Mathematical and computational modeling in biology at multiple scales

A variety of topics are reviewed in the area of mathematical and computational modeling in biology, covering the range of scales from populations of organisms to electrons in atoms. The use of maximum entropy as an inference tool in the fields of biology and drug discovery is discussed. Mathematical and computational methods and models in the areas of epidemiology, cell physiology and cancer are surveyed. The technique of molecular dynamics is covered, with special attention to force fields for protein simulations and methods for the calculation of solvation free energies. The utility of quantum mechanical methods in biophysical and biochemical modeling is explored. The field of computational enzymology is examined.     

Isocitrate dehydrogenase 1 R132C mutation occurs exclusively in microsatellite stable colorectal cancers with the CpG island methylator phenotype

The CpG Island Methylator Phenotype (CIMP) is fundamental to an important subset of colorectal cancer; however, its cause is unknown. CIMP is associated with microsatellite instability but is also found in BRAF mutant microsatellite stable cancers that are associated with poor prognosis. The isocitrate dehydrogenase 1 (IDH1) gene causes CIMP in glioma due to an activating mutation that produces the 2-hydroxyglutarate oncometabolite. We therefore examined IDH1 alteration as a potential cause of CIMP in colorectal cancer. The IDH1 mutational hotspot was screened in 86 CIMP-positive and 80 CIMP-negative cancers. The entire coding sequence was examined in 81 CIMP-positive colorectal cancers. Forty-seven cancers varying by CIMP-status and IDH1 mutation status were examined using Illumina 450K DNA methylation microarrays. The R132C IDH1 mutation was detected in 4/166 cancers. All IDH1 mutations were in CIMP cancers that were BRAF mutant and microsatellite stable (4/45, 8.9%). Unsupervised hierarchical cluster analysis identified an IDH1 mutation-like methylation signature in approximately half of the CIMP-positive cancers. IDH1 mutation appears to cause CIMP in a small proportion of BRAF mutant, microsatellite stable colorectal cancers. This study provides a precedent that a single gene mutation may cause CIMP in colorectal cancer, and that this will be associated with a specific epigenetic signature and clinicopathological features.     

Excess amino acid polymorphism in mitochondrial DNA: contrasts among genes from Drosophila, mice, and humans

Recent studies of mitochondrial DNA (mtDNA) variation in mammals and Drosophila have shown an excess of amino acid variation within species (replacement polymorphism) relative to the number of silent and replacement differences fixed between species. To examine further this pattern of nonneutral mtDNA evolution, we present sequence data for the ND3 and ND5 genes from 59 lines of Drosophila melanogaster and 29 lines of D. simulans. Of interest are the frequency spectra of silent and replacement polymorphisms, and potential variation among genes and taxa in the departures from neutral expectations. The Drosophila ND3 and ND5 data show no significant excess of replacement polymorphism using the McDonald-Kreitman test. These data are in contrast to significant departures from neutrality for the ND3 gene in mammals and other genes in Drosophila mtDNA (cytochrome b and ATPase 6). Pooled across genes, however, both Drosophila and human mtDNA show very significant excesses of amino acid polymorphism. Silent polymorphisms at ND5 show a significantly higher variance in frequency than replacement polymorphisms, and the latter show a significant skew toward low frequencies (Tajima's D = -1.954). These patterns are interpreted in light of the nearly neutral theory where mildly deleterious amino acid haplotypes are observed as ephemeral variants within species but do not contribute to divergence. The patterns of polymorphism and divergence at charge-altering amino acid sites are presented for the Drosophila ND5 gene to examine the evolution of functionally distinct mutations. Excess charge-altering polymorphism is observed at the carboxyl terminal and excess charge-altering divergence is detected at the amino terminal. While the mildly deleterious model fits as a net effect in the evolution of nonrecombining mitochondrial genomes, these data suggest that opposing evolutionary pressures may act on different regions of mitochondrial genes and genomes.      

Characterization of cross-bridge elasticity and kinetics of cross-bridge cycling during force development in single smooth muscle cells

Force development in smooth muscle, as in skeletal muscle, is believed to reflect recruitment of force-generating myosin cross-bridges. However, little is known about the events underlying cross-bridge recruitment as the muscle cell approaches peak isometric force and then enters a period of tension maintenance. In the present studies on single smooth muscle cells isolated from the toad (Bufo marinus) stomach muscularis, active muscle stiffness, calculated from the force response to small sinusoidal length changes (0.5% cell length, 250 Hz), was utilized to estimate the relative number of attached cross-bridges. By comparing stiffness during initial force development to stiffness during force redevelopment immediately after a quick release imposed at peak force, we propose that the instantaneous active stiffness of the cell reflects both a linearly elastic cross-bridge element having 1.5 times the compliance of the cross-bridge in frog skeletal muscle and a series elastic component having an exponential length-force relationship. At the onset of force development, the ratio of stiffness to force was 2.5 times greater than at peak isometric force. These data suggest that, upon activation, cross-bridges attach in at least two states (i.e., low-force-producing and high-force-producing) and redistribute to a steady state distribution at peak isometric force. The possibility that the cross-bridge cycling rate was modulated with time was also investigated by analyzing the time course of tension recovery to small, rapid step length changes (0.5% cell length in 2.5 ms) imposed during initial force development, at peak force, and after 15 s of tension maintenance. The rate of tension recovery slowed continuously throughout force development following activation and slowed further as force was maintained. Our results suggest that the kinetics of force production in smooth muscle may involve a redistribution of cross-bridge populations between two attached states and that the average cycling rate of these cross-bridges becomes slower with time during contraction.     

