Electrical Sizing of Particles in Suspensions: I. Theory

The processes involved during the passage of a suspended particle through a small cylindrical orifice across which exists an electric field are considered in detail. Expressions are derived for the resulting change in current in terms of the ratios of particle to orifice volume and particle to suspending fluid resistivity, and particle shape. Graphs are presented of the electric field and of the fluid velocity as functions of position within the orifice, and of the shape factor of spheroids as a function of their axial ratio and orientation in the electric field. The effects of the electric and hydrodynamic fields on the orientation of nonspherical particles and on the deformation of nonrigid spheres is treated, and the migration of particles towards the orifice axis is discussed. Oscillograms of current pulses produced by rigid, nonconducting spheres in various orifices are shown and compared with the theoretical predictions.     

Electrical Sizing of Particles in Suspensions: III. Rigid Spheroids and Red Blood Cells

The processes involved during the passage of a suspended particle through a small cylindrical orifice across which exists an electric field are investigated experimentally for an approximate prolate spheroid in the form of two tangent, rigid spheres (ragweed pollen particles) and for fresh, human red blood cells. Oscillograms of current pulses produced by both types of particles are presented and discussed in terms of particle shape and orientation and the effects of the hydrodynamic field. It is concluded that all the particles enter the orifice with their major axes aligned parallel to the orifice axis (electric field), but that during their passage some are rotated by the hydrodynamic field. Cells with their equatorial plane perpendicular to a radius of the orifice change their orientation with respect to the electric field as they are rotated, the others do not; only in the former case is there any deformation. It is shown that the bimodal or skewed size distributions can be explained on this basis, and that size (shape factor × volume) is actually a normally distributed variable (P > 95%). The average size of samples from 10 healthy adults was found to be 102.7 μ³ with a coefficient of variation of 1.8%. For a volume of 87 μ³, this corresponds to a shape factor of 1.18, an axial ratio (assuming a perfect oblate spheroid) of 0.26, and an equivalent major axis of 8.6 μ. The effect of high electric fields on red cell size distributions is mentioned.     

Specific problems using electronic particle counters

Some specific problems of electronic particle counters (Coulter Counter, Elzone) are discussed. Conductivity of the medium does not influence the size response of the instrument, but might change the size of the particles through osmotic stress. An important problem of electronic particle counters is count loss by coincidence of passage of particles through the orifice and caused by dead time of the instruments. Several correction equations were tried out. It turned out that the count losses were much higher than the ones predicted by the manufacturers. In instruments equipped with multi-channel size analysers dead time count loss is much more important than the count loss by coincidence. A maximal counting frequency of 200 counts/second is recommended for accurate work. The width of the size distribution of particles depended on the diameter of the aperture tube.     

Electrical Counting and Sizing of Mammalian Cells in Suspension

A recently developed method of determining the number and size of particles suspended in a conducting solution is to pump the suspension through a small orifice having an immersed electrode on each side to supply electrical current. The current changes due to the passage of particles of resistivity different from that of the solution. Theoretical expressions are developed which relate the current change caused by such particles to their volume and shape. It is found that most biological cells may be treated as dielectric particles whose capacitive effects are negligible. Electrolytic tank measurements on models confirm the theoretical development, and electric field plots of model orifices are used to predict the observed pulse shapes. An equivalent circuit of the orifice-electrode system is analyzed and shows that the current pulse may be made conductivity-independent when observed with a zero input impedance amplifier.     

