Modeling Calcium Concentration and Biochemical Reactions

Almost all regions of the brain receive one or more neuromodulatory inputs, and disrupting these inputs produces deficits in neuronal function. Neuromodulators act through intracellular second messenger pathways to influence the electrical properties of neurons, integration of synaptic inputs, spatio-temporal firing dynamics of neuronal networks, and, ultimately, systems behavior. Second messengers pathways consist of series of bimolecular reactions, enzymatic reactions, and diffusion. Calcium is the second messenger molecule with the most effectors, and thus is highly regulated by buffers, pumps and intracellular stores. Computational modeling provides an innovative, yet practical method to evaluate the spatial extent, time course and interaction among second messenger pathways, and the interaction of second messengers with neuron electrical properties. These processes occur both in compartments where the number of molecules are large enough to describe reactions deterministically (e.g. cell body), and in compartments where the number of molecules is small enough that reactions occur stochastically (e.g. spines). – In this tutorial, I explain how to develop models of second messenger pathways and calcium dynamics. The first part of the tutorial explains the equations used to model bimolecular reactions, enzyme reactions, calcium release channels, calcium pumps and diffusion. The second part explains some of the GENESIS, Kinetikit and Chemesis objects that implement the appropriate equations. In depth explanation of calcium and second messenger models is provided by reviewing code, both in XPP, Chemesis and Kinetikit, that implements simple models of calcium dynamics and second messenger cascades.

Determination of the minimum alveolar concentration of isoflurane in Shetland ponies using constant current or constant voltage electrical stimulation

OBJECTIVE: To determine the minimum alveolar concentration (MAC) of isoflurane in Shetland ponies using a sequence of three different supramaximal noxious stimulations at each tested concentration of isoflurane rather than a single stimulation. STUDY DESIGN: Prospective, experimental trial. ANIMALS: Seven 4-year-old, gelding Shetland ponies. METHODS: The MAC of isoflurane was determined for each pony. Three different modes of electrical stimulation were applied consecutively (2 minute intervals): two using constant voltage (90 V) on the gingiva via needle- (CVneedle) or surface-electrodes (CVsurface) and one using constant current (CC; 40 mA) via surface electrodes applied to the skin over the digital nerve. The ability to clearly interpret the responses as positive, the latency of the evoked responses and the inter-electrode resistance were recorded for each stimulus. RESULTS: Individual isoflurane MAC (%) values ranged from 0.60 to 1.17 with a mean (+/-SD) of 0.97 (+/-0.17). The responses were more clearly interpreted with CC, but did not reach statistical significance. The CVsurface mode produced responses with a longer delay. The CVneedle mode was accompanied by variable inter-electrode resistances resulting in uncontrolled stimulus intensity. At 0.9 MAC, the third stimulation induced more positive responses than the first stimulation, independent of the mode of stimulation used. CONCLUSIONS: The MAC of isoflurane in the Shetland ponies was lower than expected with considerable variability among individuals. Constant current surface electrode stimulations were the most repeatable. A summation over the sequence of three supramaximal stimulations was observed around 0.9 MAC. CLINICAL RELEVANCE: The possibility that Shetland ponies require less isoflurane than horses needs further investigation. Constant current surface-electrode stimulations were the most repeatable. Repetitive supramaximal stimuli may have evoked movements at isoflurane concentrations that provide immobility when single supramaximal stimulation was applied.

Concentration-dependent isoflurane effects on withdrawal reflexes in pigs and the role of the stimulation paradigm

In this prospective two-phase experimental trial, 10 pigs were anaesthetized twice with isoflurane only. In the first phase, the individual minimum alveolar concentration (MAC) was determined and in the second phase the effects on withdrawal reflexes of increasing end-tidal isoflurane concentrations (from 1.6% to 2.8%) were assessed. Single, 10 and 60 repeated electrical stimulations were used to evoke withdrawal reflexes which were recorded and quantified by electromyography. Recruitment curves for reflex amplitude for increasing stimulation intensities and isoflurane concentrations were constructed. Isoflurane MAC was 1.9+/-0.3%. Reflexes evoked by repeated stimulation were suppressed at isoflurane concentrations significantly higher than those which suppressed complex movements during MAC determination (P=0.014 and P=0.006 for 10 and 60 repeated stimuli respectively). Isoflurane up to 2.8% was still not able to abolish reflex activity evoked by repeated stimulations in all pigs. Single stimulation reflexes were suppressed at significantly lower concentrations than repeated stimulation reflexes (P=0.008 and P=0.004 for 10 and 60 repeated stimuli, respectively). Reflex amplitude was significantly correlated with isoflurane concentration (P<0.001, r=-0.85) independent of the individual MAC. The findings indicate that the level at which isoflurane suppresses withdrawal reflexes is dependent on the stimulation paradigm (single vs. repeated electrical stimulation), and there is limited value in expressing reflex withdrawal suppression in terms of MAC as purposeful and reflex movements are independently affected by isoflurane in individual animals.

