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N B Grover

Publications and source records attributed to N B Grover.

At least 19 recordsLinked to original sources
PubMed2006

Diffusion with attrition.

This article treats the problem of the sharp front observed when a diffusing substance interacts irreversibly with binding sites within the medium. The model consists of two simultaneous partial differential equations that are nonlinear and cannot be solved in closed form. The parameters are the diffusion coefficient D in the direction under consideration (x), the interaction constant k, the binding-site concentration mu and the boundary concentration of the diffusing ion c(0). Our aim is to develop methods to enable the estimation of these parameters from the experimental data. An analytical solution for the case k --> infinity, as found by others, is given first and then a finite element analysis package is used to obtain numerical solutions for the general case. Graphs are presented to illustrate the effects of the various parameters. Simple graphical procedures are described to compute mu and c (0). The position of the advancing front xi then provides, together with mu, a way to estimate D. A mathematical identity relating D and x and a second one involving D, k and t help to reduce the complexity of the problem. A new, measurable quantity S(t) is defined as [see text] where f is the total concentration (free + bound) of the diffusing ion at time t, and detailed plots are furnished that permit the computation of k directly from S(t), mu and D. The accuracy with which such methods can be expected to determine the various parameters of the model is considered at some length. Finally, in a concluding section, we simulate typical experimental data, examine the validity of our methods, and see how their accuracy is affected by controlled amounts of various kinds of noise.

Biometry↗
PubMed2004

Bacterial shape maintenance: an evaluation of various models.

In this article, we examine a large number of combinations of growth models, with separate attention to cell volume, cylindrical surface-area, polar caps, nascent poles, onset of constriction, precision of cell division and interdivision-time dispersion, for Escherichia coli cells growing in steady state at various doubling times. Our main conclusion is striking, and quite general: exponential cylindrical surface-area growth is not possible, irrespective of the behaviour of cell volume, the polar regions, the nascent poles, or any other feature of cell growth-such cells never reach steady state. The same is true of linear cylindrical surface-area growth, regardless of when during the cell cycle the doubling in growth rate takes place. Only after the introduction of feedback into the surface-area growth law, do the cultures attain steady state, all of them. The other components of the models contribute only marginally to the properties of the steady state. Thus, whether the feedback applies just to the cylindrical portion of the cell or to its entire surface area affects only the coefficient of variation of cell radius and the radius-volume correlation. The dynamics of old-pole maintenance, constant area or constant shape, influences the radius-length and radius-volume correlations and, to a much lesser extent, the coefficients of variation of cell radius and length; how the nascent poles grow, whether linearly or exponentially, does not seem to matter at all. The absolute dimensions of the cells are set by the growth rate of the culture and have almost no effect when the feedback is taken to apply to the entire cell surface area; when it is limited to the cylindrical portion of the cell, however, both radius-length and radius-volume correlations increase with increasing doubling time. Comparison with published values was inconclusive. The nature of cell surface-area growth has therefore been settled, but whether the volume increases by simple-exponential or by pseudo-exponential growth, or whether the old poles maintain a constant shape or a constant area during the cell cycle, can be determined only with more precise experimental data. The form of nascent-pole growth is not resolvable by present techniques.

Cell Cycle↗
PubMed2004

Synchronous cultures from the baby machine. A model for animal cells.

A baby-machine system that produces newborn Escherichia coli cells from cultures immobilised on a membrane was developed many years ago in an attempt to attain optimal synchrony with minimal disturbance of steady-state growth, and a model designed to characterise the nature and quality of the synchrony of such cells in a quantitative manner has been published. The baby machine has now been adapted for animal cells, and the present article is an attempt to modify the model to include these cells as well. The model consists of five elements, giving rise to five adjustable parameters (and a proportionality constant): a major, essentially synchronous group of cells with ages distributed normally about zero; a minor, random component from a steady-state population on the membrane that had undergone only very little age selection during the elution process; a fixed background count, to allow for the signals recorded by the electronic particle counter produced by debris and electronic noise; a time-shift, to account for differences between time of cell division and end of sample collection; and the coefficient of variation of the interdivision-time distribution, taken to be reciprocal-normal. It is this last feature, a reciprocal-normal rather than a Pearson type III interdivision-time distribution, that distinguishes this version of the model from its predecessor. The model is fitted by unconstrained non-linear least-squares to data from three different leukemia cell lines. The standard errors of the parameters are quite small in all cases, making their estimates highly significant; the quality of the fit is striking. The five parameters of the model can be divided into two nuisance parameters, two that are associated with the methodology and one that describes an inherent property of the cell itself; it turns out that both methodology parameters are zero in all three data sets studied. We also discuss the partition of the transition-time dispersion between the age distribution of the newborn cells and the age distribution of dividing cells and show that a reliable estimate of the corresponding parameters requires an experiment that extends over at least two and a half doubling times.