Precision of size determination of resistive electronic particle counters

The precision of the size determination of resistive particlecounting systems was studied by: (i) measuring the apparentsize of a single particle cycled repeatedly through the sensingelectrodes: (ii) by measuring the apparent size distributionof a population of particles of known and limited size range.(iii) by moving individual particles through a large-scale modelof the electrode assembly, and (iv) by measuring the size ofalgal cells microscopically and (subsequently) with a resistivecounting system. Three systematic errors were indicated (i)An ‘edge error’ results when a particle passes throughthe orifice near the perimeter of the orifice (     

Spatial configuration of charge and hydrophobicity tune particle transport through mucus

Mucus is a selectively permeable hydrogel that protects wet epithelia from pathogen invasion and poses a barrier to drug delivery. Determining the parameters of a particle that promote or prevent passage through mucus is critical, as it will enable predictions about the mucosal passage of pathogens and inform the design of therapeutics. The effect of particle net charge and size on mucosal transport has been characterized using simple model particles; however, predictions of mucosal passage remain challenging. Here, we utilize rationally designed peptides to examine the integrated contributions of charge, hydrophobicity, and spatial configuration on mucosal transport. We find that net charge does not entirely predict transport. Specifically, for cationic peptides, the inclusion of hydrophobic residues and the position of charged and hydrophobic residues within the peptide impact mucosal transport. We have developed a simple model of mucosal transport that predicts how previously unexplored amino acid sequences achieve slow versus fast passage through mucus. This model may be used as a basis to predict transport behavior of natural peptide-based particles, such as antimicrobial peptides or viruses, and assist in the engineering of synthetic sequences with desired transport properties.     

Mixing and propulsion of the contents of the reticulo-rumen]

Roughage intake and digestion by ruminants involve complex interactions between the roughage constituents, the microorganisms in the reticulo-rumen (RR) and its motility. Ruminal digestion requires intense activity, ie comminution of feed particles and mixing and propulsion of digesta. The regular repetition of the contraction sequences in the RR every 50 to 70 s subjects the digesta to a consistent pattern of movements. The particles are distributed according to their functional density which depends on the density of the plant structure of the particle, the liquid inside the particle and also the gas, ie on the degree of particle fermentation. An interwoven mat of large low-density particles fills the dorsal sac and the top of the ventral sac of rumen. This mat traps part of the small high density particles. Squeezed by the contractions, the interwoven mat acts like a filter and lets a liquid containing small particles of high density pass into the bottom of the ventral sac. This liquid then flows into the reticulum and passes through the reticulo-omasal orifice (ROO). Chewing during rumination reduces particle size, eliminates particle gas and aids in separating the low-density particles, which are less fermented, from the heavy residues. The outflow of digesta, made possible by the opening of the ROO during the second phase of the reticular contraction, is highly selective. The effluent does not contain particles greater than 2 mm in size in sheep and 4 mm in cattle. This is due to the buoyancy of the large particles in the reticulum, to the self-filtration of the digesta during the passage through the ROO and possibly to backflow from the omasum to the reticulum. Finally, RR motor activity, ie continuously mixing the digesta and monitoring the evacuation of gas and outflow of digesta, allows the homeostasis in the rumen necessary to microbial fermentation. The characteristics of the ingested particles, their rates of size reduction and density increase, the consistency of digesta and the intensity of the rumen wall stimulations are all factors which depend on the nature of feed and intake level. Via mechanisms which are not yet all well known and/or quantified, these factors act upon the efficiency of the mixing and propulsion of the reticulo-ruminal content and thus upon the retention time of the feed in the RR as well as its digestive utilisation.(ABSTRACT TRUNCATED AT 400 WORDS)     

Sizing particles with a Coulter counter

A theorem is presented which permits a determination of the amplitude of the signal generated by the passage of a particle of arbitrary shape through a Coulter counter. The theorem is applied to particles of two shapes, a sphere and a prolate spheroid. For the sphere the signal is directly proportional to the volume of the particle. For the spheroid the result is a complicated function of the shape. Two spheroids of the same volume but different shapes will give different signals.     

Flow-system measurement of cell impedance properties.

