Molecular map of the desmosomal plaque.

Recent biochemical and molecular approaches have begun to establish the protein interactions that lead to desmosome assembly. To determine whether these associations occur in native desmosomes we have performed ultrastructural localisation of specific domains of the major desmosomal components and have used the results to construct a molecular map of the desmosomal plaque. Antibodies directed against the amino- and carboxy-terminal domains of desmoplakin, plakoglobin and plakophilin 1, and against the carboxy-terminal domains of desmoglein 3, desmocollin 2a and desmocollin 2b, were used for immunogold labelling of ultrathin cryosections of bovine nasal epidermis. For each antibody, the mean distance of the gold particles, and thus the detected epitope, from the cytoplasmic surface of the plasma membrane was determined quantitatively. Results showed that: (i) plakophilin, although previously shown to bind intermediate filaments in vitro, is localised extremely close to the plasma membrane, rather than in the region where intermediate filaments are seen to insert into the desmosomal plaque; (ii) while the 'a' form of desmocollin overlaps with plakoglobin and desmoplakin, the shorter 'b' form may be spatially separated from them; (iii) desmoglein 3 extends across the entire outer plaque, beyond both desmocollins; (iv) the amino terminus of desmoplakin lies within the outer dense plaque and the carboxy terminus some 40 nm distant in the zone of intermediate filament attachment. This is consistent with a parallel arrangement of desmoplakin in dimers or higher order aggregates and with the predicted length of desmoplakin II, indicating that desmoplakin I may be folded or coiled. Thus several predictions from previous work were borne out by this study, but in other cases our observations yielded unexpected results. These results have significant implications relating to molecular interactions in desmosomes and emphasise the importance of applying multiple and complementary approaches to biological investigations.

Contributions of individual molecular species to the Hill coefficient for ligand binding by an oligomeric protein.

New insights into the Hill coefficient (n) as a measure of cooperativity are obtained by resolving Y, the fractional ligand binding to an oligomeric protein, into a series of integral nth-order reactions. For identical sites within a single conformational state, the weighted sum of each reaction multiplied by its net order gives a Hill coefficient at Y = 0.5 of n50 = 1.0, indicative of non-cooperative binding. However, the disappearance of unliganded oligomers (S0) reflects the higher-order reactions, with their weighted sum (for a tetramer) leading to a Hill coefficient at S0 = 0.5 of n50* = -1.27. For an oligomer with two conformational states (such as represented by the T and R states in the Monod-Wyman-Changeux model) capable of generating highly cooperative binding, the same nth-order reactions apply, but with different weights. For oxygen binding to hemoglobin, n50 is resolved into three components with net reaction orders of n = -2, 2, and 4 (with weights of 0.067, 0.15, and 0.754 corresponding, respectively, to the contributions of singly, triply and quadruply liganded molecules) to give n50 = 3.18. However, the cooperativity of the "state" function, R' (the normalized fraction of molecules in the R state), as characterized by n50' (the Hill coefficient at R' = 0.5) is distinct from n50. If the T-R equilibrium lies very far in favor of either state, then even when the two states differ widely in their intrinsic affinity for ligand, the lower limit of cooperativity for Y is n50 = 1.0, but the Hill coefficient for R' cannot fall below n50' = 1.27 (for a tetramer). Hence, the lower limit of n50' is equal to the absolute value of n50* describing the disappearance of S0 for an oligomer with a single conformational state.

Distinct desmocollin isoforms occur in the same desmosomes and show reciprocally graded distributions in bovine nasal epidermis.

The adhesive core of the desmosome is composed of cadherin-like glycoproteins of two families, desmocollins and desmogleins. Three isoforms of each are expressed in a tissue-specific and developmentally regulated pattern. In bovine nasal epidermis, the three desmocollin (Dsc) isoforms are expressed in overlapping domains; Dsc3 expression is strongest in the basal layer, while Dsc2 and Dsc1 are strongly expressed in the suprabasal layers. Herein we have investigated whether different isoforms are assembled into the same or distinct desmosomes by performing double immunogold labeling using isoform-specific antibodies directed against Dsc1 and Dsc3. The results show that individual desmosomes harbor both isoforms in regions where their expression territories overlap. Quantification showed that the ratio of the proteins in each desmosome altered gradually from basal to immediately suprabasal and upper suprabasal layers, labeling for Dsc1 increasing and Dsc3 decreasing. Thus desmosomes are constantly modified as cells move up the epidermis, with continuing turnover of the desmosomal glycoproteins. Statistical analysis of the quantitative data showed a possible relationship between the distributions of the two isoforms. This gradual change in desmosomal composition may constitute a vertical adhesive gradient within the epidermis, having important consequences for cell positioning and differentiation.