Animals↗
PubMed2003

Osmosis: a macroscopic phenomenon, a microscopic view.

At present, physical chemistry employs the tools of thermodynamics to treat osmosis across a semipermeable membrane. We propose a model in terms of momentum transfer, the inherent asymmetry of which leads quantitatively to the van't Hoff relationship; qualitatively, the solute molecules can be looked upon as micropumps that suck solvent through the pores in the membrane.

Models, Biological↗
PubMed2001

Synchronous cultures from the baby machine: anatomy of a model.

The baby-machine system, which produces newborn Escherichia coli cells from cultures immobilized on a membrane, was developed many years ago in an attempt to attain optimal synchrony with minimal disturbance of steady-state growth. In the present article, we describe in some detail a model designed to analyse such cells with a view to characterizing the nature and quality of the synchrony in a quantitative manner; it can also serve to evaluate the methodology itself, its potential and its limitations. The model consists of five elements, giving rise to five adjustable parameters (and a proportionality constant): a major, essentially synchronous group of cells with ages distributed normally about zero; a minor, random component from a steady-state population on the membrane that had undergone only very little age selection during the elution process; a fixed background count, to account for the signals recorded by the electronic particle counter produced by debris and electronic noise; a time-shift, to allow for differences between collection time and sampling time; and the coefficient of variation of the interdivision-time distribution, taken to be a Pearson type III. The model is fitted by nonlinear least-squares to data from cells grown in glucose minimal medium. The standard errors of the parameters are quite small, making their estimates all highly significant; the quality of the fit is striking. We also provide a simple yet rigorous procedure for correcting cell counts obtained in an electronic particle counter for the effect of coincidence. An example using real data produces an excellent fit.

Cell Culture Techniques↗
PubMed2001

Cell-cycle research with synchronous cultures: an evaluation.

The baby-machine system, which produces new-born Escherichia coli cells from cultures immobilized on a membrane, was developed many years ago in an attempt to attain optimal synchrony with minimal disturbance of steady-state growth. In the present article, we put forward a model to describe the behaviour of cells produced by this method, and provide quantitative evaluation of the parameters involved, at each of four different growth rates. Considering the high level of selection achievable with this technique and the natural dispersion in interdivision times, we believe that the output of the baby machine is probably close to optimal in terms of both quality and persistence of synchrony. We show that considerable information on events in the cell cycle can be obtained from populations with age distributions very much broader than those achieved with the baby machine and differing only modestly from steady state. The data presented here, together with the long and fruitful history of findings employing the baby-machine technique, suggest that minimisation of stress on cells is the single most important factor for successful cell-cycle analysis.

Amino Acids↗
PubMed2001

Dimensional regulation of cell-cycle events in Escherichia coli during steady-state growth.

Two opposing models have been put forward in the literature to describe the changes in the shape of individual Escherichia coli cells in steady-state growth that take place during the cell cycle: the Length model, which maintains that the regulating dimension is cell length, and the Volume model, which asserts it to be cell volume. In addition, the former model envisages cell diameter as decreasing with length up to constriction whereas the latter sees it as being constrained by the rigid cell wall. These two models differ in the correlations they predict between the various cellular dimensions (diameter, length, volume) not only across the entire population of bacteria but also, and especially, within subpopulations that define specific cell-cycle events (division, for example, or onset of constriction); the coefficients of variation at these specific events are also expected to be very different. Observations from cells prepared for electron microscopy (air-dried) and for phase-contrast microscopy (hydrated) appeared qualitatively largely in accordance with the predictions of the Length model. To obtain a more quantitative comparison, simulations were carried out of populations defined by each of the models; again, the results favoured the Length model. Finally, in age-selected cells using membrane elution, the diameter-length and diameter-volume correlations were in complete agreement with the Length model, as were the coefficients of variation. It is concluded that, at least with respect to cell-cycle events such as onset of constriction and cell division, length rather than volume is the controlling dimension.

Cell Cycle↗
PubMed1998

The significance of non-significance.

We discuss the implications of empirical results that are statistically non-significant. Figures illustrate the interrelations among effect size, sample sizes and their dispersion, and the power of the experiment. All calculations (detailed in Appendix) are based on actual noncentral t-distributions, with no simplifying mathematical or statistical assumptions, and the contribution of each tail is determined separately. We emphasize the importance of reporting, wherever possible, the a priori power of a study so that the reader can see what the chances were of rejecting a null hypothesis that was false. As a practical alternative, we propose that non-significant inference be qualified by an estimate of the sample size that would be required in a subsequent experiment in order to attain an acceptable level of power under the assumption that the observed effect size in the sample is the same as the true effect size in the population; appropriate plots are provided for a power of 0.8. We also point out that successive outcomes of independent experiments each of which may not be statistically significant on its own, can be easily combined to give an overall p value that often turns out to be significant. And finally, in the event that the p value is high and the power sufficient, a non-significant result may stand and be published as such.

