A mathematical model of in vivo bovine blastocyst developmental to gestational Day 15.

Bovine embryo growth involves a complex interaction between the developing embryo and the growth-promoting potential of the uterine environment. We have previously established links between embryonic factors (embryo stage, embryo gene expression), maternal factors (progesterone, body condition score), and embryonic growth to 8 d after bulk transfer of Day 7 in vitro-produced blastocysts. In this study we recovered blastocysts on Days 7 and 15 after artificial insemination to test the hypothesis that in vivo and in vitro embryos follow a similar growth program. We conducted our study using 4 commercial farms and repeated our study over 2 yr (2014, 2015), with data available from 2 of the 4 farms in the second year. Morphological and gene expression measurements (196 candidate genes) of the Day 7 embryos were measured and the progesterone concentration of the cows were measured throughout the reproductive cycle as a reflection of the state of the uterine environment. These data were also used to assess the interaction between the uterine environment and the developing embryo and to examine how well Day 7 embryo stage can be predicted from the Day 7 gene expression profile. Progesterone was not a strong predictor of in vivo embryo growth to Day 15. This contrasts with a range of Day 7 embryo transfer studies which demonstrated that progesterone is a very good predictor of embryo growth to Day 15. Our analysis demonstrates that in vivo embryos are 3 times less sensitive to progesterone than in vitro-transferred embryos (up to Day 15). This highlights that caution must be applied when extrapolating the results of in vitro embryo transfer studies to the in vivo situation. The similar variance in measured and predicted (based on Day 15 length) Day 7 embryo stage indicate low stochastic perturbations for in vivo embryo growth (large stochastic growth effects would generate a significantly larger standard deviation in measured embryo length on Day 15). We also identified that Day 7 embryo stage could be predicted based on the Day 7 gene expression profile (58% overall success rate for classification of 5 embryo stages). Our analysis also associated genes with each developmental stage and demonstrates the high level of temporal regulation of genes that occurs during early embryonic development.

Varying plantain content in temperate ryegrass-white clover pastures affects urinary-nitrogen excretion of non-lactating dairy cows.

Dairy cow urine patches contain high rates of nitrogen (N; >500 kg N/ha) and represent the main source of N loss from grazed pastoral systems. Emerging research has identified plantain (Plantago lanceolata) as a key forage to potentially reduce urine N (UN) losses from dairy cows. This experiment examined the effect of increasing proportions of plantain in the diet of dairy cows on UN excretion relative to a ryegrass-white clover diet. Twenty mixed aged non-lactating dairy cows were randomly assigned to one of five treatment diets; 0 %, 20 %, 40 %, 60 % or 100 % plantain (dry matter basis), with the remainder comprised of ryegrass-white clover pasture and grass-silage. Cows were fitted with urine sensors to measure urination event N concentration, volume and frequency. Daily N intake increased with increasing proportions of plantain in the diet due to the greater N concentration of plantain. Conversely, mean UN concentration was reduced as the proportion of plantain in the diet increased. Urine-N concentration was >40 % lower for cows on 100 % plantain compared with 0 % plantain (0.46 and 0.81 % N respectively). There was no treatment effect on the total daily amount of UN excreted, indicating a dilution effect of plantain as total daily urine volumes markedly increased with increasing plantain diets. Nitrogen load per urination event was lower for cows on 100 % plantain than 0 % despite greater N intake, with no significant difference for the intermediate treatment groups. The reduced N load per event for cows on >60 % plantain could help to reduce N leaching losses at the urine patch level. This experiment suggests that a reduction in UN concentration can be achieved on low levels of plantain (20 % of the diet), but >60 % plantain diets are required to reduce N load per event.

Anisotropic nutrient transport in three-dimensional single species bacterial biofilms.

