Algorithm and Complexity for a Network Assortativity Measure

We show that finding a graph realization with the minimum Randi\'c index for a given degree sequence is solvable in polynomial time by formulating the problem as a minimum weight perfect b-matching problem. However, the realization found via this reduction is not guaranteed to be connected. Approximating the minimum weight b-matching problem subject to a connectivity constraint is shown to be NP-Hard. For instances in which the optimal solution to the minimum Randi\'c index problem is not connected, we describe a heuristic to connect the graph using pairwise edge exchanges that preserves the degree sequence. In our computational experiments, the heuristic performs well and the Randi\'c index of the realization after our heuristic is within 3% of the unconstrained optimal value on average. Although we focus on minimizing the Randi\'c index, our results extend to maximizing the Randi\'c index as well. Applications of the Randi\'c index to synchronization of neuronal networks controlling respiration in mammals and to normalizing cortical thickness networks in diagnosing individuals with dementia are provided.Comment: Added additional section on application

Plasticity in transmission strategies of the malaria parasite, Plasmodium chabaudi : environmental and genetic effects

Parasites may alter their behaviour to cope with changes in the within-host environment. In particular, investment in transmission may alter in response to the availability of parasite resources or host immune responses. However, experimental and theoretical studies have drawn conflicting conclusions regarding parasites' optimal (adaptive) responses to deterioration in habitat quality. We analyse data from acute infections with six genotypes of the rodent malaria species to quantify how investment in transmission (gametocytes) is influenced by the within-host environment. Using a minimum of modelling assumptions, we find that proportional investment in gametocytogenesis increases sharply with host anaemia and also increases at low parasite densities. Further, stronger dependence of investment on parasite density is associated with greater virulence of the parasite genotype. Our study provides a robust quantitative framework for studying parasites' responses to the host environment and whether these responses are adaptive, which is crucial for predicting the short-term and evolutionary impact of transmission-blocking treatments for parasitic diseases

Complex CatSper-dependent and independent [Ca2⁺]i signalling in human spermatozoa induced by follicular fluid

STUDY QUESTION: Does progesterone in human follicular fluid (hFF) activate CatSper and do other components of hFF modulate this effect and/or contribute separately to hFF-induced Ca2+ signaling?SUMMARY ANSWER: hFF potently stimulates CatSper and increases [Ca2+]i, primarily due to high concentrations of progesterone, however,other components of hFF also contribute to [Ca2+]i signaling, including modulation of CatSper channel activity and inhibition of [Ca2+]i oscillations.WHAT IS KNOWN ALREADY: CatSper, the principal Ca2+ channel in spermatozoa, is progesterone-sensitive and essential for fertility. Both hFF and progesterone, which is present in hFF, influence sperm function and increase their [Ca2+]i.STUDY DESIGN, SIZE, DURATION: This basic medical research study used semen samples from >40 donors and hFF from >50 patients who were undergoing surgical oocyte retrieval for IVF/ICSI.PARTICIPANTS/MATERIALS, SETTING, METHODS: Semen donors and patients were recruited in accordance with local ethics approval (13/ES/0091) from the East of Scotland Research Ethics Service REC1. Activities of CatSper and KSper were assessed by patch clamp electrophysiology. Sperm [Ca2+]i responses were examined in sperm populations and single cells. Computer-assisted sperm analysis (CASA) parameters and penetration into viscous media were used to assess functional effects.MAIN RESULTS AND THE ROLE OF CHANCE: hFF and progesterone significantly potentiated CatSper currents. Under quasiphysiologicalconditions, hFF (up to 50%) failed to alter membrane K+ conductance or current reversal potential. hFF and progesterone (at an equivalent concentration) stimulated similar biphasic [Ca2+]i signals both in sperm populations and single cells. At a high hFF concentration (10%), the sustained (plateau) component of the [Ca2+]i signal was consistently greater than that induced by progesterone alone. In single cell recordings, 1% hFF-induced [Ca2+]i oscillations similarly to progesterone but with 10% hFF generation of [Ca2+]i oscillations was suppressed. After treatment to ‘strip’ lipid-derived mediators, hFF failed to significantly stimulate CatSper currents but induced small [Ca2+]i responsesthat were greater than those induced by the equivalent concentration of progesterone after stripping. Similar [Ca2+]i responses were observed when sperm pretreated with 3 μM progesterone (to desensitize progesterone responses) were stimulated with hFF or stripped hFF. hFF stimulated viscous media penetration and was more effective than the equivalent does of progesterone.LARGE SCALE DATA: N/A.LIMITATIONS, REASONS FOR CAUTION: This was an in vitro study. Caution must be taken when extrapolating these results in vivo.WIDER IMPLICATIONS OF THE FINDINGS: This study directly demonstrates that hFF activates CatSper and establishes that the biologically important effects of hFF reflect, at least in part, action on this channel, primarily via progesterone. However, these experiments also demonstrate that other components of hFF both contribute to the [Ca2+]i signal and modulate the activation of CatSper. Simple in vitro experiments performed out of the context of the complex in vivo environment need to be interpreted with caution

