Analysis of the Dynamics of a Bacillus subtilis Spore Germination Protein Complex during Spore Germination and Outgrowth

Germination of Bacillus subtilis spores is normally initiated when nutrients from the environment interact with germinant receptors (GRs) in the spores'' inner membrane (IM), in which most of the lipids are immobile. GRs and another germination protein, GerD, colocalize in the IM of dormant spores in a small focus termed the “germinosome,” and this colocalization or focus formation is dependent upon GerD, which is also essential for rapid GR-dependent spore germination. To determine the fate of the germinosome and germination proteins during spore germination and outgrowth, we employed differential interference microscopy and epifluorescence microscopy to track germinating spores with fluorescent fusions to germination proteins and used Western blot analyses to measure germination protein levels. We found that after initiation of spore germination, the germinosome foci ultimately changed into larger disperse patterns, with ≥75% of spore populations displaying this pattern in spores germinated for 1 h, although >80% of spores germinated for 30 min retained the germinosome foci. Western blot analysis revealed that levels of GR proteins and the SpoVA proteins essential for dipicolinic acid release changed minimally during this period, although GerD levels decreased ∼50% within 15 min in germinated spores. Since the dispersion of the germinosome during germination was slower than the decrease in GerD levels, either germinosome stability is not compromised by ∼2-fold decreases in GerD levels or other factors, such as restoration of rapid IM lipid mobility, are also significant in germinosome dispersion as spore germination proceeds.     

Data-Driven Method to Estimate Nonlinear Chemical Equivalence

There is great need to express the impacts of chemicals found in the environment in terms of effects from alternative chemicals of interest. Methods currently employed in fields such as life-cycle assessment, risk assessment, mixtures toxicology, and pharmacology rely mostly on heuristic arguments to justify the use of linear relationships in the construction of “equivalency factors,” which aim to model these concentration-concentration correlations. However, the use of linear models, even at low concentrations, oversimplifies the nonlinear nature of the concentration-response curve, therefore introducing error into calculations involving these factors. We address this problem by reporting a method to determine a concentration-concentration relationship between two chemicals based on the full extent of experimentally derived concentration-response curves. Although this method can be easily generalized, we develop and illustrate it from the perspective of toxicology, in which we provide equations relating the sigmoid and non-monotone, or “biphasic,” responses typical of the field. The resulting concentration-concentration relationships are manifestly nonlinear for nearly any chemical level, even at the very low concentrations common to environmental measurements. We demonstrate the method using real-world examples of toxicological data which may exhibit sigmoid and biphasic mortality curves. Finally, we use our models to calculate equivalency factors, and show that traditional results are recovered only when the concentration-response curves are “parallel,” which has been noted before, but we make formal here by providing mathematical conditions on the validity of this approach.     

Integrated Kinetic and Probabilistic Modeling of the Growth Potential of Bacterial Populations

When bacteria are exposed to osmotic stress, some cells recover and grow, while others die or are unculturable. This leads to a viable count growth curve where the cell number decreases before the onset of the exponential growth phase. From such curves, it is impossible to estimate what proportion of the initial cells generates the growth because it leads to an ill-conditioned numerical problem. Here, we applied a combination of experimental and statistical methods, based on optical density measurements, to infer both the probability of growth and the maximum specific growth rate of the culture. We quantified the growth potential of a bacterial population as a quantity composed from the probability of growth and the “suitability” of the growing subpopulation to the new environment. We found that, for all three laboratory media studied, the probability of growth decreased while the “work to be done” by the growing subpopulation (defined as the negative logarithm of their suitability parameter) increased with NaCl concentration. The results suggest that the effect of medium on the probability of growth could be described by a simple shift parameter, a differential NaCl concentration that can be accounted for by the change in the medium composition. Finally, we highlighted the need for further understanding of the effect of the osmoprotectant glycine betaine on metabolism.     

