The Need for Simple Dynamic Equations to Describe Plant Competition

A dynamic single-equation model for plant interaction is comparedwith the competition mechanism implicit in larger simulationmodels. When light is the limiting factor, both mechanisms canbe written in the same mathematical form containing a ‘drivingforce’ and a restriction factor. In the single-equationmodel the driving force is derived directly from the RGR ofa competition-free plant. In more comprehensive models, detailedinformation on the growth of plant organs has to be generatedby submodels. When factors other than light are limiting growth, the representationof competition in crop simulation models is complex; the single-equationmodel has the same form irrespective of which factor is limitinggrowth. It is argued that simple dynamic models should be developedfor complex processes. Plant competition, dynamic model     

A New Model to Describe Flow Behaviour of Concentrated Orange Juice

The knowledge of rheological behaviour of juices and fruit derivatives is very useful both in the prediction of their stability and in process design, and it depends on the type of juice and on the raw material with which they are produced. Most of the equations that have been used to quantify flow behaviour describe the evolution of shear stress with the change of shear rate. Nevertheless, the essential variable in equipment design is viscosity. In this way, a mathematical model to easily describe the evolution of apparent viscosity of these non-Newtonian fluids with the shear rate would be very useful. In this work, a mathematical expression has been developed, fitted to experimental data and compared with the Herschel–Bulkley one. The obtained parameters with concentrated orange juice followed these trends: equilibrium apparent viscosity (η _∞) scarcely changed with temperature. Static apparent viscosity (η ₀) decreased with increasing temperature, contrary to what happened with the flow behaviour constant k.     

A Model to Describe the Partitioning of Photosynthate during Vegetative Plant Growth

An approach is described to the problem of modelling quantitativelythe partitioning of photosynthate during vegetative plant growth.Two plant processes are important in the scheme: the first ofthese is the utilization of substrate for growth and how thisutilization depends upon substrate concentration, the secondconcerns the transport of substrate between different plantparts and how this depends upon the substrate concentrationsin the plant parts. In both cases simple phenomenological relationshave been assumed which seem to be in reasonable accord withexperimental data and with more basic theoretical considerations.The model is able to describe some of the features of steady-statevegetative plant growth in a natural manner. The limitationsof the present formulation are considered, and the implicationsof this type of approach for whole-plant models are discussed.     

A Horizontal Alignment Tool for Numerical Trend Discovery in Sequence Data: Application to Protein Hydropathy

An algorithm is presented that returns the optimal pairwise gapped alignment of two sets of signed numerical sequence values. One distinguishing feature of this algorithm is a flexible comparison engine (based on both relative shape and absolute similarity measures) that does not rely on explicit gap penalties. Additionally, an empirical probability model is developed to estimate the significance of the returned alignment with respect to randomized data. The algorithm''s utility for biological hypothesis formulation is demonstrated with test cases including database search and pairwise alignment of protein hydropathy. However, the algorithm and probability model could possibly be extended to accommodate other diverse types of protein or nucleic acid data, including positional thermodynamic stability and mRNA translation efficiency. The algorithm requires only numerical values as input and will readily compare data other than protein hydropathy. The tool is therefore expected to complement, rather than replace, existing sequence and structure based tools and may inform medical discovery, as exemplified by proposed similarity between a chlamydial ORFan protein and bacterial colicin pore-forming domain. The source code, documentation, and a basic web-server application are available.     

A Model Based on Facilitated Passive Diffusion is Needed to Describe Root Water Entry through Aquaporins

Despite abundant evidence that water transfer from soil to xylem occurs along a pathway regulated by aquaporins (AQPs) water entry is still modeled using principles of ordinary passive diffusion. Problems with this model have been known for some time and include variable intrinsic properties of conductivity Lp, changing reflection coefficients, σ, and an inability to accurately resolve osmotic differentials between the soil and xylem. Here we propose a model of water entry based on principles of facilitated passive diffusion and following Michaelis-Menten formalism. If one accepts that water entry is controlled, at least in part, by AQPs, then a model of ordinary passive diffusion is precluded, as it does not allow for facilitation kinetics. By contrast, recognition of facilitated water entry through protein channels could explain shortcomings of ordinary passive diffusion, such as diurnal variability in conductivity which we have recently shown is directly correlated to diurnal changes in PsPIP2-1 mRNA levels in Pisum sativum.Key Words: aquaporins, root water entry, facilitated passive diffusion, simple passive diffusion, biophysical models     

