A model-based approach for assessing in vivo combination therapy interactions

We present an approach for evaluating the efficacy of combination antitumor agent schedules that accounts for order and timing of drug administration. Our model-based approach compares in vivo tumor volume data over a time course and offers a quantitative definition for additivity of drug effects, relative to which synergism and antagonism are interpreted. We begin by fitting data from individual mice receiving at most one drug to a differential equation tumor growth/drug effect model and combine individual parameter estimates to obtain population statistics. Using two null hypotheses: (i) combination therapy is consistent with additivity or (ii) combination therapy is equivalent to treating with the more effective single agent alone, we compute predicted tumor growth trajectories and their distribution for combination treated animals. We illustrate this approach by comparing entire observed and expected tumor volume trajectories for a data set in which HER-2/neu-overexpressing MCF-7 human breast cancer xenografts are treated with a humanized, anti-HER-2 monoclonal antibody (rhuMAb HER-2), doxorubicin, or one of five proposed combination therapy schedules.

The binding conformation of Taxol in β-tubulin: A model based on electron crystallographic density

The chemotherapeutic drug Taxol is known to interact within a specific site on β-tubulin. Although the general location of the site has been defined by photoaffinity labeling and electron crystallography, the original data were insufficient to make an absolute determination of the bound conformation. We have now correlated the crystallographic density with analysis of Taxol conformations and have found the unique solution to be a T-shaped Taxol structure. This T-shaped or butterfly structure is optimized within the β-tubulin site and exhibits functional similarity to a portion of the B9-B10 loop in the α-tubulin subunit. The model provides structural rationalization for a sizeable body of Taxol structure–activity relationship data, including binding affinity, photoaffinity labeling, and acquired mutation in human cancer cells.

Psychophysical evidence for fast region-based segmentation processes in motion and color.

Theories of image segmentation suggest that the human visual system may use two distinct processes to segregate figure from background: a local process that uses local feature contrasts to mark borders of coherent regions and a global process that groups similar features over a larger spatial scale. We performed psychophysical experiments to determine whether and to what extent the global similarity process contributes to image segmentation by motion and color. Our results show that for color, as well as for motion, segmentation occurs first by an integrative process on a coarse spatial scale, demonstrating that for both modalities the global process is faster than one based on local feature contrasts. Segmentation by motion builds up over time, whereas segmentation by color does not, indicating a fundamental difference between the modalities. Our data suggest that segmentation by motion proceeds first via a cooperative linking over space of local motion signals, generating almost immediate perceptual coherence even of physically incoherent signals. This global segmentation process occurs faster than the detection of absolute motion, providing further evidence for the existence of two motion processes with distinct dynamic properties.

Biological impact on mineral dissolution: Application of the lichen model to understanding mineral weathering in the rhizosphere

Microorganisms modify rates and mechanisms of chemical and physical weathering and clay growth, thus playing fundamental roles in soil and sediment formation. Because processes in soils are inherently complex and difficult to study, we employ a model based on the lichen–mineral system to identify the fundamental interactions. Fixed carbon released by the photosynthetic symbiont stimulates growth of fungi and other microorganisms. These microorganisms directly or indirectly induce mineral disaggregation, hydration, dissolution, and secondary mineral formation. Model polysaccharides were used to investigate direct mediation of mineral surface reactions by extracellular polymers. Polysaccharides can suppress or enhance rates of chemical weathering by up to three orders of magnitude, depending on the pH, mineral surface structure and composition, and organic functional groups. Mg, Mn, Fe, Al, and Si are redistributed into clays that strongly adsorb ions. Microbes contribute to dissolution of insoluble secondary phosphates, possibly via release of organic acids. These reactions significantly impact soil fertility. Below fungi–mineral interfaces, mineral surfaces are exposed to dissolved metabolic byproducts. Through this indirect process, microorganisms can accelerate mineral dissolution, leading to enhanced porosity and permeability and colonization by microbial communities.

Aggregation and disaggregation of senile plaques in Alzheimer disease

We quantitatively analyzed, using laser scanning confocal microscopy, the three-dimensional structure of individual senile plaques in Alzheimer disease. We carried out the quantitative analysis using statistical methods to gain insights about the processes that govern Aβ peptide deposition. Our results show that plaques are complex porous structures with characteristic pore sizes. We interpret plaque morphology in the context of a new dynamical model based on competing aggregation and disaggregation processes in kinetic steady-state equilibrium with an additional diffusion process allowing Aβ deposits to diffuse over the surface of plaques.