Molecular analysis of HLA-DQB1 alleles in childhood common acute lymphoblastic leukaemia.

Epidemiological studies suggest that childhood common acute lymphoblastic leukaemia (c-ALL) may be the rare outcome of early post-natal infection with a common infectious agent. One of the factors that may determine whether a child succumbs to c-ALL is how it responds to the candidate infection. Since immune responses to infection are under the partial control of (human leucocyte antigen) HLA genes, an association between an HLA allele and c-ALL could provide support for an infectious aetiology. To define the limit of c-ALL susceptibility within the HLA region, we have compared HLA-DQB1 allele frequencies in a cohort of 62 children with c-ALL with 76 newborn controls, using group-specific polymerase chain reaction (PCR) amplification, and single-strand conformation polymorphism (SSCP) analysis. We find that a significant excess of children with c-ALL type for DQB1*05 [relative risk (RR): 2.54, uncorrected P=0.038], and a marginal excess with DQB1*0501 (RR: 2.18; P=0.095). Only 3 of the 62 children with c-ALL have the other susceptibility allele, DPB1*0201 as well as DQB1*0501, whereas 15 had one or the other allele. This suggests that HLA-associated susceptibility may be determined independently by at least two loci, and is not due to linkage disequilibrium. The combined relative risk of the two groups of children with DPB1*0201 and/or DQB1*0501 is 2.76 (P=0.0076). Analysis of amino acids encoded by exon 2 of DQB1 reveal additional complexity, with significant (P<0.05) or borderline-significant increases in Gly26, His30, Val57, Glu66-Val67 encoding motifs in c-ALL compared with controls. Since these amino acids are not restricted to DQB1*0501, our results suggest that, as with DPB1, the increased risk of c-ALL associated with DQB1 is determined by specific amino acid encoding motifs rather than by an individual allele. These results also suggest that HLA-associated susceptibility to c-ALL may not be restricted to the region bounded by DPB1 and DQB1.

A statistical theory for flow cytometry profiles in terms of the binding of ligands to cell surface receptors and changes in gene expression.

Flow cytometry analysis is a technique used for obtaining light scattering and fluorescence intensity data in order to characterise a chosen cell line. From a sample of the data obtained, it is desired to infer the distribution of cell size, cell granularity and occupancy of cell surface receptors, by constructing histograms for the variables of interest. Often an attempt is made, for instance, to account for the changes in shape of these histograms in terms of alterations in gene expression, etc. In this paper we analyse the way that changes in the sample histograms can be interpreted in three frequently encountered situations, namely (a) when there is one cell line exposed to alterations in chemical potential of ligand, (b) when there are two cell lines exposed separately to saturating concentrations of the same ligand, and (c) when two ligands are added in saturating amounts, first separately, then together, to the same cell line. We demonstrate that, under a wide range of assumptions, the change in histogram shape can be accounted for in terms of a proportionate and absolute component and examples are given to illustrate this. Finally, a computer program to analyse experimental data in terms of estimated shift and stretch parameters is described.

Quantitative analysis of wound healing.

In this article, we initially review several problems associated with the design and interpretation of certain types of experiments currently used to study wound healing, drawing attention to the fact that applications for standard statistical techniques in the analysis of the experimental results are often of limited value. We then argue that, because of the special nature of wound healing data, curve fitting of empirical model equations can often provide a convenient way to summarize treatment effects with large data sets. The various ways in which this technique could be used to facilitate the interpretation of experimental wound healing results are then explored. To illustrate this approach, we then took several wound healing experiments and introduced possible models that could be used, paying particular attention to simple equations with the smallest possible number of parameters. For each equation, the way that the parameters of the model could be interpreted with regard to the biologic effects represented is given. Examples are given to show the application of each model discussed theoretically in the interpretation of some typical experimental data sets.

Mathematical models for growth in alligator (Alligator mississippiensis) embryos developing at different incubation temperatures.

