We are searching data for your request:
Upon completion, a link will appear to access the found materials.
Here it says that scattering is inversely proportional to cell number but also says that we can observe greater absorbance as cell number increases.
So does turbidometeric method work on cell mass or number ?
Your text says that scattering is proportional to cell number, which is correct. It is not inversely proportional, as you stated.
Cell counting is any of various methods for the counting or similar quantification of cells in the life sciences, including medical diagnosis and treatment. It is an important subset of cytometry, with applications in research and clinical practice. For example, the complete blood count can help a physician to determine why a patient feels unwell and what to do to help. Cell counts within liquid media (such as blood, plasma, lymph, or laboratory rinsate) are usually expressed as a number of cells per unit of volume, thus expressing a concentration (for example, 5,000 cells per milliliter).
Measurement of Bacterial Growth: 3 Ways
This article throws light upon the three ways for the measurement of bacterial growth. The ways are: 1. Determination of the Number of Cells. 2. Determination of Cell Mass 3. Determination of Cell Activity.
Way # 1. Determination of the Number of Cells Directly:
A known volume of cell suspension (0.01 ml) is spread uniformly over a glass slide within a specific area (1 sq. cm). The smear is then fixed, stained, examined under the oil immersion lens, and the cells counted.
Since it is impractical to scan the entire area, it is customary to count the cells in a few microscopic fields. The total cell count is determined by calculating the total number of microscopic fields per 1 sq cm is of cell suspension. To obtain the total cell count following calculations is required.
(a) Area of the microscopic field = Ï€ r 2
r (oil immersion lens) = 0.08 mm
Area of the field under the oil immersion lens
Ï€r 2 =3.14 Ã— (0.08 mm) 2 = 0.02 sq mm
(b) Area of the smear 1 sq cm = 100 sq mm
. . . No. of microscopic fields 100/0.02 = 5,000
Average number of bacteria per field Ã— 5000 = number of cells/1 sq cm i.e. Number of cells/0.01 ml of the suspension.
Counting Chamber Method:
Special microscope slides are available with chambers designed to contain a cell suspension above an accurately rules area etched into the glass. The Petroff-Hausser chamber or haemocytometer (because it was originally devised for counting blood cells) is rules with squares of known area, and is so constructed that a film of known depth can be introduced between the slide and the cover slip.
Consequently, the volume of the liquid overlying each squire is accurately known.
Proportional Count Method:
A standard suspension of particles, for example, plastic- beads, where the number of particles per volume is known, is mixed with an equal amount of cell suspension. This mixed suspension is spread on the slide, fixed and stained.
The particles and the cells in each microscopic field are then counted. An average count of the particles and the cell is taken from the number of fields. For example, suppose an average count of 5 particles and 30 cells per field is obtained.
If the number of particles in 1 ml of standard suspension is 10,000 then the number of cells per 1 ml of suspension is:
30/5Ã— 10,000 = 60,000 cells/ml
In this method there is no need to measure the amount of the suspension spread on the slide.
An electronic instrument called the Coulter counter can also be used for the direct enumeration of cells in a suspension. Fig. 18.31 demonstrates the principles of the Coulter counter. The instrument is capable of accurately counting thousands of cells in a few seconds.
The suspending fluid, however, must be free of inaminate particles (e.g. dust), since smaller ones will score as cells and larger ones will plug the aperture through which the cells pass.
Direct counting methods are rapid and simple. The morphology of cells can also be observed when they are counted under the microscope. The major disadvantage of these methods is that is gives a total cell count which includes both viable and non-viable cells.
Accuracy also declines with very dense and very dilute suspensions because of clumping and statistical errors, respectively. Very dense suspensions, however, can be counted if they are diluted appropriately.
Determination of the Number of Cells Indirectly by the Plate Count:
The plate count is based upon the assumption that each organism trapped in on a nutrient agar medium will multiply and produce a visible colony. The number of colonies therefore is the same as the number of viable cells inoculated into the medium. In this procedure (Fig. 18.32) an appropriately diluted cell suspension is introduced into a petri dish.
An appropriate melted agar medium is poured into the petri dish and is thoroughly mixed with the inoculum by rotating the plate. After the solidification of the medium, the plates are inverted and incubated for 18 to 24 hours. A plate having 30 to 300 colonies is selected for counting the number of organisms.
The plate count has certain disadvantages. If the suspension contains different microbial species, then all of them may not grow on the medium used and under the specified conditions of growth. Secondly, if the suspension is not homogeneous and contains aggregates of cells, the resulting colony count will be lower than the actual number of organisms, since each aggregate will produce only one colony.
The plate-count technique is used routinely with satisfactory results for the estimation of bacterial population in milk, water food, and other materials. The method is highly sensitive, i.e. extremely high or very low populations can be counted. However, the most obvious advantage of the method is that is counts only living organisms.
Membrane Filters Count:
This method is the same in principle as that of a plate count. A suspension of micro-organisms, such as in water or air, if filtered through a millipore filter membrane. The organisms are retained on the filter disc. The disc is then placed in a petri dish containing a suitable medium. The plates are incubated and the colonies are observed on the membrane surface.
The method has distinct advantages over the plate count. A large volume of the sample can be analyzed, especially when the number of organisms is very few. Secondly various types of micro-organisms can be detected by using selective media in the plates and under different conditions of growth.
Way # 2. Determination of the cell mass.
(a) Measurement of Dry Weight of Cells:
This is the most direct approach for quantitative measurement of a mass of cells. The sample is centrifuged or filtered and the residue or the pellet is washed a number of times to remove all extraneous matter. The residue is then dried and weighed.
However, it can be used only with very dense cell suspensions. This method is tedious and is applicable mainly in research investigations. It is commonly used for measuring growth of moulds in certain phases of industrial work.
Measurement of Cell Nitrogen:
The major constituent of cell material is protein, and nitrogen is a characteristic constituent of protein. A bacterial population or cell crop can be measured in terms of cell nitrogen. The cells are to be harvested as described in the first technique, and then the cell nitrogen is estimated by chemical analysis. This is also a tedious method, and can be used only with dense cell suspension.
