Comparison of nonlinear models to describe the feather growth and development curve in yellow-feathered chickens

Feathers play a critical role in thermoregulation and directly influence poultry production. Poor feathering adversely affects living appearance and carcass quality, thus reducing profits. However, producers tend to ignore the importance of feather development and do not know the laws of feather growth and development. The objective of this study was to fit growth curves to describe the growth and development of feathers in yellow-feathered broilers during the embryonic and posthatching periods using different nonlinear functions (Gompertz, logistic and Bertalanffy). Feather mass and length were determined during the embryonic development and posthatching stages to identify which growth model most accurately described the feather growth pattern. The results showed that chick embryos began to grow feathers at approximately embryonic (E) day 10, and the feathers grew rapidly from E13 to E17. There was little change from E17 to the day of hatching (DOH). During the embryonic period, the Gompertz function (Y = 798.48e^{−203 431exp(−0.87t)}, Akaike’s information criterion (AIC) = −0.950 × 10³, Bayesian information criterion (BIC) = −0.711 × 10³ and mean square error (MSE) = 559.308) provided the best fit for the feather growth curve compared with the other two functions. After hatching, feather mass and length changed little from the DOH to day (D) 14, increased rapidly from D21 to D91 and then grew slowly after D91. The first stage of feather molting occurred from 2 to 3 weeks of age when the down feathers were mostly shed and replaced with juvenile feathers, and the second stage occurred at approximately 13 to 15 weeks of age. The three nonlinear functions could overall fit the feather growth curve well, but the Bertalanffy model (Y = 116.88 × (1−0.86e^−0.02t)³, AIC = 1.065 × 10⁵, BIC = 1.077 × 10⁵ and MSE = 11.308) showed the highest degree of fit among the models. Therefore, the Gompertz model exhibited the best goodness of fit for the feather growth curve during the embryonic development, while the Bertalanffy model was the most suitable model due to its accurate ability to predict the growth and development of feathers during the growth period, which is an important commercial characteristic of yellow-feathered chickens.     

Comparison of non-linear growth models to describe the growth curve in West African Dwarf sheep

The objectives of this study were to compare the goodness of fit of four non-linear growth models, i.e. Brody, Gompertz, Logistic and Von Bertalanffy, in West African Dwarf (WAD) sheep. A total of 5274 monthly weight records from birth up to 180 days of age from 889 lambs, collected during 2001 to 2004 in Betecoucou breeding farm in Benin were used. In the preliminary analysis, the General Linear Model Procedure of the Statistical Analysis Systems Institute was applied to the dataset to identify the significant effects of the sex of lamb (male and female), type of birth (single and twin), season of birth (rainy season and dry season), parity of dam (1, 2 and 3) and year of birth (2001, 2002, 2003 and 2004) on the observed birth weight and monthly weight up to 6 months of age. The models parameters (A, B and k), coefficient of determination (R²), mean square error (MSE) were calculated using language of technical computing package Matlab®, 2006. The mean values of A, B and k were substituted into each model to calculate the corresponding Akaike’s Information Criterion (AIC). Among the four growth functions, the Brody model has been selected for its accuracy of fit according to the higher R², lower MSE and AIC. Finally, the parameters A, B and k were adjusted in Matlab®, 2006 for the sex of lamb, year of birth, season of birth, birth type and the parity of ewe, providing a specific slope of the Brody growth curve. The results of this study suggest that Brody model can be useful for WAD sheep breeding in Betecoucou farm conditions through growth monitoring.     

Analysis and identification of stochastic compartment models in pharmacokinetics: implication for cancer chemotherapy

One of the fundamental problems in pharmacokinetics is determining the parameters of multicompartment models from the measured excretion rate and observations on one of the compartments. Since it is frequently impractical to obtain observations for all physiological compartments, and due to the inherent variations in biological systems, a stochastic approach to multicompartment analysis is suggested. The objective of this article is to consider the identification of multicompartment models from a stochastic point of view, with particular emphasis on two- and three-compartment models.The essential part of this investigation is the statistical simulation of the C-T curves of the observed compartment for different biological conditions. We then present a probabilistic characterization of the multirandom parameter family of the rate constant matrix and evaluate the statistical properties of the solution processes for the unobservable compartments.     