From residue matching patterns to protein folding topographies: General model and bovine pancreatic trypsin inhibitor

A coarse-grained model for protein-folding dynamics is introduced based on a discretized representation of torsional modes. The model, based on the Ramachandran map of the local torsional potential surface and the class (hydrophobic/polar/neutral) of each residue, recognizes patterns of both torsional conformations and hydrophobic-polar contacts, with tolerance for imperfect patterns. It incorporates empirical rates for formation of secondary and tertiary structure. The method yields a topological representation of the evolving local torsional configuration of the folding protein, modulo the basins of the Ramachandran map. The folding process is modeled as a sequence of transitions from one contact pattern to another, as the torsional patterns evolve. We test the model by applying it to the folding process of bovine pancreatic trypsin inhibitor, obtaining a kinetic description of the transitions between the contact patterns visited by the protein along the dominant folding pathway. The kinetics and detailed balance make it possible to invert the result to obtain a coarse topographic description of the potential energy surface along the dominant folding pathway, in effect to go backward or forward between a topological representation of the chain conformation and a topographical description of the potential energy surface governing the folding process. As a result, the strong structure-seeking character of bovine pancreatic trypsin inhibitor and the principal features of its folding pathway are reproduced in a reasonably quantitative way.

Two amino acid substitutions convert a guanylyl cyclase, RetGC-1, into an adenylyl cyclase

Guanylyl cyclases (GCs) and adenylyl cyclases (ACs) have fundamental roles in a wide range of cellular processes. Whereas GCs use GTP as a substrate to form cGMP, ACs catalyze the analogous conversion of ATP to cAMP. Previously, a model based on the structure of adenylate cyclase was used to predict the structure of the nucleotide-binding pocket of a membrane guanylyl cyclase, RetGC-1. Based on this model, we replaced specific amino acids in the guanine-binding pocket of GC with their counterparts from AC. A change of two amino acids, E925K together with C995D, is sufficient to completely alter the nucleotide specificity from GTP to ATP. These experiments strongly validate the AC-derived RetGC-1 structural model and functionally confirm the role of these residues in nucleotide discrimination.

Evidence in support of a four transmembrane-pore-transmembrane topology model for the Arabidopsis thaliana Na+/K+ translocating AtHKT1 protein, a member of the superfamily of K+ transporters

The Arabidopsis thaliana AtHKT1 protein, a Na+/K+ transporter, is capable of mediating inward Na+ currents in Xenopus laevis oocytes and K+ uptake in Escherichia coli. HKT1 proteins are members of a superfamily of K+ transporters. These proteins have been proposed to contain eight transmembrane segments and four pore-forming regions arranged in a mode similar to that of a K+ channel tetramer. However, computer analysis of the AtHKT1 sequence identified eleven potential transmembrane segments. We have investigated the membrane topology of AtHKT1 with three different techniques. First, a gene fusion alkaline phosphatase study in E. coli clearly defined the topology of the N-terminal and middle region of AtHKT1, but the model for membrane folding of the C-terminal region had to be refined. Second, with a reticulocyte-lysate supplemented with dog-pancreas microsomes, we demonstrated that N-glycosylation occurs at position 429 of AtHKT1. An engineered unglycosylated protein variant, N429Q, mediated Na+ currents in X. laevis oocytes with the same characteristics as the wild-type protein, indicating that N-glycosylation is not essential for the functional expression and membrane targeting of AtHKT1. Five potential glycosylation sites were introduced into the N429Q. Their pattern of glycosylation supported the model based on the E. coli-alkaline phosphatase data. Third, immunocytochemical experiments with FLAG-tagged AtHKT1 in HEK293 cells revealed that the N and C termini of AtHKT1, and the regions containing residues 135–142 and 377–384, face the cytosol, whereas the region of residues 55–62 is exposed to the outside. Taken together, our results show that AtHKT1 contains eight transmembrane-spanning segments.

A model of self-thinning through local competition.

Explanations of self-thinning in plant populations have focused on plant shape and packing. A dynamic model based on the structure of local interactions successfully reproduces the pattern and can be approximated to identify key parameters and relationships. The approach generates testable new explanations for differences between species and populations, unifies self-thinning with other patterns in plant population dynamics, and indicates why organisms other than plants can follow the law.