(b) Turbidity Measurements:
A most widely used technique of measuring cell mass is by observing the light-scattering capacity of the sample. A suspension of unicellular organisms is placed in a colorimeter or spectrophotometer, and light is passed through it. The amount of the light absorbed or scattered is proportional to the mass of cells in the path of light.
When cells are growing exponentially, increase in cell mass is directly related to cell number. This is a rapid and accurate method to estimate dry weight or cell number in unit volume, provided a standard curve is first prepared. A standard curve can be prepared by measuring bacterial growth simultaneously by two methods, and then establishing a relationship between the values obtained.
For example, an aliquot of samples is removed from the cell suspension, dried, and the weights per milliliter determined. From the cell suspensions dilutions are prepared, and the organisms are counted by plate-count. At the same time turbidity measurements of the cell suspension are also determined.
Any two sets of the data can then be plotted (cell weights or cell number against turbidity), as illustrated in Figure 18.33 to obtain a standard curve. For practical purposes, and within certain range of concentrations, a linear or straight-line relationship exists. Thus, by indirectly measuring the turbidity of the suspension, cell weight or cell number can be determined with the help of the standard curve.
This method however, has some limitations. Turbidity is most effective with suspensions of moderate density. Suspensions with very high or very low density give erroneous results. Secondly, it is not possible to measure cultures that are deeply coloured or contain suspended material other than cells. It must be recognized that turbidity measures both living as well as dead cells.
Limulus Amebocyte Lysate test using the Turbidimetric method
The principle of the LAL test is the coagulation reaction that occurs when the amebocytes extracted from the Limulus Polyphemus crab enter into contact with bacterial endotoxins. The endotoxins trigger a series of chain reactions that result in the proteins falling in gel form. The importance of conducting this test to all pharmaceutical products, food or any other type of product that is going to come into contact with humans lies in the harm that the Gram-negative bacteria can cause in the organism. These bacteria are the ones that release the endotoxins when they are attacked by the defence mechanism of humans and their cellular wall is broken. The release of endotoxins causes an immune response, which results in the release of cytokines. High levels of cytokines in the blood can cause severe respiratory conditions, processes associated to the death of a great quantity of cells and even death of the infected organism.
When turbidimetry is used in LAL tests, what we measure is the turbidity of the solution when the coagulant begins to be formed. The insoluble protein is responsible for the appearance of a gel in the tube where the test takes place. Having the patterns of the endotoxin, we can measure the turbidity through a spectrophotometrical method and this measurement allows us to quantify the amount of endotoxins that are present, which is why the results of this test are always relative. The analysis can be conducted through the turbidimetric endpoint method or through the kinetic turbidimetric method.
In the turbidimetric endpoint test, we need to take the reading of the turbidity at a determined period of time. This leads to manipulation errors and it has a disadvantage in that the reading cannot be taken correctly in a single sample and therefore the entire process will need to be repeated or that there is only a single moment to make the measurement and the measurement needs to be precise. If the reading is not taken at the moment indicated, the gelation continues. For these reasons, this method is not used much.
The kinetic turbidimetric method, on the other hand, has been more successful, in part because of the technological advancements in the past few decades that have made it possible to connect readings of multimedia plates along with temperature control and the whole process of data collection being totally computerized. Another characteristic feature of this method that makes it very popular when it is time to develop a LAL test is its low limit of detection and the wide range of endotoxin concentrations in which the measurements can take place, being able to construct normal curves in a concentration range of up to 100 endotoxin units per a millilitre of the solution.
The relationship between the appearance of the turbidity in the LAL test and the endotoxin concentration is exponential. Therefore, we can get a straight line using the antilogarithms of variable time and the concentration antilogarithms of the solution patterns. With the straight line we get from the regression, we can know the endotoxin concentrations in the samples subject to the study in the subsequent experiments. The temperature factor plays a fundamental role in these tests. In order to get a good level of reproducibility and precision in the results, we need to make sure we control the temperature. It is necessary to work at the temperature indicated in each protocol.
Different variations of the LAL test have been investigated using turbidimetry, which have yielded rapid tests of endotoxin detection conducting the test at higher temperatures than the normal ones, which are around 37 ºC, or, for instance, the introduction of the reagents in nano particles.
The PYROSTAR™ ES-F and the PYROSTAR™ ES-F/Plate reagents are products by Wako that serve for bacterial endotoxin detection by applying the scientific method of turbidimetry. These products are sold to be used in measurements made for research-related purposes. Under no circumstances should they be used as diagnostic methods.
In order to use the reagent PYROSTAR™ ES-F/Plate, it is necessary to have a microplate reader like the Tecan Sunrise™ Microplate Reader and the corresponding software. The actual procedure consists of making measurements to have a calibration curve that covers between 10 units less and 10 units more than what the samples are predicted to be found. Measurements are made in positive and negative controls and the samples are measured in duplicate to ensure the quality of the measurements. Measurements should be taken every 40 seconds at 405 nm and at a temperature of 37 ºC on each one of the dishes of the microplate once the reagent PYROSTAR™ ES-F/Plate is added to the samples. The microplate reader monitors the turbidity of the samples in order to determine the time that the turbidity takes to appear, and with the transmittance data, the software calculates the regression curve that allows us to determine the concentration of endotoxins. This reagent includes the Curdlan (β-1, 3-glucan) to remove the interference that this compound produces and is sold with standard control endotoxin or without this substance.
Wako also manufactures a photometric instrument that can be used to measure the speed of change in the turbidity of the solution in the LAL test, called the Toxinometer® ET-6000. This instrument uses a LED of 430 nm wavelength as a source of light and also has the advantage of on-board temperature control, which is very important in this test.
Change in the amount of a cell component
In situations where determining the number of microorganisms is difficult or undesirable for other reasons, the use of indirect methods can be an excellent alternative. These methods measure some quantifiable cell property that increases as a direct result of microbial growth.
