Parameter identification of the calvin photosynthesis cycle

Summary This article is concerned with the determination of kinetic parameters of the Calvin photosynthesis cycle which is described by seventeen nonlinear ordinary differential equations. It is shown that the task requires dynamic data for several sets of initial conditions. The numerical technique is based upon an algorithm for non-linear optimization and Gear's numerical integration scheme for stiff systems of differential equations. The sensitivity of the parameters to noise in the data is tested with a method adapted from Rosenbrook and Storey. A preliminary set of parameters has been obtained from a preliminary set of experimental data. The numerical methods are then tested with synthetic data derived from these parameters. The mathematical model and the results obtained in the simulation are used as an aid in designing new experiments.     

Trgrps — an interactive algorithm for group recogniton with an example from spartinetea

Summary TRGRPS can detect groups or signal if discrete groups cannot be found in a sample. The present paper elaborates on the concepts, describes the algorithm and provides illustrations from syntaxonomy. A computer program (TRGRPS.BAS) is available from the author upon request.Contribution from the Working Group for Data Processing in Phytosociology, International Society for Vegetation Science. For nomenclature of species see Lausi, Beeftink & Kortekaas (1975).The research project, from which this paper summarizes partial results, is supported by a National Research Council of Canada grant. Computer time was provided by the University of Western Ontario.     

Centres of diversity quantified—A maximum variance approach to a biogeographic problem

Summary A quantitative method that optimizes the mapping of species diversity in phytogeographic studies is described. Diversity is computed on the basis of species number per unit area. The optimal size of unit area for which diversity is computed is held to be that which maximises the diversity difference between species-rich and species-poor regions. An example is given using Turkish Papaver. A very high correspondence is found between intuitive insights based on long study and the computer-generated diversity maps. Phytogeographic elements were also determined by computer after gridding Turkey at the scale discovered to be optimal for diversity and scoring the grid squares for presence-absence of each species. In this case, too, quite high correspondence was found between the computer and intuitive results.Nomenclature follows Cullen (1965).The authors express their thanks to Mr. K. Roberts, University of Western Ontario Computing Centre of writing the original maximum variance program and to the National Research Council of Canada for supporting the computing side of the project.     

Quantitative evaluation of temporal similarity in abundance of animal species

Summary A quantitative method is suggested for measuring the similarity of seasonal abundance patterns of different animal species. The method was applied to two sets of field data and produced biologically meaningful and interesting results.     

Assessment of Mechanobiological Models for the Numerical Simulation of Tissue Differentiation around Immediately Loaded Implants

Nowadays, there is a growing consensus on the impact of mechanical loading on bone biology. A bone chamber provides a mechanically isolated in vivo environment in which the influence of different parameters on the tissue response around loaded implants can be investigated. This also provides data to assess the feasibility of different mechanobiological models that mathematically describe the mechanoregulation of tissue differentiation. Before comparing numerical results to animal experimental results, it is necessary to investigate the influence of the different model parameters on the outcome of the simulations. A 2D finite element model of the tissue inside the bone chamber was created. The differentiation models developed by Prendergast, et al. [“Biophysical stimuli on cells during tissue differentiation at implant interfaces”, Journal of Biomechanics, 30(6), (1997), 539–548], Huiskes et al. [“A biomechanical regulatory model for periprosthetic fibrous-tissue differentiation”, Journal of Material Science: Materials in Medicine, 8 (1997) 785–788] and by Claes and Heigele [“Magnitudes of local stress and strain along bony surfaces predict the course and type of fracture healing”, Journal of Biomechanics, 32(3), (1999) 255–266] were implemented and integrated in the finite element code. The fluid component in the first model has an important effect on the predicted differentiation patterns. It has a direct effect on the predicted degree of maturation of bone and a substantial indirect effect on the simulated deformations and hence the predicted phenotypes of the tissue in the chamber. Finally, the presence of fluid also causes time-dependent behavior.

Both models lead to qualitative and quantitative differences in predicted differentiation patterns. Because of the different nature of the tissue phenotypes used to describe the differentiation processes, it is however hard to compare both models in terms of their validity.     

Progress Curves Analysis as an Alternative for Exploration of Activation-inhibition Phenomena in Cholinesterases

The kinetic behaviour of insect acetylcholinesterases deviates from the Michaelis-Menten pattern. These deviations are known as activation or inhibition at various substrate concentrations and can be more or less observable depending on mutations around the active site of the enzyme. Most kinetic studies on these enzymes still rely on initial rate measurements. It is demonstrated here that according to this method one of the deviations can be overlooked. We attempt to point out that in such cases a detailed step-by-step progress curves analysis is successful. The study is focused on two different methods of analysing progress curves: (i) the first one is based on an integrated initial rate equation which can sufficiently fit truncated progress curves under corresponding conditions; and (ii) the other one precludes the algebraic formulae, but uses numerical integration for searching a non analytical solution of ordinary differential equations describing a kinetic model. All methods are tested on three different acetylcholinesterase mutants from Drosophila melanogaster. The results indicate that kinetic parameters for the E107K mutant with highly expressive activation and inhibition can be well evaluated applying any analysis method. It is quite different for E107W and E107Y mutants where latent activation is present, but discovered only using one or the other progress curves analysis methods.     

Robust numerical solution for the two parameter solute solvent transport model

Prediction of solute and solvent transport in cells is central to developing and testing cryopreservation protocols. As we show here, however, the models used can be difficult to accurately numerically integrate in some key cases, and thus are a challenge to implement when determining the time dependent cell state during cryoprotectant equilibration and cooling. Exact solution techniques exist for overcoming this problem, but their implementation is also challenging: inversion of a nonlinear function is required that negates much of the utility of the approach. This communication describes a simple approach for more robust numerical integration that can be implemented using any numerical differential equation solver, and can facilitate arbitrarily accurate solutions to transport models without the complication of inversion formulae or complicated numerical integration schemes. Further, a simple relevant example of red blood cell equilibration with 40% glycerol is presented with comments on extending the approach to other settings.