A Mathematical Model of Cell Cycle Progression Applied to the MCF-7 Breast Cancer Cell Line

In this paper, we present a model of cell cycle progression and apply it to cells of the MCF-7 breast cancer cell line. We consider cells existing in the three typical cell cycle phases determined using flow cytometry: the G1, S, and G2/M phases. We further break each phase up into model phases in order to capture certain features such as cells remaining in phases for a minimum amount of time. The model is also able to capture the environmentally responsive part of the G1 phase, allowing for quantification of the number of environmentally responsive cells at each point in time. The model parameters are carefully chosen using data from various sources in the biological literature. The model is then validated against a variety of experiments, and the excellent fit with experimental results allows for insight into the mechanisms that influence observed biological phenomena. In particular, the model is used to question the common assumption that a ‘slow cycling population’ is necessary to explain some results. Finally, an extension is proposed, where cell death is included in order to accurately model the effects of tamoxifen, a common first line anticancer drug in breast cancer patients. We conclude that the model has strong potential to be used as an aid in future experiments to gain further insight into cell cycle progression and cell death.     

Viscoelastic properties of passive skeletal muscle in compression: stress-relaxation behaviour and constitutive modelling

The compressive properties of skeletal muscle are important in impact biomechanics, rehabilitation engineering and surgical simulation. However, the mechanical behaviour of muscle tissue in compression remains poorly characterised. In this paper, the time-dependent properties of passive skeletal muscle were investigated using a combined experimental and theoretical approach. Uniaxial ramp and hold compression tests were performed in vitro on fresh porcine skeletal muscle at various rates and orientations of the tissue fibres. Results show that above a very small compression rate, the viscoelastic component plays a significant role in muscle mechanical properties; it represents approximately 50% of the total stress reached at a compression rate of 0.5% s⁻¹. A stiffening effect with compression rate is observed especially in directions closer to the muscle fibres. Skeletal muscle viscoelastic behaviour is thus dependent on compression rate and fibre orientation.

A model is proposed to represent the observed experimental behaviour, which is based on the quasi-linear viscoelasticity framework. A previously developed strain-dependent Young's Moduli formulation was extended with Prony series to account for the tissue viscoelastic properties. Parameters of the model were obtained by fitting to stress-relaxation data obtained in the muscle fibre, cross-fibre and 45° directions. The model then successfully predicted stress-relaxation behaviour at 60° from the fibre direction (errors <25%). Simultaneous fitting to data obtained at compression rates of 0.5% s⁻¹, 1% s⁻¹ and 10% s⁻¹ was performed and the model provided a good fit to the data as well as good predictions of muscle behaviour at rates of 0.05% s⁻¹ and 5% s⁻¹ (errors <25%).     

The origins of uncooperative rhizobia

Mutualisms are thought to be destabilized by exploitative mutants that receive benefits from partners without reciprocation. Nonetheless, there is surprisingly little evidence for the spread of exploitation in mutualist populations. In particular mutualisms, non‐beneficial partners are commonplace and this raises the question of whether exploitation is invading as an adaptive strategy. Here, we highlight the legume–rhizobium mutualism as a key test case. Rhizobial bacteria fix nitrogen in legume roots in exchange for carbon from their hosts. However, non‐beneficial rhizobia are widespread, including non‐fixing and non‐nodulating strains. Recent research has shown that legumes can punish some uncooperative rhizobia and substantially reduce their fitness, but these sanctions must not be universally effective. Important questions about uncooperative rhizobia remain unresolved. (1) Is it adaptive for rhizobia to be uncooperative with hosts? (2) Do uncooperative rhizobia evolve from cooperative ancestors? (3) What are the mechanisms of rhizobial exploitation? We describe experimental approaches and testable hypotheses that address these gaps in our knowledge.     

The relative advantages of plasticity and fixity in different environments: when is it good for a plant to adjust?