Towards Systematic Discovery of Signaling Networks in Budding Yeast Filamentous Growth Stress Response Using Interventional Phosphorylation Data

Reversible phosphorylation is one of the major mechanisms of signal transduction, and signaling networks are critical regulators of cell growth and development. However, few of these networks have been delineated completely. Towards this end, quantitative phosphoproteomics is emerging as a useful tool enabling large-scale determination of relative phosphorylation levels. However, phosphoproteomics differs from classical proteomics by a more extensive sampling limitation due to the limited number of detectable sites per protein. Here, we propose a comprehensive quantitative analysis pipeline customized for phosphoproteome data from interventional experiments for identifying key proteins in specific pathways, discovering the protein-protein interactions and inferring the signaling network. We also made an effort to partially compensate for the missing value problem, a chronic issue for proteomics studies. The dataset used for this study was generated using SILAC (Stable Isotope Labeling with Amino acids in Cell culture) technique with interventional experiments (kinase-dead mutations). The major components of the pipeline include phosphopeptide meta-analysis, correlation network analysis and causal relationship discovery. We have successfully applied our pipeline to interventional experiments identifying phosphorylation events underlying the transition to a filamentous growth form in Saccharomyces cerevisiae. We identified 5 high-confidence proteins from meta-analysis, and 19 hub proteins from correlation analysis (Pbi2p and Hsp42p were identified by both analyses). All these proteins are involved in stress responses. Nine of them have direct or indirect evidence of involvement in filamentous growth. In addition, we tested four of our predicted proteins, Nth1p, Pbi2p, Pdr12p and Rcn2p, by interventional phenotypic experiments and all of them present differential invasive growth, providing prospective validation of our approach. This comprehensive pipeline presents a systematic way for discovering signaling networks using interventional phosphoproteome data and can suggest candidate proteins for further investigation. We anticipate the methodology to be applicable as well to other interventional studies via different experimental platforms.     

Commitment of Mathematicians in Medicine: A Personal Experience, and Generalisations

I will present here a personal point of view on the commitment of mathematicians in medicine. Starting from my personal experience, I will suggest generalisations including favourable signs and caveats to show how mathematicians can be welcome and helpful in medicine, both in a theoretical and in a practical way.     

Budding Yeast for Budding Geneticists: A Primer on the Saccharomyces cerevisiae Model System

The budding yeast Saccharomyces cerevisiae is a powerful model organism for studying fundamental aspects of eukaryotic cell biology. This Primer article presents a brief historical perspective on the emergence of this organism as a premier experimental system over the course of the past century. An overview of the central features of the S. cerevisiae genome, including the nature of its genetic elements and general organization, is also provided. Some of the most common experimental tools and resources available to yeast geneticists are presented in a way designed to engage and challenge undergraduate and graduate students eager to learn more about the experimental amenability of budding yeast. Finally, a discussion of several major discoveries derived from yeast studies highlights the far-reaching impact that the yeast system has had and will continue to have on our understanding of a variety of cellular processes relevant to all eukaryotes, including humans.     

