Estimating transition probabilities from aggregate samples plus partial transition data

Longitudinal studies often collect only aggregate data, which allows only inefficient transition probability estimates. Barring enormous aggregate samples, improving the efficiency of transition probability estimates seems to be impossible without additional partial-transition data. This paper discusses several sampling plans that collect data of both types, as well as a methodology that combines them into efficient estimates of transition probabilities. The method handles both fixed and time-dependent categorical covariates and requires no assumptions (e.g., time homogeneity, Markov) about the population evolution.     

Computation of relaxation matrix elements from incomplete NOESY data sets

Summary The structural determination of biological molecules in solution by NMR relies on the determination of a set of interatomic distances obtained by measurement of intramolecular nuclear Overhauser effects (NOE). It is shown in this paper that it is possible to obtain the accurate relaxation rate (and hence the interatomic distance) from the direct measurement of a single NOE signal. The precise analysis of a NOESY peak evolution with respect to the mixing time allows the evaluation of the relaxation parameters for the pair of spins under consideration. This is done without any assumption on the relaxation of unmeasured spins, or on the movement of the molecule. The theoretical basis of this method is presented. In order to evaluate the proposed method, a simulated case on the protein BPTI is studied, which shows that the method performs very well even in the case of noisy data sets.     

Reconstitution of Arachin from Isolated Subunits

Six subunits of arachin were isolated in urea solution. They were then reassociated by removing urea by co-dialysis against 20 mM sodium phosphate buffer (pH 7.9), containing 30% sucrose, 0.1 M> sodium chloride and 7 mM β-mercaptoethanol, without agitation at 25°C. The reconstitution yield was greater than 90%. The reconstituted molecule was indistinguishable from intact arachin in disc electrophoretic mobility, subunit composition, sedimentation behavior depending upon ionic strength, circular dichroism, ultraviolet absorption and fluorescence emission spectra, and stabilities against heating, proteases and guanidine hydrochloride. The reconstituted arachin was, therefore, suggested to be in native state.

On the other hand, we found that co-dialysis of four or five subunits of arachin formed hexamer which contained the corresponding four or five subunits. These hexamers were more labile than intact arachin against heating. These facts suggest that the assembly of all six subunits to a hexamer will most advantage the quaternary structure of arachin.     

Establishing the stochastic nature of intracellular calcium oscillations from experimental data

Calcium has been established as a key messenger in both intra- and intercellular signaling. Experimentally observed intracellular calcium responses to different agonists show a variety of behaviors from simple spiking to complex oscillatory regimes. Here we study typical experimental traces of calcium oscillations in hepatocytes obtained in response to phenylephrine and ATP. The traces were analyzed with methods of nonlinear time series analysis in order to determine the stochastic/deterministic nature of the intracellular calcium oscillations. Despite the fact that the oscillations appear, visually, to be deterministic yet perturbed by noise, our analyses provide strong evidence that the measured calcium traces in hepatocytes are prevalently of stochastic nature. In particular, bursting calcium oscillations are temporally correlated Gaussian series distorted by a monotonic, instantaneous, time-independent function, whilst the spiking behavior appears to have a dynamical nonlinear component whereby the overall determinism level is still low. The biological importance of this finding is discussed in relation to the mechanisms incorporated in mathematical models as well as the role of stochasticity and determinism at cellular and tissue levels which resemble typical statistical and thermodynamic effects in physics.     

Derivation of antibody distribution from experimental binding data.

It can be demonstrated that antibody populations cannot be suitably described in terms of a Sips distribution. Use of the Stieltjes transform allows instead derivation, from experimental binding data, of the most probable distribution of the association constants. From graphical interpolation of the experimental data four parameters can be obtained, which characterize a satisfactory bimodal distribution. By this procedure, analysis of data taken at different times of a humoral immune response, indicates that the relative abundance of the two sub-populations, rather than their mean association constant, is mainly affected by time or by variations of antigen dose. By use of the same procedure it is also possible to show that, at least as far as haptens are concerned, the slope of the 50% antigen-binding plot, often taken as a measure of the “avidity” of antibodies, is instead a function of the relative weight of the two sub-populations and of the spread of each of them.     

Fitting experimental data to models that use morphological data from public databases

Ideally detailed neuron models should make use of morphological and electrophysiological data from the same cell. However, this rarely happens. Typically a modeler will choose a cell morphology from a public database, assign standard values for R _a, C _m, and other parameters and then do the modeling study. The assumption is that the model will produce results representative of what might be obtained experimentally. To test this assumption we developed models of CA1 hippocampal pyramidal neurons using 4 different morphologies obtained from 3 public databases. The multiple run fitter in NEURON was used to fit parameter values in each of the 4 morphological models to match experimental data recorded from 19 CA1 pyramidal cells. Fits with fixed standard parameter values produced results that were generally not representative of our experimental data. However, when parameter values were allowed to vary, excellent fits were obtained in almost all cases, but the fitted parameter values were very different among the 4 reconstructions and did not match standard values. The differences in fitted values can be explained by very different diameters, total lengths, membrane areas and volumes among the reconstructed cells, reflecting either cell heterogeneity or issues with the reconstruction data. The fitted values compensated for these differences to make the database cells and experimental cells more similar electrotonically. We conclude that models using fully reconstructed morphologies need to be calibrated with experimental data (even when morphological and electrophysiological data come from the same cell), model results should be generated with multiple reconstructions, morphological and experimental cells should come from the same strain of animal at the same age, and blind use of standard parameter values in models that use reconstruction data may not produce representative experimental results. Action Editor: Steve Redman     

Reconstitution of the malate/aspartate shuttle from mitochondria

The isolated aspartate/glutamate carrier and oxoglutarate carrier from mitochondria were coreconstituted into phospholipid vesicles. Reconstitution of the functionally active carrier proteins with high protein/lipid ratios was achieved by detergent removal on hydrophobic ion-exchange columns. A simplified version of the mitochondrial malate/aspartate shuttle was constructed by inclusion of glutamate-oxaloacetate transaminase and the substrates aspartate and oxaloacetate within the interior of the liposomes. Addition of external glutamate led to internal production of oxoglutarate which could be exchanged against externally added labeled malate. The reconstitution procedure was characterized with respect to the optimum ratio of reconstituted carrier proteins, the lipid concentration, and the concentration of internal substrates.     