Effects of Initial Body Condition, Frame Size and Concentration of Dietary Energy on Carcass Value of Finished Steers

Yearling steers were sorted into four groups based on hip height and fat cover at the start of the finishing period. Each group of sorted steers was fed diets containing 0.59 or 0.64 Mcal NEg per pound of diet. The value of each carcass was determined by use of the Oklahoma State University Boxed Beef Calculator. Sorting to increase hip height decreased the percentage of Choice carcasses and fat cover, increased ribeye area, and had no effect on carcass weight or yield grades 1 and 2. Sorting to decrease initial fat cover decreased carcass weight, carcass fat cover, and percentage of choice carcasses and increased the proportion of yield grades 1 and 2 carcasses. Concentration of energy in the finishing diet had no effect on carcass measurements. Increasing the percentage of yield grades 1 and 2 carcasses did not result in increased economic value of the carcasses when quality grades were lower and when there was a wide spread between Choice and Select carcasses, as occurred in 1996. With less spread between Choice and Select, as in 1997, sorting the cattle to increase yield grades 1 and 2 resulted in increased value, especially for close-trim boxed beef. The results of this study emphasize the importance of knowing how carcasses will grade before selecting a valuebased market for selling cattle.

Effects of Initial Fat Thickness, Hip Height, and Concentration of Dietary Energy on Growth of Area of the Longissimus dorsi Muscle and Subcutaneous Fat of Yearling Steers

Steers were sorted into four groups based on hip height and fat cover at the start of the finishing period. Each group of sorted steers was fed diets containing 0.59 or 0.64 Mcal NEg per lb. of diet dry matter. Steers with less initial fat cover (0.08 in.) compared with those with more (0.17) had less carcass fat cover 103 days later. The steers with less fat cover accumulated fat at a faster rate, but this was not apparent prior to 80 days. Accretion of fat was best predicted by an exponential growth equation, and was not affected by the two concentrations of energy fed in this study. Steers with greater initial height accumulated fat cover at a slower rate than shorter steers. This difference was interpreted to mean that large-frame steers accumulate subcutaneous fat at a slower rate than medium-frame steers. Increase in area of the ribeye was best described by a linear equation. Initial fat cover, hip height, and concentrations of energy in the diet did not affect rate of growth of this muscle. Predicting carcass fat cover from the initial ultrasound measurement of fat thickness found 46 of the 51 carcasses with less than 0.4 in. of fat cover. Twelve carcasses predicted to have less than 0.4 in. of fat cover had more than 0.4 in. Five carcasses predicted to have more than 0.4 in. actually had less than that. Accurate initial measurements of initial fat thickness with ultrasound might be a useful measurement to sort cattle for specific marketing grids.

Effects of Initial Body Condition, Frame Size and Concentration of Dietary Energy on Performance of Finishing Steers

Steers were sorted into four groups based on hip height and fat cover at the start of the finishing period. Each group of sorted steers was fed a diet containing 0.59 or 0.64 Mcal NEg per pound of diet. Steers with less initial fat cover (.08 in.) gained slightly faster, consumed less feed, and therefore tended to be more efficient than steers with greater finish (.16 in.). Steers fed the lower-energy diet consumed more feed, gained similarly, and were less efficient than steers fed the higher-energy diet. The NRC computer model to evaluate beef cattle diets underpredicted performance of cattle in this experiment, but accurately predicted the differences in gain and feed efficiency observed between the leaner and fatter steers and between the two diets. In this study, the shorter steers (49.4 vs 52.2 in. initial height at the hip) gained faster with slightly greater feed intake and the same feed conversion.