Interpreting 16S rDNA T-RFLP Data: Application of Self-Organizing Maps and Principal Component Analysis to Describe Community Dynamics and Convergence

Interpreting the large amount of data generated by rapid profiling techniques, such as T-RFLP, DGGE, and DNA arrays, is a difficult problem facing microbial ecologists. This study compares the ability of two very different ordination methods, principal component analysis (PCA) and self-organizing map neural networks (SOMs), to analyze 16S-DNA terminal restriction-fragment length polymorphism (T-RFLP) profiles from microbial communities in glucose-fed methanogenic bioreactors during startup and changes in operational parameters. Our goal was not only to identify which samples were similar, but also to decipher community dynamics and describe specific phylotypes, i.e., phylogenetically similar organisms, that behaved similarly in different reactors. Fifteen samples were taken over 56 volume changes from each of two bioreactors inoculated from river sediment (S2) and anaerobic digester sludge (M3) and from a well-established control reactor (R1). PCA of bacterial T-RFLP profiles indicated that both the S2 and M3 communities changed rapidly during the first nine volume changes, and then became relatively stable. PCA also showed that an HRT of 8 or 6 days had no effect on either reactor communtity, while an HRT of 2 days changed community structure significantly in both reactors. The SOM clustered the terminal restriction fragments according to when each fragment was most abundant in a reactor community, resulting in four clearly discernible groups. Thirteen fragments behaved similarly in both reactors, eight of which composed a significant proportion of the microbial community as judged by the relative abundance of the fragment in the T-RFLP profiles. Six Bacteria terminal restriction fragments shared between the two communities matched cloned 16S rDNA sequences from the reactors related to Spirochaeta, Aminobacterium, Thermotoga, and Clostridium species. Convergence also occurred within the acetoclastic methanogen community, resulting in a predominance of Methanosarcina siciliae-related organisms. The results demonstrate that both PCA and SOM analysis are useful in the analysis of T-RFLP data; however, the SOM was better at resolving patterns in more complex and variable data than PCA ordination.     

A Modified Self-thinning Equation to Describe Size/Density Relationships for Defoliated Swards

Use of the self-thinning rule to describe size/density compensation(SDC) in defoliated swards is examined. It is shown that defoliationrelated variation in leaf area and associated morphogeneticchanges in plant structure necessitate slope corrections, designatedC_a and C_r , respectively. The theory predicts that reduced leafarea in more heavily defoliated swards will result in SDC atslopes more negative than -3/2 (variable leaf area SDC), andthat there will be a transition to -3/2 (constant leaf area)SDC at higher herbage mass. Empirical data from previous experiments with Lolium perenneL. and Medicago sativa L. are examined, and appear to confirmthe theoretical predictions, including the slope change at thepoint of transition from variable to constant leaf area SDC.This transition point, designated d_i , is subject to interspecificvariation and is related to the mature shoot size of a particularspecies. Some applications of this theory are discussed, andin particular a sward productivity index is proposed.Copyright1995, 1999 Academic Press Variable leaf area self-thinning, size/density compensation, Lolium perenne, Medicago sativa, sward productivity index     

Application of Random Coefficient Regression Model to Myopia Data: A Case Study

A one-year birth cohort from Northern Finland has been followed up since 1966. As a part of this study, we are in this paper concerned with analysing the progression of myopia (nearsightness) up to the age of 20 years. The random coefficient regression model was chosen for the analysis because of the large individual variation in the development of myopia. Maximum likelihood estimates for the parameters in the model were obtained via the expectation maximization (EM) algorithm. It is shown how the estimated model can be used to predict future observations for an individual using the previously recorded refractive error measurements as well as other relevant data on the patient in question.     

A Biophysical Model of Neuronal Dendrites' Integrative Properties: Relations to Morphological Data

We used a biophysical model to probe the basic integrative properties of primate pallidal neurons in order to obtain a better understanding of Basal Ganglia physiology. The first results we present here deal mainly with the way dendritic morphology influences these properties. Neuronal morphology has been quantitatatively analyzed in 3D. Single fast excitatory synaptic inputs resulting in AMPA receptors activations have been simulated, without regenerative voltage dependent conductances. Dendrites of both pallidal segments (GPi and GPe) showed a strong dependence of the synaptic efficacy upon distance from soma, but even the most distal dendritic synaptic sites were able to substantially depolarize the cell body. The mean synaptic efficacy was the same in both populations, but the attenuation of propagated post-synaptic potentials was higher in GPi neurons. All these features were very dependent on the dendritic diameters which appear to constitute a key parameter in these neuronal populations both with respect to the integration of afferent information and to the differences between cells in performing this task.