Growth index of culture formula

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How to calculate the growth rate of bacteria??

Barry G. In the s—s, determination of bacterial growth rates was an important tool in microbial genetics, biochemistry, molecular biology, and microbial physiology.

The exciting technical developments of the s and the s eclipsed that tool; as a result, many investigators today lack experience with growth rate measurements. Recently, investigators in a number of areas have started to use measurements of bacterial growth rates for a variety of purposes.

Those measurements have been greatly facilitated by the availability of microwell plate readers that permit the simultaneous measurements on up to different cultures. Only the exponential logarithmic portions of the resulting growth curves are useful for determining growth rates, and manual determination of that portion and calculation of growth rates can be tedious for high-throughput purposes.

Here, we introduce the program GrowthRates that uses plate reader output files to automatically determine the exponential portion of the curve and to automatically calculate the growth rate, the maximum culture density, and the duration of the growth lag phase. GrowthRates is freely available for Macintosh, Windows, and Linux. We discuss the effects of culture volume, the classical bacterial growth curve, and the differences between determinations in rich media and minimal mineral salts media.

This protocol covers calibration of the plate reader, growth of culture inocula for both rich and minimal media, and experimental setup. As a guide to reliability, we report typical day-to-day variation in growth rates and variation within experiments with respect to position of wells within the plates. Growth rates have long been used in microbiology to quantify phenotypic properties. Experimental evolution studies have often used growth rates as a measure of fitness Hall ; Dykhuizen and Dean In this century, determination of growth rates fell out of common use as exciting, high-throughput molecular tools for characterizing bacteria were developed.

Classical methods of growth rate determinations are both tedious and labor intensive. The introduction of automated microtiter plate readers has brought high-throughput analysis for growth rate measurements and has resulted in a renewed use of growth rate data in a variety of areas including regulation of gene expression Swint-Kruse L, personal commununication and diverse areas of microbiology including antibacterial activities of biological fluids Feher et al.

The application of most interest to evolutionary biologists is likely a measure of fitness, including fitness cost of streptomycin resistance Paulander et al. Before the advent of plate readers, cultures were grown in Erlenmeyer flasks or tubes, in constant temperature rooms or in water baths, and on shakers or rotating drums to provide sufficient aeration.

At intervals of a few minutes, a sample would be sterilely removed, transferred to a cuvette in a spectrophotometer, and the apparent absorption optical density [OD] of the culture would be measured and recorded.

Typically, the OD versus time points would be plotted on a semilog graph paper, and those points that appeared to fall along a straight line would be used to calculate the growth rate. At best, one could measure the growth rates of about 20 cultures at a time, and those measurements would require the full-time attention of an investigator over a period of most of the day. Following the collection of data, calculation of the growth rates—whether manually or by entering all the data into a computer—was tedious and required extra time.

Now, the investigator inoculates cultures into wells in a microtiter plate, puts the plate into a reader, enters a few commands, and returns a few hours later to find all of the data neatly recorded in an electronic file. In the meantime, the plate reader has measured the OD in each of the wells at frequent intervals. All that remains is to use that data to obtain the desired growth rates. It is at this final stage that problems begin to arise, and many investigators are unsure how to calculate growth rates and unsure which of the time points should be used.

Effective use of that program, however, requires understanding the important aspects and limitations of growth rate measurements. This protocol and our program GrowthRates are intended for laboratories that use standard plate readers such as the BioTek and Spectra-Max readers.

There are dedicated instruments such as the Bioscreen reader that are designed specifically for measuring growth rates.

Those considerably more expensive instruments incorporate their own proprietary software. Others have discussed the issue of analyzing the growth data from microtiter plate readers and have written programs to facilitate that analysis Holowachuk et al. An approach similar to ours was described Breidt et al. An approach that uses a Microsoft Excel spreadsheet with an embedded macro has been described Warringer and Blomberg and is available upon request to the authors. This approach includes the nonlinear portion of the ln OD versus time curve and attempts to correct for the nonlinear relationship between ln OD and cell number at high cell densities.

This correction, however, will depend upon the geometry of the detector and on the particle size and so may not be applicable to different instruments or to larger microorganisms such as yeast. None of the earlier articles, however, provides an explicit, step-by-step protocol for determination of bacterial growth rates.