A variety of model-based (growth models) and model-free (cubic splines, exponentials) equations were fitted using weighted-nonlinear least squares regression to embryonic growth data from Alligator mississippiensis eggs incubated at 30 and 33 degrees C. Goodness of fit was estimated using a chi 2 on the sum of squared, weighted residuals, and run and sign tests on the residuals. One of the growth models used (Preece & Baines, 1978) was found to be superior to the classical growth models (exponential, monomolecular, logistic, Gompertz, von Bertalanffy) and gave an adequate fit to all longitudinal measures taken from the embryonic body and embryonic mass. However, measurements taken from the head could not be fitted by growth models but were adequately fitted by weighted least squares cubic splines. Data for the stage of development were best fitted by a sum of 2 exponentials with a transition point. Comparison of the maximum growth rates and parameter values, indicated that the growth data at 30 degrees C could be scaled to 33 degrees C to multiplying the time by a scaling factor of 1.2. This is equivalent to a Q10 of about 1.86 or, after solving the Arrhenius equation, an E++ of 46.9 kJmol-1. This may be interpreted as indicating a common rate-limiting step in development at the 2 temperatures.

A statistical model and computer program to estimate association constants for the binding of fluorescent-labelled monoclonal antibodies to cell surface antigens and to interpret shifts in flow cytometry data resulting from alterations in gene expression.

Flow cytometry is used to obtain estimates for the distribution of fluorescent ligands bound to cell surface receptors throughout a cell sample. The equipment used provides light scattering parameters and also cell staining data in the form of dot plots and histograms of fluorescence intensities and the frequency of occurrence of particular fluorescence intensities. It is then assumed that fluorescence intensity is proportional to the number of labelled ligands bound to surface receptors. In this paper we present an outline of a statistical theory to account for the stretching and translation of such flow cytometry profiles which occur either as a result of alterations in gene expression, or from changing the sub-saturating concentration of fluorescent-labelled monoclonal antibodies or lectins used to stain the cells. We describe how the theory has been incorporated into two programs CSAFIT (cell surface antigen fit) and MAKCSA (make data to test CSAFIT). The program CSAFIT can be used to estimate two parameters, alpha and beta, by constrained non-linear regression analysis of the flow cytometry profiles. If the shift results from changes in the concentration of a staining agent then the estimates alpha and beta calculated by CSAFIT are functions of the ligand concentration, the ligand type and the cell line characteristics. They quantify the stretch and translation events that are encountered in flow cytometry. So when the parameter estimates alpha and beta are then further analysed as functions of ligand concentration, estimates for the average association constant K for the binding-site/ligand interaction can be obtained. This paper describes details of the development of programs CSAFIT and MAKCSA. We also discuss the distribution of parameter estimates calculated by CSAFIT and the overall performance of CSAFIT as assessed by simulation studies using data generated by MAKCSA.

Analysis of gene-dosage effects on the expression of CD18 by trisomy 21 lymphoblastoid cell-lines using a statistical model to fit flow cytometry profiles.

It is not clear whether Down syndrome, the phenotypic expression of constitutional trisomy for chromosome 21 (T21), is the result of generalised disruption of homeostasis resulting from genetic imbalance, or the over-expression of specific genes on chromosome 21. In order to understand the effect of gene dosage more clearly, we have analysed the predicted and actual levels of expression of the leucocyte integrin beta subunit CD 18 on the surface of T21 leucocytes. Previous studies showed that CD18 expression by T21 lymphoid cell lines (LCL) is greater than on normal LCL. We have now developed a computer model that compares the observed and predicted CD18 flow cytometric profiles for trisomy 21 LCL. Three parameters (alpha, beta and gamma) have been defined that measure different aspects of gene dosage. Using the computer model to calculate these parameters, we have carried out a series of paired comparisons between normal and T21 LCL. The results show that, in some T21 LCL, increased CD18 expression is proportional to the existing gene dosage, in another set the effect is additive, whereas in others there is a combination of proportional and additive effects. The results suggest that gene regulation can exert pleiotropic effects on gene-dosage, and is consistent with a model in which gene dosage itself is the cause of disrupted homeostasis.

The kinetics of adsorption of human immunoglobulin G to poly(vinyl chloride) enzyme-linked-immunoadsorbent-assay vessel walls.

Experiments were performed to measure the effect of pH, ionic strength, temperature, organic solvents, pretreatment with gelatin and Tween 20 on the rate and extent of binding of human IgG to the walls of poly(vinyl chloride) e.l.i.s.a. vessels. It is demonstrated that, over a wide range of experimental conditions, the binding is controlled by rate-limiting diffusion to the walls, followed by a rapid and irreversible adsorption. A mathematical model is derived and shown to give a good fit to the experimental data points.

Fetal and maternal blood volumes in shed human placentae: discrepant results comparing morphometry to haemoglobin content.

