The role of cavitation in liposome formation

Liposome size is a vital parameter of many quantitative biophysical studies. Sonication, or exposure to ultrasound, is used widely to manufacture artificial liposomes, yet little is known about the mechanism by which liposomes are affected by ultrasound. Cavitation, or the oscillation of small gas bubbles in a pressure-varying field, has been shown to be responsible for many biophysical effects of ultrasound on cells. In this study, we correlate the presence and type of cavitation with a decrease in liposome size. Aqueous lipid suspensions surrounding a hydrophone were exposed to various intensities of ultrasound and hydrostatic pressures before measuring their size distribution with dynamic light scattering. As expected, increasing ultrasound intensity at atmospheric pressure decreased the average liposome diameter. The presence of collapse cavitation was manifested in the acoustic spectrum at high ultrasonic intensities. Increasing hydrostatic pressure was shown to inhibit the presence of collapse cavitation. Collapse cavitation, however, did not correlate with decreases in liposome size, as changes in size still occurred when collapse cavitation was inhibited either by lowering ultrasound intensity or by increasing static pressure. We propose a mechanism whereby stable cavitation, another type of cavitation present in sound fields, causes fluid shearing of liposomes and reduction of liposome size. A mathematical model was developed based on the Rayleigh-Plesset equation of bubble dynamics and principles of acoustic microstreaming to estimate the shear field magnitude around an oscillating bubble. This model predicts the ultrasound intensities and pressures needed to create shear fields sufficient to cause liposome size change, and correlates well with our experimental data.     

An experimental and theoretical analysis of ultrasound-induced permeabilization of cell membranes

Application of ultrasound transiently permeabilizes cell membranes and offers a nonchemical, nonviral, and noninvasive method for cellular drug delivery. Although the ability of ultrasound to increase transmembrane transport has been well demonstrated, a systematic dependence of transport on ultrasound parameters is not known. This study examined cell viability and cellular uptake of calcein using 3T3 mouse cell suspension as a model system. Cells were exposed to varying acoustic energy doses at four different frequencies in the low frequency regime (20-100 kHz). At all frequencies, cell viability decreased with increasing acoustic energy dose, while the fraction of cells exhibiting uptake of calcein showed a maximum at an intermediate energy dose. Acoustic spectra under various ultrasound conditions were also collected and assessed for the magnitude of broadband noise and subharmonic peaks. While the cell viability and transport data did not show any correlation with subharmonic (f/2) emission, they correlated with the broadband noise, suggesting a dominant contribution of transient cavitation. A theoretical model was developed to relate reversible and irreversible membrane permeabilization to the number of transient cavitation events. The model showed that nearly every stage of transient cavitation, including bubble expansion, collapse, and subsequent shock waves may contribute to membrane permeabilization. For each mechanism, the volume around the bubble within which bubbles induce reversible and irreversible membrane permeabilization was determined. Predictions of the model are consistent with experimental data.     

Detection of ultrasonic cavitation based on low-frequency analysis of acoustic signal

The acoustic cavitation phenomenon constitutes a potential hazard in ultrasound diagnostics and therapy so that early and effective detection of cavitation is of great interest. However, cavitation might even bring a higher risk especially when an echocontrast agent based on microbubbles is used. The major goal of the present work was to develop a cavitation detection method based on increased level of cavitation noise in the range of low frequencies (about 1 Hz). This method was applied in vitro using a model of body fluid containing a model echocontrast agent, such as 5% solution of lyophilized egg albumin, which was sonicated by ultrasound disintegrator. Ultrasound signal evokes cavitation in microbubble suspension accompanied by a certain level of cavitation acoustic noise. The level of noise voltage increased in the frequency range of 0.1 to 2 Hz in the presence of cavitation. Hence, this method makes it possible to determine the value of cavitation threshold. In addition, we examined how the cavitation threshold is affected by temperature and viscosity. It was found that the cavitation threshold decreased with growing temperature while it increased with growing viscosity.     

