A substitution in cGMP-dependent protein kinase 1 associated with aortic disease induces an active conformation in the absence of cGMP.

Type 1 cGMP-dependent protein kinases (PKGs) play important roles in human cardiovascular physiology, regulating vascular tone and smooth-muscle cell phenotype. A mutation in the human PRKG1 gene encoding cGMP-dependent protein kinase 1 (PKG1) leads to thoracic aortic aneurysms and dissections. The mutation causes an arginine-to-glutamine (RQ) substitution within the first cGMP-binding pocket in PKG1. This substitution disrupts cGMP binding to the pocket, but it also unexpectedly causes PKG1 to have high activity in the absence of cGMP via an unknown mechanism. Here, we identified the molecular mechanism whereby the RQ mutation increases basal kinase activity in the human PKG1α and PKG1ß isoforms. Although we found that the RQ substitution (R177Q in PKG1α and R192Q in PKG1ß) increases PKG1α and PKG1ß autophosphorylation in vitro, we did not detect increased autophosphorylation of the PKG1α or PKG1ß RQ variant isolated from transiently transfected 293T cells, indicating that increased basal activity of the RQ variants in cells was not driven by PKG1 autophosphorylation. Replacement of Arg-177 in PKG1α with alanine or methionine also increased basal activity. PKG1 exists as a parallel homodimer linked by an N-terminal leucine zipper, and we show that the WT chain in WT-RQ heterodimers partly reduces basal activity of the RQ chain. Using hydrogen/deuterium-exchange MS, we found that the RQ substitution causes PKG1ß to adopt an active conformation in the absence of cGMP, similar to that of cGMP-bound WT enzyme. We conclude that the RQ substitution in PKG1 increases its basal activity by disrupting the formation of an inactive conformation.

Modelling the Evolution of Traits in a Two-Sex Population, with an Application to Grandmothering.

We present a mathematical simplification for the evolutionary dynamics of a heritable trait within a two-sex population. This trait is assumed to control the timing of sex-specific life-history events, such as the age of sexual maturity and end of female fertility, and each sex has a distinct fitness trade-off associated with the trait. We provide a formula for the fitness landscape of the population and show a natural extension of the result to an arbitrary number of heritable traits. Our method can be viewed as a dynamical systems generalisation of the Price equation to include two sexes, age structure and multiple traits. We use this formula to examine the effect of grandmothering, whereby post-fertile females subsidise their daughter's fertility by provisioning grandchildren. Grandmothering can drive a shift towards increasingly male-biased mating sex ratios due to a post-fertile life stage in females, while male fertility continues to older ages. Our fitness landscapes show a net increase in fitness for both males and females at longer lifespans, and as a result, we find that grandmothering alone provides an evolutionary trajectory to higher longevities.

Further Mathematical Modelling of Mating Sex Ratios & Male Strategies with Special Relevance to Human Life History.

Influential models of male reproductive strategies have often ignored the importance of mate guarding, focusing instead on trade-offs between fitness gained through care for dependants in a pair bond versus fitness from continued competition for additional mates. Here we follow suggestions that mate guarding is a distinct alternative strategy that plays a crucial role, with special relevance to the evolution of our own lineage. Human pair bonding may have evolved in concert with the evolution of our grandmothering life history, which entails a shift to male-biased sex ratios in the fertile ages. As that sex ratio becomes more male biased, payoffs for mate-guarding increase due to partner scarcity. We present an ordinary differential equation model of mutually exclusive strategies (dependant care, multiple mating, and mate guarding), calculate steady-state frequencies and perform bifurcation analysis on parameters of care and guarding efficiency. Mate guarding triumphs over alternate strategies when populations are male biased, and guarding is fully efficient. When guarding does not ensure complete certainty of paternity, and multiple maters are able to gain some paternity from guarders, multiple mating can coexist with guarding. At female-biased sex ratios, multiple mating takes over, unless the benefit of care to the number of surviving offspring produced by the mates of carers is large.

Evolution of longevity, age at last birth and sexual conflict with grandmothering.

We use a two-sex partial differential equation (PDE) model based on the Grandmother hypothesis. We build on an earlier model by Kim et al. (2014) by allowing for evolution in both longevity and age at last birth, and also assuming that post-fertile females support only their daughters' fertility. Similarly to Kim et al. (2014), we find that only two locally stable equilibria exist: one corresponding to great ape-like longevities and the other corresponding to hunter-gatherer longevities. Our results show that grandmothering enables the transition between these two equilibria, without extending the end of fertility. Moreover, sensitivity analyses of the model show that male competition, arising from a skew in the mating sex ratio towards males, plays a significant role in determining whether the transition from great ape-like longevities to higher longevities is possible and the equilibrium value of the average adult lifespan. Whereas grandmothering effects have a significant impact on the equilibrium value of the average age at last birth and enable the transition to higher longevities, they have an insignificant impact on the equilibrium value of the average adult lifespan.

A validation study of a smartphone application for functional mobility assessment of the elderly.

