Algorithms for 13C metabolic flux analysis

The metabolism of an organism consists of a network of biochemical reactions that transform small molecules, or metabolites, into others in order to produce energy and building blocks for essential macromolecules. The goal of metabolic flux analysis is to uncover the rates, or the fluxes, of those biochemical reactions. In a steady state, the sum of the fluxes that produce an internal metabolite is equal to the sum of the fluxes that consume the same molecule. Thus the steady state imposes linear balance constraints to the fluxes. In general, the balance constraints imposed by the steady state are not sufficient to uncover all the fluxes of a metabolic network. The fluxes through cycles and alternative pathways between the same source and target metabolites remain unknown. More information about the fluxes can be obtained from isotopic labelling experiments, where a cell population is fed with labelled nutrients, such as glucose that contains 13C atoms. Labels are then transferred by biochemical reactions to other metabolites. The relative abundances of different labelling patterns in internal metabolites depend on the fluxes of pathways producing them. Thus, the relative abundances of different labelling patterns contain information about the fluxes that cannot be uncovered from the balance constraints derived from the steady state. The field of research that estimates the fluxes utilizing the measured constraints to the relative abundances of different labelling patterns induced by 13C labelled nutrients is called 13C metabolic flux analysis. There exist two approaches of 13C metabolic flux analysis. In the optimization approach, a non-linear optimization task, where candidate fluxes are iteratively generated until they fit to the measured abundances of different labelling patterns, is constructed. In the direct approach, linear balance constraints given by the steady state are augmented with linear constraints derived from the abundances of different labelling patterns of metabolites. Thus, mathematically involved non-linear optimization methods that can get stuck to the local optima can be avoided. On the other hand, the direct approach may require more measurement data than the optimization approach to obtain the same flux information. Furthermore, the optimization framework can easily be applied regardless of the labelling measurement technology and with all network topologies. In this thesis we present a formal computational framework for direct 13C metabolic flux analysis. The aim of our study is to construct as many linear constraints to the fluxes from the 13C labelling measurements using only computational methods that avoid non-linear techniques and are independent from the type of measurement data, the labelling of external nutrients and the topology of the metabolic network. The presented framework is the first representative of the direct approach for 13C metabolic flux analysis that is free from restricting assumptions made about these parameters.In our framework, measurement data is first propagated from the measured metabolites to other metabolites. The propagation is facilitated by the flow analysis of metabolite fragments in the network. Then new linear constraints to the fluxes are derived from the propagated data by applying the techniques of linear algebra.Based on the results of the fragment flow analysis, we also present an experiment planning method that selects sets of metabolites whose relative abundances of different labelling patterns are most useful for 13C metabolic flux analysis. Furthermore, we give computational tools to process raw 13C labelling data produced by tandem mass spectrometry to a form suitable for 13C metabolic flux analysis.

Flight metabolic rate in the Glanville fritillary butterfly

Dispersal is a highly important life history trait. In fragmented landscapes the long-term persistence of populations depends on dispersal. Evolution of dispersal is affected by costs and benefits and these may differ between different landscapes. This results in differences in the strength and direction of natural selection on dispersal in fragmented landscapes. Dispersal has been shown to be a nonrandom process that is associated with traits such as flight ability in insects. This thesis examines genetic and physiological traits affecting dispersal in the Glanville fritillary butterfly (Melitaea cinxia). Flight metabolic rate is a repeatable trait representing flight ability. Unlike in many vertebrates, resting metabolic rate cannot be used as a surrogate of maximum metabolic rate as no strong correlation between the two was found in the Glanville fritillary. Resting and flight metabolic rate are affected by environmental variables, most notably temperature. However, only flight metabolic rate has a strong genetic component. Molecular variation in the much-studied candidate locus phosphoglucose isomerase (Pgi), which encodes the glycolytic enzyme PGI, has an effect on carbohydrate metabolism in flight. This effect is temperature dependent: in low to moderate temperatures individuals with the heterozygous genotype at the single nucleotide polymorphism (SNP) AA111 have higher flight metabolic rate than the common homozygous genotype. At high temperatures the situation is reversed. This finding suggests that variation in enzyme properties is indeed translated to organismal performance. High-resolution data on individual female Glanville fritillaries moving freely in the field were recorded using harmonic radar. There was a strong positive correlation between flight metabolic rate and dispersal rate. Flight metabolic rate explained one third of the observed variation in the one-hour movement distance. A fine-scaled analysis of mobility showed that mobility peaked at intermediate ambient temperatures but the two common Pgi genotypes differed in their reaction norms to temperature. As with flight metabolic rate, heterozygotes at SNP AA111 were the most active genotype in low to moderate temperatures. The results show that molecular variation is associated with variation in dispersal rate through the link of flight physiology under the influence of environmental conditions. The evolutionary pressures for dispersal differ between males and females. The effect of flight metabolic rate on dispersal was examined in both sexes in field and laboratory conditions. The relationship between flight metabolic rate and dispersal rate in the field and flight duration in the laboratory were found to differ between the two sexes. In females the relationship was positive, but in males the longest distances and flight durations were recorded for individuals with low flight metabolic rate. These findings may reflect male investment in mate locating. Instead of dispersing, males with high flight metabolic rate may establish territories and follow a perching strategy when locating females and hence move less on the landscape level. Males with low metabolic rate may be forced to disperse due to low competitive success or may show adaptations to an alternative strategy: patrolling. In the light of life history trade-offs and the rate of living theory having high metabolic rate may carry a cost in the form of shortened lifespan. Experiments relating flight metabolic rate to longevity showed a clear correlation in the opposite direction: high flight metabolic rate was associated with long lifespan. This suggests that individuals with high metabolic rate do not pay an extra physiological cost for their high flight capacity, rather there are positive correlations between different measures of fitness. These results highlight the importance of condition.