The ability for a biofilm to grow and function is critically dependent on the nutrient availability, and this in turn is dependent on the structure of the biofilm. This relationship is therefore an important factor influencing biofilm maturation. Nutrient transport in bacterial biofilms is complex; however, mathematical models that describe the transport of particles within biofilms have made three simplifying assumptions: the effective diffusion coefficient (EDC) is constant, the EDC is that of water, and/or the EDC is isotropic. Using a Monte Carlo simulation, we determined the EDC, both parallel to and perpendicular to the substratum, within 131 real, single species, three-dimensional biofilms that were constructed from confocal laser scanning microscopy images. Our study showed that diffusion within bacterial biofilms was anisotropic and depth dependent. The heterogeneous distribution of bacteria varied between and within species, reducing the rate of diffusion of particles via steric hindrance. In biofilms with low porosity, the EDCs for nutrient transport perpendicular to the substratum were significantly lower than the EDCs for nutrient transport parallel to the substratum. Here, we propose a reaction-diffusion model to describe the nutrient concentration within a bacterial biofilm that accounts for the depth dependence of the EDC.

Urine sensor-based determination of repeatable cow urination traits in autumn, winter and spring.

Nitrogen (N) excreted in urine by grazing ruminants is the main source of N loss from pasture-based agriculture. In this study we used cow-attached urine sensors to measure the between-cow, between-day, within day diel and between-season patterns in the urination events from grazing cattle. The urine sensor was deployed for four days to estimate the time, frequency, duration, flow rate, volume, N concentration and N load of individual urination events from 13 to 15 cows per trial in autumn, winter, and spring. Repeat measurements were also obtained on cows in the autumn, winter, and spring trials. There was seasonal variation in the urination traits, with lower N output per event and N output per day in autumn. The urination events exhibited significant diel patterns, with a 2 to 5-fold diel variation in all urination traits. The diel patterns for each urination trait also displayed three distinct peaks and three distinct minima at times that were approximately consistent between seasons. We also established between-cow variability in the diel amplitude of each urination trait. Low amplitude diel cows are likely to have a lower N loss potential as they excrete a lower proportion of very large N load events, which far exceed the ability of pasture to utilize the excreted N. The duration of urination can predict event volume (RMSE = 0.8 L) and the combination of duration and frequency can predict event N load (R2 = 0.67). The between-cow variability in the urination event traits had coefficients of variation that range from 10 to 20% (ratio of standard deviation to the mean), and the between-day variation in the urination traits ranged from 7 to 20%. There is therefore potential to identify cows that for a fixed N intake excrete a lower N load per urination event over an entire season.

A mathematical model of pregnancy recognition in mammals.

In this paper we develop a mathematical model of the luteal phase of the reproductive cycle in mammals with the aim to generate a systems understanding of pregnancy recognition. Pregnancy recognition is initiated by the production of interferon tau (IFNtau) by the growing conceptus. This ensures that the maternal corpus luteum (CL) remains viable to secrete progesterone, which is critical for providing a uterine microenvironment suitable for embryonic growth. Our mathematical model describes the interactions among the CL, the reproductive hormones and the hormone receptors in the uterus. It also characterises the complex interactions amongst the uterine oestrogen, progesterone and oxytocin receptors that control the sensitivity of the uterus to oestrogen, progesterone and oxytocin, respectively. The model is represented by a dynamical system and exhibits qualitative features consistent with the known experimental results in sheep. A key factor identified was a time-dependent threshold for the IFNtau signal below which the presence of the embryo might not be recognised and thus pregnancy would likely fail. Furthermore, the model indicated that if the IFNtau signal is later than around day 13 of the cycle, then pregnancy will not be recognised irrespective of the IFNtau concentration. The thresholds in the concentration and time of the IFNtau signal is a screening mechanism whereby only embryos of sufficient quality are able to prevent luteolysis (i.e. regression of the CL). The effect of progesterone secretion rate from the CL on pregnancy recognition was investigated. The model suggests that if the secretion rate is low then the initiation of the IFNtau signal is delayed, which in turn compromises the likelihood of a pregnancy being recognised by the CL. Furthermore, pregnancy recognition does not occur below a critical threshold in the progesterone secretion rate. In summary, the model can be used to identify the most favourable conditions for pregnancy recognition.