The maternal blood volume (MBV) and fetal blood volume (FBV) of shed human placentae delivered by caesarean section at term were measured using a morphometric technique and from the placental content of adult and fetal haemoglobin. MBV was 35.3 +/- 1.5 (s.e.m.) per cent by the former and 11.0 +/- 1.5 per cent by the latter technique. FBV was 11.0 +/- 0.7 and 9.0 +/- 0.6 per cent respectively (n = 6). Measurement of the dimensions of individual villi initially photomicrographed in 0.9 per cent NaCl and subsequently re-photographed in fixative suggested that individual villi shrank to 0.7 of their initial volume during fixation. It is suggested that morphometric measurement of MBV may lead to approximately a threefold overestimate because of relative MBV expansion and villous tissue shrinkage during the process of fixation without alteration in overall placental volume.

Molecular charge effects on the protein permeability of the guinea-pig placenta.

The effect of molecular charge on protein permeability of the dually perfused guinea-pig placenta has been investigated by measurement of the permeability surface area products (PS) and observation of the ultrastructural localization of cationic horseradish peroxidase (cHRP) and anionic horseradish peroxidase (aHRP) molecules. Steady-state PS calculated from the experimental data was 0.032 +/- 0.0045 and 0.0045 +/- 0.0008 ml min-1 (mean +/- s.e.m.) for cHRP and aHRP respectively (P less than 0.01). The PS for a diffusional marker, 51Cr-ethylenediaminetetraacetic acid, showed no significant difference between the two groups. Ultrastructurally, placentae perfused with cHRP showed fewer microvilli and a dilated interstitial space compared with placentae perfused with aHRP; large vacuoles were also found in the syncytiotrophoblast in the former but not in the latter tissue. Reaction product in placentae perfused with cHRP was localized to the maternal-facing plasma membrane of the syncytiotrophoblast, in vacuoles and vesicles of the syncytiotrophoblast, and also in the basement membrane of the interstitial space, whereas placentae perfused with aHRP only had reaction product in vesicles in the syncytiotrophoblast. These results suggest that anionic sites in the guinea-pig placenta affect its permeability to charged proteins, cationic molecules inducing structural changes associated with increased permeability.

The use of non-linear regression analysis and the F test for model discrimination with dose-response curves and ligand binding data.

Computer fitting of binding data is discussed and it is concluded that the main problem is the choice of starting estimates and internal scaling parameters, not the optimization software. Solving linear overdetermined systems of equations for starting estimates is investigated. A function, Q, is introduced to study model discrimination with binding isotherms and the behaviour of Q as a function of model parameters is calculated for the case of 2 and 3 sites. The power function of the F test is estimated for models with 2 to 5 binding sites and necessary constraints on parameters for correct model discrimination are given. The sampling distribution of F test statistics is compared to an exact F distribution using the Chi-squared and Kolmogorov-Smirnov tests. For low order modes (n less than 3) the F test statistics are approximately F distributed but for higher order models the test statistics are skewed to the left of the F distribution. The parameter covariance matrix obtained by inverting the Hessian matrix of the objective function is shown to be a good approximation to the estimate obtained by Monte Carlo sampling for low order models (n less than 3). It is concluded that analysis of up to 2 or 3 binding sites presents few problems and linear, normal statistical results are valid. To identify correctly 4 sites is much more difficult, requiring very precise data and extreme parameter values. Discrimination of 5 from 4 sites is an upper limit to the usefulness of the F test.

The non-Michaelian action of thrombin on peptide p-nitroanilide substrates.

1. v([S]) kinetic data were obtained for the hydrolysis of the chromogenic substrates H-D-Phe-L-Pip-L-Arg-pNA (S-2238), H-D-Ile-L-Pro-L-Arg-pNA (S-2288), Tos-Gly-L-Pro-L-Arg-pNA (Tos-Ch-TH) and Cbz-Gly-L-Pro-L-Arg-pNA (Cbz-Ch-TH) by native human thrombin under different experimental conditions (Pip is pipecolyl, pNA is p-nitroanilide, Tos is tosyl and Cbz is benzyloxycarbonyl). 2. The data were fitted to rational functions of order 1:1, 2:2 and 3:3 by using non-linear regression. Discrimination between equations of different degree was made using the F-test. 3. In all, 24 curves were fitted. In 17 cases degree 2:2 was significantly better than degree 1:1 at a confidence level of 95%. In no case was any further significant improvement found with functions of degree 3:3. 3. Our results allow us to assert that native human thrombin is an enzyme that does not allow Michaelian kinetic behaviour when acting on chromogenic substrates. Instead, the empirically obtained steady-state data require mechanisms whose rate equation is at least of degree 2:2.