The simplest technique of this sort is to measure the weight of cells in a sample. Portions of a culture can be taken at particular intervals and centrifuged at high speed to sediment bacterial cells to the bottom of a vessel. The sedimented cells (called a cell pellet) are then washed to remove contaminating salt, and dried in an oven at 100-105 °C to remove all water, leaving only the mass of components that make up the population of cells. An increase in the dry weight of the cells correlates closely with cell growth. However, this method will count dead as well as living cells. There might also be conditions where the dry weight per cell changes over time or under different conditions. For example, some bacteria that excrete polysaccharides will have a much higher dry weight per cell when growing on high sugar levels (when polysaccharides are produced) than on low. If the species under study forms large clumps of cells such as those that grow filamentously, dry weight is a better measurement of the cell population than is a viable plate count.
It is also possible to follow the change in the amount of a cellular component instead of the entire mass of the cell. This method may be chosen because determining dry weights is difficult or when the total weight of the cell is not giving an accurate picture of the number of individuals in a population. In this case, only one component of the cell is followed such as total protein or total DNA. This has some of the same advantages and disadvantages listed above for dry weight. Additionally, the measurement of a cellular component is more labor-intensive than previously mentioned methods since the component of interest has to be partially purified and then subjected to an analysis designed to measure the desired molecule. The assumption in choosing a single component such as DNA is that that component will be relatively constant per cell. This assumption has a problem when growth rates are different because cells growing at high rates actually have more DNA per cell because of multiple initiations of replication.
A final widely used method for the determination of cell number is a turbidometric measurement or light scattering. This technique depends on the fact that as the number of cells in a solution increases, the solution becomes increasingly turbid (cloudy). The solution looks turbid because light passing through it is scattered by the microorganisms present and the turbidity is proportional to the number of microorganisms in the solution. The turbidity of a culture can be measured using a photometer or a spectrophotometer. The difference between these instruments is the type of light they pass through the sample. Photometers, such as the Klett-Summerson device, use a red, green or blue filter providing a broad spectrum of light. Spectrophotometers use prisms or diffraction gratings supplying a narrow band of wavelengths to the sample. Both instruments measure the amount of transmitted light, the light that makes it from the light source through the sample to the detector.
Figure 4.16. Measuring the turbidity of a culture. A spectrophotometer or photometer quantifies the amount of turbidity of a culture. The amount of light scattered from a solution is proportional to cell number. The instruments measures light that is not scattered by the sample.
When measuring light scattering it is important to consider the wavelength of light used a bacterial culture. Microorganisms may contain numerous macromolecules that will absorb light, including DNA (254 nm), proteins (280 nm), cytochromes (400-500 nm), and possible cell pigments. When measuring bacteria by light scattering it is best to pick a wavelength where absorption is at a minimum and for most bacterial cultures wavelengths around 600 nm are a good choice. However, the exact wavelength chosen is species specific.
The amount of light transmitted through a sample is inversely proportional to cell number and can be expressed in the following equation.
Figure 4.17. The transmittance equation. The ratio of light hitting the sample (I0) to light passing through a sample (I) is the transmittance.
Where T is the light transmitted, I0 is the light entering the sample and I is the light passing through to the detector.
Due to the nature of light scattering, transmittance decreases geometrically as the cell numbers increase. It is more intuitive to think of the units increasing as growth increases and for most bacterial analysis, transmittance is converted into absorbance using the following equation.
Figure 4.18. Absorbance. The absorbance of a sample it the negative log base 10 of the transmittance.
Absorbance increases in a linear fashion as the cell number increases. When measuring growth of a culture the term optical density (OD) is normally used to more correctly represent the light scattering that is occurring under optimal conditions, little light is actually absorbed by the culture so the term absorbance is misleading. For most unicellular organisms changes in OD are proportional to changes in cell number (within certain limits) and therefore can be used as a method to follow cell growth. If a precise cell number for a given OD is desired, a standard curve can be generated, where viable plate count or cell mass is plotted as a function of OD. It also wise to develop a standard curve to verify that the OD is actually an accurate portrayal of cell growth. After the standard curve is made, it is then possible to simply measure the OD of the culture and read the cell number from the curve.
The turbidity of a culture is dependent upon the shape and internal light-absorbing components of the microorganism and therefore turbidity readings are species-specific and cannot be compared between different microbes or even between different strains of the same species. As above, there are microbes that change cell size or shape at different stages of growth, which introduces some inaccuracy to this method of cell counting. Also both living and dead cells scatter light and are therefore counted. However, the method is very rapid and simple to perform and provides reliable results when used with care, so it is an extremely common method of real time analysis of prokaryotic populations. In fact it is one of the methods we will use for measuring cell number in the experiment on bacterial growth. Turbidometric measurements also do not destroy the sample.
Kinetics of ligand binding and signaling
Karolina Gherbi , . Steven J. Charlton , in GPCRs , 2020
10.2.2.4 Flow cytometry
Flow cytometry is another fluorescence-based technique, measuring the fluorescence of individual cells ( Edwards and Sklar, 2015 ). Cells in suspension are focused into a sample stream with a diameter of a single cell and pass through a laser beam of equivalent diameter, which excites the fluorophores attached to the cell, and the emission of the fluorophores is subsequently recorded. The narrowness of the flow cytometer means that the fluorescence observed will be primarily cell-associated. Importantly, many fluorescent ligands are quenched in aqueous solution, meaning flow cytometry does not require a filtration step to remove fluorophores in the solution ( Edwards and Sklar, 2015 ). The earliest flow cytometry-based investigation into GPCR ligand binding kinetics monitored the association and dissociation of fluorescein-labeled N-formyl peptide to formyl peptide receptors ( Sklar et al., 1984 ). Since then, flow cytometry has been used to monitor the kinetics of fluorescent ligand binding at the adenosine A3 receptor ( Kozma et al., 2012, 2013 ), free fatty acid receptor 1 ( Hara et al., 2009 ), the yeast α-factor receptor( Bajaj et al., 2004 ), and the P2Y14 receptor ( Kiselev et al., 2015 ).