The pathway from arachidonic to docosapentaenoic acid (20:4n-6 to 22:5n-6) and from eicosapentaenoic to docosahexaenoic acid (20:5n-3 to 22:6n-3) studied in testicular cells from immature rats

The concentration-dependent metabolism of 1-¹⁴C-labelled precursors of 22:5n-6 and 22:6n-3 was compared in rat testis cells. The amounts of [¹⁴C]22- and 24-carbon metabolites were measured by HPLC. The conversion of [1-¹⁴C]20:5n-3 to [3-¹⁴C]22:6n-3 was more efficient than that of [1-¹⁴C]20:4n-6 to [3-¹⁴C]22:5n-6. At low substrate concentration (4 μM) it was 3.4 times more efficient, reduced to 2.3 times at high substrate concentration (40 μM). The conversion of [1-¹⁴C]22:5n-3 to [1-¹⁴C]22:6n-3 was 1.7 times more efficient than that of [1-¹⁴C]22:4n-6 to [1-¹⁴C]22:5n-6 using a low, but almost equally efficient using a high substrate concentration. When unlabelled 20:5n-3 was added to a cell suspension incubated with [1-¹⁴C]20:4n-6 or unlabelled 22:5n-3 to a cell suspension incubated with [1-¹⁴C]22:4n-6, the unlabelled n-3 fatty acids strongly inhibited the conversion of [1-¹⁴C]20:4n-6 or [1-¹⁴C]22:4n-6 to [¹⁴C]22:5n-6. In the reciprocal experiment, unlabelled 20:4n-6 and 22:4n-6 only weakly inhibited the conversion of [1-¹⁴C]20:5n-3 and [1-¹⁴C]22:5n-3 to [¹⁴C]22:6n-3. The results indicate that if both n-6 and n-3 fatty acids are present, the n-3 fatty acids are preferred over the n-6 fatty acids in the elongation from 20- to 22- and from 22- to 24-carbon atom fatty acids. In vivo the demand for 22-carbon fatty acids for spermatogenesis in the rat may exceed the supply of n-3 precursors and thus facilitate the formation of 22:5n-6 from the more abundant n-6 precursors.     

Relationship between loading dose and infusion rate to achieve any fraction of the steady-state level in any compartment model

When a drug is infused at a constant rate K₀, the time necessary for the concentration to reach a satisfying threshold of effectiveness may be too long. To achieve this level faster, it is useful to give simultaneously a dose D, of the same drug by intravenous injection. This paper proposes the calculation, as a function of K₀ and model parameters, of the loading dose D necessary to reach, in a time T, any fraction of the asymptotic value of the amount of drug in a compartment receiving a constant rate infusion, for any n-compartment model. As an example, the expression of D for mammillary and catenary pharmacokinetic models is derived.     

Assessment and parameter identification of simplified models to describe the kinetics of semi-continuous biomethane production from anaerobic digestion of green and food waste

Biochemical reactions occurring during anaerobic digestion have been modelled using reaction kinetic equations such as first-order, Contois and Monod which are then combined to form mechanistic models. This work considers models which include between one and three biochemical reactions to investigate if the choice of the reaction rate equation, complexity of the model structure as well as the inclusion of inhibition plays a key role in the ability of the model to describe the methane production from the semi-continuous anaerobic digestion of green waste (GW) and food waste (FW). A parameter estimation method was used to investigate the most important phenomena influencing the biogas production process. Experimental data were used to numerically estimate the model parameters and the quality of fit was quantified. Results obtained reveal that the model structure (i.e. number of reactions, inhibition) has a much stronger influence on the quality of fit compared with the choice of kinetic rate equations. In the case of GW there was only a marginal improvement when moving from a one to two reaction model, and none with inclusion of inhibition or three reactions. However, the behaviour of FW digestion was more complex and required either a two or three reaction model with inhibition functions for both ammonia and volatile fatty acids. Parameter values for the best fitting models are given for use by other authors.     

