Some novel techniques of parameter estimation for the dynamical models in biological systems

Inverse problems based on using experimental data to estimate unknown parameters of a system often arise in biological and chaotic systems. In this paper, we consider parameter estimation in systems biology involving linear and non-linear complex dynamical models, including the Michaelis–Menten enzyme kinetic system, a dynamical model of competence induction in Bacillus subtilis bacteria and a model of feedback bypass in B. subtilis bacteria. We propose some novel techniques for inverse problems. Firstly, we establish an approximation of a non-linear differential algebraic equation that corresponds to the given biological systems. Secondly, we use the Picard contraction mapping, collage methods and numerical integration techniques to convert the parameter estimation into a minimization problem of the parameters. We propose two optimization techniques: a grid approximation method and a modified hybrid Nelder–Mead simplex search and particle swarm optimization (MH-NMSS-PSO) for non-linear parameter estimation. The two techniques are used for parameter estimation in a model of competence induction in B. subtilis bacteria with noisy data. The MH-NMSS-PSO scheme is applied to a dynamical model of competence induction in B. subtilis bacteria based on experimental data and the model for feedback bypass. Numerical results demonstrate the effectiveness of our approach.

Exploring the parameter space of a rabbit ventricular action potential model to investigate the effect of variation on action potential and calcium transients

Computational models for cardiomyocyte action potentials (AP) often make use of a large parameter set. This parameter set can contain some elements that are fitted to experimental data independently of any other element, some elements that are derived concurrently with other elements to match experimental data, and some elements that are derived purely from phenomenological fitting to produce the desired AP output. Furthermore, models can make use of several different data sets, not always derived for the same conditions or even the same species. It is consequently uncertain whether the parameter set for a given model is physiologically accurate. Furthermore, it is only recently that the possibility of degeneracy in parameter values in producing a given simulation output has started to be addressed. In this study, we examine the effects of varying two parameters (the L-type calcium current (I(CaL)) and the delayed rectifier potassium current (I(Ks))) in a computational model of a rabbit ventricular cardiomyocyte AP on both the membrane potential (V(m)) and calcium (Ca(2+)) transient. It will subsequently be determined if there is degeneracy in this model to these parameter values, which will have important implications on the stability of these models to cell-to-cell parameter variation, and also whether the current methodology for generating parameter values is flawed. The accuracy of AP duration (APD) as an indicator of AP shape will also be assessed.

Numerical exploration of the defect’s effect on mechanical properties of nanowires under torsion

Molecular dynamics (MD) simulations have been carried out to investigate the defect’s effect on the mechanical properties of single-crystal copper nanowire with different surface defects, under torsion deformation. The torsional rigidity is found insensitive to the surface defects and the critical angle appears an obvious decrease due to the surface defects, the largest decrease is found for the nanowire with surface horizon defect. The deformation mechanism appears different degrees of influence due to surface defects. The surface defects play a role of dislocation sources. Comparing with single intrinsic stacking faults formation for the perfect nanowire, much affluent deformation processes have been activated because of surface defects, for instance, we find the twins formation for the nanowire with a surface 45o defect.

Simulations of the effect of waveguide cross-section on quantum dot – plasmon coupling

Quantum dot - plasmon waveguide systems are of interest for the active control of plasmon propagation, and consequently, the development of active nanophotonic devices such as nano-sized optical transistors. This paper is concerned with how varying aspect ratio of the waveguide crosssection affects the quantum dot - plasmon coupling. We compare a stripe waveguide with an equivalent nanowire, illustrating that both waveguides have a similar coupling strength to a nearby quantum dot for small waveguide cross-section, thereby indicating that stripe lithographic waveguides have strong potential use in quantum dot –plasmon waveguide systems. We also demonstrate that changing the aspect ratio of both stripe and wire waveguides can increase the spontaneous emission rate of the quantum dot into the plasmon mode, by up to a factor of five. The results of this paper will contribute to the optimisation of quantum dot - plasmon waveguide systems and help pave the way for the development of active nanophotonics devices.