A mathematical analysis of obstructed diffusion within skeletal muscle.

Molecules are transported through the myofilament lattice of skeletal muscle fibers during muscle activation. The myofilaments, along with the myosin heads, sarcoplasmic reticulum, t-tubules, and mitochondria, obstruct the diffusion of molecules through the muscle fiber. In this work, we studied the process of obstructed diffusion within the myofilament lattice using Monte Carlo simulation, level-set and homogenization theory. We found that these intracellular obstacles significantly reduce the diffusion of material through skeletal muscle and generate diffusion anisotropy that is consistent with experimentally observed slower diffusion in the radial than the longitudinal direction. Our model also predicts that protein size has a significant effect on the diffusion of material through muscle, which is consistent with experimental measurements. Protein diffusion on the myofilament lattice is also anomalous (i.e., it does not obey Brownian motion) for proteins that are close in size to the myofilament spacing. The obstructed transport of Ca2+ and ATP-bound Ca2+ through the myofilament lattice also generates smaller Ca2+ transients. In addition, we used homogenization theory to discover that the nonhomogeneous distribution in the troponin binding sites has no effect on the macroscopic Ca2+ dynamics. The nonuniform sarcoplasmic reticulum Ca2+-ATPase pump distribution also introduces small asymmetries in the myoplasmic Ca2+ transients.

Application of Hyperspectral imaging to predict the pH, intramuscular fatty acid content and composition of lamb M. longissimus lumborum at 24h post mortem.

Cost-effective, rapid and objective measurement of lamb quality on a routine basis is an important step for lamb value chains wishing to manage lamb product quality. Hyperspectral imaging (HSI) technology has shown promise as a solution for objective non-invasive prediction of meat quality. The performance of HSI applied 24h post mortem to lamb M. longissimus lumborum (LL) within a processing plant environment was assessed over two sampling years to evaluate its suitability for an objective lamb meat quality assurance tool. Calibration and validation steps were undertaken to evaluate HSI prediction performance for predicting fatty acid content and composition (n=1020 lambs) and pH (n=2406 lambs). Practical considerations of reference meat quality data quality and validation strategies are discussed. HSI can be used to predict meat quality parameters of lamb LL with varying accuracy levels, but ongoing calibration and validation across seasons is required to improve robustness of HSI for objective non-invasive assessment of lamb meat quality.

A mathematical model of fatty acid metabolism and VLDL assembly in human liver.

The lipid composition of very-low-density lipoprotein (VLDL) in plasma is crucial for human health. A pre-requisite for the alteration of VLDL composition is a co-ordinated understanding of the complex interactions in VLDL assembly. In order to determine the potential effects of changes in substrate availability on VLDL lipid composition, we constructed, parameterized and evaluated a mechanistic mathematical model of the biosynthesis of triglycerides, phospholipids, and cholesterol esters and the assembly of VLDL in human hepatocytes. Using published data on human liver metabolism, the model was also used to provide insight into the complex process of lipid metabolism and to estimate the affinities of different liver enzymes for different fatty acids (FA). For example, we found that Delta6-desaturase is 19 times more selective for C18:3n-3 than C18:2n-6, stearoyl-CoA-desaturase is 2.7 times more selective for C18:0 than C16:0, Delta5-desaturase desaturates C20:4n-3 preferentially over C20:3n-6 and FA elongase preferentially elongates C18:3n-6. The model was also used to predict the plasma free fatty acid (FFA) composition required to generate a prescribed change in plasma lipoprotein FA composition. Furthermore, the model was tested against a published human feeding trial that investigated the effect of changes in dietary FA composition on human plasma lipid FA composition. The model is a useful tool for predicting the effect of changes in plasma FFA composition on plasma lipoprotein lipid FA composition.

Estimation of microbial growth using population measurements subject to a detection limit.