Live Cell Imaging of Germination and Outgrowth of Individual Bacillus subtilis Spores; the Effect of Heat Stress Quantitatively Analyzed with SporeTracker

Spore-forming bacteria are a special problem for the food industry as some of them are able to survive preservation processes. Bacillus spp. spores can remain in a dormant, stress resistant state for a long period of time. Vegetative cells are formed by germination of spores followed by a more extended outgrowth phase. Spore germination and outgrowth progression are often very heterogeneous and therefore, predictions of microbial stability of food products are exceedingly difficult. Mechanistic details of the cause of this heterogeneity are necessary. In order to examine spore heterogeneity we made a novel closed air-containing chamber for live imaging. This chamber was used to analyze Bacillus subtilis spore germination, outgrowth, as well as subsequent vegetative growth. Typically, we examined around 90 starting spores/cells for ≥4 hours per experiment. Image analysis with the purposely built program “SporeTracker” allows for automated data processing from germination to outgrowth and vegetative doubling. In order to check the efficiency of the chamber, growth and division of B. subtilis vegetative cells were monitored. The observed generation times of vegetative cells were comparable to those obtained in well-aerated shake flask cultures. The influence of a heat stress of 85°C for 10 min on germination, outgrowth, and subsequent vegetative growth was investigated in detail. Compared to control samples fewer spores germinated (41.1% less) and fewer grew out (48.4% less) after the treatment. The heat treatment had a significant influence on the average time to the start of germination (increased) and the distribution and average of the duration of germination itself (increased). However, the distribution and the mean outgrowth time and the generation time of vegetative cells, emerging from untreated and thermally injured spores, were similar.     

Survival of Clostridium botulinum Spores

Radiation survival curves of spores of Clostridium botulinum strain 33A exhibited an exponential reduction which accounted for most of the population, followed by a “tail” comprising a very small residual number [7 to 0.7 spore(s) per ml] which resisted death in the range between 3.0 and 9.0 Mrad dose levels. The “tail” was not caused by protective spore substances released into the suspensions during irradiation, by the presence of accumulated radiation “inactivated” spores, or by heat shock of pre-irradiated spores. The theoretical number of spore targets which must be inactivated by irradiation was estimated both by a graphical and by a computation method to be about 80, and the D value was calculated to be 0.295 and 0.396 Mrad, respectively, in buffer and in pork pea broth.     

Monitoring Rates and Heterogeneity of High-Pressure Germination of Bacillus Spores by Phase-Contrast Microscopy of Individual Spores

Germination of Bacillus spores with a high pressure (HP) of ∼150 MPa is via activation of spores'' germinant receptors (GRs). The HP germination of multiple individual Bacillus subtilis spores in a diamond anvil cell (DAC) was monitored with phase-contrast microscopy. Major conclusions were that (i) >95% of wild-type spores germinated in 40 min in a DAC at ∼150 MPa and 37°C but individual spores'' germination kinetics were heterogeneous; (ii) individual spores'' HP germination kinetic parameters were similar to those of nutrient-triggered germination with a variable lag time (T_lag) prior to a period of the rapid release (ΔT_release) of the spores'' dipicolinic acid in a 1:1 chelate with Ca²⁺ (CaDPA); (iii) spore germination at 50 MPa had longer average T_lag values than that at ∼150 MPa, but the ΔT_release values at the two pressures were identical and HPs of <10 MPa did not induce germination; (iv) B. subtilis spores that lacked the cortex-lytic enzyme CwlJ and that were germinated with an HP of 150 MPa exhibited average ΔT_release values ∼15-fold longer than those for wild-type spores, but the two types of spores exhibited similar average T_lag values; and (v) the germination of wild-type spores given a ≥30-s 140-MPa HP pulse followed by a constant pressure of 1 MPa was the same as that of spores exposed to a constant pressure of 140 MPa that was continued for ≥35 min; (vi) however, after short 150-MPa HP pulses and incubation at 0.1 MPa (ambient pressure), spore germination stopped 5 to 10 min after the HP was released. These results suggest that an HP of ∼150 MPa for ≤30 s is sufficient to fully activate spores'' GRs, which remain activated at 1 MPa but can deactivate at ambient pressure.     