BACKGROUND: To minimize the reaction time and position judgment error using stopwatch-timed measures, we developed a smartphone application to measure performance in the five-time sit-to-stand (FTSTS) and timed up-and-go (TUG) tests. OBJECTIVE: This study aimed to validate this smartphone application by comparing its measurement with a laboratory-based reference condition. METHODS: Thirty-two healthy elderly people were asked to perform the FTSTS and TUG tests in a randomized sequence. During the tests, their performance was concurrently measured by the smartphone application and a force sensor installed in the backrest of a chair. The intraclass correlation coefficient [ICC(2,1)] and Bland-Altman analysis were used to calculate the measurement consistency and agreement, respectively, between these two methods. RESULTS: The smartphone application demonstrated excellent measurement consistency with the lab-based reference condition for the FTSTS test [ICC(2,1) = 0.988] and TUG test [ICC(2,1) = 0.946]. We observed a positive bias of 0.27 seconds (95% limits of agreement, -1.22 to 1.76 seconds) for the FTSTS test and 0.48 seconds (95% limits of agreement, -1.66 to 2.63 seconds) for the TUG test. CONCLUSION: We cross-validated the newly developed smartphone application with the laboratory-based reference condition during the examination of FTSTS and TUG test performance in healthy elderly.

Mathematical modelling of spatial sorting and evolution in a host-parasite system.

There have been numerous empirical and agent-based modelling studies on the spatial self-structuring of traits, particularly in regard to dispersal ability (termed spatial sorting) of cane toads in northern Australia, but few mathematical modelling studies. In this study, we formulate a reaction-diffusion based partial-integro-differential equation model based on an earlier model by Bouin et al. (2012) to examine this spatial self-structuring of traits in both a cane toad population and lungworm parasite population, which evolves with the cane toad population. In particular, the traits we focus on are dispersal ability for the cane toad population and both prepatent period and larval size for the lungworm parasite population. Apart from the spatial self-structuring of these traits, our results confirm a number of observations made in empirical and agent-based studies; particularly, that there is a noticeable lag between the host and parasite population which is critically dependent on the parasite functional response to host densities, that older populations regress back to lower dispersal speeds and that spatial sorting can still occur with a disadvantage in reproductivity and/or survival in more motile individuals. Moreover, we find that such a disadvantage in reproductivity and/or survival is unlikely to be large if spatial sorting is to have a noticeable effect on the rate of range expansion, as it has been observed to have over the last 60 years in northern Australia.

Modelling the impact of marine reserves on a population with depensatory dynamics.

In this study, we use a spatially implicit, stage-structured model to evaluate marine reserve effectiveness for a fish population exhibiting depensatory (strong Allee) effects in its dynamics. We examine the stability and sensitivity of the equilibria of the modelled system with regards to key system parameters and find that for a reasonable set of parameters, populations can be protected from a collapse if a small percentage of the total area is set aside in reserves. Furthermore, the overall abundance of the population is predicted to achieve a maximum at a certain ratio A of reserve area to fished area, which depends heavily on the other system parameters such as the net export rate of fish from the marine reserves to the fished areas. This finding runs contrary to the contested "equivalence at best" result when comparing fishery management through traditional catch or effort control and management through marine reserves. Lastly, we analyse the problem from a bioeconomics perspective by computing the optimal harvesting policy using Pontryagin's Maximum Principle, which suggests that the value for A which maximizes the optimal equilibrium fishery yield also maximizes population abundance when the cost per unit harvest is constant, but can increase substantially when the cost per unit harvest increases with the area being harvested.

An age-structured approach to modelling behavioural variation maintained by life-history trade-offs.

There have been numerous empirical studies on the fitness consequences of behavioural syndromes in various animal taxa; however, the ecological and evolutionary implications on a population level are still poorly understood. To better understand these implications, we develop a non-linear age-structured mathematical model to qualitatively examine the evolutionary consequences of a heritable boldness personality trait within an animal population. We assume that this heritable boldness trait is positively correlated with boldness towards predators and intraspecific aggressiveness. This assumption leads to a growth/reproductive success versus mortality trade-off, which is thoroughly investigated and documented in the literature. Another life-history trade-off we include in the model is future versus current reproduction, which was shown by Wolf et al. to be a possible mechanism for the evolution of behavioural syndromes within an animal population. The stability of the system is analysed, whereby the characteristic equation is in the form of a homogeneous Fredholm equation of the second kind which depends on both the perturbation and equilibrium solution. The system is found to be stable due to the competition between individuals of similar boldness acting as a negative feedback mechanism. Using numerical simulations we examine the qualitative features of the solution to the system. In particular, we investigate the interplay between the mutation and competition strength between two individuals with different boldness, whereby we find that an increasing competition range acts to push individuals to both extremes of the shy-bold axis, while an increasing mutation range counteracts this effect. This qualitative trait of aggregation of individuals around the shy and bold extremes is also found when examining different birth, mortality and competition functions.

Modelling a Wolbachia invasion using a slow-fast dispersal reaction-diffusion approach.

This paper uses a reaction-diffusion approach to examine the dynamics in the spread of a Wolbachia infection within a population of mosquitoes in a homogeneous environment. The formulated model builds upon an earlier model by Skalski and Gilliam (Am. Nat. 161(3):441-458, 2003), which incorporates a slow and fast dispersal mode. This generates a faster wavespeed than previous reaction-diffusion approaches, which have been found to produce wavespeeds that are unrealistically slow when compared with direct observations. In addition, the model incorporates cytoplasmic incompatibility between male and female mosquitoes, which creates a strong Allee effect in the dynamics. In previous studies, linearised wavespeeds have been found to be inaccurate when a strong Allee effect is underpinning the dynamics. We provide a means to approximate the wavespeed generated by the model and show that it is in close agreement with numerical simulations. Wavespeeds are approximated for both Aedes aegypti and Drosophila simulans mosquitoes at different temperatures. These wavespeeds indicate that as the temperature decreases within the optimal temperature range for mosquito survival, the speed of a Wolbachia invasion increases for Aedes aegypti populations and decreases for Drosophila simulans populations.