# Talk:Bacterial growth

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## Yo

Hey non-user here, don't know how the hell to work this site. Make sure you read item number 3 in the Phases section. There's some very unacademic statements being tossed around ("it's better to forget this"), thought you might want to fix that up. Love <3 Edit;another users: Omg exponential growth is really hard, all those doing biotech and bio stuff, dont give up........ love frank

```— Preceding unsigned comment added by 98.228.92.241 (talk) 04:08, 13 August 2012 (UTC)
```

## Mathematical modelling

The graph is certainly incorrect if "B" is supposed to look like exponential growth. Michael Hardy 22:49, 22 May 2004 (UTC)

It says:

At exponential phase, bacteria are reproducing at their maximum rate; therefore, their number increases during this phase. It is a period of exponential growth.

This is contradictory! It cannot be growing at its maximum rate while it's growing exponentially. See exponential growth. While something is growing exponentially, its growth rate is always increasing; it's never at its maximum growth rate. I can't help suspecting this of being a case of thinking that "exponential growth" merely means extremely or surprisingly rapid growth. Besides, the description makes it sound like the growth rate is jointly proportional to the present size and the amount by which the size falls short of the carrying capacity. That would make it approximately exponential in its early phases, but nowhere near exponential when the growth rate is maximum. Michael Hardy 20:36, 15 Jul 2004 (UTC)

If the number of bacteria is increasing exponentially, and each bacterium is reproducing at maximum rate, then the rate of increase can be increasing exponentially, no problems at all. RobertStar20 22:38, 2 Nov 2004 (UTC)

If what was meant was the each bacterium separately is reproducing at maximum rate, then the article is very unclear. Moreover, if each bacterium separately is reproducing faster at time t than at any other time, then one would expect slow per capita growth a later times, and therefore the growth rate is not exponential. In exponential growth, the per capita growth rate remains constant. If that varies, then growth is not exponential. Michael Hardy 22:44, 2 Nov 2004 (UTC)
If all the individual bacterium are separately reproducing at maximum rate, then the whole colony is at its maximum rate at that point in time, i.e. it is incapable of reproducing any faster. However, I agree that the per capita growth rate at later times will be slower, so it is indeed not technically exponential. Looking at the exponential growth page, maybe the logistic function is what it really is... but isn't this a bit too mathematical perhaps? We need a word which means increasing at an increasing rate, but not necessarily exponentially. As for the graph being incorrect, it's a log y-axis, so an exponential curve will become straight... if only it were actually exponential :-). [Unrelated question: do your comments on this page automatically appear on my talk page or what?] RobertStar20 23:19, 2 Nov 2004 (UTC)

I'm not entirely happy with the way this now reads; I'd like to see something more explicit about the mathematical model before such a phrase as "exponential growth" is used in a way that makes it appear to be meant literally. But maybe no one who knows this material has worked on this article. Michael Hardy 21:07, 8 Nov 2004 (UTC)

Bacteria definetly grow exponentially. The example of growing bacteria are used constantly to introduce, reinforce and evaluate understanding in high school math courses of exponential functions. Each bacteria has a period during which it will divide. Obviously, conditions such as space, food supply, heat, light, etc... affect this rate, so we assume those factors are constant. Suppose a given strain of bacteria, let's call it B1, divides every 4 hours. Assuming we start with say, 10 bacteria, and the conditions don't change, then you will have table as follows:
``` Time (h)    Bacteria Count" 0           10 4           20 8           40 12          80 16          160 20          320 24          640 .           . .           . .           .
```
``` This growth is modelled by the equation B = 10 x (2 ^ h/4),
where B is the number of bacteria
and h is the number of hours
(x means multiply, ^ means exponent, / means divide)
```

So, the discussion is hopefully resolved with the accepted mathematical notion: Bacteria divide at a constant rate, hence their population grows exponentially.

How could that resolve the issue when the article says they do NOT grow exponentially? Michael Hardy 00:12, 12 December 2005 (UTC)
what you added to the article was utter nonsense. The point at which growth is fastest, after which it slows down, cannot be a time when it is growing exponentially. Michael Hardy 00:18, 12 December 2005 (UTC)
Sorry you feel that way. Perhaps i didn't explain it clearly? Or maybe I don't understand the confusion. Maybe someone could help me format the table above...or could you at least explain what you mean by utter nonsense? Do you mean my assumption that bacteria division is constant?

I just tried to reread your page, and it referenced the exponential growth page, which says, "Examples of exponential growth Biology. Microorganisms in a culture dish will grow exponentially, at first, after the first microorganism appears (but then logistically until the available food is exhausted, when growth stops). "

If we assume the division of bacteria occurs at a constant rate (environment, other factors are constant) then the number of bacteria in any population will grow exponentially. It's the same for many types of populations, from rabbits to humans. If you assume that there is a constant steady growth rate, then the number in a population grows exponentially over time.

Or put another way, without external stressors, a population size will grow exponentially over time.

Have I missed something? This concept is as old as Malthus at least, who, I believe, pointed out that a population grows exponentially but resources tend to grow linearly and hence each population will tend to exhaust it's resources, inevitably.