The Kinaesthetic Fusion Effect : fast-forward 30 years

This study investigated the Kinaesthetic Fusion Effect (KFE) first described by Craske and Kenny in 1981. The current study did not replicate these findings following a change in the reporting method used by participants. Participants did not perceive any reduction in the sagittal separation of a button pressed by the index finger of one arm and a probe touching the other, following repeated exposure to the tactile stimuli present on both unseen arms. This study’s failure to replicate the widely-cited KFE as described by Craske et al. (1984) suggests that it may be contingent on several aspects of visual information, especially the availability of a specific visual reference, the role of instructions regarding gaze direction, and the potential use of a line of sight strategy when referring felt positions to an interposed surface. In addition, a foreshortening effect was found; this may result from a line-of-sight judgment and represent a feature of the reporting method used. Finally, this research will benefit future studies that require participants to report the perceived locations of the unseen limbs.

The effect of ocular surface conditions on blink rate and completeness

A healthy human would be expected to show periodic blinks, making a brief closure of the eyelids. Most blinks are spontaneous, occurring regularly with no external stimulus. However a reflex blink can occur in response to external stimuli such as a bright light, a sudden loud noise, or an object approaching toward the eyes. A voluntary or forced blink is another type of blink in which the person deliberately closes the eyes and the lower eyelid raises to meet the upper eyelid. A complete blink, in which the upper eyelid touches the lower eyelid, contributes to the health of ocular surface by providing a fresh layer of tears as well as maintaining optical integrity by providing a smooth tear film over the cornea. The rate of blinking and its completeness vary depending on the task undertaken during blink assessment, the direction of gaze, the emotional state of the subjects and the method under which the blink was measured. It is also well known that wearing contact lenses (both rigid and soft lenses) can induce significant changes in blink rate and completeness. It is been established that efficient blinking plays an important role in ocular surface health during contact lens wear and for improving contact lens performance and comfort. Inefficient blinking during contact lens wear may be related to a low blink rate or incomplete blinking and can often be a reason for dry eye symptoms or ocular surface staining. It has previously been shown that upward gaze can affect blink rate, causing it to become faster. In the first experiment, it was decided to expand on previous studies in this area by examining the effect of various gaze directions (i.e. upward gaze, primary gaze, downward gaze and lateral gaze) as well as head angle (recumbent position) on normal subjects’ blink rate and completeness through the use of filming with a high-speed camera. The results of this experiment showed that as the open palpebral aperture (and exposed ocular surface area) increased from downward gaze to upward gaze, the number of blinks significantly increased (p<0.04). Also, the size of closed palpebral aperture significantly increased from downward gaze to upward gaze (p<0.005). A weak positive correlation (R² = 0.18) between the blink rate and ocular surface area was found in this study. Also, it was found that the subjects showed 81% complete blinks, 19% incomplete blinks and 2% of twitch blinks in primary gaze, consistent with previous studies. The difference in the percentage of incomplete blinks between upward gaze and downward gaze was significant (p<0.004), showing more incomplete blinks in upward gaze. The findings of this experiment suggest that while blink rate becomes slower in downward gaze, the completeness of blinking is typically better, thereby potentially reducing the risk of tear instability. On the other hand, in upward gaze while the completeness of blinking becomes worse, this is potentially offset by increased blink frequency. In addition, blink rate and completeness were not affected by lateral gaze or head angle, possibly because these conditions have similar size of the open palpebral aperture compared with primary gaze. In the second experiment, an investigation into the changes in blink rate and completeness was carried out in primary gaze and downward gaze with soft and rigid contact lenses in unadapted wearers. Not surprisingly, rigid lens wear caused a significant increase in the blink rate in both primary (p<0.001) and downward gaze (p<0.02). After fitting rigid contact lenses, the closed palpebral aperture (blink completeness) did not show any changes but the open palpebral aperture showed a significant narrowing (p<0.04). This might occur from the subjects’ attempt to avoid interaction between the upper eyelid and the edge of the lens to minimize discomfort. After applying topical anaesthetic eye drops in the eye fitted with rigid lenses, the increased blink rate dropped to values similar to that before lens insertion and the open palpebral aperture returned to baseline values, suggesting that corneal and/or lid margin sensitivity was mediating the increased blink rate and narrowed palpebral aperture. We also investigated the changes in the blink rate and completeness with soft contact lenses including a soft sphere, double slab-off toric design and periballast toric design. Soft contact lenses did not cause any significant changes in the blink rate, closed palpebral aperture, open palpebral aperture and the percentage of incomplete blinks in either primary gaze or downward gaze. After applying anaesthetic eye drops, the blink rate reduced in both primary gaze and downward gaze, however this difference was not statistically significant. The size of the closed palpebral aperture and open palpebral aperture did not show any significant changes after applying anaesthetic eye drops. However it should be noted that the effects of rigid and soft contact lenses that we observed in these studies were only the immediate reaction to contact lenses and in the longer term, it is likely that these responses will vary as the eye adapts to the presence of the lenses.