Dynamic Model of Heat Inactivation Kinetics for Bacterial Adaptation

The Weibullian-log logistic (WeLL) inactivation model was modified to account for heat adaptation by introducing a logistic adaptation factor, which rendered its “rate parameter” a function of both temperature and heating rate. The resulting model is consistent with the observation that adaptation is primarily noticeable in slow heat processes in which the cells are exposed to sublethal temperatures for a sufficiently long time. Dynamic survival patterns generated with the proposed model were in general agreement with those of Escherichia coli and Listeria monocytogenes as reported in the literature. Although the modified model''s rate equation has a cumbersome appearance, especially for thermal processes having a variable heating rate, it can be solved numerically with commercial mathematical software. The dynamic model has five survival/adaptation parameters whose determination will require a large experimental database. However, with assumed or estimated parameter values, the model can simulate survival patterns of adapting pathogens in cooked foods that can be used in risk assessment and the establishment of safe preparation conditions.Combined with heat transfer data or models, microbial survival kinetics, especially of bacteria or spores, is extensively used to determine the safety of industrial heat preservation processes like canning, extant or planned. The same is true for milder heat processes such as milk and fruit pasteurization. However, survival models are also a valuable tool to assess the safety of prepared foods, especially those made of raw meats, poultry, and eggs, where surviving pathogens can be a public health issue.The heat resistance of a bacterium, or any other microorganism, is almost always determined from a set of its isothermal survival curves, recorded at several lethal temperatures. The kinetic models, which define the heat resistance parameters, may vary, but the calculation procedure itself is usually the same. First, the experimental isothermal survival data are fitted with what is known as the “primary model.” Once fitted, the temperature dependence of this primary model''s coefficients is described by what is known as the “secondary model.” When combined with a temperature profile expression, T(t), and incorporated into the inactivation rate equation, the result is a “tertiary model,” which enables its user to predict the organism''s survival curve under any static or dynamic (i.e., nonisothermal) conditions.The traditional log-linear (“first-order kinetic”) model is the best-known primary survival model, and it is still widely used in sterility calculations in the food, pharmaceutical, and other industries. Traditionally, it has been assumed that the D value calculated with this model has a log-linear temperature dependence or, alternatively, that the temperature effect on the exponential rate constant, k, the D value''s reciprocal, follows the Arrhenius equation. However, accumulating experimental evidence in recent years indicates that bacterial heat inactivation only rarely follows the first-order kinetics and that there is no reason that it should (3, 18, 29). Nonlinear survival curves can be described by a variety of mathematical models (6). Perhaps the most frequently used in recent years is the Weibullian model, of which the traditional log-linear model is a special case—see below.Regardless of the log-linearity issue, none of the above-mentioned models accounts for adaptation, the ability of certain bacterial cells to adjust their metabolism in response to stress in order to increase their survivability (2, 10, 26, 27, 28). A notable example is Escherichia coli. Its cells can produce “heat shock proteins,” which help them to survive mild heat treatments (1, 11). Other organisms, Salmonella enterica and Bacillus cereus among them, can also develop defensive mechanisms that help them to survive in an acidic environment (8, 9, 13). Whether adaptation allows the cells to avoid injury or to repair damage once it has occurred, or both, should not concern us here. (Injury and recovery, although related, are a separate issue, one which is amply discussed in the literature. Their quantitative aspects and mathematical modeling are discussed elsewhere [5].)The cells'' ability to augment their resistance is not unlimited, and it takes time for the cells to activate the protective system and synthesize its chemical elements (10, 12). Consequently, the effect of heat adaptation on an organism''s survival pattern becomes measurable only at or at slightly above what''s known as the “sublethal” temperature range. Under dynamic conditions, therefore, adaptation can be detected only when the heating rate is sufficiently low to allow the cells to respond metabolically to the heat stress prior to their destruction.Several investigators have reported and discussed the quantitative aspects of adaptation (25, 27, 28). When it occurs, adaptation is noticed as a gap between survival curves determined at low heating rates and those predicted by kinetic models whose parameters had been determined at high lethal temperatures (7, 8, 9, 27, 28). The question is how to modify the inactivation kinetic model so that it can properly account for adaptation at low heating rates while maintaining its predictive ability at high rates and clearly lethal temperatures. Stasiewicz et al. (25) have recently given a partial answer to this question. They started with the Weibullian inactivation model (see below) and assumed that its rate parameter''s temperature dependence follows a modified version of the Arrhenius equation. Using this model and experimental data for Salmonella bacteria, they showed that a “pathway-dependent model” is more reliable than a “state-dependent model.”The objectives of our work were to develop a variant of the Weibullian-log logistic (WeLL) inactivation model to account for dynamic adaptation and to demonstrate its applicability with reported adaptive survival patterns exhibited by Escherichia coli and Listeria monocytogenes, two organisms of food safety concern.     