Flow cytometry is usually performed on whole cells in suspension but has also been performed on magnetic beads with solubilized receptors attached to them ( Hara et al., 2009 ). Just as for the imaging techniques discussed earlier, high-affinity fluorescent ligands are required as too much nonspecific binding will result in a poor signal-to-noise ratio. The main downside of flow cytometry is the significantly lower throughput compared to other techniques experiments tend to be performed in larger volume tubes ( Sklar et al., 1984 Bajaj et al., 2004 Hara et al., 2009 ), or 6, 12-, and 24-well plates ( Kozma et al., 2013 ). Additionally, while flow cytometry is homogenous, several kinetic experiments performed have still used a different well/tube for every time point ( Kozma et al., 2012, 2013 ). It is also difficult to perform very short reads, which limits this method to higher affinity ligands.
Calculating the total number of cells infected with SARS-CoV-2
We use our estimate of the total number of infectious units in the body of an infected individual to estimate the number of cells that are infected by the virus during peak infection. In order to estimate the total number of infected cells, we estimate how many infectious units are found in each infected cell as shown in Figure 2 .
Estimate of the number of infected cells and their fraction out of the potential relevant host cells.
We rely on two lines of evidence in order to estimate the number of infectious units within an infected cell at a given time. The first is data regarding the total number of infectious units produced by an infected cell throughout its lifetime also known as the yield. As we are not aware of studies directly reporting values of the yield of cells infected with SARS-CoV-2, we used values reported for other betacoronaviruses in combination with values we derived from a study ( 20 ) of replication kinetics of SARS-CoV-2. Using a plaque formation assay to count the number of infectious units, two previous studies measured the viral yield as either 10 or 600 infectious units ( 21 , 22 ). Using reported values for replication kinetics of SARS-CoV-2 ( 20 ) we estimated a yield of
10 infectious units per cell at 36 hours from infection, in agreement with the lower end of these estimates. To convert the total number of infectious units produced overall by a cell into the number of units residing in the cell at a given moment, we estimate the ratio between these two quantities to be 3 using two independent methods detailed in the SI. Combining this ratio with our estimate for the total number of units produced by a cell, we thus estimate that, at any given moment, there are somewhere between a few to a few hundreds of infectious units residing in each infected cell.
The second line of evidence concerns the density of virions within a single cell. Several studies have used transmission electron microscopy (TEM) to characterize the intracellular replication of SARS-CoV-2 virions within cells ( 23 – 26 ). Using seven TEM scans taken from those studies we estimated that the density of virions within infected cells is 10 5 virions per 1 pL (see Dataset S1). As the human cells targeted by SARS-CoV-2 have a volume of 𢒁 pL (resulting in a cellular mass of 𢒁 ng) ( 27 , 28 ), TEM data indicate there are 5 viral particles within a single infected cell at any point in time. As done above, we assume a ratio of 1 infectious unit resulting per 10 4 virions. Thus, TEM scans imply that there are infectious units that will result from the virions residing inside a cell at any given moment after the initial stages of infection.
Following those lines of evidence we conclude that at a given moment there are
10 5 virions residing inside an infected cell which translates into
10 infectious units. Using the ratio of total production to the value at a given time inside the cell, we further conclude that the overall yield from an infected cell is
10 infectious units, coinciding with the middle range of measurements from other betacoronaviruses. This estimate also agrees well with recent results from dynamical models of SARS-CoV-2 host infection ( 29 , 30 ).
We can perform a sanity check using mass considerations to see that our estimate of the number of virions is not beyond the maximal feasible amount. Each virion has a mass of 𢒁 fg ( 5 ). Hence, 10 5 virions have a mass of 𢒀.1 ng, about 10% of the total mass of a 1 ng host cell and about a third of its dry weight. While a relatively high fraction, this is still within the range observed for other viral infections ( 31 , 32 ).
Combining the estimates for the overall number of infectious units in a person near peak infection and the number of infectious units in a single cell (Cinfectious units per cell), we can calculate the number of infected cells around peak infection:
How does this estimate compare to the number of potential host cells for the virus? The best-characterized route of infection for SARS-CoV-2 is through cells of the respiratory system, specifically the pneumocytes (
10 11 cells ), alveolar macrophages (
10 10 cells) and the mucus cells in the nasal cavity (
10 9 cells) ( 27 , 28 ). Other cell types, like enterocytes (gut epithelial cells) can also be infected ( 33 ) but they represent a similar number of cells ( 34 ) and therefore don’t change the order of magnitude of the potential host cells. As such, our best estimate for the size of the pool of cell types that SARS-CoV-2 likely infects is thus
10 11 cells, and the number of cells infected during peak infection therefore represents a small fraction of this potential pool (1 in 10 5 7 ).
Robert E. Brackett , in Postharvest Handling , 1993
1. Plate counts
The standard plate count , sometimes also referred to as the total plate count, is probably the most widely used technique for evaluating microorganisms in foods. The purpose, as its name implies, is to estimate the number of viable microorganism cells in a given sample of food. Although the standard plate count provides information about the total microbial load in a food, it also has some limitations. First, the standard plate count only tells how many cells but not what kinds of cells are present. Second, only relatively rapidly growing aerobic organisms such as bacteria are enumerated. Anaerobic bacteria and many fungi will not grow under the conditions used with the standard plate count. Thus, many important organisms are missed by this procedure.
In general, it is not necessary to determine the populations of microorganisms of fresh produce to assure quality. Populations of microorganisms in fruits and vegetables often bear little relationship to quality. The main application for the standard plate count in the fruit and vegetable industry is in monitoring sanitation procedures or in tracing microbiological problems. For example, this technique could be used to determine that various pieces of equipment are being cleaned and sanitized properly. Low populations of microorganisms would indicate that equipment is being maintained properly whereas an increase might point out inadequacies in cleaning procedures. However, what actually constitutes “low” or “high” populations depends on the piece of equipment and on what is considered a normal population. Before such data can be used in a meaningful way, baseline populations reflecting adequately cleaned equipment should be determined. Details of the standard plate count are described by Busta et al. (1984) .