Analysis of Variance↗
PubMed1996

Studies in psychoneuroimmunology: psychological, immunological, and neuroendocrinological parameters in Israeli civilians during and after a period of Scud missile attacks.

Twenty-two male volunteers in Jerusalem were subjected to a battery of psychological tests at the height of the Iraqi Scud missile attacks on Israeli cities during the 1991 Persian Gulf War and again after the cessation of hostilities. Venous blood samples were taken at each time point. The separated mononuclear cells and plasma were cryopreserved, and a spectrum of immunological and neuroendocrine assays were performed on the preserved samples. Psychological testing indicated levels of anxiety were higher during the war than they were after the war ended, and both anxiety and anger during the hostilities were significantly elevated in comparison with prewar data. During the war, specific war-related pressures were greater than everyday pressures, and problem-focused coping was more evident than emotion-focused coping. Natural-killer cell activity and cell-mediated lympholysis were significantly elevated during the war, as were plasma levels of adrenocorticotrophic hormone, neurotensin, and substance P. The only biological test parameter found to be reduced during the war period was mononuclear cell thymidine incorporated in nonstimulated cultures.

Adaptation, Psychological↗
PubMed1995

Characterization of cell-cycle-specific events in synchronous cultures of Escherichia coli: a theoretical evaluation.

Synchronous growth studies are often used to assess the presence, timing and duration of periodic phenomena in the bacterial cell cycle. In an effort to evaluate the quality and quantity of information on cycle-specific events that can reasonably be expected from such inquiries, a model was constructed of a synchronous culture of Escherichia coli cells as would be derived from a growing population immobilized on a surface, and applied to the case of one stable and one unstable cellular component. The results indicated that, while the presence of cycle-specific events may be easily detectable, their timing and duration are very difficult to establish in synchronous growth experiments. Furthermore, differences in timing can be misconstrued as differences in duration, and vice versa, when interpretations are based on the qualitative analysis of the data.

Cell Cycle↗
PubMed1995

On microbial states of growth.

It is crucial to the reproducibility of results and their proper interpretation that the conditions under which experiments are carried out be defined with rigour and consistency. In this review we attempt to clarify the differences and interrelationships among steady, balanced and exponential states of culture growth. Basic thermodynamic concepts are used to introduce the idea of steady-state growth in open, biological systems. The classical, sometimes conflicting, definitions of steady-state and balanced growth are presented, and a consistent terminology is proposed. The conditions under which a culture in balanced growth is also in exponential growth and in steady-state growth are indicated. It is pointed out that steady-state growth always implies both balanced and exponential growth, and examples in which the converse does not hold are described. More complex situations are then characterized and the terminology extended accordingly. This leads to the notion of normal growth and growth that can be synchronous or otherwise unbalanced but still reproducible, and to the condition of approximate steady state manifested by growth in batch culture and by asymmetrically dividing cells, which is analysed in some detail.

Bacteria↗
PubMed1994

Nucleoid partitioning and the division plane in Escherichia coli.

Escherichia coli nucleoids were visualized after the DNA of OsO4-fixed but hydrated cells was stained with the fluorochrome DAPI (4',6-diamidino-2-phenylindole dihydrochloride hydrate). In slowly growing cells, the nucleoids are rod shaped and seem to move along the major cell axis, whereas in rapidly growing, wider cells they consist of two- to four-lobed structures that often appear to advance along axes lying perpendicular or oblique to the major axis of the cell. To test the idea that the increase in cell diameter following nutritional shift-up is caused by the increased amount of DNA in the nucleoid, the cells were subjected to DNA synthesis inhibition. In the absence of DNA replication, the nucleoids continued to move in the growing filaments and were pulled apart into small domains along the length of the cell. When these cells were then transferred to a richer medium, their diameters increased, especially in the region enclosing the nucleoid. It thus appears that the nucleoid motive force does not depend on DNA synthesis and that cell diameter is determined not by the amount of DNA per chromosome but rather by the synthetic activity surrounding the nucleoid. Under the non-steady-state but balanced growth conditions induced by thymine limitation, nucleoids become separated into small lobules, often lying in asymmetric configurations along the cell periphery, and oblique and asymmetric division planes occur in more than half of the constricting cells. We suggest that such irregular DNA movement affects both the angle of the division plane and its position.

Cell Division↗
PubMed1993

Shape changes in Escherichia coli B/r A during agar filtration.