Analysis of the Loss in Heat and Acid Resistance during Germination of Spores of Bacillus Species

A major event in the nutrient germination of spores of Bacillus species is release of the spores'' large depot of dipicolinic acid (DPA). This event is preceded by both commitment, in which spores continue through germination even if germinants are removed, and loss of spore heat resistance. The latter event is puzzling, since spore heat resistance is due largely to core water content, which does not change until DPA is released during germination. We now find that for spores of two Bacillus species, the early loss in heat resistance during germination is most likely due to release of committed spores'' DPA at temperatures not lethal for dormant spores. Loss in spore acid resistance during germination also paralleled commitment and was also associated with the release of DPA from committed spores at acid concentrations not lethal for dormant spores. These observations plus previous findings that DPA release during germination is preceded by a significant release of spore core cations suggest that there is a significant change in spore inner membrane permeability at commitment. Presumably, this altered membrane cannot retain DPA during heat or acid treatments innocuous for dormant spores, resulting in DPA-less spores that are rapidly killed.     

Temperature and photocontrol of onoclea spore germination

Germination of Onoclea sensibilis L. spores is controlled by light and temperature. Temperatures of 30 C can induce maximal germination in the dark to a level of 60 to 95% of that induced by a saturating dose of red light (0.38 joules/square meter) providing the spores are placed at the elevated temperature immediately after being sown. Maximum dark germination occurs with a minimum exposure of 16 to 24 hours at 30 C, suggesting that the temperature treatment is required for the induction of germination rather than for the germination process per se. Interaction of temperature and light for induction of germination shows nonadditive behavior. Germination induced by light and temperature applied consecutively never exceeded that which could be induced by a saturating dose of red light alone. Imbibition of the spores at 25 C in the dark for 12 or more hours prior to incubation at 30 C results in a loss of thermosensitivity. Dose response curves for red light induction of germination after varying times of imbibition at 25 C show no concomitant loss of sensitivity of the spores to red irradiation. This suggests that the mechanism and/or pathway of thermoinduction of germination differs from that of photoinduction. The loss of thermosensitivity as a result of presoaking at 25 C can be prevented if the spores are imbibed at 25 C in osmotic agents such as 0.3 molar mannitol or 0.1 gram per liter of polyethylene glycol 400 or in 0.08% dimethylsulfoxide or 10 micrograms per milliliter of herbicide SAN 9789 (4-chloro-5-(methylamino)-2-(α,α,α-trifluoro-m-tolyl-3-(2H)pyridazinone). The latter two substances are hypothesized to act upon membranes. These results suggest that the degree of hydration and possibly changes in membrane properties play a role in the change in sensitivity of Onoclea spores to temperature.     

Predicting Rotator Cuff Tears Using Data Mining and Bayesian Likelihood Ratios

Objectives

Rotator cuff tear is a common cause of shoulder diseases. Correct diagnosis of rotator cuff tears can save patients from further invasive, costly and painful tests. This study used predictive data mining and Bayesian theory to improve the accuracy of diagnosing rotator cuff tears by clinical examination alone.

Methods

In this retrospective study, 169 patients who had a preliminary diagnosis of rotator cuff tear on the basis of clinical evaluation followed by confirmatory MRI between 2007 and 2011 were identified. MRI was used as a reference standard to classify rotator cuff tears. The predictor variable was the clinical assessment results, which consisted of 16 attributes. This study employed 2 data mining methods (ANN and the decision tree) and a statistical method (logistic regression) to classify the rotator cuff diagnosis into “tear” and “no tear” groups. Likelihood ratio and Bayesian theory were applied to estimate the probability of rotator cuff tears based on the results of the prediction models.

Results

Our proposed data mining procedures outperformed the classic statistical method. The correction rate, sensitivity, specificity and area under the ROC curve of predicting a rotator cuff tear were statistical better in the ANN and decision tree models compared to logistic regression. Based on likelihood ratios derived from our prediction models, Fagan''s nomogram could be constructed to assess the probability of a patient who has a rotator cuff tear using a pretest probability and a prediction result (tear or no tear).