Does turbidometeric method count cell number or cell mass? - Biology
Methods for Measurement of Cell Numbers
Measuring techniques involve direct counts, visually or instrumentally, and indirect viable cell counts.
1. Direct microscopic counts are possible using special slides known as counting chambers. Dead cells cannot be distinguished from living ones. Only dense suspensions can be counted (>10 7 cells per ml), but samples can be concentrated by centrifugation or filtration to increase sensitivity.
A variation of the direct microscopic count has been used to observe and measure growth of bacteria in natural environments. In order to detect and prove that thermophilic bacteria were growing in boiling hot springs, T.D. Brock immersed microscope slides in the springs and withdrew them periodically for microscopic observation. The bacteria in the boiling water attached to the glass slides naturally and grew as microcolonies on the surface.
2. Electronic counting chambers count numbers and measure size distribution of cells. For cells the size of bacteria the suspending medium must be very clean. Such electronic devices are more often used to count eucaryotic cells such as blood cells.
3. Indirect viable cell counts, also called plate counts, involve plating out (spreading) a sample of a culture on a nutrient agar surface. The sample or cell suspension can be diluted in a nontoxic diluent (e.g. water or saline) before plating. If plated on a suitable medium, each viable unit grows and forms a colony. Each colony that can be counted is called a colony forming unit (cfu) and the number of cfu's is related to the viable number of bacteria in the sample.
Advantages of the technique are its sensitivity (theoretically, a single cell can be detected), and it allows for inspection and positive identification of the organism counted. Disadvantages are (1) only living cells develop colonies that are counted (2) clumps or chains of cells develop into a single colony (3) colonies develop only from those organisms for which the cultural conditions are suitable for growth. The latter makes the technique virtually useless to characterize or count the total number of bacteria in complex microbial ecosystems such as soil or the animal rumen or gastrointestinal tract. Genetic probes can be used to demonstrate the diversity and relative abundance of procaryotes in such an environment, but many species identified by genetic techniques have so far proven unculturable.
Table 1. Some Methods used to measure bacterial growth
|Direct microscopic count||Enumeration of bacteria in milk or cellular vaccines||Cannot distinguish living from nonliving cells|
|Viable cell count (colony counts)||Enumeration of bacteria in milk, foods, soil, water, laboratory cultures, etc.||Very sensitive if plating conditions are optimal|
|Turbidity measurement||Estimations of large numbers of bacteria in clear liquid media and broths||Fast and nondestructive, but cannot detect cell densities less than 10 7 cells per ml|
|Measurement of total N or protein||Measurement of total cell yield from very dense cultures||only practical application is in the research laboratory|
|Measurement of Biochemical activity e.g. O2 uptake CO2 production, ATP production, etc.||Microbiological assays||Requires a fixed standard to relate chemical activity to cell mass and/or cell numbers|
|Measurement of dry weight or wet weight of cells or volume of cells after centrifugation||Measurement of total cell yield in cultures||probably more sensitive than total N or total protein measurements|
Figure 2. Bacterial colonies growing on a plate of nutrient agar. Hans Knoll Institute. Jena, Germany.
Why is it necessary to develop new statistical methodology for sequence count data? If large numbers of replicates were available, questions of data distribution could be avoided by using non-parametric methods, such as rank-based or permutation tests. However, it is desirable (and possible) to consider experiments with smaller numbers of replicates per condition. In order to compare an observed difference with an expected random variation, we can improve our picture of the latter in two ways: first, we can use distribution families, such as normal, Poisson and negative binomial distributions, in order to determine the higher moments, and hence the tail behavior, of statistics for differential expression, based on observed low order moments such as mean and variance. Second, we can share information, for instance, distributional parameters, between genes, based on the notion that data from different genes follow similar patterns of variability. Here, we have described an instance of such an approach, and we will now discuss the choices we have made.
Choice of distribution
While for large counts, normal distributions might provide a good approximation of between-replicate variability, this is not the case for lower count values, whose discreteness and skewness mean that probability estimates computed from a normal approximation would be inadequate.
For the Poisson approximation, a key paper is the work by Marioni et al. , who studied the technical reproducibility of RNA-Seq. They extracted total RNA from two tissue samples, one from the liver and one from the kidneys of the same individual. From each RNA sample they took seven aliquots, prepared a library from each aliquot according to the protocol recommended by Illumina and sampled each library on one lane of a Solexa genome analyzer. For each gene, they then calculated the variance of the seven counts from the same tissue sample and found very good agreement with the variance predicted by a Poisson model. In line with our arguments in Section Model, Poisson shot noise is the minimum amount of variation to expect in a counting process. Thus, Marioni et al. concluded that the technical reproducibility of RNA-Seq is excellent, and that the variation between technical replicates is close to the shot noise limit. From this vantage point, Marioni et al. (and similarly Bullard et al. ) suggested to use the Poisson model (and Fisher's exact test, or a likelihood ratio test as an approximation to it) to test whether a gene is differentially expressed between their two samples. It is important to note that a rejection from such a test only informs us that the difference between the average counts in the two samples is larger than one would expect between technical replicates. Hence, we do not know whether this difference is due to the different tissue type, kidney instead of liver, or whether a difference of the same magnitude could have been found as well if one had compared two samples from different parts of the same liver, or from livers of two individuals.
Figure 1 shows that shot noise is only dominant for very low count values, while already for moderate counts, the effect of the biological variation between samples exceeds the shot noise by orders of magnitude.
This is confirmed by comparison of technical with biological replicates . In Figure 7 we used DESeq to obtain variance estimates for the data of Nagalakshmi et al. . The analysis indicates that the difference between technical replicates barely exceeds shot noise level, while biological replicates differ much more. Tests for differential expression that are based on a Poisson model, such as those discussed in References [6, 7, 20, 22, 23] should thus be interpreted with caution, as they may severely underestimate the effect of biological variability, in particular for highly expressed genes.