Relation of transition probabilities in the Leslie model to those from experimental cumulative distributions

We explore the relationship between transition probabilities in the Leslie model and those derived from experimental cumulative distributions. The nature of the two kinds of probabilities are discussed, and a formula derived for converting from one to the other. A numerical example is given to illustrate the differences.     

Modelling the CO2 gas exchange of grassland vegetation from experimental data

Pseudo-cubic spline functions were applied to the two atmospheric CO₂ concentrations of 340 and 600 l·l^–1 CO₂ for describing the average daily CO₂ gas exchange rates of simplifed grassland model ecosystems. Measurements used were from daily means of photon flux density (PhAR), temperature and relative air humidity, phytomass of each day, leaf area indexes, average phenological states of the vegetation (1–15), and water exchange rates of the entire model ecosystems. The functions were validated with, data from the same experimental year. We also succeeded in verifying the functions with the response data from years other than those used for constructing the model.     

Reconstitution of ATP-dependent calcium transport from streptococci

Membrane vesicles of three streptococcal strains (Streptococcus faecalis, Streptococcus lactis, and Streptococcus sanguis) were extracted with octyl-beta-D-glucoside in the presence of Escherichia coli lipid and glycerol. For reconstitution, the detergent extract was mixed with bath-sonicated E. coli lipid, in the presence of octyl-beta-D-glucoside, and proteoliposomes were formed by a 25-fold dilution. ATP-dependent calcium accumulation by proteoliposomes was comparable to that found in parent vesicles. Recovery of this calcium transport activity was dependent on the inclusion of an osmolyte protein stabilant (glycerol, etc.) during solubilization. The properties of ATP-driven calcium transport were studied in the reconstituted system. In proteoliposomes, ATP-linked calcium accumulation was not affected by the protonophore, carbonyl cyanide p-trifluoromethoxyphenylhydrazone, or by the ionophores, valinomycin and nigericin, in the presence of potassium, or by N,N'-dicyclohexylcarbodiimide, an inhibitor of the F0F1-ATPase. On the other hand, calcium transport was completely blocked by micromolar levels of orthovanadate; half-maximal inhibitions were observed at 0.4, 4, and 4 microM vanadate, for S. faecalis, S. lactis, and S. sanguis, respectively. This marked sensitivity to orthovanadate suggests operation of an E1E2-type ion-motive pump. These data demonstrate that, in a reconstituted system, calcium transport is not linked to an ATP-dependent proton circulation via the F0F1-ATPase, but rather is driven by a calcium-translocating ATPase. Thus, calcium extrusion from the cytosol of enteric, lactic acid, or oral streptococci is mediated by an ATP-linked process analogous to the ion-motive ATPases of eukaryotic membranes.     

Reconstitution of the sodium-calcium exchanger from cardiac sarcolemmal vesicles

The Na+-Ca2+ exchanger was extracted from cardiac sarcolemmal vesicles and reconstituted into phospholipid vesicles by a cholate-dialysis method. Reconstitution was attempted with different phospholipids. Phosphatidylcholine alone was ineffective, whereas phosphatidylcholine and phosphatidylethanolamine (1:1, w/w) showed high activity, but a significant Ca2+ uptake in the absence of Na+ gradient. Optimal reconstitution was obtained with a mixture of phosphatidylcholine and phosphatidylserine (9:1, mol/mol). The reconstituted proteoliposomes showed an ouabain-sensitive (Na+ + K+)-ATPase activity and a Na+-Ca2+ exchange with a specific activity comparable to that of the original vesicles. The specificity toward Na+ was also recovered. A partial purification of the exchanger was obtained by the method of transport-specificity fractionation ( Goldin , S.M. and Rhoden , V. (1978) J. Biol. Chem. 253, 2575-2583). When proteoliposomes were reconstituted with sodium oxalate inside and incubated with calcium in the presence of an outwardly directed Na+ gradient, the vesicles containing the Na+-Ca2+ exchanger specifically accumulated calcium which precipitated inside as calcium oxalate. The resulting increase in density allowed separation of the proteoliposomes containing the Na+-Ca2+ exchanger from the rest of the vesicles on a sucrose density gradient.     

Unravelling gene networks from noisy under-determined experimental perturbation data

Systems biology aims to study the properties of biological systems in terms of the properties of their molecular constituents. This occurs frequently by a process of mathematical modelling. The first step in this modelling process is to unravel the interaction structure of biological systems from experimental data. Previously, an algorithm for gene network inference from gene expression perturbation data was proposed. Here, the algorithm is extended by using regression with subset selection. The performance of the algorithm is extensively evaluated on a set of data produced with gene network models at different levels of simulated experimental noise. Regression with subset selection outperforms the previously stated matrix inverse approach in the presence of experimental noise. Furthermore, this regression approach enables us to deal with under-determination, that is, when not all genes are perturbed. The results on incomplete data sets show that the new method performs well at higher number of perturbations, even when noise levels are high. At lower number of perturbations, although still being able to recover the majority of the connections, less confidence can be placed in the recovered edges.