Single-cell analysis of [Ca²⁺]i signalling in sub-fertile men:characteristics and relation to fertilization outcome

STUDY QUESTIONWhat are the characteristics of progesterone-induced (CatSper-mediated) single cell [Ca2+]i signals in spermatozoa from sub-fertile men and how do they relate to fertilizing ability?SUMMARY ANSWERSingle cell analysis of progesterone-induced (CatSper-mediated) [Ca2+]i showed that reduced progesterone-sensitivity is a common feature of sperm from sub-fertile patients and is correlated with fertilization rate.WHAT IS KNOWN ALREADYStimulation with progesterone is a widely used method for assessing [Ca2+]i mobilization by activation of CatSper in human spermatozoa. Although data are limited, sperm population studies have indicated an association of poor [Ca2+]i response to progesterone with reduced fertilization ability.STUDY DESIGN, SIZE, DURATIONThis was a cohort study using semen samples from 21 donors and 101 patients attending the assisted conception unit at Ninewells Hospital Dundee who were undergoing ART treatment. Patients were recruited from January 2016 to June 2017.PARTICIPANTS/MATERIALS, SETTING, METHODSSemen donors and patients were recruited in accordance with local ethics approval (13/ES/0091) from the East of Scotland Research Ethics Service (EoSRES) REC1. [Ca2+]i responses were examined by single cell imaging and motility parameters assessed by computer-assisted sperm analysis (CASA).MAIN RESULTS AND THE ROLE OF CHANCEFor analysis, patient samples were divided into three groups IVF(+ve) (successful fertilization; 62 samples), IVF-FF (failed fertilization; eight samples) and ICSI (21 samples). A further 10 IVF samples showed large, spontaneous [Ca2+]i oscillations and responses to progesterone could not be analysed. All patient samples loaded with the [Ca2+]i-indicator fluo4 responded to progesterone stimulation with a biphasic increase in fluorescence (transient followed by plateau) which resembled that seen in progesterone-stimulated donor samples. The mean normalized response (progesterone-induced increase in fluorescence normalized to resting level) was significantly smaller in IVF-FF and ICSI patient groups than in donors. All samples were further analysed by plotting, for each cell, the relationship between resting fluorescence intensity and the progesterone-induced fluorescence increment. In donor samples these plots overlaid closely and had a gradient of ≈ 2 and plots for most IVF(+ve) samples closely resembled the donor distribution. However, in a subset (≈ 10%) of IVF(+ve) samples, 3/8 IVF-FF samples and one-third of ICSI samples the gradient of the plot was significantly lower, indicating that the response to progesterone of the cells in these samples was abnormally small. Examination of the relationship between gradient (regression coefficient of the plot) in IVF samples and fertilization rate showed a positive correlation. In IVF-FF and ICSI groups, the proportion of cells in which a response to progesterone could be detected was significantly lower than in donors and IVF (+ve) patients. Approximately 20% of cells in donor, IVF(+ve) and ICSI samples generated [Ca2+]i oscillations when challenged with progesterone but in IVF-FF samples only ≈ 10% of cells generated oscillations and there was a significantly greater proportion of samples where no oscillations were observed. Levels of hyperactivated motility were lower in IVF(+ve) and IVF-FF groups compared to controls, IVF-FF also having lower levels than IVF(+ve).LIMITATIONS, REASONS FOR CAUTIONThis is an in vitro study and caution must be taken when extrapolating these results in vivo.WIDER IMPLICATIONS OF THE FINDINGSThis study reveals important details of impaired [Ca2+]i signalling in sperm from sub-fertile men that cannot be detected in population studies