Noise estimates for the data of Nagalakshmi et al. . The data allow assessment of technical variability (between library preparations from aliquots of the same yeast culture) and biological variability (between two independently grown cultures). The blue curves depict the squared coefficient of variation at the common scale, wρ(q)/q 2 (see Equation (9)) for technical replicates, the red curves for biological replicates (solid lines, dT data set, dashed lines, RH data set). The data density is shown by the histogram in the top panel. The purple area marks the range of the shot noise for the range of size factors in the data set. One can see that the noise between technical replicates follows closely the shot noise limit, while the noise between biological replicates exceeds shot noise already for low count values.
Consequently, it is preferable to use a model that allows for overdispersion. While for the Poisson distribution, variance and mean are equal, the negative binomial distribution is a generalization that allow for the variance to be larger. The most advanced of the published methods using this distribution is likely edgeR . DESeq owes its basic idea to edgeR, yet differs in several aspects.
Sharing of information between genes
First, we discovered that the use of total read counts as estimates of sequencing depth, and hence for the adjustment of observed counts between samples (as recommended by Robinson et al.  and others) may result in high apparent differences between replicates, and hence in poor power to detect true differences.
DESeq uses the more robust size estimate Equation (5) in fact, edgeR's power increases when it is supplied with those size estimates instead. (Note: While this paper was under review, edgeR was amended to use the method of Oshlack and Robinson .)
For small numbers of replicates as often encountered in practice, it is not possible to obtain simultaneously reliable estimates of the variance and mean parameters of the NB distribution. EdgeR addresses this problem by estimating a single common dispersion parameter. In our method, we make use of the possibility to estimate a more flexible, mean-dependent local regression. The amount of data available in typical experiments is large enough to allow for sufficiently precise local estimation of the dispersion. Over the large dynamic range that is typical for RNA-Seq, the raw SCV often appears to change noticeably, and taking this into account allows DESeq to avoid bias towards certain areas of the dynamic range in its differential-expression calls (see Figure 2 and 4).
This flexibility is the most substantial difference between DESeq and edgeR, as simulations show that edgeR and DESeq perform comparably if provided with artificial data with constant SCV (Supplementary Note G in Additional file 1). EdgeR attempts to make up for the rigidity of the single-parameter noise model by allowing for an adjustment of the model-based variance estimate with the per-gene empirical variance. An empirical Bayes procedure, similar to the one originally developed for the limma package [24–26], determines how to combine these two sources of information optimally. However, for typical low replicate numbers, this so-called tagwise dispersion mode seems to have little effect (Figure 4) or even reduces edgeR's power (Supplementary Note F in Additional file 1).
Third, we have suggested a simple and robust way of estimating the raw variance from the data. Robinson and Smyth  employed a technique they called quantile-adjusted conditional maximum likelihood to find an unbiased estimate for the raw SCV. The quantile adjustment refers to a rank-based procedure that modifies the data such that the data seem to stem from samples of equal library size. In DESeq, differing library sizes are simply addressed by linear scaling (Equations (2) and (3)), suggesting that quantile adjustment is an unnecessary complication. The price we pay for this is that we need to make the approximation that the sum of NB variables in Equation (10) is itself NB distributed. While it seems that neither the quantile adjustment nor our approximation pose reason for concern in practice, DESeq's approach is computationally faster and, perhaps, conceptually simpler.
Fourth, our approach provides useful diagnostics. Plots such as Supplementary Figure S3 in Additional file 2 are helpful to judge the reliability of the tests. In Figure 1b and 7, it is easy to see at which mean value biological variability dominates over shot noise this information is valuable to decide whether the sequencing depth or the number of biological replicates is the limiting factor for detection power, and so helps in planning experiments. A heatmap as in Figure 5 is useful for data quality control.
Origin of Prevalent Claims in the Literature on the Number of Bacterial Cells in Humans
Microbes are found throughout the human body, mainly on the external and internal surfaces, including the gastrointestinal tract, skin, saliva, oral mucosa, and conjunctiva. Bacteria overwhelmingly outnumber eukaryotes and archaea in the human microbiome by 2–3 orders of magnitude [7,8]. We therefore sometimes operationally refer to the microbial cells in the human body as bacteria. The diversity in locations where microbes reside in the body makes estimating their overall number daunting. Yet, once their quantitative distribution shows the dominance of the colon as discussed below, the problem becomes much simpler. The vast majority of the bacteria reside in the colon, with previous estimates of about 10 14 bacteria , followed by the skin, which is estimated to harbor
As we showed recently , all papers regarding the number of bacteria in the human gastrointestinal tract that gave reference to the value stated could be traced to a single back-of-the-envelope estimate . That order of magnitude estimate was made by assuming 10 11 bacteria per gram of gut content and multiplying it by 1 liter (or about 1 kg) of alimentary tract capacity. To get a revised estimate for the overall number of bacteria in the human body, we first discuss the quantitative distribution of bacteria in the human body. After showing the dominance of gut bacteria, we revisit estimates of the total number of bacteria in the human body.
Distribution of Bacteria in Different Human Organs
Table 1 shows typical order of magnitude estimates for the number of bacteria that reside in different organs in the human body. The estimates are based on multiplying measured concentrations of bacteria by the volume of each organ [9,10]. Values are rounded up to give an order of magnitude upper bound.
Although the bacterial concentrations in the saliva and dental plaque are high, because of their small volume the overall numbers of bacteria in the mouth are less than 1% of the colon bacteria number. The concentration of bacteria in the stomach and the upper 2/3 of the small intestine (duodenum and jejunum) is only 10 3 –10 4 bacteria/mL, owing to the relatively low pH of the stomach and the fast flow of the content through the stomach and the small intestine . Table 1 reveals that the bacterial content of the colon exceeds all other organs by at least two orders of magnitude. Importantly, within the alimentary tract, the colon is the only substantial contributor to the total bacterial population, while the stomach and small intestine make negligible contributions.