Reducing Liposome Size with Ultrasound: Bimodal Size Distributions

Sonication is a simple method for reducing the size of liposomes. We report the size distributions of liposomes as a function of sonication time using three different techniques. Liposomes, mildly sonicated for just 30 sec, had bimodal distributions when surface-weighted with modes at about 140 and 750 nm. With extended sonication, the size distribution remains bimodal but the average diameter of each population decreases and the smaller population becomes more numerous. Independent measurements of liposome size using Dynamic Light Scattering (DLS), transmission electron microscopy (TEM), and the nystatin/ergosterol fusion assay all gave consistent results. The bimodal distribution (even when number-weighted) differs from the Weibull distribution commonly observed for liposomes sonicated at high powers over long periods of time and suggests that a different mechanism may be involved in mild sonication. The observations are consistent with the following mechanism for decreasing liposome size. During ultrasonic irradiation, cavitation, caused by oscillating microbubbles, produces shear fields. Large liposomes that enter these fields form long tube-like appendages that can pinch-off into smaller liposomes. This proposed mechanism is consistent with colloidal theory and the observed behavior of liposomes in shear fields.     

Reducing liposome size with ultrasound: bimodal size distributions

Sonication is a simple method for reducing the size of liposomes. We report the size distributions of liposomes as a function of sonication time using three different techniques. Liposomes, mildly sonicated for just 30 sec, had bimodal distributions when surface-weighted with modes at about 140 and 750 nm. With extended sonication, the size distribution remains bimodal but the average diameter of each population decreases and the smaller population becomes more numerous. Independent measurements of liposome size using Dynamic Light Scattering (DLS), transmission electron microscopy (TEM), and the nystatin/ergosterol fusion assay all gave consistent results. The bimodal distribution (even when number-weighted) differs from the Weibull distribution commonly observed for liposomes sonicated at high powers over long periods of time and suggests that a different mechanism may be involved in mild sonication. The observations are consistent with the following mechanism for decreasing liposome size. During ultrasonic irradiation, cavitation, caused by oscillating microbubbles, produces shear fields. Large liposomes that enter these fields form long tube-like appendages that can pinch-off into smaller liposomes. This proposed mechanism is consistent with colloidal theory and the observed behavior of liposomes in shear fields.     

Characterization and propagation of acoustic emission signals in woody plants: towards an improved acoustic emission counter

Abstract. The physics of ultrasonic acoustic emissions (AEs) was investigated for AE transmission through wood and transducers. The physical properties measured were velocity, attenuation and frequency composition of AEs produced by two sources: cavitation events in xylem and pencil lead breaks. The authors also measured the relative sensitivity of various combinations of ultrasound transducers and amplifiers to aid in the selection of a measuring system optimized for cavitation detection in woody plants. Some of the authors' conclusions are: (1) Softwoods ( Thuja, Pinus ) attenuate AEs more rapidly than hardwoods (maple, birch). (2) The velocity of AEs in wood exceeds that measured by others in water so the main medium of AE transmission must be the cellulose. (3) The strongest frequencies of AEs are in the range of 100–300 kHz. (4) Cavitation-induced AEs tend to shift to higher frequency as wood dehydration progresses. (5) One cannot determine the locus of origin of AEs from its frequency composition. (6) The frequency composition of the acoustic emissions probably cannot be determined at all with the sensors used because of their tendency to 'ring'. The data collected in this paper were used to aid in the design of an improved AE counter having a seven-fold increase in signal to noise ratio compared to counters previously used in our laboratory. The improved counter, model 4615 Drought Stress Monitor, is now commercially available from Physical Acoustics Corp., Princeton, NJ, U.S.A.     

Characterization of Dynamic Behaviour of MCF7 and MCF10A Cells in Ultrasonic Field Using Modal and Harmonic Analyses

Treatment options specifically targeting tumour cells are urgently needed in order to reduce the side effects accompanied by chemo- or radiotherapy. Differences in subcellular structure between tumour and normal cells determine their specific elasticity. These structural differences can be utilised by low-frequency ultrasound in order to specifically induce cytotoxicity of tumour cells. For further evaluation, we combined in silico FEM (finite element method) analyses and in vitro assays to bolster the significance of low-frequency ultrasound for tumour treatment. FEM simulations were able to calculate the first resonance frequency of MCF7 breast tumour cells at 21 kHz in contrast to 34 kHz for the MCF10A normal breast cells, which was due to the higher elasticity and larger size of MCF7 cells. For experimental validation of the in silico-determined resonance frequencies, equipment for ultrasonic irradiation with distinct frequencies was constructed. Differences for both cell lines in their response to low-frequent ultrasonic treatment were corroborated in 2D and in 3D cell culture assays. Treatment with ~ 24.5 kHz induced the death of MCF7 cells and MDA-MB-231 metastases cells possessing a similar elasticity; frequencies of > 29 kHz resulted in cytotoxicity of MCF10A. Fractionated treatments by ultrasonic irradiation of suspension myeloid HL60 cells resulted in a significant decrease of viable cells, mostly significant after threefold irradiation in intervals of 3 h. Most importantly in regard to a clinical application, combined ultrasonic treatment and chemotherapy with paclitaxel showed a significantly increased killing of MCF7 cells compared to both monotherapies. In summary, we were able to determine for the first time for different tumour cell lines a specific frequency of low-intensity ultrasound for induction of cell ablation. The cytotoxic effect of ultrasonic irradiation could be increased by either fractionated treatment or in combination with chemotherapy. Thus, our results will open new perspectives in tumour treatment.     

