Rapid measurement of heteronuclear transverse relaxation rates using non-uniformly sampled <i>R</i>_1<i>ρ</i> accordion experiments

Multidimensional, heteronuclear NMR relaxation methods are used extensively to characterize the dynamics of biological macromolecules. Acquisition of relaxation datasets on proteins typically requires significant measurement time, often several days. Accordion spectroscopy offers a powerful means to shorten relaxation rate measurements by encoding the “relaxation dimension” into the indirect evolution period in multidimensional experiments. Time savings can also be achieved by non-uniform sampling (NUS) of multidimensional NMR data, which is used increasingly to improve spectral resolution or increase sensitivity per unit time. However, NUS is not commonly implemented in relaxation experiments, because most reconstruction algorithms are inherently nonlinear, leading to problems when estimating signal intensities, relaxation rate constants and their error bounds. We have previously shown how to avoid these shortcomings by combining accordion spectroscopy with NUS, followed by data reconstruction using sparse exponential mode analysis, thereby achieving a dramatic decrease in the total length of longitudinal relaxation experiments. Here, we present the corresponding transverse relaxation experiment, taking into account the special considerations required for its successful implementation in the framework of the accordion-NUS approach. We attain the highest possible precision in the relaxation rate constants by optimizing the NUS scheme with respect to the Cramér–Rao lower bound of the variance of the estimated parameter, given the total number of sampling points and the spectrum-specific signal characteristics. The resulting accordion-NUS R1ρ relaxation experiment achieves comparable precision in the parameter estimates compared to conventional CPMG (Carr–Purcell–Meiboom–Gill) R2 or spin-lock R1ρ experiments while saving an order of magnitude in experiment time.

Rapid measurement of heteronuclear transverse relaxation rates using non-uniformly sampled R_1ρ accordion experiments

Multidimensional, heteronuclear NMR relaxation methods are used extensively to characterize the dynamics of biological macromolecules. Acquisition of relaxation datasets on proteins typically require significant measurement time, often several days. Accordion spectroscopy offers a powerful means to shorten relaxation rate measurements by encoding the 'relaxation dimension' into the indirect evolution period in multidimensional experiments. Time savings can also be achieved by nonuniform sampling (NUS) of multidimensional NMR data, which is used increasingly to improve spectral resolution or increase sensitivity per unit time. However, NUS is not commonly implemented in relaxation experiments, because most reconstruction algorithms are inherently nonlinear, leading to problems when estimating signal intensities, relaxation rate constants and their error bounds. We have previously shown how to avoid these shortcomings by combining accordion spectroscopy with NUS, followed by data reconstruction using sparse exponential mode analysis, thereby achieving a dramatic decrease in the total length of longitudinal relaxation experiments. Here, we present the corresponding transverse relaxation experiment, taking into account the special considerations required for its successfully implementation in the framework of the accordion-NUS approach. We attain the highest possible precision in the relaxation rate constants by optimizing the NUS scheme with respect to the Cramér-Rao lower bound of the variance of the estimated parameter, given the total number of sampling points and the spectrum-specific signal characteristics. The resulting accordion-NUS R1ρ relaxation experiment achieves comparable precision in the parameter estimates, compared to conventional CPMG R2 or spin-lock R1ρ experiments, while saving an order of magnitude in experiment time.

Indirect Evolution and Aggregate-Taking Behavior in a Football League: Utility Maximization, Profit Maximization, and Success

An evolutionary model of European football was applied to analyze a two-stage indirect evolution game in which teams choose their utility function in the first stage, and their optimal talent investments in the second stage. Given the second-stage optimal aggregate-taking strategy (ATS) of talent investment, it was shown that teams may choose a mix of profit or win maximization as their objective, where the former is of considerably higher relevance with linear weights for profits, and is more successful in the utility function. With linear weights for profit and win maximization, maximizing profits is the only evolutionarily stable strategy (ESS) of teams. The results change if quadratic weights for profits and wins are employed. With increasing talent productivity, win maximization dominates in the static and in the dynamic versions of the model. As a consequence, it is an open question whether the commercialization of football (and other sports) leagues will lead to more profit or win maximization.

Indirect evolution of social fitness inequalities and facultative social exploitation

Microbial genotypes with similarly high proficiency at a cooperative behaviour in genetically pure groups often exhibit fitness inequalities caused by social interaction in mixed groups. Winning competitors in this scenario have been referred to as ‘cheaters’ in some studies. Such interaction-specific fitness inequalities, as well as social exploitation (in which interaction between genotypes increases absolute fitness), might evolve due to selection for competitiveness at the focal behaviour or might arise non-adaptively due to pleiotropy, hitchhiking or genetic drift. The bacterium Myxococcus xanthus sporulates during cooperative development of multicellular fruiting bodies. Using M. xanthus lineages that underwent experimental evolution in allopatry without selection on sporulation, we demonstrate that interaction-specific fitness inequalities and facultative social exploitation during development readily evolved indirectly among descendant lineages. Fitness inequalities between evolved genotypes were not caused by divergence in developmental speed, as faster-developing strains were not over-represented among competition winners. In competitions between ancestors and several evolved strains, all evolved genotypes produced more spores than the ancestors, including losers of evolved-versus-evolved competitions, indicating that adaptation in non-developmental contexts pleiotropically increased competitiveness for spore production. Overall, our results suggest that fitness inequalities caused by social interaction during cooperative processes may often evolve non-adaptively in natural populations.

Rapid and widespread de novo evolution of kin discrimination

Diverse forms of kin discrimination, broadly defined as alteration of social behavior as a function of genetic relatedness among interactants, are common among social organisms from microbes to humans. However, the evolutionary origins and causes of kin-discriminatory behavior remain largely obscure. One form of kin discrimination observed in microbes is the failure of genetically distinct colonies to merge freely upon encounter. Here, we first use natural isolates of the highly social bacterium Myxococcus xanthus to show that colony-merger incompatibilities can be strong barriers to social interaction, particularly by reducing chimerism in multicellular fruiting bodies that develop near colony-territory borders. We then use experimental laboratory populations to test hypotheses regarding the evolutionary origins of kin discrimination. We show that the generic process of adaptation, irrespective of selective environment, is sufficient to repeatedly generate kin-discriminatory behaviors between evolved populations and their common ancestor. Further, we find that kin discrimination pervasively evolves indirectly between allopatric replicate populations that adapt to the same ecological habitat and that this occurs generically in many distinct habitats. Patterns of interpopulation discrimination imply that kin discrimination phenotypes evolved via many diverse genetic mechanisms and mutation-accumulation patterns support this inference. Strong incompatibility phenotypes emerged abruptly in some populations but strengthened gradually in others. The indirect evolution of kin discrimination in an asexual microbe is analogous to the indirect evolution of reproductive incompatibility in sexual eukaryotes and linguistic incompatibility among human cultures, the commonality being indirect, noncoordinated divergence of complex systems evolving in isolation.

On Delegation in Contests and the Survival of Payoff Maximizing Behavior

In two-player contests, optimal delegation involves giving the agent incentives to maximize the principal's payoff while in contests with more than two players incentives will be different from the principal's payoff maximization. These results are related to the evolutionary stability of payoff-maximizing preferences in the model of indirect evolution in general symmetric games, which depends on the slope of the reaction function being zero at equilibrium. Further examples of the relationship are also discussed.