Landscape as a model: the importance of geometry

In all models, but especially in those used to predict uncertain processes (e.g., climate change and nonnative species establishment), it is important to identify and remove any sources of bias that may confound results. This is critical in models designed to help support decisionmaking. The geometry used to represent virtual landscapes in spatially explicit models is a potential source of bias. The majority of spatial models use regular square geometry, although regular hexagonal landscapes have also been used. However, there are other ways in which space can be represented in spatially explicit models. For the first time, we explicitly compare the range of alternative geometries available to the modeller, and present a mechanism by which uncertainty in the representation of landscapes can be incorporated. We test how geometry can affect cell-to-cell movement across homogeneous virtual landscapes and compare regular geometries with a suite of irregular mosaics. We show that regular geometries have the potential to systematically bias the direction and distance of movement, whereas even individual instances of landscapes with irregular geometry do not. We also examine how geometry can affect the gross representation of real-world landscapes, and again show that individual instances of regular geometries will always create qualitative and quantitative errors. These can be reduced by the use of multiple randomized instances, though this still creates scale-dependent biases. In contrast, virtual landscapes formed using irregular geometries can represent complex real-world landscapes without error. We found that the potential for bias caused by regular geometries can be effectively eliminated by subdividing virtual landscapes using irregular geometry. The use of irregular geometry appears to offer spatial modellers other potential advantages, which are as yet underdeveloped. We recommend their use in all spatially explicit models, but especially for predictive models that are used in decisionmaking.     

Improving Tikhonov regularization with linearly constrained optimization: application to the inverse epicardial potential solution.

Two methods to improve on the accuracy of the Tikhonov regularization technique commonly used for the stable recovery of solutions to ill-posed problems are presented. These methods do not require a priori knowledge of the properties of the solution or of the error. Rather they exploit the observed properties of overregularized and underregularized Tikhonov solutions so as to impose linear constraints on the sought-after solution. The two methods were applied to the inverse problem of electrocardiography using a spherical heart-torso model and simulated inner-sphere (epicardial) and outer-sphere (body) potential distributions. It is shown that if the overregularized and underregularized Tikhonov solutions are chosen properly, the two methods yield epicardial solutions that are not only more accurate than the optimal Tikhonov solution but also provide other qualitative information, such as correct position of the extrema, not obtainable using ordinary Tikhonov regularization. A heuristic method to select the overregularized and underregularized solutions is discussed.     

Influence of the muscle fibre end geometry on the extracellular potentials

Intra- and extracellular action potentials of isolated frog muscle fibres were recorded at different distances to the end of the fibre. The first and second time derivatives of the intracellular action potentials were also recorded. The intracellular action potentials and their first and second time derivatives were almost the same regardless of the place of recording. With the decrease in the axial distance to the end the extracellular action potentials changed gradually in a complicated manner from a shape similar to the second time derivative into a shape similar to the first time derivative. Extracellular potentials, having two negative maxima, were recorded over the terminal taper part of the fibres.These alterations were simulated by a mathematical model. It was shown that the changes in the shape of the extracellular action potentials around the end of the fibres were mainly due to the existence of the fibre end though a better correspondence of the experimentally recorded and the calculated extracellular action potentials was obtained when the morphology of the fibre end was taken into consideration.     

Computational issues in mapping variation affecting susceptibility to complex disorders: the chicken and the egg

Linkage mapping strategies for complex disorders have evolved under a variety of constraints. Some of these constraints reflect the nature of complex disorders and are manifest in limitations on the kinds of data that can be collected, while others were (at least historically) strictly computational. This paper focuses on how computational issues have impacted the design of studies on complex disorders and, conversely, how our study designs have influenced the computational issues that have been addressed. We now have unprecedented computational resources, but also face unprecedented computational and methodological challenges as we move from the linkage mapping of genes influencing susceptibility to complex disorders toward the identification of the actual variation affecting susceptibility to these disorders. The near-term computational and methodological issues we must address will be profoundly influenced by the study designs of the recent past. But future study designs, as well as our investments in computational and methodological research, ought to be developed considering the computational and informatics resources we now have at hand.     