Use of chemical dosimetry for comparison of ultrasound and ionizing radiation effects on cavitation

A comparison of the effects of ultrasound produced by low- and high-frequency ultrasonic apparatuses upon biological systems is one of the basic problems when studying ultrasound cavitation effects. One possibility for how to compare these effects is the indirect method which uses well-known physical quantities characterizing the interaction of ionizing radiation with matter and which also converts these quantities to one common physical quantity. The comparison was performed with two methods applied to the chemical dosimetry of ionizing radiation. The first method employed a two-component dosimeter which is composed of 50 % chloroform and 50 % re-distilled water (i.e. Taplin dosimeter). The other method used a modified iodide dosimeter prepared from a 0.5 M potassium iodide solution. After irradiation or ultrasound exposure, measurable chemical changes occurred in both dosimeters. The longer the exposure, the greater the chemical changes. These effects are described by the relationship of these changes versus the exposure times in both dosimeters. The UZD 21 ultrasonic disintegrator (with a frequency of 20 kHz, 50 % power output) was used as a low-frequency ultrasound source, and the BTL-07 therapeutic instrument (with a frequency of 1 MHz and intensity of 2 W/cm2) was used as a high-frequency cavitation ultrasound source. For comparison, a 60 Co gamma source was applied (60 Co, gamma energies of 1.17 and 1.33 MeV, activity of 14 PBq). Results of this study have demonstrated that the sonochemical products are generated during exposure in the exposed samples of both dosimeters for all apparatuses used. The amount of these products depends linearly upon the exposure time. The resulting cavitation effects were recalculated to a gray-equivalent dose (the proposed unit is cavitation gray [cavitGy]) based on the sonochemical effects compared to the effects of ionizing radiation from the 60 Co source.     

Ultrasound sensitive enzyme-membrane

Summary Glucose oxidase (GOD) was immobilized on an acetylcellulose membrane filter (pore size: 0.45 m) with dipalmitoyl phosphatidyl-choline (DPPC). The activity of the GOD-DPPC membrane appeared during ultrasonic irradiation while the GOD activity disappeared when the irradiation was stopped. The apparent GOD activity (the value of the output current decrease of an oxygen electrode in the reaction mixture) gradually increased with increasing ultrasonic power below 3 W. On the other hand, it decreased with the increase in ultrasonic power over 4 W because dissolved oxygen in the reaction mixture in creased as ultrasonic cavitation was generated. The response of the membrane decreased with increasing ultrasonic frequency and the response of the membrane to ultrasound waves (20 KHz, 3 W) was reproducible. The membrane was stable for at least 2 months at 5°C. We conclude that the GOD-DPPC membrane can be regarded as a ultrasound sensitive membrane.     

Inhibition of barnacle cyprid settlement using low frequency and intensity ultrasound

Low frequency, low intensity ultrasound was demonstrated as an effective inhibitor of barnacle cyprid settlement. When the same substratum vibration amplitude (10.05 nm) and acoustic pressure (5 kPa) were applied, ultrasound at a frequency of 23?kHz significantly reduced cyprid settlement. The mechanism appeared to differ from the ultrasonic cavitation induced inhibition previously reported as no increased mortality was observed, and no change in the exploratory behaviour of cyprids was observed when they were exposed to this continuous ultrasonic irradiation regime. The application of ultrasound treatment in an intermittent mode of '5?min on and 20?min off' at 20-25?kHz and at the low intensity of 5?kPa produced the same effect as the continuous application of 23?kHz. This energy efficient approach to the use of low frequency, low intensity ultrasound may present a promising and efficient strategy regarding irradiation treatment for antifouling applications.     