A flow-system technique has been developed that detects the high-frequency resistance and capacitance changes in a sensing orifice due to the passage of cells through the orifice. The resistance and capacitance changes are related to cell properties such as size, plasma membrane capacitance, and electrical resistivity of the cell interior. The relationship between measured impedances and cellular properties is discussed, and the prototype instrument for making such measurements is described. The instrument can simultaneously detect the dc Coulter volume and two ac parameters related to the complex ac impedance change. Some initial tests of the instrument using plastic microspheres and Chinese hamster ovary cells are described.     

Factors involved in the generation and replication of rhabdovirus defective T particles.

Previous indications that cloned B virions might be genetically predisposed to generate a particular defective T particle are shown to be inaccurate. T particle generation was found to be a much more random process than was previously believed. We show that the previously observed generation of particular sizes of T particles by B virion pools is due to the random generation of T particles during preparation of first-passage pools of cloned B virions, and these breed true during the additional passages needed to produce visible quantities of T particles. It is also shown that different host cell lines selectively amplify different T particles, suggesting a strong role of host cell factors in T particle replication. Surprisingly, our line of HeLa cells did not generate or replicate detectable T particles of vesicular stomatitis virus (VSV) Indiana after either serial undiluted passage or direct addition of T particles, even though the added T particles strongly interfered with B virion replication. In contrast to VSV, rabies virus generates large amounts of T particles during the first passage of cloned B virions, and every rabies-infected baby hamster kidney-21 cell culture evolves into a persistent carrier state. We find that T particle RNA is biologically inactive although T particle nucleocapsid ribonucleoprotein replicates and interferes in cells coinfected with B virions. Efforts to study the mechanism of T particle generation by in vitro attempts to generate T particles or modify their size (using sheared ribonucleoprotein or chemical or UV mutagenesis) were unsuccessful. The kinetics of UV and nitrous acid inactivation of T particles indicate a smaller target size relative to B virions, even after correcting for lengths of RNA molecules. The intercalating dye proflavine does not photosensitize VSV B virions or T particles when present during replication, indicating that there is little or no RNA base pairing in the helical nucleocapsids of either.     

Electrical sizing of particles in suspensions. II. Experiments with rigid spheres

Experimental verification is provided for the theoretical expressions (see preceding article, I. Theory) describing the electrical processes that take place during the passage of an aqueous suspension of rigid, nonconducting spheres (ragweed pollen) through an orifice across which there exists an electrical field, for a large range of orifice dimensions; the instrumentation developed is considered in some detail. The effective length of an orifice as deduced from conductivity measurements is shown to be essentially the same as that predicted theoretically. Absolute volume distributions are presented of a suspension of polystyrene latex spheres as determined electrically (mean 11.17 μ³, c. v. 4.2%) and with an electron microscope (mean 11.01 μ³, c. v. 4.1%). Conflicting experimental results reported in the literature are discussed.     

A selection model to estimate the interaction between food particles and the post-canine teeth in human mastication.

Food comminution during chewing is the composite result of selection and breakage. In the selection process, every food particle has a chance of being placed between the antagonistic post-canine teeth and being subjected to subsequent breakage. The selection chance, being the ratio between the number of selected and offered particles, has been mathematically described as a function of the number of particles offered, in terms of the number of breakage sites available on the teeth and particle affinity, i.e. the fraction of breakage sites occupied by one particle. The assumption has been made that particles are successively selected during a jaw-closing phase and that the selection chance of subsequent particles having the opportunity to occupy a breakage site proportionally decreases with the unoccupied fraction of the breakage sites left. The number of selected particles of a single size then asymptotically approaches the total number of breakage sites available for that size, when the number of particles offered increases. The critical particle number, derived from the measure of particle affinity, indicates the number of particles by which the breakage sites become saturated. The selection model for single particle sizes has been successfully applied to describe one-chew experiments, using various numbers and sizes of particles made of a silicone-rubber. After pseudo-chewing movements the subjects were unexpectedly instructed to carry out a real chew on particles (half-cubes). Undamaged, hence non-selected half-cubes could afterwards be distinguished from broken particles. The model has been extended to a particle mixture to describe the selection of particles of a certain size while other particles of different sizes are present. If a two-way competition between smaller and larger particles is assumed, the model predicts that the ratios of the selection chances between different particle sizes do not depend upon the numbers of the particles in the mixture.     