Relative sensitivity of photosynthesis and respiration to freeze-thaw stress in herbaceous species : importance of realistic freeze-thaw protocols

The relative effect of a freeze-thaw cycle on photosynthesis, respiration, and ion leakage of potato leaf tissue was examined in two potato species, Solanum acaule Bitt. and Solanum commersonii Dun. Photosynthesis was found to be much more sensitive to freezing stress than was respiration, and demonstrated more than a 60% inhibition before any impairment of respiratory function was observed. Photosynthesis showed a slight to moderate inhibition when only 5 to 10% of the total electrolytes had leaked from the tissue (reversible injury). This was in contrast to respiration which showed no impairment until temperatures at which about 50% ion leakage (irreversible injury) had occurred. The influence of freeze-thaw protocol was further examined in S. acaule and S. commersonii, in order to explore discrepancies in the literature as to the relative sensitivities of photosynthesis and respiration. As bath cooling rates increased from 1°C/hour to about 3 or 6°C/hour, there was a dramatic increase in the level of damage to all measured cellular functions. The initiation of ice formation in deeply supercooled tissue caused even greater damage. As the cooling rates used in stress treatments increased, the differential sensitivity between photosynthesis and respiration nearly disappeared. Examination of agriculturally relevant, climatological data from an 11 year period confirmed that air cooling rates in the freezing range do not exceed 2°C/hour. It was demonstrated, in the studies presented here, that simply increasing the actual cooling rate from 1.0 to 2.9°C/hour, in frozen tissue from paired leaflet halves, meant the difference between cell survival and cell death.     

Oblique double layer potentials for the direct and inverse problems of electrocardiology

A mathematical analysis of a model of the cardiac bioelectric sources generating the potential field in a bounded conducting volume is carried out. A boundary integral representation of the potential is given, which shows that, if the anisotropy of the cardiac muscle is taken into account, the bioelectric sources are characterized by an “oblique” double layer on the excitation wavefront. Boundedness conditions for the potential and jump relationships across the front are investigated. Uniqueness results for the inverse problem (i.e. the determination of the wavefront surface, given the potential on the volume boundary) are established.     

Computational fluid dynamics simulations in realistic 3-D geometries of the total cavopulmonary anastomosis: the influence of the inferior caval anastomosis

Fluid dynamics of Total Cavo-Pulmonary Connection (TCPC) were studied in 3-D models based on real dimensions obtained by Magnetic Resonance (MR) images. Models differ in terms of shape (intra- or extra-cardiac conduit) and cross section (with or without patch enlargement) of the inferior caval (IVC) anastomosis connection. Realistic pulsatile flows were submitted to both the venae cavae, while porous portions were added at the end of the pulmonary arteries to reproduce the pulmonary afterload. The dissipated power and the flow distribution into the lungs were calculated at different values of pulmonary arteriolar resistances (PAR). The most important results are: i) power dissipation in different TCPC designs is influenced by the actual cross sectional area of the IVC anastomosis and ii) the inclusion of a patch minimizes the dissipated power (range 4-13 mW vs. 14-56 mW). Results also show that the perfusion of the right lung is between 15% and 30% of the whole IVC blood flow when the PAR are evenly distributed between the right and the left lung.     

Computational study of the elastic properties of Rheum rhabarbarum tissues via surrogate models of tissue geometry

Plant petioles and stems are hierarchical cellular structures, displaying geometrical features defined at multiple length scales. One or more of the intermediate hierarchical levels consists of tissues in which the cellular distribution is quasi-random, a factor that affects the elastic properties of the tissues. The current work focuses on the finite element analysis (FEA) of the constituent tissues of the plant Rheum rhabarbarum (rhubarb). The geometric model is generated via a recently introduced method: the finite edge centroidal Voronoi tessellation (FECVT), which is capable to capture the gradients of cellularity and diversified pattern of cellular materials, as opposed to current approaches in literature. The effective stiffness of the tissues is obtained by using an accurate numerical homogenization technique via detailed finite element analysis of the models of sub-regions of the tissues. As opposed to a large-scale representative volume element (RVE), statistical volume elements (SVE) are considered in this work to model tissue microstructures that are highly random. 2D finite element analyses demonstrate that the distribution of cells in collenchyma and parenchyma tissue make them stiffer in two different directions, while the overall effect of the combined tissues results in approximately equal stiffness in both directions. The rhubarb tissues, on the other hand, are more compliant than periodic and quasi-uniform random cellular materials by a factor of up to 47% and 44%, respectively. The variations of the stiffness shows the stiffening role that cell shape, size, and graded cellular distribution play in the mechanics of the rhubarb tissue.     