Toussaint and Conconi provide an explicit protocol for measuring growth rates in yeast; however, much of that protocol is very specific to yeast and is less generally applicable than is the protocol mentioned later. They describe an algorithm to calculate growth rates and lag times, but details of the basis of calculating growth rates and lag times are not provided. A perl script to implement their algorithm is available upon request, but the utility of that script depends on knowing how to use perl, whereas the compiled program GrowthRates requires no special computer skills.

The purpose of a growth rate measurement is to determine the rate of change in the number of cells in a culture per unit time. This requires estimating the cell density at a series of time points. Whether done by a modern plate reader or by the classical shake flask and spectrophotometer approach, the number of cells per milliliter of culture is estimated from the turbidity of the culture that is measured by the plate reader or spectrophotometer and is estimated as OD.

Spectrophotometers measure the fraction of light that is absorbed by a solution and report that as absorbance units. The absorption of a solution depends on the wavelength of the light, so the typical unit is reported as A , where the subscript indicates the wavelength in nanometers and A is the negative log of transmittance the fraction of incident light that is detected.

However, a bacterial culture is not a solution; it is a suspension of bacterial cell particles. Light is not as much absorbed as it is scattered, and there is only a limited range over which the measured absorbance is proportional to the number of cells per milliliter.

For that reason, it is preferable to refer to OD rather than to absorbance. Typically, OD is determined at a wavelength of nm, in which case, we measure OD If we want to infer the true culture density from OD , it is essential to determine the range over which OD measurements are directly proportional to culture density.

For most purposes, however, the absolute culture density is unimportant. When OD is measured in a classical spectrophotometer, the sample is put into a cuvette with a fixed light path, typically 1. When OD is measured in a plate reader, the length of the light path within which light scattering occurs is determined by the volume in the well.

Thus, the same culture that gives an OD of 0. Figure 1 shows a typical growth curve. A lag phase where growth is absent is followed by an acceleration phase during which the growth rate increases until a constant growth rate is achieved during the exponential phase. Most of the time, we are only interested in the growth rate during the exponential phase, which is the rate reported by the GrowthRates program. In some cases, we may also be interested in the maximum OD that is reached or in the duration of the lag phase.

GrowthRates reports both of those parameters, but it reports the lag phase by extrapolating the slope of the exponential phase back to the initial OD; that is, it treats the lag as though no growth occurred until the end of the lag phase at which point growth becomes instantly exponential. Although unrealistic, this approach allows comparisons of relative lag times without having to account for details of the acceleration phase.

Typical bacterial growth curve: ln OD is plotted versus time. The points that fall along the straight line represent the exponential growth phase. Here, the lag time is shown as the time to enter exponential phase and really includes the time during which growth accelerates. The plate reader should be capable of maintaining a constant temperature and should be able to shake the plate between readings. Step 1 only needs to be done once, but it is important to calibrate your system.

Step 1. This step is needed only if it is important to relate OD to absolute cell density. If you use both rich media typically yellow or brown in color and minimal media typically colorless , this step should be performed for cultures in both media.

Grow a culture to midexponential phase to ensure maximum cell viability. Make a serial 1. However, 1. Using a well that contains the same volume and medium as you will subsequently use in all experiments, set the absorbance to read zero.

Determine the OD of each dilution in the plate reader using the same volume as you will subsequently use in all experiments. This requires only one reading, not a time series. Determine the reproducibility of growth rates across wells. Some people have observed that cultures in the outer edge wells grow slightly faster than those in the inner core wells.

This property may depend upon the particular plate reader, the volumes in the wells, etc, but it is important to know about the uniformity across the plates in your setup. If you find significant differences between edge and core wells, you may not want to use the edge wells. Inoculate identical cultures into all wells except a control well that contain uninoculated medium and determine the growth rates. Repeating the experiment on three different days provides a good measure of the variation with respect to well position as well as a good measure of the day-to-day reproducibility of absolute growth rates.

The duration of the lag phase and the shape of the curve during the acceleration phase depend on the physiological state of the cells in the inoculum, the fraction of viable cells in the inoculum, and the handling of the inoculum cultures. Especially if you intend to monitor and interpret the duration of the lag phase, it is important to grow the inoculum cultures consistently. Inocula should be grown at the same temperature as the temperature at which the growth rate will be measured.