In this paper we develop a maximum likelihood estimation procedure for determining the mean and variance in microbial population size from microbial population measurements subject to a detection limit. Existing estimation methods generally set non-detectable measurements equal to the detection limit and are highly biased. Because changes in the mean and variance in the microbial population size are typical in industrial processes we also outline statistical tests for detecting such changes when measurements are subject to a detection limit, which is critical for process control. In an industrial process there may also potentially be variability in the microbial growth rate due to variation in the microbial strain, environment, and food characteristics. Accordingly, we also present a maximum likelihood procedure for estimating microbial growth model parameters and their variance components from microbial population measurements subject to a detection limit. Such information can be used to generate the mean and variance through time of the microbial population size, which is vital for the application of predictive microbiological models to risk assessment and food product shelf-life estimation.

A risk assessment approach applied to the growth of Erwinia carotovora in vegetable juice for variable temperature conditions.

Risk assessment for food spoilage relies on probabilistic models of microbial growth to predict the likelihood that microbial populations will exceed predefined spoilage levels. To assist in the design and management of industrial food quality systems, predictive microbiological models have to incorporate major risk factors such as the variability in the microbial strain, environment and initial contamination levels. In addition, the application of results measured under laboratory conditions to the less controlled environment of an industrial process usually also involves uncertainty. Extra information regarding this uncertainty must be factored into industrial microbial risk assessment. In this paper, based on our previous analysis of the growth of Erwinia carotovora we show how different factors contribute to the risk of microbial spoilage of vegetable juice and we demonstrate an effective way of including these factors into risk assessment models. The association of risk components with different unavoidable and manageable factors is also valuable for the development of optimal strategies for reducing microbial risk.

Determining insulin sensitivity from glucose tolerance tests in sheep.

A mathematical model of the dynamics of insulin and glucose during a frequently sampled intravenous glucose tolerance test (IVGTT) in sheep was developed that characterizes the large second-phase insulin secretion response in sheep during IVGTT. The model was fit to measurements of the glucose and insulin dynamics during standard IVGTT ( = 42) and modified IVGTT ( = 40), where insulin was injected 60 min after the initiation of the IVGTT. The correlation between log insulin sensitivity determined by hyperglycemic clamps (HGC) and standard IVGTT was = 0.43 ( = 0.005). The correlation between log insulin sensitivity determined by HGC and modified IVGTT was = 0.51 ( = 0.002). The model, therefore, provides a method to determine insulin sensitivity through a cheaper and more easily performed IVGTT. We validated our estimation procedure using 2 independent experiments on the effect of 1) pregnancy and 2) being born preterm and exposed to dextrose or dextrose with insulin on HGC-derived insulin sensitivity. The IVGTT-derived insulin sensitivity was significantly greater in pregnant ewes than in prepregnant ewes (difference of 0.39 ± 0.12 log n ng mL; < 0.05), and this was consistent with the significantly greater hyperinsulinemic euglycemic clamp-derived insulin sensitivity in pregnant ewes than in prepregnant ewes (difference of 4.03 ± 0.66 µmol mL kg min ng; < 0.001). There was no significant effect of being born preterm on IVGTT/HGC-derived insulin sensitivity. Basal insulin, insulin sensitivity, insulin production, and insulin clearance were lower in prepregnant ewes ( < 0.05). That is, prepregnant ewes have a lower insulin equilibrium status and less responsive insulin turnover. There was also a significant effect of insulin therapy on the rate of insulin clearance in preterm lambs ( < 0.05). This effect was independently significant of its covariance with all other model parameters. Therefore, it can be interpreted as a direct effect on the rate of insulin clearance by the insulin treatment. All other parameter responses to the insulin treatment effect can be regarded as being due to the covariance between these parameters. These analyses demonstrate that treatment effects on insulin sensitivity can be detected using IVGTT experiments.

The effects of age, weight, and sire on pregnancy rate in cattle.