Conclusions

Our predictive data mining models, combined with likelihood ratios and Bayesian theory, appear to be good tools to classify rotator cuff tears as well as determine the probability of the presence of the disease to enhance diagnostic decision making for rotator cuff tears.     

The Effects of Heat Activation on Bacillus Spore Germination,with Nutrients or under High Pressure,with or without Various Germination Proteins

Nutrient germination of spores of Bacillus species occurs through germinant receptors (GRs) in spores'' inner membrane (IM) in a process stimulated by sublethal heat activation. Bacillus subtilis spores maximum germination rates via different GRs required different 75°C heat activation times: 15 min for l-valine germination via the GerA GR and 4 h for germination with the l-asparagine–glucose–fructose–K⁺ mixture via the GerB and GerK GRs, with GerK requiring the most heat activation. In some cases, optimal heat activation decreased nutrient concentrations for half-maximal germination rates. Germination of spores via various GRs by high pressure (HP) of 150 MPa exhibited heat activation requirements similar to those of nutrient germination, and the loss of the GerD protein, required for optimal GR function, did not eliminate heat activation requirements for maximal germination rates. These results are consistent with heat activation acting primarily on GRs. However, (i) heat activation had no effects on GR or GerD protein conformation, as probed by biotinylation by an external reagent; (ii) spores prepared at low and high temperatures that affect spores'' IM properties exhibited large differences in heat activation requirements for nutrient germination; and (iii) spore germination by 550 MPa of HP was also affected by heat activation, but the effects were relatively GR independent. The last results are consistent with heat activation affecting spores'' IM and only indirectly affecting GRs. The 150- and 550-MPa HP germinations of Bacillus amyloliquefaciens spores, a potential surrogate for Clostridium botulinum spores in HP treatments of foods, were also stimulated by heat activation.     

Analysis of the Effects of a gerP Mutation on the Germination of Spores of Bacillus subtilis

As previously reported, gerP Bacillus subtilis spores were defective in nutrient germination triggered via various germinant receptors (GRs), and the defect was eliminated by severe spore coat defects. The gerP spores'' GR-dependent germination had a longer lag time between addition of germinants and initiation of rapid release of spores'' dipicolinic acid (DPA), but times for release of >90% of DPA from individual spores were identical for wild-type and gerP spores. The gerP spores were also defective in GR-independent germination by DPA with its associated Ca²⁺ divalent cation (CaDPA) but germinated better than wild-type spores with the GR-independent germinant dodecylamine. The gerP spores exhibited no increased sensitivity to hypochlorite, suggesting that these spores have no significant coat defect. Overexpression of GRs in gerP spores did lead to faster germination via the overexpressed GR, but this was still slower than germination of comparable gerP⁺ spores. Unlike wild-type spores, for which maximal nutrient germinant concentrations were between 500 μM and 2 mM for l-alanine and ≤10 mM for l-valine, rates of gerP spore germination increased up to between 200 mM and 1 M l-alanine and 100 mM l-valine, and at 1 M l-alanine, the rates of germination of wild-type and gerP spores with or without all alanine racemases were almost identical. A high pressure of 150 MPa that triggers spore germination by activating GRs also triggered germination of wild-type and gerP spores identically. All these results support the suggestion that GerP proteins facilitate access of nutrient germinants to their cognate GRs in spores'' inner membrane.     

Limited period of graviresponsiveness in germinating spores of Ceratopteris richardii

Rhizoids of the fern Ceratopteris richardii Brogn. usually emerge 40 h after germination is initiated by light, and more than 90% of them emerge growing in a downward direction. However, when the spores are germinated on a clinostat, the emerging rhizoids show no preferential orientation. This indicates that under normal 1 · g conditions the initial growth direction of rhizoids can be oriented by gravity. If the orientation of the spores is changed 3 h or less after the start of germination, the growth direction of most emerging rhizoids becomes downward relative to the new orientation. However, if the orientation of the spores is changed by 180° 8 h or more after germination is initiated by light, most rhizoids emerge growing upward; i.e., the same direction as if there had been no orientation change. Emerged rhizoids also do not change their direction of growth if their orientation is changed. These results indicate that the growth direction of emerging rhizoids is set by gravity prior to actual emergence, and that the time of full orientation responsiveness is limited to a period ranging from the initiation of germination to about 3–4 h after the start of germination. There is a gravity-oriented nuclear movement beginning at about 13 h after germination, and this movement appears to predict the initial growth direction of rhizoids.These studies were made possible by grant NAGW 1519 to S.J.R. and grant NGT-51065 to E.S.E., both from the National Aeronautics and Space Administration.     

