A generalization of Gompertz law compatible with the Gyllenberg-Webb theory for tumour growth

We present a new extension of Gompertz law for tumour growth and anti-tumour therapy. After discussing its qualitative and analytical properties, we show, in the spirit of [16], that, like the standard Gompertz model, it is fully compatible with the two-population model of Gyllenberg and Webb, formulated in [14] in order to provide a theoretical basis to Gompertz law. Compatibility with the model proposed in [17] is also investigated. Comparisons with some experimental data confirm the practical applicability of the model. Numerical simulations about the method performance are presented.     

An algorithm to fit the Gompertz function to growth curves

An algorithm to fit the Gompertz growth Junction is presented.This algorithm is easy to program on a microcomputer. The algorithmis based on employing a searching technique to solve a set ofequations derived from the Gompertz function. Its applicationmay prove valuable when access to a computer mainframe is difficult.Such a method may be useful in construction of a specific growthcurve in biology, or as a managerial tool in livestock enterprise,as well as in the clinical treatment of tumors. Demonstrationof the successful application of this algorithm in experimentallivestock growth data are presented.     

The contribution of latent inhibition to reduced generalization after pre-exposure to the test stimulus

Two experiments assessed the contribution of latent inhibition to the generalization-reducing effects of pre-exposure to the test stimulus using a taste aversion procedure in rats. In both experiments, lithium chloride induced illness was paired with a flavor compound (AX) of either salt or sugar (A or B) and hydrochloric acid (X). Generalization of the resulting aversion to a test compound (BX), was assessed after varying pre-exposure to BX, X, and B. Experiment 1 showed that generalization to BX was less when BX itself had been exposed than equivalent pre-exposure to either B and X separately or to B and a new compound (CX). Experiment 2 showed that levels of generalization varied directly as a function of the amount of pre-exposure to BX. The findings show that latent inhibition alone cannot account for the generalization-reducing effect of pre-exposure to BX.     

(An algorithm for determining values of parameters of the Gompertz growth function)]

In the literature some attempts were made to analyse and to construct models for biological growth processes and to describe the quantitative aspects of a growth characteristic's changes in time using the Gompertz' function y=aexp(-exp(b--ct)). In this paper differential equations are derived having the Gompertz' function as solution. The goodness of fit after adjusting a chosen analytical expression to the courses of measured values is able to give hints at the reliability of that expression as a true model. This possibility of verification was hardly practiced in past because of lacking in proper numerical procedures for performing the nonlinear regression. An ALGOL program for iterative adjusting the parameters of the GOMPERTZ' function (with or without a constant term) to measured values is given in an appendix of the present paper. Starting values for the nonlinear parameters b and c will be evaluated by Internal Least Squares using one of the derived differential equations. For this algorithm an ALGOL program is given in the appendix too. The growth of human embryo serves as an example to demonstrate the numerical procedures and related programs for evaluating the starting values of the parameters and for their iterative improvement until reaching a minimum for the remainding variance between calculated and measured courses.     

Modelling of Scenedesmus obliquus; function of nutrients with modified Gompertz model

This study attempted to investigate variation in biovolume of Scenedesmus obliquus, in the modified Johnson medium at 20+/-2 degrees C, under 16kergcm(-2)s(-1) continuous illumination. The experiments were carried out at four nitrate (8, 12, 16, and 20mM) and four phosphate (0.1, 0.3, 0.5 and 0.7mM) concentrations at pH 7 and 8. The best response for algal growth was found at 0.3mM phosphate and 12mM nitrate at pH 7, as it was obtained from weight averaging method. Besides, optimum phosphate and nitrate concentrations significantly distinguished (p<0.01) from other concentrations according to Turkey's HSD test. Key features of the growth of S. obliquus under phosphate and nitrate influenced batch culture was successfully predicted by modified Gompertz model. Through the cultivations, specific growth rate (mu) ranged from 0.30 to 1.02 day(-1), while biovolume doubling time (td) varied from 0.68 to 2.30 days. There were important differences (p<0.05) for both mu and td among response variables. Both nutrients displayed noteworthy effect (p<0.01) on the algal biovolume.     