The goal was to estimate the heritabilities and genetic variances for pregnancy rate (PR) and calving date (CD) in Angus cattle along with the effect of weight, age, and sire on PR and CD. The data consisted of 4,999 records on PR and CD. Statistical models included year as a fixed effect; premating/postmating weight and age as covariates; and sire of embryo, maternal grandsire (MGS), and permanent maternal environmental effects as random effects. The models also included the interactions between herd and weight (weight change). Direct and maternal effects on PR and CD were estimated using sire MGS and animal models in REML. Pregnancy rate increased from age 2 to 6 and decreased from age 7 to 11 (P < 0.01) and this effect was independent of the culling strategy. There was a quadratic effect of premating cow weight independent of age on PR, with lower PR for low weights (P < 0.01). Overall, cows with a premating weight of 550 kg had the greatest PR. Cows that lost weight during mating had lower PR (P < 0.01). The maternal additive heritability for PR was 0.001 ± 0.012 and the direct additive heritability was 0.024 ± 0.020. The ratio of permanent maternal environmental variance to phenotypic variance was significant (0.048 ± 0.017; P < 0.01). This demonstrates that permanent maternal environmental effects play a major role in the repeatability of PR (0.049 ± 0.015; P < 0.01). The maternal additive heritability for CD was 0.040 ± 0.022, and the direct additive heritability was 0.076 ± 0.045. The ratio of permanent maternal environmental variance to phenotypic variance was low (0.014 ± 0.017) and the repeatability for CD was significant (0.0544 ± 0.0180; P < 0.01). This suggests that maternal genetic effects are as important as direct genetic effects on CD. There was a positive quadratic relationship between premating cow weight and CD with delayed calving for low/high weights (P < 0.01). Cows that lost weight over mating also had a later CD (P < 0.01). Comparisons of a weight-selected herd to the control herd showed differences (P < 0.05) in the optimal premating weight for early calving (control, 480 kg, and weight selected, 615 kg). Calving date was also more sensitive to changes in weight over mating in the weight selection herd (P < 0.05). Therefore, the set point in the weight-fertility axis and the sensitivity of fertility to changes in weight both changed in the weight selection herd.

A new, improved and generalizable approach for the analysis of biological data generated by -omic platforms.

The principles embodied by the Developmental Origins of Health and Disease (DOHaD) view of 'life history' trajectory are increasingly underpinned by biological data arising from molecular-based epigenomic and transcriptomic studies. Although a number of 'omic' platforms are now routinely and widely used in biology and medicine, data generation is frequently confounded by a frequency distribution in the measurement error (an inherent feature of the chemistry and physics of the measurement process), which adversely affect the accuracy of estimation and thus, the inference of relationships to other biological measures such as phenotype. Based on empirical derived data, we have previously derived a probability density function to capture such errors and thus improve the confidence of estimation and inference based on such data. Here we use published open source data sets to calculate parameter values relevant to the most widely used epigenomic and transcriptomic technologies Then by using our own data sets, we illustrate the benefits of this approach by specific application, to measurement of DNA methylation in this instance, in cases where levels of methylation at specific genomic sites represents either (1) a response variable or (2) an independent variable. Further, we extend this formulation to consideration of the 'bivariate' case, in which the co-dependency of methylation levels at two distinct genomic sites is tested for biological significance. These tools not only allow greater accuracy of measurement and improved confidence of functional inference, but in the case of epigenomic data at least, also reveal otherwise cryptic information.

Partitioning of the variance in the growth parameters of Erwinia carotovora on vegetable products.

The objective of this paper was to estimate and partition the variability in the microbial growth model parameters describing the growth of Erwinia carotovora on pasteurised and non-pasteurised vegetable juice from laboratory experiments performed under different temperature-varying conditions. We partitioned the model parameter variance and covariance components into effects due to temperature profile and replicate using a maximum likelihood technique. Temperature profile and replicate were treated as random effects and the food substrate was treated as a fixed effect. The replicate variance component was small indicating a high level of control in this experiment. Our analysis of the combined E. carotovora growth data sets used the Baranyi primary microbial growth model along with the Ratkowsky secondary growth model. The variability in the microbial growth parameters estimated from these microbial growth experiments is essential for predicting the mean and variance through time of the E. carotovora population size in a product supply chain and is the basis for microbiological risk assessment and food product shelf-life estimation. The variance partitioning made here also assists in the management of optimal product distribution networks by identifying elements of the supply chain contributing most to product variability.