Step 2. Rich medium, overnight cultures. Inoculate rich medium LB, Mueller-Hinton broth, 2xYT [all available from Difco] or other undefined medium and grow the culture overnight to saturation. This approach can result in a high proportion of inviable cells and viable cells that are in a physiological state that requires considerable adaptation before the culture starts to grow.

The result tend to be long with variable lag times. Rich medium, overnight oxygen-limited cultures. Inoculate 10 ml of rich medium in a tightly sealed 15 ml centrifuge tube. Allow the culture to stand overnight without shaking.

The culture density will be limited by the available dissolved oxygen, and as a result, there will be fewer dead cells, and viable cells will be in a physiological state that allows rapid resumption of growth. The result is shorter and more consistent lag times. Minimal medium, saturated overnight cultures.

Minimal, or defined, media such as M9 Difco include only the resources required for the particular strain to grow. Typically, this means a buffered solution containing a carbon source, a nitrogen source, inorganic phosphorus, trace elements, and any required amino acids, nucleosides, and so forth. Undefined supplements, such as yeast extract, tryptone, casamino acids, and so forth, are not included in minimal media. If those resources are provided in excess, cultures will grow to saturation.

Care should be taken, when possible, to avoid dramatic shifts in carbon sources to avoid diauxic growth due to catabolite repression. For instance, E.

I want to compare the growth rate of each Pseudomonas aeruginosa. generation time by Frederich Fiddel equation and calculate growth rate mathematically As the OD of the culture increases you will need to dilute culture samples before. growth of a batch culture the following equation holds: in the culture, v is the number growth rate constant, and 7 is the mean generation time (in (Novick, ; Powell, a); it cannot then be assumed that the index of viability, a, is.

Population Growth Vs. Replacement Reproduction vs. Zero Pop.

Barry G.

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Empirical sigmoidal models have been widely applied as primary models to describe microbial growth in foods. In a case study, the performance was compared of two models based on empirical parameters and two models based on biological parameters. These models were fitted to experimental data for Lactobacillus plantarum in six isothermal conditions. Both are the main parameters of the mathematical models used to describe microbial growth over time for a single set of environmental conditions, and such models are called primary models Whiting and Buchanan, The temperature is an important variable in food microbiology, since it varies during the production and distribution chain modifying the microbial growth rate and suitability. In this context, the estimation of the primary model parameters must be done with exactness, for each growth temperature, leading to secondary models that represent well the influence of the temperature on the primary models parameters Whiting and Buchanan,

Good agreement was demonstrated between specific rate of ribosome synthesis and specific growth rate of Acinetobacter calcoaceticus. A new molecular-biology-based method was developed to determine the specific growth rate of a distinct microbial population in an environmental sample by measurement of the specific rate of ribosome synthesis. When exposed to chloramphenicol, the bacterial cells continue to generate preS rRNA while the mature 16S rRNA remains constant 9 , excluding low rates of degradation. Monitoring preS rRNA synthesis has been used in previous work 2 , 5 , 8 , 9 as an indicator of growth response, and preS rRNA synthesis has been shown 5 to dramatically increase compared to the sum of preS and mature 16S rRNA levels. RT-RiboSyn expands on this concept to determine a specific rate of ribosome synthesis by using a primer that specifically targets a population of interest. The optical densities of the four cultures were measured periodically at nm by using a spectrophotometer, and the specific growth rates were determined for the time of sample collection. RNA was extracted from the subsamples by using the phenol-chloroform method 7 , followed by purification with an RNAqueous kit Ambion, Inc. A trend line was fitted to these data, and the equation was determined. Using the slope of the equation, the ribosome doubling time was determined.

Bacteria reproduce at regular intervals. An example might be every 20 minutes.

Introduction: It is often necessary in experimental research to quantify the dividing capabilities of cells when investigating manipulations of the cells or their environment. The growth of cell populations can be modelled by assuming each cell divides into two, and the rate of growth depends on the length of the cell cycle. However, the simplicity of this idea may lead to misinterpretations in some circumstances.