Logistic growth curve of chickens: a comparison of techniques to estimate parameters

Parameters of a mathematical function of growth, fit to the body weight curve of two randombred control populations of each sex of chickens from hatching through 45 weeks of age, were estimated. The logistic function was chosen from among growth formulae that express rate of gain as a function of weight at a given time and gain to be made. Two logistic parameters, growth-rate constant and age at the point of inflection, were estimated by the methods of sample quantiles and nonlinear regression from weekly mean body weights of 225 males and 281 females of the Rhode Island Red (RIR) line, and 164 males and 239 females of the White Leghorn (WL) line. Males had a larger growth-rate constant than females of the same line. The RIR line had a larger rate constant than the WL line, for each sex. Age at the point of inflection was similar for males and females in the RIR line, but smaller for males than females in the WL line. Sample quantiles yielded larger, less precise estimates of the growth-rate constant than nonlinear regression. Estimates of age at the point of inflection were usually smaller using sample quantiles.     

Principles of chromatin organization in yeast: relevance of polymer models to describe nuclear organization and dynamics

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Estimation of the photosynthesis/irradiance (P/I) curve parameters from light and dark bottle experiments

Light and dark bottle experiments, carried out in three systemsin the Netherlands, were used to estimate the parameters ofmodels relating the oxygen production rate to incident lightintensity. The maximum production rate (P_M) and the light saturationconstant (I_S) were estimated using both gross and nett oxygenproduction data. In the latter case, the community oxygen consumptionrate (R_ox was also estimated. Eight models were compared withrespect to goodness of fit, as has been accomplished previouslyby Jassby and Platt (Limnol. Oceanogr., 21, 540–547, 1976)and many others. This study, however, emphasizes the problemof parameter correlation and the consequential usefulness ofthese type of experiments to identify the P/I curve parameters.The results show that at a 90% level of confidence, the modelscannot be distinguished with respect to goodness of fit. However,the models do show distinct differences in parameter correlation.Parameter correlation was shown to be related to the shape ofthe curve. P/I curves with high convexity were shown to be lesssensitive for parameter correlation. In particular, models showinglow convexity suffer from over-paraineterisation, which meansthat on the basis of the observed production rates it is difficultto discriminate between the parameters. Also, alternative modelformulations, using P_M and the initial slope (), were investigated.These formulations produced less parameter correlation. However,for models with low convexity, showing high parameter correlationanyway, the reduction is limited. The use of nett oxygen productiondata does not show a significant difference in fit at a 90%confidence level. However, measured R_ox from dark bottle experimentstends to be higher than the values found by estimating R_ox fromnett oxygen production.     

Comparison of parameters estimated from A/Ci and A/Cc curve analysis

The parameters estimated from traditional A/C _i curve analysis are dependent upon some underlying assumptions that substomatal CO₂ concentration (C _i) equals the chloroplast CO₂ concentration (C _c) and the C _i value at which the A/C _i curve switches between Rubisco- and electron transport-limited portions of the curve (C _i-t) is set to a constant. However, the assumptions reduced the accuracy of parameter estimation significantly without taking the influence of C _i-t value and mesophyll conductance (g _m) on parameters into account. Based on the analysis of Larix gmelinii’s A/C _i curves, it showed the C _i-t value varied significantly, ranging from 24 Pa to 72 Pa and averaging 38 Pa. t-test demonstrated there were significant differences in parameters respectively estimated from A/C _i and A/C _c curve analysis (p<0.01). Compared with the maximum ribulose-1,5-bisphosphate carboxylase/oxygenase (Rubisco) carboxylation rate (V_cmax), the maximum electron transport rate (J_max) and J_max/V_cmax estimated from A/C _c curve analysis which considers the effects of g _m limit and simultaneously fits parameters with the whole A/C _c curve, mean V_cmax estimated from A/C _i curve analysis (V_cmax-C _i) was underestimated by 37.49%; mean Jmax estimated from A/C _i curve analysis (J_max-C _i) was overestimated by 17.8% and (J_max-C _i)/(V_cmax-C _i) was overestimated by 24.2%. However, there was a significant linear relationship between V_cmax estimated from A/C _i curve analysis and V_cmax estimated from A/C _c curve analysis, so was it J_max (p<0.05).     