Monoculture parameters successfully predict coculture growth kinetics of Bacteroides thetaiotaomicron and two Bifidobacterium strains.

Microorganisms rarely live in isolation but are most often found in a consortium. This provides the potential for cross-feeding and nutrient competition among the microbial species, which make it challenging to predict the growth kinetics in coculture. In this paper we developed a mathematical model to describe substrate consumption and subsequent microbial growth and metabolite production for bacteria grown in monoculture. The model characterized substrate utilization kinetics of 18 Bifidobacterium strains. Some bifidobacterial strains demonstrated preferential degradation of oligofructose in that sugars with low degree of polymerization (DP) (DP≤3 or 4) were metabolized before sugars of higher DP, or vice versa. Thus, we expanded the model to describe the preferential degradation of oligofructose. In addition, we adapted the model to describe the competition between human colonic bacteria Bacteroides thetaiotaomicron LMG 11262 and Bifidobacterium longum LMG 11047 or Bifidobacterium breve Yakult for inulin as well as cross-feeding of breakdown products from the extracellular hydrolysis of inulin by B. thetaiotaomicron LMG 11262. We found that the coculture growth kinetics could be predicted based on the respective monoculture growth kinetics. Using growth kinetics from monoculture experiments to predict coculture dynamics will reduce the number of in vitro experiments required to parameterize multi-culture models.

Effect of age, weight, and sire on embryo and fetal survival in sheep.

The goal was to estimate the heritabilities and genetic variances for embryo and fetal survival (ES) in sheep along with the effect of premating ewe weight, age, and bilateral or unilateral ovulation on ES. The data consisted of 11,369 records on ovulation rate and litter size. Statistical models for ES included year and ovulation rate as fixed effects, premating ewe weight, and age as covariates, and sire of embryo, maternal grandsire (MGS), and permanent maternal environmental effects of the ewe as random effects. The variance components were estimated using REML. In ewes that survived to yr 6, the mean litter size was 1.87, 2.05, 2.01, 2.07, and 1.91 ± 0.04 in ewes of age 2, 3, 4, 5, and 6 yr, respectively. Litter size was less in ewes of age 2 and 6 yr compared to ewes of age 3, 4, and 5 yr (P < 0.01). Ovulation rate was lower at age 2 yr and increased from age 2 to 6 yr (P < 0.05). Two-year-old ewes had lower ES than 3-yr-old ewes (P < 0.01) and the probability of ES decreased after age 3 yr (P < 0.01). Thus, ES contributes significantly to lower fertility in 2-yr-old ewes. In ewes with high ovulation rates (i.e., 5 corpora lutea, CL), more balanced ovulations (i.e., 2 or 3 CL on each ovary) tended (P = 0.06) to be associated with increased ES. A quadratic relationship was observed between ewe weight and litter size (P < 0.01) and a positive linear relationship between premating ewe weight and ovulation rate (P < 0.01). A quadratic effect of ewe weight on ES was observed, with decreased ES for low and high ewe weights (P < 0.01). The optimal ewe weight for ES increased with ovulation rate, which is consistent with the requirement of greater body reserves for maintaining a larger number of fetuses during gestation. A quadratic relationship between ewe weight and the probability that a ewe is able to maintain a pregnancy was also observed (P < 0.05). Pregnancy loss is due to failure of the embryo or fetus or failure of the dam to maintain the pregnancy. The sire of the embryo only influences the embryo, whereas the MGS influences both the ewe and the embryo. The heritability for the direct additive effect on ES in ewes that lambed was 0.0081 ± 0.0139, and the heritability for the maternal additive effect was 0.0447 ± 0.0242. The permanent maternal environmental variance component was significant and explained 8.5% of the phenotypic variance. Thus, genetically, the dam's ability to maintain a pregnancy has 5.5 times the effect on pregnancy loss than the embryo's ability to survive, and this, in turn, was only half the size of the permanent environmental effect. Therefore, selection among dams based on the mean embryonic survival of their embryos will provide an effective way to improve embryonic survival.