The influence of different disturbance frequencies on the species richness,diversity and equitability of phytoplankton in shallow lakes

The relationships between the species richness, diversity and equitability of phytoplankton is discussed in the context of Connell's (1978, Science 199: 1304–1310) Intermediate Disturbance Hypothesis (IDH). The records of 759 vertical phytoplankton samples, which were obtained from four shallow central European lakes (Balaton, Neusiedlersee, and two small artificial ponds) at daily to weekly intervals were analysed.

1. The Shannon-Weaver function was used to measure diversity of the recorded species compositionof the phytoplankton. It is shown on fictitious data that compositional diversity is sensitive to the numberof coequilibrating species provided that the suspected interrelationship between diversity and ‘complexity’is amenable to the application of this method.
2. The disturbance scale that was developed on the basis of the field records fits well to Reynolds'(1988, Verh. int. Ver. Limnol. 23: 683–691) derivation: < 3 days qualifies as high frequency, approximatel3–8 days as intermediate frequency and > 8–9 days as low frequency of disturbance for phytoplankton.
3. Arithmetical means of the compositional diversity of phytoplankton under different frequencies ofdisturbance support the hypothesis that maximal diversity appears at intermediate frequencies.
4. There are different reasons for decrease in diversity at higher and lower frequencies. Inequitabilitydiminishes diversity at low disturbance; while species number decreases at high frequencies.
5. The case of Neusiedlersee calls attention to the fact that it is difficult, if at all possible, to differentiatebetween the indices under continuous stress and high frequency of disturbance in lakes in temperateregions. Similar species number-equitability pattern are induced by both and it is also presumablethat high frequency disturbance can itself effect a serious stress.
6. The striking effects that regular major periodic events (e.g. significant changes in the grazing pressureat the onset of the clear-water phase, autumnal cooling) in the plankton have on its species diversity areevident. Thus, the relative importance of intermediate frequency disturbances has its own seasonality:it is increasingly important in periods (partly in the spring, but mostly in the summer-autumn equilibriumphases), in which competition among phytoplankton species is increasing. This observation suggestsa way by which the stochasticity-based IDH can be incorporated into rather more deterministicexplanations (e.g. PEG-model; Sommer et al., 1986. Archiv für Hydrobiologie 106: 433–471) of planktonsuccession.
7. The most controversial issue and, therefore, the main difficulty, with IDH is that it not onlymaintains species richness in an ecosystem but it also supposes its presence. The lack of either earlyor late successional species in a given community can inactivate the mechanism. From the point of viewof the diversity-species richness relationship, the persistence of disturbance at given frequencies is ofgreater importance than the temporal alterations themselves in the evolutionary ecology of the phytoplankton.
8. For characteristically unperturbed phytoplankton communities (no case was studied here), equilibriumconcepts (niche diversification, etc.) should be more strongly applicable to their diversity andspecies richness.

     

Ultrasound acoustic emissions from dehydrating leaves of deciduous and evergreen trees

While drying, detached leaves produced ultrasound acoustic emissions (UAE) comparable to emissions from stem and twig wood. Experiments on Ilex aquifolium L. showed that the main source of these signals was cavitation in the veins, to which conduits and fibres probably both contributed. Regions of the leaf blade with abundant mesophyll and only small veins emitted few signals. More signals were counted on the adaxial side of the midrib than on the abaxial one and on the proximal third than on the distal one, in accordance with the anatomical structure. Sound attenuation was pronounced. Eight species were compared with respect to cavitation behaviour, field water relations and pressure–volume curves, and the data showed differences in cumulative number of events and resistance of leaves to cavitation. Data were generally in good agreement with anatomical structure and habitat preferences. The number of signals per conduit counted on cross-sections was in some leaves much higher than unity, which suggests short xylem elements or an acoustic activity of cells other than conduits. There was no correlation between cavitation threshold or cumulative number of signals and the degree of sclerophylly; unexpectedly, there was a correlation between the cumulative number of signals at a water potential of -1.3 MPa and the bulk modulus of elasticity.     

Interactions of inertial cavitation bubbles with stratum corneum lipid bilayers during low-frequency sonophoresis

Interactions of acoustic cavitation bubbles with biological tissues play an important role in biomedical applications of ultrasound. Acoustic cavitation plays a particularly important role in enhancing transdermal transport of macromolecules, thereby offering a noninvasive mode of drug delivery (sonophoresis). Ultrasound-enhanced transdermal transport is mediated by inertial cavitation, where collapses of cavitation bubbles microscopically disrupt the lipid bilayers of the stratum corneum. In this study, we describe a theoretical analysis of the interactions of cavitation bubbles with the stratum corneum lipid bilayers. Three modes of bubble-stratum corneum interactions including shock wave emission, microjet penetration into the stratum corneum, and impact of microjet on the stratum corneum are considered. By relating the mechanical effects of these events on the stratum corneum structure, the relationship between the number of cavitation events and collapse pressures with experimentally measured increase in skin permeability was established. Theoretical predictions were compared to experimentally measured parameters of cavitation events.     