Revisiting the Original Back-of-the-Envelope Estimate for the Number of Bacteria in the Colon
The primary source for the often cited value of
10 14 bacteria in the body dates back to the 1970s  and only consists of a sentence-long “derivation,” which assumes the volume of the alimentary tract to be 1 liter, and multiplies this volume by the number density of bacteria, known to be about 10 11 bacteria per gram of wet content. Such estimates are often very illuminating, yet it is useful to revisit them as more empirical data accumulates. This pioneering estimate of 10 14 bacteria in the intestine is based on assuming a constant bacterial density over the 1 liter of alimentary tract volume (converting from volume to mass via a density of 1 g/mL). Yet, the parts of the alimentary tract proximal to the colon contain a negligible number of bacteria in comparison to the colon content, as can be appreciated from Table 1. We thus conclude that the relevant volume for the high bacteria density of 10 11 bacteria/g is only that of the colon. As discussed in Box 1, we integrated data sources on the volume of the colon to arrive at 0.4 L.
Box 1. The Volume of the Human Colon Content
This is a critical parameter in our calculation. We used a value of 0.4 L based on the following studies (see also S1 Data, tab ColonContent). The volume of the colon content of the reference adult man was previously estimated as 340 mL (355 g at density of 1.04 g/mL ), based on various indirect methods including flow measurements, barium meal X-ray measurements and postmortem examination . A recent study  gives more detailed data about the volume of undisturbed colon that was gathered by MRI scans. The authors report a height-standardized colonic inner volume for males of 97 ± 24 mL/m 3 (where the best fit was found when dividing the colonic volume by the cube of the height). Taking a height of 1.70 m for the reference man , we arrive at a colon volume of 480 ± 120 mL (where unless noted otherwise ± refers to the standard deviation [SD]). This volume includes an unreported volume of gas and did not include the rectum. Most recently, studies analyzing MRI images of the colon provided the most detailed and complete data. The inner colon volume in that cohort was 760 mL in total [16,17]. This cohort was, however, significantly taller than the reference man. Normalizing for height, we arrive at 600 mL total volume for a standard man. In order to deduct the volume occupied by gas, stool fraction in this report was estimated at ≈70% of colon volume leading to 430 mL of standardized wet colon content. Therefore, this most reliable analysis together with earlier studies support an average value of about 0.4 L.
We can sanity-check this volume estimate by looking at the volume of stool that flows through the colon. An adult human is reported to produce on average 100–200 grams of wet stool per day . The colonic transit time is negatively correlated with the daily fecal output, and its normal values are about 25–40 hours [18,19]. By multiplying the daily output and the colon transit time, we thus get a volume estimate of 150–250 mL, which is somewhat lower than but consistent with the values above, given the uncertainties and very crude estimate that did not account for water in the colon that is absorbed before defecation. To summarize, the volume of colon content as evaluated by recent analyses of MRI images is in keeping with previous estimates and fecal transit dynamics. Values for a reference adult man averaged 0.4 L (standard error of the mean [SEM] 17%, coefficient of variation [CV] 25%), which will be used in calculations below. Following a typical meal, the volume changes by about 10% , while each defecation event reduces the content by a quarter to a third .
The Total Number of Bacteria in the Body
We are now able to repeat the original calculation for the number of bacteria in the colon . Given 0.9·10 11 bacteria/g wet stool as derived in Box 2 and 0.4 L of colon, we find 3.8·10 13 bacteria in the colon with a standard error uncertainty of 25% and a variation of 52% SD over a population of 70 kg males. Considering that the contribution to the total number of bacteria from other organs is at most 10 12 , we use 3.8·10 13 as our estimate for the number of bacteria across the whole body of the "reference man."
Box 2. Concentration of Bacteria in the Colon
The most widely used approach for measuring the bacterial cell density in the colon is by examining bacteria content in stool samples. This assumes that stool samples give adequate representation of colon content. We return to this assumption in the discussion. The first such experiments date back to the 1960s and 1970s [20,21]. In those early studies, counting was based on direct microscopic clump counts from diluted stool samples. Later experiments [22,23] used DAPI nucleic acid staining and fluorescent in situ hybridization [FISH] to bacterial 16S RNA. Values are usually reported as bacteria per gram of dry stool. For our calculation, we are interested in the bacteria content for the wet rather than dry content of the colon. To move from bacteria /g dry stool to bacteria /g wet stool we use the fraction of dry matter as reported in each article. Table 2 reports the values we extracted from 14 studies in the literature and translated them to a common basis enabling comparison.
We note that the uncertainty estimate value takes into account known variation in the colon volume, bacteria density, etc., but cannot account for unquantified systematic biases. One prominent such bias is the knowledge gap on differences between the actual bacteria density in the colon, with all its spatial heterogeneity, and the measurements of concentration in feces, which serve as the proxy for estimating bacteria number.
What is the total mass of bacteria in the body? From the total colon content of about 0.4 kg and a bacteria mass fraction of about one-half [21,24], we get a contribution of about 0.2 kg (wet weight) from bacteria to the overall mass of the colon content. Given the dominance of bacteria in the colon over all other microbiota populations in the body, we conclude that there is about 0.2 kg of bacteria in the body overall. Given the water content of bacteria, the total dry weight of bacteria in the body is about 50–100g. This value is consistent with a parallel alternative estimate for the total mass of bacteria that multiplies the average mass of a gut bacterium of about 5 pg (wet weight, corresponding to a dry weight of 1–2 pg, see S1 Appendix) with the updated total number of bacteria. We note that this empirically observed average gut bacterium is several times bigger than the conveniently chosen “standard” 1 μm 3 volume and 1 pg wet mass bacterium often referred to in textbooks. The total bacteria mass we find represents about 0.3% of the overall body weight, significantly updating previous statements that 1%–3% of the body mass is composed of bacteria or that a normal human hosts 1–3 kg of bacteria .
The Number of Human Cells in a “Standard” Adult Male
Many literature sources make general statements on the number of cells in the human body ranging between 10 12 to 10 14 cells [26,27]. An order of magnitude back-of-the-envelope argument behind such values is shown in Box 3.
