Analysis of linear trade models and relation to scale economies

We discuss linear Ricardo models with a range of parameters. We show that the exact boundary of the region of equilibria of these models is obtained by solving a simple integer programming problem. We show that there is also an exact correspondence between many of the equilibria resulting from families of linear models and the multiple equilibria of economies of scale models.

Singular value decomposition for genome-wide expression data processing and modeling

We describe the use of singular value decomposition in transforming genome-wide expression data from genes × arrays space to reduced diagonalized “eigengenes” × “eigenarrays” space, where the eigengenes (or eigenarrays) are unique orthonormal superpositions of the genes (or arrays). Normalizing the data by filtering out the eigengenes (and eigenarrays) that are inferred to represent noise or experimental artifacts enables meaningful comparison of the expression of different genes across different arrays in different experiments. Sorting the data according to the eigengenes and eigenarrays gives a global picture of the dynamics of gene expression, in which individual genes and arrays appear to be classified into groups of similar regulation and function, or similar cellular state and biological phenotype, respectively. After normalization and sorting, the significant eigengenes and eigenarrays can be associated with observed genome-wide effects of regulators, or with measured samples, in which these regulators are overactive or underactive, respectively.

A combined kinetic and modeling study of the catalytic center subsites of human angiogenin.

Kinetic analysis and molecular modeling have been used to map the ribonucleolytic center of angiogenin (Ang). Pyrimidine nucleotides were found to interact very weakly with Ang, consistent with the inaccessible B1 pyrimidine binding site revealed by x-ray crystallography. Ang also lacks an effective phosphate binding site on the 5' side of B1. Although the B2 site that preferentially binds purines on the 3' side of B1 is also weak, its associated phosphate subsites make substantial contributions: both 3',5'-ADP and 5'-ADP have Ki values 6-fold lower than for 5'-AMP, and adding a 3'-phosphate to the substrate CpA increases Kcat/Km by 9-fold. Thus Ang has a functional P2 site on the 3' side of B2 and a site for a second phosphate on the 5' side of B2. Modeling of an Ang-d(ApTpApA) complex suggested that Arg-5 forms part of the P2 site and that a 2'-phosphate might bind more tightly than a 3'-phosphate. Both predictions were confirmed kinetically. The subsite map obtained by this combined approach indicated that 5'-diphosphoadenosine 2'-phosphate might be a more potent inhibitor than any of the nucleotides tested thus far. Indeed, its Ki value of 150 microM is 50-fold lower than that for the best nucleotide previously reported and 400-fold lower than the Km for the best dinucleotide substrate. This compound may serve as a suitable starting point for the eventual design of tight-binding inhibitors of Ang as antiangiogenic agents for human therapy.

Quantitative modeling of stochastic systems in molecular biology by using stochastic Petri nets

An integrated understanding of molecular and developmental biology must consider the large number of molecular species involved and the low concentrations of many species in vivo. Quantitative stochastic models of molecular interaction networks can be expressed as stochastic Petri nets (SPNs), a mathematical formalism developed in computer science. Existing software can be used to define molecular interaction networks as SPNs and solve such models for the probability distributions of molecular species. This approach allows biologists to focus on the content of models and their interpretation, rather than their implementation. The standardized format of SPNs also facilitates the replication, extension, and transfer of models between researchers. A simple chemical system is presented to demonstrate the link between stochastic models of molecular interactions and SPNs. The approach is illustrated with examples of models of genetic and biochemical phenomena where the UltraSAN package is used to present results from numerical analysis and the outcome of simulations.

A global budget for fine root biomass, surface area, and nutrient contents

Global biogeochemical models have improved dramatically in the last decade in their representation of the biosphere. Although leaf area data are an important input to such models and are readily available globally, global root distributions for modeling water and nutrient uptake and carbon cycling have not been available. This analysis provides global distributions for fine root biomass, length, and surface area with depth in the soil, and global estimates of nutrient pools in fine roots. Calculated root surface area is almost always greater than leaf area, more than an order of magnitude so in grasslands. The average C:N:P ratio in living fine roots is 450:11:1, and global fine root carbon is more than 5% of all carbon contained in the atmosphere. Assuming conservatively that fine roots turn over once per year, they represent 33% of global annual net primary productivity.