Functional and ecological xylem anatomy

Cohesion-tension transport of water is an energetically efficient way to carry large amounts of water from the roots up to the leaves. However, the cohesion-tension mechanism places the xylem water under negative hydrostatic pressure (P_x), rendering it susceptible to cavitation. There are conflicts among the structural requirements for minimizing cavitation on the one hand vs maximizing efficiency of transport and construction on the other. Cavitation by freeze-thaw events is triggered by in situ air bubble formation and is much more likely to occur as conduit diameter increases, creating a direct conflict between conducting efficiency and sensitivity to freezing induced xylem failure. Temperate ring-porous trees and vines with wide diameter conduits tend to have a shorter growing season than conifers and diffuse-porous trees with narrow conduits. Cavitation by water stress occurs by air seeding at interconduit pit membranes. Pit membrane structure is at least partially uncoupled from conduit size, leading to a much less pronounced trade-off between conducting efficiency and cavitation by drought than by freezing. Although wider conduits are generally more susceptible to drought-induced cavitation within an organ, across organs or species this trend is very weak. Different trade-offs become apparent at the level of the pit membranes that interconnect neighbouring conduits. Increasing porosity of pit membranes should enhance conductance but also make conduits more susceptible to air seeding. Increasing the size or number of pit membranes would also enhance conductance, but may weaken the strength of the conduit wall against implosion. The need to avoid conduit collapse under negative pressure creates a significant trade-off between cavitation resistance and xylem construction cost, as revealed by relationships between conduit wall strength, wood density and cavitation pressure. Trade-offs involving cavitation resistance may explain the correlations between wood anatomy, cavitation resistance, and the physiological range of negative pressure experienced by species in their native habitats.     

High mortality and enhanced recovery: modelling the countervailing effects of disturbance on population dynamics

Disturbances cause high mortality in populations while simultaneously enhancing population growth by improving habitats. These countervailing effects make it difficult to predict population dynamics following disturbance events. To address this challenge, we derived a novel form of the logistic growth equation that permits time‐varying carrying capacity and growth rate. We combined this equation with concepts drawn from disturbance ecology to create a general model for population dynamics in disturbance‐prone systems. A river flooding example using three insect species (a fast life‐cycle mayfly, a slow life‐cycle dragonfly and an ostracod) found optimal tradeoffs between disturbance frequency vs. magnitude and a close fit to empirical data in 62% of cases. A savanna fire analysis identified fire frequencies of 3–4 years that maximised population size of a perennial grass. The model shows promise for predicting population dynamics after multiple disturbance events and for management of river flows and fire regimes.     

Repeat disturbances have cumulative impacts on stream communities

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Induced allopolyploidization of autotetraploidBrassica campestris

Seeds of a variety of allogamous Brown Sarson (Brassica campestris) were irradiated with gamma rays either before or after duplication of their chromosome number by colchicine. Tetraploids from seeds irradiated before duplication had mean quadrivalent and chiasma frequencies of 1.85 and 28.35 respectively. Those from seeds irradiated after duplication had frequencies of 2.82 and 29.94, while unirradiated tetraploids had 2.77 and 30.53 respectively. Small structural aberrations inducing preferential pairing are assumed to have caused the lower quadrivalent frequency after the first treatment. The results suggest that it may be more expedient to induced, allopolyploidlike chromosome behaviour by irradiation at the diploid than at the tetraploid level.     