A simple derivation of the Gompertz law for human mortality

The Gompertz law of dependence of human mortality rate on age is derived from a simple model of death as a result of an exponentially rare escape of abnormal cells from immunological response.     

A contribution to spline-regression

Considered are polynomial spline-regressions by which functions with individual behaviour over parts of their domain may be approximated (in square mean) in a favourable manner by successive polynomials. Concerning the connections of the individual polynoms different conditions may be imposed as to continuity and smoothness. Beside of the calculation of the regression parameters essential results are the construction of confidence regions for the regression function and the formulation of tests for special dependence. Hints for practical application are given and a concrete example from agriculture is presented.     

Parameter Estimation of the Gompertz Population

The Gompertz distribution has been used to model human mortality and fit actuarial tables. In the recent years, this distribution has been studied by some authors. The MLE estimates for the parameters of the Gompertz distribution were disucssed by GARG, RAO and REDMOND (1970). The purpose of this paper is to develop an exact confidence interval and an exact joint confidence region for the parameters of the Gompertz distribution.     

The contribution of ionic interactions to the conformational stability and function of polygalacturonase from A. niger

Aspergillus niger produces multiple forms of polygalacturonases with molecular masses ranging from 30 to 60 kDa. The high molecular weight polygalacturonase (61 ± 2 kDa) from A. niger possesses a pH optimum of 4.3 and a pI of 3.9. The enzyme exhibited high sensitivity, both in terms of activity and structure, in the pH range of 4.3–7.0. The enzyme was irreversibly inactivated at pH 7.0. The enzyme is predominantly rich in parallel β structure. There is unfolding of the enzyme molecule between 4.3 and 7.0 resulting in irreversible loss of secondary and tertiary structure with the exposure of hydrophobic surfaces. ANS binding measurements, intrinsic fluorescence and acrylamide quenching measurements have confirmed the unfolding and exposure of hydrophobic surfaces. The midpoint of pH transition for both activity and secondary structure is 6.2 ± 0.1. The pH-induced changes of polygalacturonase confirm the role of histidine residues in structure and activity of the enzyme. The irreversible nature of inactivation is due to the unfolding induced exposure of hydrophobic surfaces leading to association/aggregation of the molecule. Size exclusion chromatography measurements have established the association of enzyme at higher pH. Urea induced unfolding measurements at pH 4.3 and 7.0 have confirmed the loss in stability as we approach neutral pH.     

A contribution to the world selenium map

Atomic absorption spectrophotometric method was used to determine the serum selenium levels of 86 healthy individuals. Variations in age, sex, and geographically different urban regions of Yugoslavia were investigated. A group of 63 healthy children, ages 8–15 yr, were examined. Mean±standard deviation of the serum selenium concentration was 57±9 μg/L; age and geographic area had no effect on the Se status of children, but the difference between boys and girls was significant (P<0.05). A group of 23 men from Zagreb, ages 22–37 yr, were examined. The group was divided into three age subgroups and no difference was found among these groups. The mean Se concentration was 69±18 μg/L, and a statistically significant difference was found only between the group of adults and the group of children (P<0.05).     