Insulin transport within skeletal muscle transverse tubule networks.

It has recently been observed in situ in mice that insulin takes approximately 10 min to be transported 20 microm into the t-tubule networks of skeletal muscle fibers. The mechanisms for this slow transport are unknown. It has been suggested that the biochemical composition of the t-tubular space that may include large molecules acting as gels and increased viscosity in the narrow tubules may explain this slow diffusion. In this article, we construct a mathematical model of insulin transport within the t-tubule network to determine potential mechanisms responsible for this slow insulin transport process. Our model includes insulin diffusion, insulin binding to insulin receptors, t-tubule network tortuosity, interstitial fluid viscosity, hydrodynamic wall effects, and insulin receptor internalization and recycling. The model predicted that depending on fiber type there is a 2-15 min delay in the arrival time of insulin between the sarcolemma and inner t-tubules (located 20 microm from the sarcolemma) after insulin injection. This is consistent with the experimental data. Increased viscosity in the narrow t-tubules and large molecules acting as gels are not the primary mechanisms responsible for the slow insulin diffusion. The primary mechanisms responsible for the slow insulin transport are insulin binding to insulin receptors and network tortuosity.

Mathematically modeling the effects of electrically stimulating skeletal muscle.

A framework for modeling the activation of skeletal muscle is presented for studying functional electrical stimulation. A mathematical model of the cellular responses of skeletal muscle, created at AgResearch (Ruakura, New Zealand www.agresearch.co.nz), has been integrated with an anatomical, finite element model of the semitendinosus muscle, which was constructed from CT scans of the hind limb of a sheep. The tibial nerve was also constructed from digitized CT scans, and has been modeled using the Hodgkin Huxley neural model. The relevant cellular equations have been solved over these geometries. The results obtained, i.e speed of action potential propagation through the nerve and muscle, and the duration of twitch force, agree with published values.

A Hodgkin-Huxley model exhibiting bursting oscillations.

We investigate bursting behaviour generated in an electrophysiological model of pituitary corticotrophs. The active and silent phases of this mode of bursting are generated by moving between two stable oscillatory solutions. The bursting is indirectly driven by slow modulation of the endoplasmic reticulum Ca2+ concentration. The model exhibits different modes of bursting, and we investigate mode transitions and similar modes of bursting in other Hodgkin-Huxley models. Bifurcation analysis and the use of null-surfaces facilitate a geometric interpretation of the model bursting modes and action potential generation, respectively.

CRH-induced electrical activity and calcium signalling in pituitary corticotrophs.

Pituitary corticotroph cells generate repetitive action potentials and associated Ca2+ transients in response to the agonist corticotropin releasing hormone (CRH). There is indirect evidence suggesting that the agonist, by way of complex intracellular mechanisms, modulates the voltage sensitivity of the L-type Ca2+ channels embedded in the plasma membrane. We have previously constructed a Hodgkin-Huxley-type model of this process, which indicated that an increase in the L-type Ca2+ current is sufficient to generate repetitive action potentials (LeBeau et al. (1997). Biophys. J.73, 1263-1275). CRH is also believed to inhibit an inwardly rectifying K+ current. In this paper, we have found that a CRH-induced inhibition of the inwardly rectifying K+ current increases the model action potential firing frequency, [Ca2+]i transients and membrane excitability. This dual modulatory action of CRH on inward rectifier and voltage-gated Ca2+ channels better describes the observed CRH-induced effects. This structural alteration to the model along with parameter changes bring the model firing frequency in line with experimental data. We also show that the model exhibits experimentally observed bursting behaviour, where the depolarization spike is followed by small oscillations in the membrane potential.