We have investigated the phenomenon of shape distortion in a sample of 1,552 Escherichia coli B/r A cells in balanced exponential growth, during preparation for electron microscopy by agar filtration. Mixed preparations of bacterial cells and polystyrene latex spheres were shadow cast at low angle and the resulting shadows used to obtain quantitative estimates for the dimensions of the dehydrated cells; these then serve as a basis for a model of its shape in three dimensions. A statistical analysis of the projections of clustered cells and the intervening fissures, in nonshadow-cast preparations, provides an estimate of the effects of drying. The average width of the dehydrated cell (450 nm) is about 20 nm greater than the diameter of the live bacterium, whereas its length (1,398 nm) is approximately 40 nm less.

Agar↗
PubMed1993

Control of mini-R1 plasmid replication: a computer simulation.

A molecular model for the control of plasmid R1 replication has been proposed by Nordström, Molin and Light (Plasmid 12, 71-90, 1984), involving three genes: repA, copA, copB. RepA codes for a polypeptide whose synthesis is required for initiation; replication is controlled by regulating this synthesis. CopA encodes a small, unstable, untranslated RNA molecule that inhibits translation of the repA message whereas copB produces a protein that inhibits transcription from the repA promoter. We have recast this model into precise mathematical terms and tested it by computer simulation of a synchronous culture in steady-state balanced growth, composed of individual Escherichia coli cells harboring the small, unstable derivative, mini-R1. All single-cell steady-state distributions obtained are independent of initial conditions, and the average values of various plasmid-related variables are similar to those measured experimentally. The relationship between the number of replication events per cell and the copy number at birth, as predicted by the model, mitigates against a sensitive correction mechanism for cells born with other than average copy number and is much closer quantitatively to a nonresponse system, although there is a weak dependence on copy number. The effect of the convergent transcription initiated at the repA and copB promoters on the expression of the copA gene is found to contribute little to the stability of mini-R1 replicons under steady-state growth conditions or to their potential for survival following infection. In fact, the role of the entire CopB control loop is shown to be quite minor, both in steady state and after infection. It is pointed out that genetic manipulations are far more easily performed in silico than in vivo but that results of the kind presented here are very often possible only when simulating individual cells.

Computer Simulation↗
PubMed1993

Partition of plasmid R1: a computer simulation.

A computer-simulated population of individual Escherichia coli cells harboring plasmid R1 parA+/parB- has been used to analyze three possible modes of plasmid segregation: equi-partition, in which plasmids are partitioned equally to daughter cells at cell division; single-site inheritance, in which the products of the most recent replication event are partitioned equally and the remaining plasmids are distributed randomly; and pair-site partition, in which a single, randomly chosen plasmid is actively partitioned to each daughter cell at division and the rest are distributed randomly. Comparison between predicted and experimental plasmid loss-frequency enabled us to rule out the first of these models as a likely mode of action in R1 but was inconclusive regarding the other two. The parA region would therefore seem to partition actively only one pair of plasmids to each daughter cell, the precise selection rule involved remaining unresolved. This question is not easily decided with current technology, as we show, but our simulation results also predict that the isolation of rep(Ts) mutants will provide an experimental system in which a clear distinction is possible between two plasmids that are the products of the most recent replication event and two that are chosen strictly at random.

Computer Simulation↗
PubMed1993

Dimensional rearrangement of Escherichia coli B/r cells during a nutritional shift-down.

In a search for the mechanism underlying dimensional changes in bacteria, the glucose analogue methyl alpha-D-glucoside was used to effect a rapid reduction in the mass growth rate of Escherichia coli by competitively inhibiting glucose uptake, a so-called nutritional shift-down. The new steady-state cell mass and volume were reached after 1 h, during which the rate of cell division was maintained; rearrangement of the linear dimensions (cell length, diameter), however, required an additional 2 h and caused an undershoot in cell length, consistent with the view that E. coli is slow to modify its diameter. The results are compared with the overshoot in cell length that occurs following nutritional shift-up.

Cell Division↗
PubMed1992

Aggregation of Escherichia coli B/r A during agar filtration: effect on morphometric measurements.

We have investigated the phenomenon of particle aggregation in a sample of 71,038 Escherichia coli B/r A cells in balanced exponential growth, during preparation for electron microscopy by agar filtration. The bacteria were photographed in a transmission electron microscope and the dimensions and spatial relationships among all the members of each aggregate were recorded using an interactive image processing system. The proportion of aggregated cells, 22%, is much greater than that found by direct count in a light microscope (7%), implying that most aggregation takes place during the preparation stages. The aggregated cells are about 1% narrower than the free cells, because of mutual compression, and 1.5% longer, because of a selection bias in favor of longer cells. From a statistical analysis of the data, we conclude that the clustering of cells into aggregates in the course of sample preparation is the result of random encounters during the settling on the collodion membrane and of the changing surface tension during the drying process. A method is proposed to correct morphometric measurements for the distortion caused by cellular aggregation of this kind.

Agar↗