 2008
Reducing the load of spatial scales in a calcium model
by
Shawn Means
University of Auckland
Multiscale models of calcium dynamics often rely crucially on accurate
representations of the calcium concentration in restricted spaces. However, connecting a local model of a microdomain to the model of calcium dynamics in the bulk of the cell is often computationally expensive. We present a method which reduces this expense on a model of calcium dynamics for a cardiac cell which resolves the multiple spatial scales of the dyadic cleft (order 10 nm) and the bulk interior (order 1 um). The method involves using a combined analytical / numerical solution scheme coupled via appropriate boundary conditions.
Date received: November 16, 2008
Computational neural models embedded in virtual animals
by
Mike Paulin
University of Otago
It is now possible to build complex integrative models of animals, with brains and bodies, which can act autonomously in virtual environments. These models extend scientists’ ability to visualize the relevant physics and biology, and to develop and test theories despite the essential complexity of neural systems. Wrapping the detailed physics, engineering, mathematical abstraction and numerical complexity in a form that looks and behaves like an animal, and can be measured and explored like the real thing, provides an interface not only between experimental biologists and mathematical/computational modelers, but also between scientists and the lay public. I will demonstrate a model of the electrosensory system of the spiny dogfish, Squalus acanthias. The dogfish’s ability to isolate weak signals in a noisy environment is due to a brainstem structure called the dorsal octavolateral nucleus. The virtual dogfish has a computational model of this neural structure, receiving realistic sense data from a realistic physical model of the environment. The human auditory system contains an analogous brainstem structure called the dorsal cochlear nucleus, albeit much less accessible to experimentation than the dogfish’s dorsal nucleus. Understanding the dogfish electrosensory hindbrain may lead to new designs for signal filters, in particular for applications in human hearing.
Date received: October 27, 2008
Who eats whom? Population dynamics in the ocean
by
Mike Plank
University of Canterbury
Marine ecosystems have a very high degree of size structure, meaning that body size (which typically spans several orders of magnitude from plankton to large fish) is the most important determinant of who eats whom. Many marine ecosystems have the remarkable property that total biomass in logarithmically sized bins is almost invariant with respect to body size. In this talk, I will present a stochastic, individual-based model of predation, growth and death, and show how this scales up to a size-structured population model. Depending on certain ecological parameters, this model can have a stable steady state (which is related to the invariance of biomass property), or can exhibit travelling wave solutions.
Date received: November 23, 2008
Optimal movement in the prey capture behaviour of weakly electric fish
by
Claire Postlethwaite
University of Auckland
Coauthors: Malcolm MacIver, Mary Silber, Tiffany Psemeneki, Jangir Selmanikov
Animal behaviour arises through a complex mixture of biomechanical, neuronal, sensory, and control constraints. By focusing on a simple, stereotyped movement, the prey capture strike of a weakly electric fish, we show that the trajectory of a strike is one which minimises effort. Specifically, we model the fish as a rigid ellipsoid moving through a fluid with no viscosity, governed by Kirchhoff's equations, and generate trajectories which are optimal with respect to a mechanical cost function. We compare these to measured prey capture strikes of weakly electric fish. The fish has certain movement limitations which are not incorporated in the mathematical model, such as not being able to move sideways. Nonetheless, we show quantitatively that the computed least-cost trajectories are remarkably similar to the measured trajectories.
Date received: October 19, 2008
Development of a model-based tracking algorithm for reconstruction of 3D spider motion.
by
Kiri Pullar
University of Otago
Coauthors: Mike Paulin
An algorithm that recovers 3D body pose from video sequences has numerous applications such as motion capture, gesture recognition, surveillance of people or animals and animation for movies or computer games. The aim of this work is to develop a tracking approach that exploits our knowledge of physics to enable makerless motion capture of a spider during locomotion.
The basic elements of our tracking approach are an articulated body model, extracted features from video frames and Bayesian filtering. Articulated objects like the spider present a number of difficulties for successful tracking. The three key challenges are: large number of degrees of freedom (a complete model requires ~64 DOF), fast, non-linear motion and self occlusion of limbs. I intend to overcome these complications by beginning with a simple inverted pendulum based model, then adding complexity such as multiple links, springs and constraints until I have a physics based model that can be applied to the tracking of 3D spider motion.
Date received: October 27, 2008
Multitype contact processes: stochastic spatial competition models
by
Joseph Stover
University of Canterbury
The contact process is the basic interacting particle system used for creating stochastic spatial biological models. A new type of particle is introduced for each species or even for stages of growth within a species. Analytical studies have proven extremely difficult for these types of models, but mean field analysis and computer simulations can provide some insight into their behavior.
Date received: November 2, 2008
Modelling the interaction of prolactin and LIF signalling in the bovine mammary gland
by
Kumar Vetharaniam
AgResearch Limited, New Zealand
Coauthors: Kuljeet Singh
The hormone prolactin plays a major part in controlling the synthesis of all the major milk components and is important for maintaining lactation. A key pathway through which prolactin acts involves the activation of STAT-5 proteins which then translocate to the nucleus and mediate the transcription of prolactin’s target genes. A potential inhibitor of PRL action is activated STAT-3, which up-regulates the SOCS-3 protein which in turn blocks STAT-5 activation. Experiments have lead to speculation that increased levels of STAT-3 may be responsible for turning off milk production, and suggest a possible role for LIF, a factor known to activate STAT-3.
We have constructed a mathematical model, consisting of a set of coupled, delay-differential equations, which describes prolactin and LIF signalling along the STAT pathways. This model allows us to investigate under what conditions the appearance of LIF could stop milk synthesis by blocking prolactin, and also to investigate possible interventions to ameliorate the effect of STAT-3.
Date received: October 30, 2008
Modelling the calcium dynamics in airway smooth muscle cells
by
Inga Wang
University of Auckland
Asthma is a condition characterized by airway hyper-responsiveness, which results in reversible increases in airway smooth muscle (ASM) contraction, and variable amounts of inflammation of the bronchial mucosa. Hence the understanding of the regulation and mechanics of ASM contraction and the surrounding lung tissue is crucial for medical research. The ASM contraction is regulated by the changes in intracellular calcium concentration and the responsiveness of the ASM to this calcium. In this talk, I will present a model of calcium dynamics in ASM cells.
Date received: November 15, 2008
Dynamics in reaction-diffusion excitable systems
by
Wenjun Zhang
University of Auckland
Excitable systems of reaction-diffusion equations are used to model many biophysical processes, including changes of calcium concentration in various cell types. Understanding the interaction between soliton and periodic waves is important in these systems. By moving to travelling waves coordinates and using ideas from geometric singular perturbation theory, we show how complicated bifurcations associated with this interaction arise from the singular limit. We illustrate the method with examples of calcium models and the FitzHugh-Nagumo model.
Date received: November 11, 2008