Continuing coevolution of virus and defective interfering particles and of viral genome sequences during undiluted passages: virus mutants exhibiting nearly complete resistance to formerly dominant defective interfering particles

We quantitatively analyzed the interference interactions between defective interfering (DI) particles and mutants of cloned vesicular stomatitis virus passaged undiluted hundreds of times in BHK-21 cells. DI particles which predominated at different times in these serial passages always interfered most strongly (and very efficiently) with virus isolated a number of passages before the isolation of the DI particles. Virus isolated at the same passage level as the predominant DI particles usually exhibited severalfold resistance to these DI particles. Virus mutants (Sdi- mutants) isolated during subsequent passages always showed increasing resistance to these DI particles, followed by decreasing resistance as new DI particles arose to predominate and exert their own selective pressures on the virus mutant population. It appears that such coevolution of virus and DI particle populations proceeds indefinitely through multiple cycles of selection of virus mutants resistant to a certain DI particle (or DI particle class), followed by mutants resistant to a newly predominant DI particle, etc. At the peak of resistance, virus mutants were isolated which were essentially completely resistant to a particular DI particle; i.e., they were several hundred thousand-fold resistant, and they formed plaques of normal size and numbers in the presence of extremely high multiplicities of the DI particle. However, they were sensitive to interference by other DI particles. Recurring population interactions of this kind can promote rapid virus evolution. Complete sequencing of the N (nucleocapsid) and NS (polymerase associated) genes of numerous Sdi- mutants collected at passage intervals showed very few changes in the NS protein, but the N gene gradually accumulated a series of stable nucleotide and amino acid substitutions, some of which correlated with extensive changes in the Sdi- phenotype. Likewise, the 5' termini (and their complementary plus-strand 3' termini) continued to accumulate extensive base substitutions which were strikingly confined to the first 47 nucleotides. We also observed addition and deletion mutations in noncoding regions of the viral genome at a level suggesting that they probably occur at a high frequency throughout the genome, but usually with lethal or debilitating consequences when they occur in coding regions.     

Estimation of flattening coefficient for absorption and circular dichroism using simulation

The absorbance and circular dichroism (CD) of suspensions is lower than if the same amount of chromophore were uniformly distributed throughout the medium. Several mathematical treatments of this absorption flattening phenomenon have been presented using various assumptions and approximations. This article demonstrates an alternative simulation approach that allows relaxation of assumptions. On current desktop computers, the algorithm runs quickly with enough particles and light paths considered to get answers that are usually accurate to better than 3%. Results from the simulation agree with the most popular analytical model for 0.01 volume fraction of particles, showing that the extent of flattening depends mainly on the absorbance through a particle diameter. Unlike previous models, the simulation can show that flattening is significantly lower when volume fraction increases to 0.1 but is higher when the particles have a size distribution. The simulation can predict the slope of the nearly linear relationship between flattening of CD and the absorbance of the suspension. This provides a method to correct experimental CD data where volume fraction and particle size are known.     

Adenosine diphosphate-induced aggregation of human platelets in flow through tubes. I. Measurement of concentration and size of single platelets and aggregates.