Enhanced single copy integration events in corn via particle bombardment using low quantities of DNA

Transgene copy number is an important criterion for determining the utility of transgenic events. Single copy integration events are highly desirable when the objective is to produce marker free plants through segregation or when it is necessary to introgress different transgenes into commercial cultivars from different transgenic events. In contrast multi-copy events are advocated by several authors for higher expression of the transgene. Till recently, it was thought that employment of the particle gun for transformation results in the production of a high proportion of multi-copy events often with complex integration pattern when compared to Agrobacterium-mediated transformation. However, it has been demonstrated that usage of cassette DNA for bombardment in place of whole plasmids would result in simple insertion pattern of the transgenes. While investigating the effect of varying the cassette DNA amount on stable transformation, the frequency of occurrence of low copy events was observed to increase when lower doses of cassette DNA was employed for bombardment. Large scale experimentation with rigorous statistical analysis performed to verify the above observations employing Helium gun and the Electric discharge gun for gene delivery confirmed the above observations. Helium gun experiments involving production of more than 1,600 corn events consistently yielded single copy events at higher frequencies at lower cassette DNA load (46% at 2.5 ng/shot) as compared to higher cassette DNA load (29% at 25 ng/shot) across 18 independent experiments. Results were nearly identical with the Electric discharge particle gun device where single copy events were recovered at frequencies of 54% at 2.5 ng cassettes DNA per shot as compared to 18% at 25 ng cassette DNA per shot. The transformation frequency declined from 41 to 34% (Helium gun) and from 48 to 31% (Electric discharge gun) with reduction in cassette DNA quantity from 25 to 2.5 ng per shot. This reduction in the transformation frequency is more than compensated by the savings in time and effort involved in the production and screening of events if the desired outcome is single copy events. These results demonstrate the flexibility of the particle gun method for controlling the frequency of production of either low copy or high copy events by altering the quantity of cassette DNA used for bombardment. The transgene expression levels over generations in relation to its integration need further investigations.     

Genetic stability of gene-targeted immunoglobulin loci. II. Influence of the cell line and the vector linearization site

The site-specific integration of exogenous gene fragments by homologous recombination provides a convenient method for altering the immunoglobulin loci of B cells and specifically designing antibody molecules. To introduce a human isotype into the heavy chain locus of mouse hybridoma cells we compared the recombination frequencies of vectors that could be linearized either as integration or as replacement constructs in different cell lines. Integration as well as replacement recombination was observed, irrespective of the location of the site at which the vector was cleaved. Integration events involving the human IgG1 vectors were lost at high frequency due to secondary vector excision, so that all stable recombinations were found to be replacement events. Replacement recombination of an integration vector involves an illegitimate crossover at least at the 3′ side and sometimes gives rise to deletion of the C_H1 domain. However, a homologous event at the 3′ side is more efficient than an illegitimate one, so that a homology that is distributed on both sides of the heterologous region promotes targeting at higher frequency than a contiguous sequence of the same total length. The position of the linearization site in the vector markedly influenced the targeting efficiency, but surprisingly, whether a double-strand break in the homology or in the heterology region more efficiently promoted integration was dependent on the cell line. In all cells, however, cleavage of the vector outside the homology region favoured stable replacements with a bias against C_H1-truncated clones. We further show that the frequency of replacements induced by integration vectors is not correlated to the homology length and cannot be increased by irradiation of the cells. Our findings indicate that for targeting the IgH locus other mechanisms might be involved than at other loci. Received: 20 January 1997 / Accepted: 9 June 1997     

Methodologies for estimating the sample size required for genetic conservation of outbreeding crops

Summary The main purpose of germplasm banks is to preserve the genetic variability existing in crop species. The effectiveness of the regeneration of collections stored in gene banks is affected by factors such as sample size, random genetic drift, and seed viability. The objective of this paper is to review probability models and population genetics theory to determine the choice of sample size used for seed regeneration. A number of conclusions can be drawn from the results. First, the size of the sample depends largely on the frequency of the least common allele or genotype. Genotypes or alleles occurring at frequencies of more than 10% can be preserved with a sample size of 40 individuals. A sample size of 100 individuals will preserve genotypes (alleles) that occur at frequencies of 5%. If the frequency of rare genotypes (alleles) drops below 5%, larger sample sizes are required. A second conclusion is that for two, three, and four alleles per locus the sample size required to include a copy of each allele depends more on the frequency of the rare allele or alleles than on the number. Samples of 300 to 400 are required to preserve alleles that are present at a frequency of 1%. Third, if seed is bulked, the expected number of parents involved in any sample drawn from the bulk will be less than the number of parents included in the bulk. Fourth, to maintain a rate of breeding (F) of 1 %, the effective population size (N _e) should be at least 150 for three alleles, and 300 for four alleles. Fifth, equalizing the reproductive output of each family to two progeny doubles the effective size of the population. Based on the results presented here, a practical option is considered for regenerating maize seed in a program constrained by limited funds.Part of this paper was presented at the Global Maize Germplasm Workshop, CIMMYT, El Batan, Mexico, March 6–12, 1988