Conditions when statistical tests for model discrimination have high power. Some examples from pharmacokinetics, ligand binding, transient and steady-state enzyme kinetics.

The situation where data pairs xi, yi are actually generated by a true model, f(delta, x), but erroneously fitted by a deficient model, g(phi, x), is explored. A function, Q(delta), is described which is the average squared distance between f(delta, x) and the best-fit false model, g(phi, x). For a range of x covering 5-95% 'saturation' of f(delta, x), Q(delta) is calculated numerically for sums of exponentials, binding functions and rational functions. In each case, the region of delta when the second model in the series can be reliably differentiated from the first by statistical tests is described.

Bile salt-stimulated lipase and esterase activity in human milk after collection, storage, and heating: nutritional implications.

In a study of human milk obtained in the first month of lactation, lipase and esterase activity were assayed. Bile salt-stimulated lipase (BSSL) and bile salt-stimulated esterase (BSSE) activities in colostrum were similar to corresponding enzyme activities in transitional milk and in mature milk. BSSL and BSSE were significantly (P less than 0.001) correlated to one another, which suggests that lipase and esterase activities in milk are due to the same enzyme. When milk was allowed to stand at room temperature, in a refrigerator, or subjected to freezing and thawing, wide fluctuations were observed in lipase and esterase activities, but there was no systematic tendency for enzyme activity to increase or decrease. Heating milk to various temperatures between 40-55 degrees C resulted in progressive loss of enzyme activity. The activation energy for the process which inactivates the enzyme was found by linear regression to the Arrhenius plot to be 2 X 10(5) J X mole-1. Our findings suggest that lipase and esterase activity in human milk which is donated to hospitals and stored frozen can make a valuable contribution to fat digestion in the newborn infant, but pasteurization destroys the enzyme.

Evidence concerning a possible steady state rate equation for E. coli alkaline phosphatase.

Steady state data was obtained for alkaline phosphatase over a wide range of experimental conditions using two substrates, four inhibitors, two modifiers and several pH, ionic strength and temperatures values. The data was fitted by rational functions of degree 1:1, 2:2 and 3:3 using a non-linear regression program and then the F-test was used to assess the goodness of fit. A proportion of the curves could only be fitted by 2:2 functions but many of them could be adequately fitted by 1:1 functions. No statistically significant improvement in fit occurred with 3:3 functions. Data was simulated using a computer program to see what sort of curves could be generated by a two sites mechanism proposed for alkaline phosphatase and this study showed it is difficult to detect cubic terms in this rate equation. It was concluded that alkaline phosphatase does not obey Michaelis-Menten kinetics. Rather, the steady state data require a mechanism of at least second degree but do not exclude a rate equation of third degree.

Simple enzyme kinetic mechanisms that can give all possible velocity profiles with chemically reasonable rate constant values.

It is shown that all rate profiles and double reciprocal plots possible for arbitrary rational functions of degree n:n can be given by enzyme mechanisms in which rate constant values are limited by physical constraints. The significance of this finding in the theory of complex kinetics is explained, and the application in the area of non-linear regression analysis of complex kinetic data and model discrimination, is discussed.

Inhibition of enzyme-catalysed reactions by excess substrate. A theoretical and Monte Carlo study of turning points in v(S) graphs.

Some difficulties associated with observing and defining substrate inhibition curves are discussed. Then a new method for measuring the steepness of substrate inhibition curves is derived and a parameter, lambda, is defined to measure the steepness of descent from a maximum or steepness of ascent from a minimum in v(S) plots. A mathematical theorem is presented to show how the magnitude of lambda is limited by the degree of the rate equation. Conditions for satisfactory Monte Carlo simulations of enzyme mechanisms are explored and the constraints necessary to generate v(S) curves with profiles in physiological ranges of substrate concentrations are investigated using 16 enzyme mechanisms. The probability of detecting substrate inhibition is estimated. It is shown that there exists a lower limit to the substrate concentration at which maxima can occur in v(S) plots but no upper limit and also that enzyme mechanisms can approach but never achieve the maximum steepness of descent possible for arbitrary rational functions with non-negative coefficients.

Kinetic analysis of cell spreading. I. Theory and modelling of curves.

The spreading of cells on suitably treated surfaces is briefly discussed and the need to analyse this phenomenon numerically is emphasized. Possible mathematical models for fitting experimental data are classified as statistical, kinetic or empirical and examples of each of these types are given. A possible protocol for analysing cell spreading kinetics and determining goodness of fit and parameter redundancy is presented.