Numbers of Individual Nutrient Germinant Receptors and Other Germination Proteins in Spores of Bacillus subtilis

Germination of dormant Bacillus subtilis spores with specific nutrient germinants is dependent on a number of inner membrane (IM) proteins, including (i) the GerA, GerB, and GerK germinant receptors (GRs) that respond to nutrient germinants; (ii) the GerD protein, essential for optimal GR function; and (iii) SpoVA proteins, essential for the release of the spore-specific molecule dipicolinic acid (DPA) during spore germination. Levels of GR A and C subunit proteins, GerD, and SpoVAD in wild-type spores were determined by Western blot analysis of spore fractions or total disrupted spores by comparison with known amounts of purified proteins. Surprisingly, after disruption of decoated B. subtilis spores with lysozyme and fractionation, ∼90% of IM fatty acids and GR subunits remained with the spores'' insoluble integument fraction, indicating that yields of purified IM are low. The total lysate from disrupted wild-type spores contained ∼2,500 total GRs/spore: GerAA and GerAC subunits each at ∼1,100 molecules/spore and GerBC and GerKA subunits each at ∼700 molecules/spore. Levels of the GerBA subunit determined previously were also predicted to be ∼700 molecules/spore. These results indicate that the A/C subunit stoichiometry in GRs is most likely 1:1, with GerA being the most abundant GR. GerD and SpoVAD levels were ∼3,500 and ∼6,500 molecules/spore, respectively. These values will be helpful in formulating mathematic models of spore germination kinetics as well as setting lower limits on the size of the GR-GerD complex in the spores'' IM, termed the germinosome.     

Ethylene Oxide Gaseous Sterilization: I. Concentration and Temperature Effects

The relationships of reaction temperature and concentration of gaseous ethylene oxide to the time required for inactivation of air-dried Bacillus subtilis var. niger spores are more complex than previously reported. A plot of temperature vs. the logarithm of “thermochemical death time” (TCDT) resulted in a straight line between 18 and 57 C for systems of “high” ethylene oxide concentration. The TCDT values were independent of ethylene oxide concentrations above certain temperature-dependent limits. A given ethylene oxide concentration produced a TCDT curve identical in the upper temperature regions with that for higher concentrations. As the temperature was lowered beyond a critical point, this curve diverged from that for higher concentrations, as a straight line of lesser slope. Thus, a series of curves exists for a range of ethylene oxide concentrations. They are characterized by two segments, both logarithmic, intersecting at a critical temperature for each concentration. The intersecting point is at a temperature inversely related to the ethylene oxide gas concentration. The temperature quotient for the high temperature segments of all systems was 1.8. This value was characteristic for ethylene oxide concentrations of 440 and 880 mg/liter at temperatures above 40.6 and 33.4 C, respectively. Below these critical temperatures, the Q₁₀ values for the respective systems were 3.2 and 2.3.     

Adaptation in Cones: A General Model

Three features appear to characterize steady-state light adaptation in vertebrate cone photoreceptors: (a) the shape of the “log intensity-response” curve at different levels of adaptation is the same, the only change with adaptation is in the position of the point on the curve about which the cones operate; (b) at high adapting intensities the operating point becomes fixed in position; (c) this fixed position is at the steepest point of the log intensity-response curve. These three features can be described by a mathematical model.     