Effect of cold water immersion on repeated cycling performance and limb blood flow

The purpose of the present study was to compare the effects of cold water immersion (CWI) and active recovery (ACT) on resting limb blood flow, rectal temperature and repeated cycling performance in the heat. Ten subjects completed two testing sessions separated by 1 week; each trial consisted of an initial all-out 35-min exercise bout, one of two 15-min recovery interventions (randomised: CWI or ACT), followed by a 40-min passive recovery period before repeating the 35-min exercise bout. Performance was measured as the change in total work completed during the exercise bouts. Resting limb blood flow, heart rate, rectal temperature and blood lactate were recorded throughout the testing sessions. There was a significant decline in performance after ACT (mean (SD) −1.81% (1.05%)) compared with CWI where performance remained unchanged (0.10% (0.71%)). Rectal temperature was reduced after CWI (36.8°C (1.0°C)) compared with ACT (38.3°C (0.4°C)), as was blood flow to the arms (CWI 3.64 (1.47) ml/100 ml/min; ACT 16.85 (3.57) ml/100 ml/min) and legs (CW 4.83 (2.49) ml/100 ml/min; ACT 4.83 (2.49) ml/100 ml/min). Leg blood flow at the end of the second exercise bout was not different between the active (15.25 (4.33) ml/100 ml/min) and cold trials (14.99 (4.96) ml/100 ml/min), whereas rectal temperature (CWI 38.1°C (0.3°C); ACT 38.8°C (0.2°C)) and arm blood flow (CWI 20.55 (3.78) ml/100 ml/min; ACT 23.83 (5.32) ml/100 ml/min) remained depressed until the end of the cold trial. These findings indicate that CWI is an effective intervention for maintaining repeat cycling performance in the heat and this performance benefit is associated with alterations in core temperature and limb blood flow.

Higher-order spectral analysis of nonlinear ocean surface gravity waves

Higher-order spectral analysis is used to detect the presence of secondary and tertiary forced waves associated with the nonlinearity of energetic swell observed in 8- and 13-m water depths. Higher-order spectral analysis techniques are first described and then applied to the field data, followed by a summary of the results.

Higher-Order spectra of nonlinear polynomial models for Chua's circuit

Polynomial models are shown to simulate accurately the quadratic and cubic nonlinear interactions (e.g. higher-order spectra) of time series of voltages measured in Chua's circuit. For circuit parameters resulting in a spiral attractor, bispectra and trispectra of the polynomial model are similar to those from the measured time series, suggesting that the individual interactions between triads and quartets of Fourier components that govern the process dynamics are modeled accurately. For parameters that produce the double-scroll attractor, both measured and modeled time series have small bispectra, but nonzero trispectra, consistent with higher-than-second order nonlinearities dominating the chaos.

An analytical solution for diffusion and nonlinear uptake of oxygen in a spherical cell

We develop a new analytical solution for a reactive transport model that describes the steady-state distribution of oxygen subject to diffusive transport and nonlinear uptake in a sphere. This model was originally reported by Lin (Journal of Theoretical Biology, 1976 v60, pp449–457) to represent the distribution of oxygen inside a cell and has since been studied extensively by both the numerical analysis and formal analysis communities. Here we extend these previous studies by deriving an analytical solution to a generalized reaction-diffusion equation that encompasses Lin’s model as a particular case. We evaluate the solution for the parameter combinations presented by Lin and show that the new solutions are identical to a grid-independent numerical approximation.