A century of generalization

We review data from both ethology and psychology about generalization, that is how animals respond to sets of stimuli including familiar and novel stimuli. Our main conclusion is that patterns of generalization are largely independent of systematic group (evidence is available for insects, fish, amphibians, reptiles, birds and mammals, including humans), behavioural context (feeding, drinking, courting, etc.), sensory modality (light, sound, etc.) and of whether reaction to stimuli is learned or genetically inherited. These universalities suggest that generalization originates from general properties of nervous systems, and that evolutionary strategies to cope with novelty and variability in stimulation may be limited. Two major shapes of the generalization gradient can be identified, corresponding to two types of stimulus dimensions. When changes in stimulation involve a rearrangement of a constant amount of stimulation on the sense organs, the generalization gradient peaks close to familiar stimuli, and peak responding is not much higher than responding to familiar stimuli. Contrary to what is often claimed, such gradients are better described by Gaussian curves than by exponentials. When the stimulus dimension involves a variation in the intensity of stimulation, the gradient is often monotonic, and responding to some novel stimuli is considerably stronger than responding to familiar stimuli. Lastly, when several or many familiar stimuli are close to each other predictable biases in responding occur, along all studied dimensions. We do not find differences between biases referred to as peak shift and biases referred to as supernormal stimulation. We conclude by discussing theoretical issues.     

Domain bridging interactions. A necessary contribution to the function and structure of Escherichia coli aspartate transcarbamoylase

Aspartate transcarbamoylase undergoes a domain closure in the catalytic chains upon binding of the substrates that initiates the allosteric transition. Interdomain bridging interactions between Glu(50) and both Arg(167) and Arg(234) have been shown to be critical for stabilization of the R state. A hybrid version of the enzyme has been generated in vitro containing one wild-type catalytic subunit, one catalytic subunit in which Glu(50) in each catalytic chain has been replaced by Ala (E50A), and wild-type regulatory subunits. Thus, the hybrid enzyme has one catalytic subunit capable of domain closure and one catalytic subunit incapable of domain closure. The hybrid does not behave as a simple mixture of the constituent subunits; it exhibits lower catalytic activity and higher aspartate affinity than would be expected. As opposed to the wild-type enzyme, the hybrid is inhibited allosterically by CTP at saturating substrate concentrations. As opposed to the E50A holoenzyme, the hybrid is not allosterically activated by ATP at saturating substrate concentrations. Small angle x-ray scattering showed that three of the six interdomain bridging interactions in the hybrid is sufficient to cause the global structural change to the R state, establishing the critical nature of these interactions for the allosteric transition of aspartate transcarbamoylase.     

A Comparative View of Alpha Crystallins: The contribution of comparative studies to understanding function

Integration between comparative biology and cellular/molecularbiology has helped advance understanding of the structure, functionand physiology of the vertebrate small heat shock proteins A-and B-crystallin. These proteins are expressed at high concentrationin the eye lens where they contribute to transparency and refractivepower. But they also function similarly to molecular chaperonesby preventing the aggregation of denatured proteins that cancause opacities, or cataracts. -crystallins also serve a numberof other roles in and out of the lens that are still not completelyunderstood. Comparative examination of -crystallins and closelyrelated small heat shock proteins from diverse taxa has helpedprovide insights into the proteins' three-dimensional shapeand structure/function relationships. Until recently, no studieshad examined the tissue specific expression or chaperone-likeactivity of -crystallins from a non-mammalian vertebrate. Ihave been investigating the -crystallins of the zebrafish, Daniorerio, as a first step towards utilizing the bony fishes asa model group for understanding the evolution of -crystallinfunction. Zebrafish A-crystallin displays similar structureand expression and increased chaperone-like activity comparedto its human orthologue. Zebrafish B-crystallin, however, hasa truncated C-terminal extension, more limited expression andlower chaperone-like activity than its human orthologue. Thesedata suggest that A-crystallin physiological function may beconserved between zebrafish and mammals, while B-crystallinphysiological function has diverged. Understanding zebrafish-crystallin physiology is necessary before this species canbe used for developmental and genetic studies, and providesa foundation for further comparative studies.     

A contribution to the etiology of racemose cysticercosis

An aberrant case of proliferating coenurosis caused by Taenia serialis in immunosuppressed mice is described. The coenuri closely resembled examples of racemose cysticerci described in the literature and the present results are discussed with reference to human cases of asexually proliferating larval cestode infections.