Current-voltage relationships of potassium channels in the plasmalemma ofAcetabularia

Summary The outer membrane of mechanically prepared protoplasmic droplets fromAcetabularia mediterranea has been investigated by patch-clamp techniques. These membranes are shown to consist of physiologically intact plasmalemma. With the Cl^– pump inhibited, microscopic currents through K⁺-selective channels were studied. These currents compare well with macroscopic K⁺ currents as previously determined by standard microelectrode techniques and tracer flux measurements. There is about one K⁺ channel per m² in the plasmalemma. The current-voltage relationship (I–V curve) of the main open channel (channel A) is sigmoid over a voltage range between about –100 and +100 mV with saturation currents of about ±10 pA. A second species (or different state of channel A) of K⁺-selective channels (channel B) differs from channel A by smaller saturation currents (about ±7 pA) and a much smaller open probability. The open probability of channel A increases from almost zero at large negative voltages to about 1/2 at large positive voltages. Taking the closed times into account, the mean steady-stateI–V curve of channel A displays outward rectification about the equilibrium voltage for K⁺ and negative slope conductance at larger negative voltages. The open channelI–V curve of the open channels A and B, the changes of theI–V curve of the open channel A upon variation of the external K⁺ concentration, as well as the mean steady-stateI–V curves of channel A are described by simple reaction kinetic models, the parameters of which are determined to fit the experimental data. The results are discussed with respect to data from other K⁺ channels in plants and with respect to regulation of the cytoplasmic K⁺ concentration inAcetabularia.     

Shapes and functions of species–area curves: a review of possible models

Aim This paper reviews possible candidate models that may be used in theoretical modelling and empirical studies of species–area relationships (SARs). The SAR is an important and well‐proven tool in ecology. The power and the exponential functions are by far the models that are best known and most frequently applied to species–area data, but they might not be the most appropriate. Recent work indicates that the shape of species–area curves in arithmetic space is often not convex but sigmoid and also has an upper asymptote. Methods Characteristics of six convex and eight sigmoid models are discussed and interpretations of different parameters summarized. The convex models include the power, exponential, Monod, negative exponential, asymptotic regression and rational functions, and the sigmoid models include the logistic, Gompertz, extreme value, Morgan–Mercer–Flodin, Hill, Michaelis–Menten, Lomolino and Chapman–Richards functions plus the cumulative Weibull and beta‐P distributions. Conclusions There are two main types of species–area curves: sample curves that are inherently convex and isolate curves, which are sigmoid. Both types may have an upper asymptote. A few have attempted to fit convex asymptotic and/or sigmoid models to species–area data instead of the power or exponential models. Some of these or other models reviewed in this paper should be useful, especially if species–area models are to be based more on biological processes and patterns in nature than mere curve fitting. The negative exponential function is an example of a convex model and the cumulative Weibull distribution an example of a sigmoid model that should prove useful. A location parameter may be added to these two and some of the other models to simulate absolute minimum area requirements.     

THE REVERSIBLE HEAT ACTIVATION INDUCING GERMINATION AND INCREASED RESPIRATION IN THE ASCOSPORES OF NEUROSPORA TETRASPERMA

The heat activation of Neurospora tetrasperma ascospores is a reversible process, since activated spores may be returned to secondary dormancy by preventing respiration, and these secondarily dormant spores may be induced to germinate by reheating. Activation of the spores brings about a large increase in respiration prior to the germination of the spores. As the spores are reversibly activated or deactivated the rate of respiration is increased or is decreased. By poisoning the cells with iodoacetamide it is possible to prevent all germination without greatly inhibiting this increase in respiration. Precisely with the beginning of germination a secondary rise in respiration occurs. The respiration of the spores is cyanide sensitive. The heat activation has a critical temperature at about 49 to 52°C.; and at a constant temperature within this range, the percentage of the spores activated as plotted against the time, follows an S-shaped population curve.     