Box 3. Order of Magnitude, Naïve Estimate for the Number of Human Cells in the Body
Assume a 10 2 kg man, consisting of “representative” mammalian cells. Each mammalian cell, using a cell volume of 1,000–10,000 μm 3 , and a cell density similar to that of water, will weigh 10 −12 –10 −11 kg. We thus arrive at 10 13 –10 14 human cells in total in the body, as shown in Fig 1. For these kind of estimates, where cell mass is estimated to within an order of magnitude, factors contributing to less than 2-fold difference are neglected. Thus, we use 100 kg as the mass of a reference man instead of 70 kg and similarly ignore the contribution of extracellular mass to the total mass. These simplifications are useful in making the estimate concise and transparent.
An alternative method that does not require considering a representative "average" cell systematically counts cells by type. Such an approach was taken in a recent detailed analysis . The number of human cells in the body of each different category (by either cell type or organ system) was estimated. For each category, the cell count was obtained from a literature reference or by a calculation based on direct counts in histological cross sections. Summing over a total of 56 cell categories  resulted in an overall estimate of 3.7·10 13 human cells in the body (SD 0.8·10 13 , i.e., CV of 22%).
Updated Inventory of Human Cells in the Body
In our effort to revisit the measurements cited, we employed an approach that tries to combine the detailed, census approach with the benefits of a heuristic calculation used as a sanity check. We focused on the six cell types that were recently identified  to comprise 97% of the human cell count: red blood cells (accounting for 70%), glial cells (8%), endothelial cells (7%), dermal fibroblasts (5%), platelets (4%), and bone marrow cells (2%). The other 50 cell types account for the remaining 3%. In four cases (red blood cells, glial cells, endothelial cells, and dermal fibroblasts), we arrived at revised calculations as detailed in Box 4.
Box 4. Revised Estimates for the Number of Red Blood Cells, Glial Cells, Endothelial Cells, and Dermal Fibroblasts
The largest contributor to the overall number of human cells are red blood cells. Calculation of the number of red blood cells was made by taking an average blood volume of 4.9 L (SEM 1.6%, CV 9%) multiplied by a mean RBC count of 5.0·10 12 cells/L (SEM 1.2%, CV 7%) (see Table 3 and S1 Data). The latter could be verified by looking at your routine complete blood count, normal values range from 4.6–6.1·10 12 cells/L for males and 4.2–5.4·10 12 cells/L for females. This led to a total of 2.5·10 13 red blood cells (SEM 2%, CV 12%). This is similar to the earlier report of 2.6·10 13 cells .
The number of glial cells was previously reported as 3·10 12 . This estimate is based on a 10:1 ratio between glial cells and neurons in the brain. This ratio of glia:neurons was held as a broadly accepted convention across the literature. However, a recent analysis  revisits this value and, after analyzing the variation across brain regions, concludes that the ratio is close to 1:1. The study concludes that there are 8.5·10 10 glial cells (CV 11%) in the brain and a similar number of neurons and so we use these updated values here.
The number of endothelial cells in the body was earlier estimated at 2.5·10 12 cells (CV 40%), based on the mean surface area of one endothelial cell  and the total surface area of the blood vessels, based on a total capillary length of 8·10 9 cm. We could not find a primary source for the total length of the capillary bed and thus decided to revisit this estimate. We used data regarding the percentage of the blood volume in each type of blood vessels . Using mean diameters for different blood vessels , we were able to derive (S1 Data) the total length of each type of vessel (arteries, veins, capillaries, etc.) and its corresponding surface area. Dividing by the mean surface area of one endothelial cell , we derive a reduced total estimate of 6·10 11 cells.
The number of dermal fibroblasts was previously estimated to be 1.85·10 12 , based on multiplying the total surface area (SA) of the human body (1.85 m 2 ) by the areal density of dermal fibroblasts . We wished to incorporate the dermal thickness (d) into the calculation. Dermal thickness was directly measured at 17 locations throughout the body , with the mean of these measurements yielding 0.11±0.04 cm. The dermis is composed of two main layers: papillary dermis (about 10% of the dermis thickness) and reticular dermis (the other 90%) . The fibroblast density is greater in the papillary dermis, with a reported areal density, σpap. of 10 6 cells/cm 2 (with 100 μm thickness of papillary, giving 10 8 cells/cm 3 ) . The fibroblast density in the middle of the dermis was reported to be about 3·10 6 cells/cm 3 , giving an areal density of σret. = 3·10 5 cells/cm 2 . Combining these we find: Nder.fib. = SA·(σpap. + σret.) = 1.85·10 4 cm 2 (10 6 + 3·10 5 ) cells/cm 2 = 2.6·10 10 cells. After this 100-fold decrease in number, dermal fibroblasts are estimated to account for only ≈0.05% of the human cell count.
Our revised calculations of the number of glial cells, endothelial cells, and dermal fibroblast yield only 0.9·10 12 cells, in contrast to 7.5·10 12 cells in the previous estimate. This leaves us with 3.0·10 13 human cells in the 70 kg “reference man,” with a calculated 2% uncertainty and 14% CV. We note that the uncertainty and CV estimates might be too optimistically low, as they are dominated by the reported high confidence of studies dealing with red blood cells but may underestimate systematic errors, omissions of some cell types, and similar factors that are hard to quantify. In Fig 2, we summarize the revised results for the contribution of the different cell types to the total number of human cells. Categories contributing >0.4% in cell count are presented. All the other categories sum up to about 2% together. We find that the body includes only 3·10 12 non-blood human cells, merely 10% of the total updated human cell count. The visualization in Fig 2 highlights that almost 90% of the cells are estimated to be enucleated cells (26·10 12 cells), mostly red blood cells and platelets, while the other ≈10% consist of ≈3·10 12 nucleated cells. The striking dominance of the hematopoietic lineage in the cell count (90% of the total) is counterintuitive given the composition of the body by mass. This is the subject of the following analysis.