Elaborating a tactile-proprioceptive illusion : the kinaesthetic fusion effect

This study investigated the Kinaesthetic Fusion Effect (KFE) first described by Craske and Kenny in 1981. In Experiment 1 the study did not replicate these findings following a change in the reporting method used by participants. Participants did not perceive any reduction in the sagittal separation of a button pressed by the index finger of one arm and a probe touching the other, following repeated exposure to the tactile stimuli present on both unseen arms. This study’s failure to replicate the widely-cited KFE as described by Craske et al. (1984) suggests that it may be contingent on several aspects of visual information, especially the availability of a specific visual reference, the role of instructions regarding gaze direction, and the potential use of a line of sight strategy when referring felt positions to an interposed surface. In addition, a foreshortening effect was found; this may result from a line-of-sight judgment and represent a feature of the reporting method used. Finally, this research will benefit future studies that require participants to report the perceived locations of the unseen limbs. Experiment 2 investigated the KFE when the visual reference was removed and participants made reports of touched position, blindfolded. A number of interesting outcomes arose from this change and may provide clarification to the phenomena.

The effect of various temperature indicators on different mortality categories in a subtropical city of Brisbane, Australia.

BACKGROUND: The relationship between temperature and mortality has been explored for decades and many temperature indicators have been applied separately. However, few data are available to show how the effects of different temperature indicators on different mortality categories, particularly in a typical subtropical climate. OBJECTIVE: To assess the associations between various temperature indicators and different mortality categories in Brisbane, Australia during 1996-2004. METHODS: We applied two methods to assess the threshold and temperature indicator for each age and death groups: mean temperature and the threshold assessed from all cause mortality was used for all mortality categories; the specific temperature indicator and the threshold for each mortality category were identified separately according to the minimisation of AIC. We conducted polynomial distributed lag non-linear model to identify effect estimates in mortality with one degree of temperature increase (or decrease) above (or below) the threshold on current days and lagged effects using both methods. RESULTS: Akaike's Information Criterion was minimized when mean temperature was used for all non-external deaths and deaths from 75 to 84 years; when minimum temperature was used for deaths from 0 to 64 years, 65-74 years, ≥ 85 years, and from the respiratory diseases; when maximum temperature was used for deaths from cardiovascular diseases. The effect estimates using certain temperature indicators were similar as mean temperature both for current day and lag effects. CONCLUSION: Different age groups and death categories were sensitive to different temperature indicators. However, the effect estimates from certain temperature indicators did not significantly differ from those of mean temperature.

Effect of accommodation on peripheral ocular aberrations

Changes in peripheral aberrations, particularly higher-order aberrations, as a function of accommodation have received little attention. Wavefront aberrations were measured for the right eyes of 9 young adult emmetropes at 38 field positions in the central 42 x 32 degrees of the visual field. Subjects accommodated monocularly to targets at vergences of either 0.3 or 4.0 D. Wavefront data for a 5 mm diameter pupil were analyzed either in terms of the vector components of refraction or Zernike coefficients and total RMS wavefront aberrations. Relative peripheral refractive error (RPRE) was myopic at both accommodation demands and showed only a slight, not statistically significant, hypermetropic shift in the vertical meridian with the higher accommodation demand. There was little change in the astigmatic components of refraction or the higher-order Zernike coefficients, apart from fourth-order spherical aberration which became more negative (by 0.10 µm) at all field locations. Although it has been suggested that nearwork and the state of peripheral refraction may play some role in myopia development, for most of our adult emmetropes any changes with accommodation in RPRE and aberration were small. Hence it seems unlikely that such changes can be of importance to late-onset myopisation.