Application of a programmable calculator in data fitting according to one and two compartment open models in clinical pharmacokinetics

The plasma or blood concentration profiles are fitted by single or two compartment open models using log-linear regression analyses. For two compartment models, “feathering” is performed at 95% equilibration time obtained from raw pharmacokinetic data. The equations have been programmed onto a Texas Instrument SR 52 pocket calculator and recorded on 8.5 × 1.7 cm magnetic strips, facilitating drug dosage regimen calculations through individual patient titrations in a clinical setting.     

STADEERS: a software package for the statistical design of experiments pertaining to the estimation of parameters in rate expressions that describe enzyme-catalyzed processes

This paper describes a computational algorithm (STADEERS-STAtisticalDesign of Exeriments in Enzyme ReactorS) for the statisticaldesign of biochemical engineering experiments. The type of experimentthat qualifies for this package involves a batch reaction catalyzedby a soluble enzyme where the activity of the enzyme decayswith time. Assuming that both the catalytic action and the deactivationof the enzyme obey known rate expressions, the present codeis helpful in the process of obtaining estimates of the kineticparameters by providing as output the times at which samplesshould be withdrawn from the reacting mixture. Starting D-optimaldesign is used as a basis for the statistical approach. ThisBASIC code is a powerful tool when fitting a rate expressionto data because it increases the effectiveness of experimentationby helping the biochemical kineticist obtain data points withthe largest possible informa tional content.     

Endocytic pathways in polarized Caco-2 cells: identification of an endosomal compartment accessible from both apical and basolateral surfaces

The enterocyte-like cell line Caco-2 forms a polarized epithelium when grown on filters. We have investigated the interaction of endocytic pathways from the apical and basolateral surfaces. The transferrin receptor was an appropriate marker for the basolateral route; uptake of radiolabeled transferrin was highly polarized, and recycling of this ligand back to the basolateral surface occurred with an efficiency of 95%, even after prolonged incubations with transferrin. Using a transferrin-peroxidase conjugate to delineate the morphological pathway, we have identified an early endocytic compartment in the basolateral cytoplasm of the cells. Longer incubations revealed a deeper endocytic compartment in the apical cytoplasm. Concanavalin A complexed to gold was used to simultaneously label the apical endocytic route. After 60 min, extensive mixing of the two labels was seen in endocytic elements throughout the apical cytoplasm, including in the Golgi area, but never in the basal cytoplasm. Using a second double labeling procedure in which antitransferrin receptor antibody complexed to gold was applied to the basolateral surface for up to 2 h and free peroxidase applied to the apical surface for shorter periods, we demonstrated that this apical marker rapidly (within 5 min) reached endosomes containing antibody-gold. Our results indicate that, in Caco-2 cells, the endocytic pathways from the apical and basolateral surfaces meet in an endosomal compartment from which transferrin can still be recycled.     

A lateral dynamics of a wheelchair: identification and analysis of tire parameters

In vehicle dynamics studies, the tire behaviour plays an important role in planar motion of the vehicle. Therefore, a correct representation of tire is a necessity. This paper describes a mathematical model for wheelchair tire based on the Magic Formula model. This model is widely used to represent forces and moments between the tire and the ground; however some experimental parameters must be determined. The purpose of this work is to identify the tire parameters for the wheelchair tire model, implementing them in a dynamic model of the wheelchair. For this, we developed an experimental test rig to measure the tires parameters for the lateral dynamics of a wheelchair. This dynamic model was made using a multi-body software and the wheelchair behaviour was analysed and discussed according to the tire parameters. The result of this work is one step further towards the understanding of wheelchair dynamics.     