Plant populations and species differ greatly in phenotypic plasticity. This could be because plasticity is advantageous under some conditions and disadvantageous or not advantageous under others. We distinguish adaptive from injurious and neutral plasticity and discuss when selection should favor adaptive plasticity over genetic differentiation or lack of phenotypic variation. It seems reasonable to hypothesize that selection is likely to favor plasticity when an environmental factor varies on the same spatial scale as the plant response unit, when the plant can respond to an environmental factor faster than the level of the factor changes, and when environmental variation is highly but not completely predictable. Phenotypic plasticity might also tend to be more advantageous when mean resource availability is high rather than low, when a response can occur late in development rather than early, and when a response is reversible rather than irreversible. There is substantial evidence for the hypothesis that predictability favors plasticity. However, available evidence does not support the hypothesis that high mean resource availability necessarily favors plasticity. Testing hypotheses about when it is good for a plant to adjust is central to understanding the diversity of plasticity in plants.     

COSTS AND BENEFITS OF PLANT RESPONSES TO DISEASE: RESISTANCE AND TOLERANCE

A major assumption of models of the evolution of plant resistance to disease is that plant resistance involves fitness costs. To test this assumption, a field experiment was performed so that a quantitative-genetic analysis could be used to detect fitness costs to Ipomoea purpurea of resistance to different fungal isolates of Colletotrichum dematium, a pathogenic fungus causing the disease anthracnose. This experiment yielded no evidence that resistance to anthracnose involves direct fitness costs. Nevertheless, trade-offs in plant fitness that were unrelated to resistance were detected between different disease environments. Tolerance, defined as the ability to compensate in part for fitness decrements caused by disease, was found to involve fitness costs. Halfsib families that were more tolerant of disease had lower fitness in the absence of disease. The possibility that the cost of tolerance could obscure fitness costs of resistance is explored.     

Individual Differences in Inhibitory Control,Not Non-Verbal Number Acuity,Correlate with Mathematics Achievement

Given the well-documented failings in mathematics education in many Western societies, there has been an increased interest in understanding the cognitive underpinnings of mathematical achievement. Recent research has proposed the existence of an Approximate Number System (ANS) which allows individuals to represent and manipulate non-verbal numerical information. Evidence has shown that performance on a measure of the ANS (a dot comparison task) is related to mathematics achievement, which has led researchers to suggest that the ANS plays a critical role in mathematics learning. Here we show that, rather than being driven by the nature of underlying numerical representations, this relationship may in fact be an artefact of the inhibitory control demands of some trials of the dot comparison task. This suggests that recent work basing mathematics assessments and interventions around dot comparison tasks may be inappropriate.     

Ribosomal RNA secondary structure: compensatory mutations and implications for phylogenetic analysis

Using sequence data from the 28S ribosomal RNA (rRNA) genes of selected vertebrates, we investigated the effects that constraints imposed by secondary structure have on the phylogenetic analysis of rRNA sequence data. Our analysis indicates that characters from both base-pairing regions (stems) and non-base-pairing regions (loops) contain phylogenetic information, as judged by the level of support of the phylogenetic results compared with a well-established tree based on both morphological and molecular data. The best results (the greatest level of support of well-accepted nodes) were obtained when the complete data set was used. However, some previously supported nodes were resolved using either the stem or loop bases alone. Stem bases sustain a greater number of compensatory mutations than would be expected at random, but the number is < 40% of that expected under a hypothesis of perfect compensation to maintain secondary structure. Therefore, we suggest that in phylogenetic analyses, the weighting of stem characters be reduced by no more than 20%, relative to that of loop characters. In contrast to previous suggestions, we do not recommend weighting of stem positions by one-half, compared with that of loop positions, because this overcompensates for the constraints that selection imposes on the secondary structure of rRNA.      

Novel biotinylated nucleotide--analogs for labeling and colorimetric detection of DNA.

A series of dATP and dCTP nucleotide analogs have been synthesized which are modified by attachment of aliphatic linkers containing a functional group to the amino-nitrogen at the hydrogen bonding positions of the bases, that is, at the 6-position of adenine and the 4-position of cytosine. These nucleotides are incorporated into DNA probes by standard nick-translation protocols. DNA probes labeled with biotin derivatives of these nucleotides are effectively hybridized to target DNA sequences and can be detected by a streptavidin and calf intestinal alkaline phosphatase conjugate with a sensitivity (0.25 pg DNA) sufficient for reproducible and rapid detection of single copy genes in a Southern blot of mammalian DNA. Also, a procedure has been developed to allow reprobing of nylon filters that have been hybridized with biotinylated probes and developed with the streptavidin/alkaline phosphatase conjugate and a standard dye system.