The Effect of Heat Treatment of Forages on Degradation Kinetics and Escape Protein Concentration

An in situ study was conducted to evaluate the effects of heat treatments on the degradation kinetics and escape protein concentrations of forages (alfalfa and berseem clover). Alfalfa collected at 4 and 7 weeks post-harvest and berseem clover collected at 5 and 7 weeks postharvest were freeze-dried and then heated to 100, 125, and 150o C for 2 hours. Heat treatment effects were determined by placing two bags of sample (for each treatment, maturity, and forage species for a given incubation times) into the rumen of one fistulated steer fed alfalfa hay. Bags were incubated for periods of 0 to 48 hours. Increasing levels of heat treatments of forages increased concentrations of neutral detergent fiber (NDF), acid detergent fiber (ADF), and acid detergent insoluble nitrogen (ADIN) and non-degradable protein (NDP), potentially degradable protein proportion (PDP), and protein escaping rumen degradation (PEP) while decreasing water soluble protein (WSP) and the rates of crude protein (CP), except immature berseem clover and cell wall (CW) degradation. PEP was greater and rate of CP degradation was lower at 100 and 150o C compared to 125o C in immature berseem clover.

The Effect of Maturity and Frost Killing of Forages on Degradation Kinetics and Escape Protein Concentration

Two consecutive in situ studies were conducted to determine the effects of maturity and frost killing of forages (alfalfa and berseem clover) on degradation kinetics and escape protein concentrations. Four maturities (3, 5, 7, and 9 weeks after second harvest) of forages collected from three locations were used to determine the effects of maturity. Four weeks after a killing frost (-2o C), berseem clover was harvested from the same locations previously sampled. To evaluate maturity, 336 DacronÒ bags containing all maturities of either alfalfa or berseem clover were placed into the rumen of two fistulated steers fed alfalfa-grass hay. Frost killing effects of berseem clover were compared with maturecut berseem clover by placing DacronÒ bags into the rumen of one fistulated steer fed alfalfa hay. Bags were incubated for periods of 0 to 48 hours. With increasing maturity, the proportion of non-degradable protein (NDP) and the rate of crude protein (CP) degradation increased in both forages. While the rate of neutral detergent fiber (NDF) degradation and potentially degradable protein proportion (PDP) increased with increasing maturity in alfalfa, the rate of NDF degradation and PDP proportion decreased and proportion of water soluble protein (WSP) increased in berseem clover. The proportion of protein escaping rumen degradation (PEP) was greater in berseem clover than alfalfa, but was not affected by maturity. Frost killing of mature berseem clover decreased WSP proportion and increased PDP proportion compared to mature berseem clover harvested live. Even though ADIN concentration was higher for frost-killed berseem clover, PEP and total escape protein concentration (CEP) was also higher for frostkilled berseem clover than mature berseem clover harvested live, due to decreases in the rate of ruminal N degradation with frost-killing.

Effects of buffering properties and undissociated acid concentration on dissolution of dental enamel in relation to pH and acid type

To quantify the relationships between buffering properties and acid erosion and hence improve models of erosive potential of acidic drinks, a pH-stat was used to measure the rate of enamel dissolution in solutions of citric, malic and lactic acids, with pH 2.4-3.6 and with acid concentrations adjusted to give buffer capacities (β) of 2-40 (mmol·l(-1))·pH(-1) for each pH. The corresponding undissociated acid concentrations, [HA], and titratable acidity to pH 5.5 (TA5.5) were calculated. In relation to β, the dissolution rate and the strength of response to β varied with acid type (lactic > malic ≥ citric) and decreased as pH increased. The patterns of variation of the dissolution rate with TA5.5 were qualitatively similar to those for β, except that increasing pH above 2.8 had less effect on dissolution in citric and malic acids and none on dissolution in lactic acid. Variations of the dissolution rate with [HA] showed no systematic dependence on acid type but some dependence on pH. The results suggest that [HA], rather than buffering per se, is a major rate-controlling factor, probably owing to the importance of undissociated acid as a readily diffusible source of H(+) ions in maintaining near-surface dissolution within the softened layer of enamel. TA5.5 was more closely correlated with [HA] than was β, and seems to be the preferred practical measure of buffering. The relationship between [HA] and TA5.5 differs between mono- and polybasic acids, so a separate analysis of products according to predominant acid type could improve multivariate models of erosive potential.