A double infusion flow system and particle sizing technique were developed to study the effect of time and shear rate on adenosine diphosphate-induced platelet aggregation in Poiseuille flow. Citrated platelet-rich plasma, PRP, and 2 microM ADP were simultaneously infused into a 40-microliters cylindrical mixing chamber at a fixed flow ratio, PRP/ADP = 9:1. After rapid mixing by a rotating magnetic stirbar, the platelet suspension flowed through 1.19 or 0.76 mm i.d. polyethylene tubing for mean transit times, t, from 0.1 to 86 s, over a range of mean tube shear rate, G, from 41.9 to 1,000 s-1. Known volumes of suspension were collected into 0.5% buffered glutaraldehyde, and all particles in the volume range 1-10(5) microns 3 were counted and sized using a model ZM particle counter (Coulter Electronics Inc., Hialeah, FL) and a logarithmic amplifier. The decrease in the single platelet concentration served as an overall index of aggregation. The decrease in the total particle concentration was used to calculate the collision capture efficiency during the early stages of aggregation, and aggregate growth was followed by changes in the volume fraction of particles of successively increasing size. Preliminary results demonstrate that both collision efficiency and particle volume fraction reveal important aspects of the aggregation process not indicated by changes in the single platelet concentration alone.     

Refractive index and thickness of the outer layer of particles of dispersed perfluorochemical-based blood substitutes

A calculation of the refractive index of particles of a disperse perfluorochemical-based (PFC-based) blood substitute has been made taking into account particular features of the structure of PFC emulsion particles and the equations earlier obtained by one of the authors in the studies on light interaction with optically inhomogeneous 2- and 3-layer spheres. The possibility of averaging by volume the refractive index of 2-layer emulsion particles has been shown. The refractive index of PFC particles has been experimentally determined using independent optical methods, and the thickness of the particle shell formed by a surfactant has been evaluated.     

Mathematical Modeling of Size Exclusion Chromatography

A mathematical model of the size exclusion chromatography (SEC) process in chromatographic columns has been developed. It considers the following three mass transfer processes in the SEC column: axial dispersion in the bulk‐fluid phase, interfacial film mass‐transfer between the stationary and mobile phases, and diffusion of solutes within the macro pores of the packing particles. Differential equations of the process model were solved by the finite difference method. Characteristics of the column and the packing particles (bed void volume fraction, particle porosity, accessible particle porosity) were obtained experimentally, as well as retention times of different molecules with known molecular weights. Experiments were performed with two different columns containing two different packing materials, Superdex 75 HR 10/30 and BioSep SEC S2000, respectively. The model has been validated by comparing theoretical and experimental retention times for the different columns.     

Ribocharin: a nuclear Mr 40,000 protein specific to precursor particles of the large ribosomal subunit

Using a monoclonal antibody (No-194) we have identified, in Xenopus laevis and other amphibia, an acidic protein of Mr 40,000 (ribocharin) which is specifically associated with the granular component of the nucleolus and nucleoplasmic 65S particles. These particles contain the nuclear 28S rRNA and apparently represent the precursor to the large ribosomal subunit in nucleocytoplasmic transit. By immunoelectron microscopy ribocharin has been localized in the granular component of the nucleolus and in interchromatin granules. During mitosis ribocharin-containing particles are associated with surfaces of chromosomes and are recollected in the reconstituting nucleoli in late telophase. We suggest that ribocharin is a specific component of precursor particles of the large ribosomal subunit, which dissociates from the 65S particle before passage through the nuclear envelope, and is reutilized in ribosome biogenesis.     

Electrical sizing of particles in suspensions IV. Lymphocytes

The factors involved during the pumping of a particle suspended in an electrolyte through a small cylindrical orifice across which exists an electric field are reviewed, and their practical application to cell volume measurement in terms of orifice geometry and particle properties is considered. Procedures are described to determine whether a particular cell type satisfies the operational criteria of a rigid, non-conducting sphere, for which the theoretical expressions can be reduced to an especially simple form under appropriate conditions. Experimental results are presented for the case of chick, mouse and human lymphocytes, all of which are shown to satisfy the above requirements. Volume distributions are provided for chick blood lymphocytes and compared with those from various lymphatic organs; representative data are also reported for different types of mouse lymphocytes. Human blood lymphocytes are found to have normally-distributed diameters (p > 98%), a property not shared by their volumes or their surface areas, nor by blood lymphocytes from the chick or from patients with chronic lymphatic leukemia. A possible implication of this finding is mentioned briefly.