Intention, foresight and ending life : a response to "The Double Effect effect" by Charles Foster, Jonathan Herring, Karen Melham and Tony Hope, (CQ 20(1))

In this paper I examine the recent arguments by Charles Foster, Jonathan Herring, Karen Melham and Tony Hope against the utility of the doctrine of double effect. One basis on which they reject the utility of the doctrine is their claim that it is notoriously difficult to apply what they identify as its 'core' component, namely, the distinction between intention and foresight. It is this contention that is the primarily focus of my article. I argue against this claim that the intention/foresight distinction remains a fundamental part of the law in those jurisdictions where intention remains an element of the offence of murder and that, accordingly, it is essential ro resolve the putative difficulties of applying the intention/foresight distinction so as to ensure the integrity of the law of murder. I argue that the main reasons advanced for the claim that the intention/foresight distinction is difficult to apply are ultimately unsustainable, and that the distinction is not as difficult to apply as the authors suggest.

Investigation of the effect of organics on the water uptake of marine aerosols

Water uptake refers to the ability of atmospheric particles to take up water vapour from the surrounding atmosphere. This is an important property that affects particle size and phase and therefore influences many characteristics of aerosols relevant to air quality and climate. However, the water uptake properties of many important atmospheric aerosol systems, including those related to the oceans, are still not fully understood. Therefore, the primary aim of this PhD research program was to investigate the water uptake properties of marine aerosols. In particular, the effect of organics on marine aerosol water uptake was investigated. Field campaigns were conducted at remote coastal sites on the east coast of Australia (Agnes Water; March-April 2007) and west coast of Ireland (Mace Head; June 2007), and laboratory measurements were performed on bubble-generated sea spray aerosols. A combined Volatility-Hygroscopicity-Tandem Differential Mobility Analyser (VH-TDMA) was employed in all experiments. This system probes the changes in the hygroscopic properties of nanoparticles as volatile organic components are progressively evaporated. It also allows particle composition to be inferred from combined volatility-hygroscopicity measurements. Frequent new particle formation and growth events were observed during the Agnes Water campaign. The VH-TDMA was used to investigate freshly nucleated particles (17-22.5 nm) and it was found that the condensation of sulphate and/or organic vapours was responsible for driving particle growth during the events. Aitken mode particles (~40 nm) were also measured with the VH-TDMA. In 3 out of 18 VH-TDMA scans evaporation of a volatile, organic component caused a very large increase in hygroscopicity that could only be explained by an increase in the absolute water uptake of the particle residuals, and not merely an increase in their relative hygroscopicity. This indicated the presence of organic components that were suppressing the hygroscopic growth of mixed particles on the timescale of humidification in the VH-TDMA (6.5 secs). It was suggested that the suppression of water uptake was caused by either a reduced rate of hygroscopic growth due to the presence of organic films, or organic-inorganic interactions in solution droplets that had a negative effect on hygroscopicity. Mixed organic-inorganic particles were rarely observed by the VH-TDMA during the summer campaign conducted at Mace Head. The majority of particles below 100 nm in clean, marine air appeared to be sulphates neutralised to varying degrees by ammonia. On one unique day, 26 June 2007, particularly large concentrations of sulphate aerosol were observed and identified as volcanic emissions from Iceland. The degree of neutralisation of the sulphate aerosol by ammonia was calculated by the VH-TDMA and found to compare well with the same quantity measured by an aerosol mass spectrometer. This was an important verification of the VH-TMDA‘s ability to identify ammoniated sulphate aerosols based on the simultaneous measurement of aerosol volatility and hygroscopicity. A series of measurements were also conducted on sea spray aerosols generated from Moreton Bay seawater samples in a laboratory-based bubble chamber. Accumulation mode sea spray particles (38-173 nm) were found to contain only a minor organic fraction (< 10%) that had little effect on particle hygroscopicity. These results are important because previous studies have observed that accumulation mode sea spray particles are predominantly organic (~80% organic mass fraction). The work presented here suggests that this is not always the case, and that there may be currently unknown factors that are controlling the transfer of organics to the aerosol phase during the bubble bursting process. Taken together, the results of this research program have significantly improved our understanding of organic-containing marine aerosols and the way they interact with water vapour in the atmosphere.