Comparative tests of ectoparasite species richness in seabirds

Background  

The diversity of parasites attacking a host varies substantially among different host species. Understanding the factors that explain these patterns of parasite diversity is critical to identifying the ecological principles underlying biodiversity. Seabirds (Charadriiformes, Pelecaniformes and Procellariiformes) and their ectoparasitic lice (Insecta: Phthiraptera) are ideal model groups in which to study correlates of parasite species richness. We evaluated the relative importance of morphological (body size, body weight, wingspan, bill length), life-history (longevity, clutch size), ecological (population size, geographical range) and behavioural (diving versus non-diving) variables as predictors of louse diversity on 413 seabird hosts species. Diversity was measured at the level of louse suborder, genus, and species, and uneven sampling of hosts was controlled for using literature citations as a proxy for sampling effort.     

Acetate metabolism in the mammary gland of the lactating ewe

Acetate metabolism in the mammary gland of lactating ewes was studied by continuous infusion of radioisotopic [U-14C]sodium acetate and measurement of mammary gland arteriovenous difference and blood flow. Entry rate of acetate into the whole body averaged 75 +/- 7 mumol min-1 kg-1 liveweight and 22.1 +/- 2.7% of total CO2 production was derived from acetate. Acetate was both utilized and produced by the mammary gland. Acetate uptake was related linearly (r2 = 0.94) to arterial concentration and gross utilization of acetate accounted for 16.2 +/- 2.6% of whole-body entry rate. Endogenous acetate production by the mammary gland increased linearly (r2 = 0.90) as milk yield rose, and accounted for 25.6 +/- 2.7% of the gross mammary utilization of acetate. The proportion of mammary CO2 derived from acetate (22.5 +/- 3.9%) was similar to that of the whole body. The uptake of acetate, 3-hydroxybutyrate, esterified fatty acids and plasma free fatty acids accounted for about 25, 13, 60 and 4% of milk fatty acid carbon respectively, after correction for the oxidation of acetate, but not of the other substrates. Metabolism of acetate in the mammary glands of lactating ewes appears quantitatively more important than that in cows, but similar to that in goats.     

Pathway Implications of Aberrant Global Methylation in Adrenocortical Cancer

Context

Adrenocortical carcinomas (ACC) are a rare tumor type with a poor five-year survival rate and limited treatment options.

Objective

Understanding of the molecular pathogenesis of this disease has been aided by genomic analyses highlighting alterations in TP53, WNT, and IGF signaling pathways. Further elucidation is needed to reveal therapeutically actionable targets in ACC.

Design

In this study, global DNA methylation levels were assessed by the Infinium HumanMethylation450 BeadChip Array on 18 ACC tumors and 6 normal adrenal tissues. A new, non-linear correlation approach, the discretization method, assessed the relationship between DNA methylation/gene expression across ACC tumors.

Results

This correlation analysis revealed epigenetic regulation of genes known to modulate TP53, WNT, and IGF signaling, as well as silencing of the tumor suppressor MARCKS, previously unreported in ACC.

Conclusions

DNA methylation may regulate genes known to play a role in ACC pathogenesis as well as known tumor suppressors.     

Effects of exogenous growth hormone on milk production and nutrient uptake by muscle and mammary tissues of dairy cows in mid-lactation

Responses to exogenous growth hormone were measured in lactating dairy cows surgically prepared to allow measurement of nutrient exchanges across mammary and hind-limb muscle tissues. Cows were injected daily with either saline or growth hormone, at a dose of 0.1 mg/kg liveweight, over periods of 6 days. During administration of growth hormone milk yield, milk fat content and yields of milk fat protein and lactose increased. Arterial plasma concentrations of glucose and non-esterified fatty acids were increased, uptake of glucose by leg muscle tissue decreased, lactate release from leg muscle tended to increase, mammary uptake of non-esterified fatty acids increased, blood flow to leg muscle tended to increase and blood flow to mammary tissue increased during injection of growth hormone. The results show that growth hormone affects supply to and utilization of key nutrients by tissues, resulting in the supply to the mammary gland of additional precursors for milk synthesis.     

Quality determination and the repair of poor quality spots in array experiments

Background  

A common feature of microarray experiments is the occurence of missing gene expression data. These missing values occur for a variety of reasons, in particular, because of the filtering of poor quality spots and the removal of undefined values when a logarithmic transformation is applied to negative background-corrected intensities. The efficiency and power of an analysis performed can be substantially reduced by having an incomplete matrix of gene intensities. Additionally, most statistical methods require a complete intensity matrix. Furthermore, biases may be introduced into analyses through missing information on some genes. Thus methods for appropriately replacing (imputing) missing data and/or weighting poor quality spots are required.