Ecological biogeography of southern ocean islands: the importance of considering spatial issues

Understanding patterns of among-island variation in species richness has long been an important question in ecology and biogeography. However, despite the clear spatial nature of the data used for such investigations, the spatial distribution of the different sampled locations is rarely explicitly considered, which may be critical for statistical and biological reasons. In a recent study, Chown et al. (1998) investigated the relationships between species richness of different indigenous and introduced taxonomic groups and a variety of variables characterizing Southern Ocean islands, and here, we use these data to address spatial issues. As predicted, we found spatial autocorrelation in species richness for terrestrial taxa with high dispersal ability or for terrestrial taxa that had time to disperse locally (introduced land birds and indigenous taxa) but not for taxa that had low opportunity to disperse to nearby islands (introduced plants, insects, and mammals), which suggests that colonization from nearby islands has played an important role in shaping present-day patterns of among-island variation in species richness. Interestingly, in several cases, the estimated effect of variables changed when spatial covariance was incorporated. Moreover, the absence of autocorrelation of some variables allowed us to confirm some important results of Chown et al. (1998), notably those involving the potential impact of human presence on the biodiversity of these islands. Overall, our results illustrate the importance of considering spatial structures in ecological studies. This is notably the case when dispersal processes can be expected to explain some of the observed patterns.     

Time is on our side: the importance of considering a recovery period when assessing flooding tolerance in plants

There is wide consensus about the significance of monitoring plant responses during flooding when evaluating specific tolerance. Nonetheless, plant recovery once water recedes has often been overlooked. This note highlights the importance of registering plant performance during a recovery phase. Two opposite types of plant growth responses, during and after flooding, are discussed. It is shown that an apparently poor performance during flooding does not necessarily involve a reduced tolerance, as plants can prioritize saving energy and carbohydrates for later resumption of vigorous growth during recovery. Conversely, maintenance of positive plant growth during flooding can imply extensive depletion of reserves, consequently constraining future plant growth. Therefore, to accurately estimate real tolerance to this stress, plant performance should be appraised during both flooding and recovery periods.     

Modelling attention in individual cells leads to a system with realistic saccade behaviours

Single cell recordings in monkey inferior temporal cortex (IT) and area V4 during visual search tasks indicate that modulation of responses by the search target object occurs in the late portion of the cell’s sensory response (Chelazzi et al. in J Neurophysiol 80:2918–2940, 1998; Cereb Cortex 11:761–772, 2001) whereas attention to a spatial location influences earlier responses (Luck et al. in J Neurophysiol 77:24–42, 1997). Previous computational models have not captured differences in the latency of these attentional effects and yet the more protracted development of the object-based effect could have implications for behaviour. We present a neurodynamic biased competition model of visual attention in which we aimed to model the timecourse of spatial and object-based attention in order to simulate cellular responses and saccade onset times observed in monkey recordings. In common with other models, a top-down prefrontal signal, related to the search target, biases activity in the ventral visual stream. However, we conclude that this bias signal is more complex than modelled elsewhere: the latency of object-based effects in V4 and IT, and saccade onset, can be accurately simulated when the target object feedback bias consists of a sensory response component in addition to a mnemonic response. These attentional effects in V4 and IT cellular responses lead to a system that is able to produce search scan paths similar to those observed in monkeys and humans, with attention being guided to locations containing behaviourally relevant stimuli. This work demonstrates that accurate modelling of the timecourse of single cell responses can lead to biologically realistic behaviours being demonstrated by the system as a whole.     

