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.     

Metabolic Profiling of Alternative NAD Biosynthetic Routes in Mouse Tissues

NAD plays essential redox and non-redox roles in cell biology. In mammals, its de novo and recycling biosynthetic pathways encompass two independent branches, the “amidated” and “deamidated” routes. Here we focused on the indispensable enzymes gating these two routes, i.e. nicotinamide mononucleotide adenylyltransferase (NMNAT), which in mammals comprises three distinct isozymes, and NAD synthetase (NADS). First, we measured the in vitro activity of the enzymes, and the levels of all their substrates and products in a number of tissues from the C57BL/6 mouse. Second, from these data, we derived in vivo estimates of enzymes''rates and quantitative contributions to NAD homeostasis. The NMNAT activity, mainly represented by nuclear NMNAT1, appears to be high and nonrate-limiting in all examined tissues, except in blood. The NADS activity, however, appears rate-limiting in lung and skeletal muscle, where its undetectable levels parallel a relative accumulation of the enzyme''s substrate NaAD (nicotinic acid adenine dinucleotide). In all tissues, the amidated NAD route was predominant, displaying highest rates in liver and kidney, and lowest in blood. In contrast, the minor deamidated route showed higher relative proportions in blood and small intestine, and higher absolute values in liver and small intestine. Such results provide the first comprehensive picture of the balance of the two alternative NAD biosynthetic routes in different mammalian tissues under physiological conditions. This fills a gap in the current knowledge of NAD biosynthesis, and provides a crucial information for the study of NAD metabolism and its role in disease.     

Cost-Effective Mapping of Benthic Habitats in Inland Reservoirs through Split-Beam Sonar,Indicator Kriging,and Historical Geologic Data

Because bottom substrate composition is an important control on the temporal and spatial location of the aquatic community, accurate maps of benthic habitats of inland lakes and reservoirs provide valuable information to managers, recreational users, and scientists. Therefore, we collected vertical, split-beam sonar data (roughness [E1], hardness [E2], and bathymetry) and sediment samples to make such maps. Statistical calibration between sonar parameters and sediment classes was problematic because the E1:E2 ratios for soft (muck and clay) sediments overlapped a lower and narrower range for hard (gravel) substrates. Thus, we used indicator kriging (IK) to map the probability that unsampled locations did not contain coarse sediments. To overcome the calibration issue we tested proxies for the natural processes and anthropogenic history of the reservoir as potential predictive variables. Of these, a geologic map proved to be the most useful. The central alluvial valley and mudflats contained mainly muck and organic-rich clays. The surrounding glacial till and shale bedrock uplands contained mainly poorly sorted gravels. Anomalies in the sonar data suggested that the organic-rich sediments also contained trapped gases, presenting additional interpretive issues for the mapping. We extended the capability of inexpensive split-beam sonar units through the incorporation of historic geologic maps and other records as well as validation with dredge samples. Through the integration of information from multiple data sets, were able to objectively identify bottom substrate and provide reservoir users with an accurate map of available benthic habitat.     

The Dipole Model and Phase Transitions in Biological Membranes

Assuming the dipole model for a membrane, approximate calculations are made which employ a dipole-dipole interaction energy. The calculations are based upon the assumption of cooperative coupling of membrane polar molecules and make use of the Bragg-Williams approximation. A theoretical estimate is made of the critical temperature at which phase changes might occur in certain biological membranes. Proposals are presented which explain how the dipole transition might relate to the sometimes observed thermal phase transitions in biological membranes.     

Ecological comparison between duckweeds in central Italy: The invasive Lemna minuta vs the native L. minor

The American duckweed Lemna minuta shows an invasive behaviour in Europe, causing weed problems in aquatic habitats there. Few studies addressed this species’ ecological requirements for a suitable establishment in a site. In this paper, L. minuta populations were analysed through field surveys so as (1) to define the autoecology of this duckweed as regards the main environmental factors characterizing invaded habitats, and (2) to identify possible overlaps/differences in ecological requirements between the alien L. minuta and the common native L. minor, with which it is often associated and in direct competition. The occurrence/abundance of the two species and environmental data were collected from 41 wetlands in central Italy. Currently, L. minuta is more common and abundant than L. minor in the study-area, despite its recent arrival there (2007). The two species have a partially overlapped autoecology. However, L. minuta differs from L. minor since it occurs in waters which are less alkaline, slightly less warm, and richer in nitrates. It shows tolerance for environmental conditions which are limiting for most of macrophytes, including L. minor, such as high shading and low water oxygenation. This enables L. minuta to increase its invasion potentiality and thus to enlarge its distribution area.     

Seasonal patterns in rainforest litterfall: Detecting endogenous and environmental influences from long‐term sampling

Tropical rainforests play an important role in the storage and cycling of global terrestrial carbon. In the carbon cycle, net primary productivity of forests is linked to soil respiration through the production and decomposition of forest litter. Climate seasonality appears to influence the production of litter although there is considerable variability within and across forests that makes accurate estimates challenging. We explored the effects of climate seasonality on litterfall dynamics in a lowland humid rainforest over a 7‐year period from 2007 to 2013, including an El Niño/La Niña cycle in 2010/2011. Litterfall was sampled fortnightly in 24 traps of 0.50 m diameter within a 1‐ha forest plot. Total mean litterfall was 10.48 ± 1.32 (±SD, dry weight) Mg ha^?1 year^?1 and seasonal in distribution. The different components of litterfall were divided into L_Leaf (63.5%), L_Wood (27.7%) and L_{FF[flowers & fruit]} (8.8%), which all demonstrated seasonal dynamics. Peak falls in L_Leaf and L_Wood were highly predictable, coinciding with maximum daily temperatures and 1 and 2 months prior to maximum monthly rainfall. The El Niño/La Niña cycle coincided with elevated local winter temperatures and peak falls of L_Leaf and L_Wood. Importantly, we establish how sampling length and generalized additive models eliminate the requirement for extensive within‐site sampling when the intention is to describe dynamics in litterfall patterns. Further, a greater understanding of seasonal cycles in litterfall allows us to distinguish between endogenous controls and environmental factors, such as El Niño events, which may have significant impacts on biochemical cycles.     

Mapping DNA damage‐dependent genetic interactions in yeast via party mating and barcode fusion genetics

Condition‐dependent genetic interactions can reveal functional relationships between genes that are not evident under standard culture conditions. State‐of‐the‐art yeast genetic interaction mapping, which relies on robotic manipulation of arrays of double‐mutant strains, does not scale readily to multi‐condition studies. Here, we describe barcode fusion genetics to map genetic interactions (BFG‐GI), by which double‐mutant strains generated via en masse “party” mating can also be monitored en masse for growth to detect genetic interactions. By using site‐specific recombination to fuse two DNA barcodes, each representing a specific gene deletion, BFG‐GI enables multiplexed quantitative tracking of double mutants via next‐generation sequencing. We applied BFG‐GI to a matrix of DNA repair genes under nine different conditions, including methyl methanesulfonate (MMS), 4‐nitroquinoline 1‐oxide (4NQO), bleomycin, zeocin, and three other DNA‐damaging environments. BFG‐GI recapitulated known genetic interactions and yielded new condition‐dependent genetic interactions. We validated and further explored a subnetwork of condition‐dependent genetic interactions involving MAG1, SLX4, and genes encoding the Shu complex, and inferred that loss of the Shu complex leads to an increase in the activation of the checkpoint protein kinase Rad53.