Superdormant Spores of Bacillus Species Have Elevated Wet-Heat Resistance and Temperature Requirements for Heat Activation

Purified superdormant spores of Bacillus cereus, B. megaterium, and B. subtilis isolated after optimal heat activation of dormant spores and subsequent germination with inosine, d-glucose, or l-valine, respectively, germinate very poorly with the original germinants used to remove dormant spores from spore populations, thus allowing isolation of the superdormant spores, and even with alternate germinants. However, these superdormant spores exhibited significant germination with the original or alternate germinants if the spores were heat activated at temperatures 8 to 15°C higher than the optimal temperatures for the original dormant spores, although the levels of superdormant spore germination were not as great as those of dormant spores. Use of mixtures of original and alternate germinants lowered the heat activation temperature optima for both dormant and superdormant spores. The superdormant spores had higher wet-heat resistance and lower core water content than the original dormant spore populations, and the environment of dipicolinic acid in the core of superdormant spores as determined by Raman spectroscopy of individual spores differed from that in dormant spores. These results provide new information about the germination, heat activation optima, and wet-heat resistance of superdormant spores and the heterogeneity in these properties between individual members of dormant spore populations.Spores of Bacillus species are formed in sporulation and are metabolically dormant and extremely resistant to a variety of stress factors (31, 32). While spores can remain dormant for long periods, if given the proper stimulus, they can rapidly “return to life” in the process of spore germination followed by outgrowth (30). Since spores are generally present in significant amounts on many foodstuffs and growing cells of a number of Bacillus species are significant agents of food spoilage and food-borne disease (32), there is continued applied interest in spore resistance and germination. While dormant spores can be killed by a treatment such as wet heat, this requires high temperatures that are costly and detrimental to food quality. Consequently, there has long been interest in triggering spore germination in foodstuffs, since germinated spores have lost the extreme resistance of dormant spores and are relatively easy to kill. However, this strategy has been difficult to apply because of the significant heterogeneity in germination rates between individual spores in populations. One reflection of this heterogeneity is the extremely variable lag times following addition of germinants but prior to initiation of germination events; while these lag times can vary from 10 to 30 min for most spores in populations, some spores have lag times of many hours or even many days (2, 12, 13, 15, 25). The spores that are extremely slow to germinate have been termed superdormant spores, and populations of superdormant spores have recently been isolated from three Bacillus species, and their germination properties characterized (9, 10). These superdormant spores germinate extremely poorly with the original germinants used to remove dormant spores from spore populations, thus allowing superdormant spore isolation, and also poorly with a number of other germinants, in particular, germinants that target nutrient germinant receptors different than those activated to isolate the superdormant spores. However, the superdormant spores germinate reasonably well with mixtures of nutrient germinants that target multiple germinant receptors. All reasons for spore superdormancy are not known, but one contributing factor is the number of nutrient germinant receptors in the spore''s inner membrane that trigger spore germination by binding to nutrient germinants (9). The levels of these receptors are most likely in the tens of molecules per spore (24), and thus stochastic variation in receptor numbers might result in some spores with such low receptor numbers that these spores germinate very poorly (23). Indeed, 20- to 200-fold elevated levels of at least one nutrient germinant receptor greatly decreases yields of superdormant spores of Bacillus subtilis (9).Spores of Bacillus species generally exhibit a requirement for an activation step in order to exhibit maximum germination (17). Usually this activation is a sublethal heat treatment that for a spore population exhibits an optimum of 60 to 100°C depending on the species. Spores are also extremely resistant to wet heat, generally requiring temperatures of 80 to 110°C to achieve rapid spore killing, with the major factor influencing the wet-heat resistance of spores of mesophilic strains being the spore core''s water content, which can be as low as 30% of wet weight as water in a fully hydrated spore (8, 19, 27, 28, 31). Invariably, increases in core water content are associated with a decrease in spore wet-heat resistance (8, 19, 22, 25). While spore populations most often exhibit log-linear kinetics of wet-heat killing, the observation of tailing in such killing curves at high levels of killing is not uncommon, suggesting there is significant heterogeneity in the wet-heat resistances of individual spores in populations (27, 28). While there has been no comparable work suggesting that there is also heterogeneity in the temperature optima for heat activation of individual spores in populations, this certainly seems possible and indeed was suggested as one cause of spore superdormancy, as yields of superdormant spores from spore populations that are not heat activated are much higher (9, 10). Consequently, the current work was initiated to test the hypothesis that superdormant spores require heat activation temperatures that are higher than those of the original dormant spores. Once this was found to be the case, the wet-heat resistance and core water content of the superdormant and original dormant spores were compared, and the environment of the spore core''s major small molecule, pyridine-2,6-dicarboxylic acid (dipicolinic acid [DPA]) was assessed by Raman spectroscopy of individual spores.