Reconciling classical and individual-based approaches in theoretical population ecology: a protocol for extracting population parameters from individual-based models

The two main approaches in theoretical population ecology-the classical approach using differential equations and the approach using individual-based modeling-seem to be incompatible. Linked to these two approaches are two different timescales: population dynamics and behavior or physiology. Thus, the question of the relationship between classical and individual-based approaches is related to the question of the mutual relationship between processes on the population and the behavioral timescales. We present a simple protocol that allows the two different approaches to be reconciled by making explicit use of the fact that processes operating on two different timescales can be treated separately. Using an individual-based model of nomadic birds as an example, we extract the population growth rate by deactivating all demographic processes-in other words, the individuals behave but do not age, die, or reproduce. The growth rate closely matches the logistic growth rate for a wide range of parameters. The implications of this result and the conditions for applying the protocol to other individual-based models are discussed. Since in physics the technique of separating timescales is linked to some concepts of self-organization, we believe that the protocol will also help to develop concepts of self-organization in ecology.     

Estimation of binding parameters of enzyme-ligand complex from fluorometric data by a curve fitting procedure: seryl-tRNA synthetase-tRNA Ser complex

A curve fitting procedure for the determination of the association constant, number of binding sites, and theoretical titration end point of an enzyme-ligand interaction monitored by fluorescence quenching titration is described and compared with classical graphical evaluation processes.     

Linear and quadratic models of point process systems: Contributions of patterned input to output

In the 1880's Volterra characterised a nonlinear system using a functional series connecting continuous input and continuous output. Norbert Wiener, in the 1940's, circumvented problems associated with the application of Volterra series to physical problems by deriving from it a new series of terms that are mutually uncorrelated with respect to Gaussian processes. Subsequently, Brillinger, in the 1970's, introduced a point-process analogue of Volterra's series connecting point-process inputs to the instantaneous rate of point-process output. We derive here a new series from this analogue in which its terms are mutually uncorrelated with respect to Poisson processes. This new series expresses how patterned input in a spike train, represented by third-order cross-cumulants, is converted into the instantaneous rate of an output point-process. Given experimental records of suitable duration, the contribution of arbitrary patterned input to an output process can, in principle, be determined. Solutions for linear and quadratic point-process models with one and two inputs and a single output are investigated. Our theoretical results are applied to isolated muscle spindle data in which the spike trains from the primary and secondary endings from the same muscle spindle are recorded in response to stimulation of one and then two static fusimotor axons in the absence and presence of a random length change imposed on the parent muscle. For a fixed mean rate of input spikes, the analysis of the experimental data makes explicit which patterns of two input spikes contribute to an output spike.     

Synergist effects of n-acetylcysteine and deferoxamine treatment on behavioral and oxidative parameters induced by chronic mild stress in rats

A growing body of evidence has pointed to a relationship between oxidative stress and depression. Thus, the present study was aimed at evaluating the effects of the antioxidants n-acetylcysteine (NAC), deferoxamine (DFX) or their combination on sweet food consumption and oxidative stress parameters in rats submitted to 40 days of exposure to chronic mild stress (CMS). Our results showed that in stressed rats treated with saline, there was a decrease in sweet food intake and treatment with NAC or NAC in combination with DFX reversed this effect. Treatment with NAC and DFX decreased the oxidative damage, which include superoxide and TBARS production in submitochondrial particles, and also thiobarbituric acid reactive substances (TBARS) levels and carbonyl proteins in the prefrontal cortex, amygdala and hippocampus. Treatment with NAC and DFX also increased the activity of the antioxidant enzymes, superoxide dismutase and catalase in the same brain areas. Even so, a combined treatment with NAC and DFX produced a stronger increase of antioxidant activities in the prefrontal cortex, amygdala and hippocampus. The results described here indicate that co-administration may induce a more pronounced antidepressant activity than each treatment alone. In conclusion, these results suggests that treatment with NAC or DFX alone or in combination on oxidative stress parameters could have positive effects against neuronal damage caused by oxidative stress in major depressive disorders.