HELANAL: a program to characterize helix geometry in proteins

A detailed analysis of structural and position dependent characteristic features of helices will give a better understanding of the secondary structure formation in globular proteins. Here we describe an algorithm that quantifies the geometry of helices in proteins on the basis of their C alpha atoms alone. The Fortran program HELANAL can extract the helices from the PDB files and then characterises the overall geometry of each helix as being linear, curved or kinked, in terms of its local structural features, viz. local helical twist and rise, virtual torsion angle, local helix origins and bending angles between successive local helix axes. Even helices with large radius of curvature are unambiguously identified as being linear or curved. The program can also be used to differentiate a kinked helix and other motifs, such as helix-loop-helix or a helix-turn-helix (with a single residue linker) with the help of local bending angles. In addition to these, the program can also be used to characterise the helix start and end as well as other types of secondary structures.     

Numerical analysis of Ca2+ signaling in rat ventricular myocytes with realistic transverse-axial tubular geometry and inhibited sarcoplasmic reticulum

The t-tubules of mammalian ventricular myocytes are invaginations of the cell membrane that occur at each Z-line. These invaginations branch within the cell to form a complex network that allows rapid propagation of the electrical signal, and hence synchronous rise of intracellular calcium (Ca(2+)). To investigate how the t-tubule microanatomy and the distribution of membrane Ca(2+) flux affect cardiac excitation-contraction coupling we developed a 3-D continuum model of Ca(2+) signaling, buffering and diffusion in rat ventricular myocytes. The transverse-axial t-tubule geometry was derived from light microscopy structural data. To solve the nonlinear reaction-diffusion system we extended SMOL software tool (http://mccammon.ucsd.edu/smol/). The analysis suggests that the quantitative understanding of the Ca(2+) signaling requires more accurate knowledge of the t-tubule ultra-structure and Ca(2+) flux distribution along the sarcolemma. The results reveal the important role for mobile and stationary Ca(2+) buffers, including the Ca(2+) indicator dye. In agreement with experiment, in the presence of fluorescence dye and inhibited sarcoplasmic reticulum, the lack of detectible differences in the depolarization-evoked Ca(2+) transients was found when the Ca(2+) flux was heterogeneously distributed along the sarcolemma. In the absence of fluorescence dye, strongly non-uniform Ca(2+) signals are predicted. Even at modest elevation of Ca(2+), reached during Ca(2+) influx, large and steep Ca(2+) gradients are found in the narrow sub-sarcolemmal space. The model predicts that the branched t-tubule structure and changes in the normal Ca(2+) flux density along the cell membrane support initiation and propagation of Ca(2+) waves in rat myocytes.     

Validation of net joint loads calculated by inverse dynamics in case of complex movements: application to balance recovery movements

The joint forces and moments driving the motion of a human subject are classically computed by an inverse dynamic calculation. However, even if this process is theoretically simple, many sources of errors may lead to huge inaccuracies in the results. Moreover, a direct comparison with in vivo measured loads or with "gold standard" values from literature is only possible for very specific studies. Therefore, assessing the inaccuracy of inverse dynamic results is not a trivial problem and a simple method is still required. This paper presents a simple method to evaluate both: (1) the consistency of the results obtained by inverse dynamics; (2) the influence of possible modifications in the inverse dynamic hypotheses. This technique concerns recursive calculation performed on full kinematic chains, and consists in evaluating the loads obtained by two different recursive strategies. It has been applied to complex 3D whole body movements of balance recovery. A recursive Newton-Euler procedure was used to compute the net joint loads. Two models were used to represent the subject bodies, considering or not the upper body as a unique rigid segment. The inertial parameters of the body segments were estimated from two different sets of scaling equations [De Leva, P., 1996. Adjustments to Zatsiorsky-Suleyanov's segment inertia parameters. Journal of Biomechanics 29, 1223-1230; Dumas, R., Chèze, L., Verriest, J.-P., 2006b. Adjustments to McConville et al. and Young et al. Body Segment Inertial Parameters. Journal of Biomechanics, in press]. Using this comparison technique, it has been shown that, for the balance recovery motions investigated: (1) the use of the scaling equations proposed by Dumas et al., instead of those proposed by De Leva, improves the consistency of the results (average relative influence up to 30% for the transversal moment); (2) the arm motions dynamically influence the recovery motion in a non negligible way (average relative influence up to 15% and 30% for the longitudinal force and the transversal moment, respectively).