Mutations as molecular tools : The metabolic-rate dependent molecular clock and DNA barcoding of allied species

Mutation and recombination are the fundamental processes leading to genetic variation in natural populations. This variation forms the raw material for evolution through natural selection and drift. Therefore, studying mutation rates may reveal information about evolutionary histories as well as phylogenetic interrelationships of organisms. In this thesis two molecular tools, DNA barcoding and the molecular clock were examined. In the first part, the efficiency of mutations to delineate closely related species was tested and the implications for conservation practices were assessed. The second part investigated the proposition that a constant mutation rate exists within invertebrates, in form of a metabolic-rate dependent molecular clock, which can be applied to accurately date speciation events. DNA barcoding aspires to be an efficient technique to not only distinguish between species but also reveal population-level variation solely relying on mutations found on a short stretch of a single gene. In this thesis barcoding was applied to discriminate between Hylochares populations from Russian Karelia and new Hylochares findings from the greater Helsinki region in Finland. Although barcoding failed to delineate the two reproductively isolated groups, their distinct morphological features and differing life-history traits led to their classification as two closely related, although separate species. The lack of genetic differentiation appears to be due to a recent divergence event not yet reflected in the beetles molecular make-up. Thus, the Russian Hylochares was described as a new species. The Finnish species, previously considered as locally extinct, was recognized as endangered. Even if, due to their identical genetic make-up, the populations had been regarded as conspecific, conservation strategies based on prior knowledge from Russia would not have guaranteed the survival of the Finnish beetle. Therefore, new conservation actions based on detailed studies of the biology and life-history of the Finnish Hylochares were conducted to protect this endemic rarity in Finland. The idea behind the strict molecular clock is that mutation rates are constant over evolutionary time and may thus be used to infer species divergence dates. However, one of the most recent theories argues that a strict clock does not tick per unit of time but that it has a constant substitution rate per unit of mass-specific metabolic energy. Therefore, according to this hypothesis, molecular clocks have to be recalibrated taking body size and temperature into account. This thesis tested the temperature effect on mutation rates in equally sized invertebrates. For the first dataset (family Eucnemidae, Coleoptera) the phylogenetic interrelationships and evolutionary history of the genus Arrhipis had to be inferred before the influence of temperature on substitution rates could be studied. Further, a second, larger invertebrate dataset (family Syrphidae, Diptera) was employed. Several methodological approaches, a number of genes and multiple molecular clock models revealed that there was no consistent relationship between temperature and mutation rate for the taxa under study. Thus, the body size effect, observed in vertebrates but controversial for invertebrates, rather than temperature may be the underlying driving force behind the metabolic-rate dependent molecular clock. Therefore, the metabolic-rate dependent molecular clock does not hold for the here studied invertebrate groups. This thesis emphasizes that molecular techniques relying on mutation rates have to be applied with caution. Whereas they may work satisfactorily under certain conditions for specific taxa, they may fail for others. The molecular clock as well as DNA barcoding should incorporate all the information and data available to obtain comprehensive estimations of the existing biodiversity and its evolutionary history.