I'd sure like to understand better if there is something I'm missing, or something I'm not explaining well. I thought the confusion was whether or not bacteria divide exponentially. They don't, or at least, as far as i understand, the rate of division is constant for given environmental factors. But because they divide, they double there number every time, which gives rise to an exponential function (base 2).

I appreciate you taking the time to respond to my comments. Please remember I am very new to Wikipedia, and if I break ediquette I don't mean to. Jess.

http://www.cellsalive.com/ecoli.htm "LOG PHASE: Once the metabolic machinery is running, they start multiplying exponentially, doubling in number every few minutes."

http://www.abc.net.au/science/experimentals/stories/s1168046.htm "Bacteria double in numbers about every 20 minutes - that's exponential growth!"

Yes, you have missed something. What you missed is what this present article says. Bacteria do grow exponentially under some circumstances, but this article is entirely explicit that those are not the circumstances considered here. Michael Hardy 00:33, 6 January 2006 (UTC)
I can't believe you're being so difficult. I just looked again: it says "exponential phase" is when they're growing fastest. Obviously a misnomer. They're growing approximately exponentially only when they're growing much more slowly. Why don't you read what this article actually says? Michael Hardy 00:35, 6 January 2006 (UTC)

4 years on and the graph is still misleading... Since this graph represents the behaviour of many millions of bacteria, all transitions should be continuous (i.e. smooth) so the lag to log should curve to a straight line, the log to lag should curve to an approximately horizontal line, before curving down to the death phase line (i'm not sure what maths governs this phase). I'm no biologist, so my expertise is limited certainly, but Michael Hardy was correct to question the graph on the basis of its maths, atleast. Perhaps we could ask the user who created the graph image to edit it.Hai2410 (talk) 17:17, 20 February 2010 (UTC)

### Determination of maximum growth rate(viagra)

First of all this is what I understand of it anyways. Once a bacterial population enter exponential phase as seen on the graph a theoretial maximum specific growth rate can be derived from from the graph.

(The difference between the theoretical and actual growth rate is determined by the concentration of limiting nutrient which is an essential growth factor necessary for bacterial growth that is consumed by bacteria before exhausting any other of the essential nutrients in the media.) The actual maximum specific growth rate or true maximum specific growth rate is determined in a chemostat. see http://mic.sgmjournals.org/cgi/reprint/151/10/3153 (for ref which states the reason they are growing approximately exponentially) They therefore could grow exponentially but they don't for these reasons.

Determining maxium specific growth rate is a two step calculation.

Step one: Determine the doubling time (generation time) the amount of time taken for the amount of cells in a population to double. (Also called doubling time) for the population. The time taken for the y value (bacterial cell number or turbidity of culture) to double. If the value doesn't increase extrapolate the line and read off your values.

Step two:

Derive maximum specific growth rate

maximum specific growth rate=Ln 2/doubling time

For the sake of the calculation, the fact that it is an approx value is close to the actual value is only going to make a small difference in the calculation of growth rate. (follow this methodology and repeat it a number of times to reduce your error). Bacteria have different maximum specific growth rates depending on the experimental conditions such as the media used if not stressed diverting the energy used for growth into non-growth processes into adaptation I think the only variable is the concentration of limiting nutrient which changes depending on the media used.

If you would like to determine the actual growth rate you need to establish a bacterial culture in a chemostat.

Alter the dilution rate of the chemostat such that the bacterial population (as measured by culture turbidity, or cell number cfu/ml) remains constant over time.

Oh yeah dilution rate = flow rate (the rate of addition of media to the chemostat) divided by the volume of the chemostat culture. also see paper maths explained better http://mic.sgmjournals.org/cgi/reprint/151/10/3153

Compare to values obained for batch culture and volia you have calculated your actual maximum specific growth rate and validated your result using two methods. The results agree (I've done it myself)

So exponential phase or is where a close approximation of exponential growth is used to calculate a close approximation of doubling time which is in turn used to derive a close approximation of maximum specific growth rate as obtained by a graph monitoring bacterial growth in batch culture is a method of determining growth.

A graph displaying exponential growth and does not look all that different from the one displayed in the figure depicting a bacterial population experiencing log growth occuring during log phase associated with this article. However it is not quite exactly strictly speaking true as true log growth cannot be derived because of the dependency on concentration of limiting nutrient in the media Lilypink (talk) 18:03, 24 January 2008 (UTC)

Actually this is part of a much larger discussion about what happens in nature and what happens in culture; the question might be phrased: "What is acclimation and what is evolution?" It is a problem inherent in typological thinking. As a point of fact, bacteria are never (it seems) adapted to an environment in which every nutrient is present completely in excess. Instead, they have all sorts of throttles on their growth, which can be removed by various means. The 'deeper' the throttle, the more difficult to remove and the more difficult to reestablish. So there are all sorts of little things that a bacteria can do to adapt to slightly more rich environs for a short time, but over time it becomes further and further adapted to a regularly rich environment. Eventually it will start picking up mutations, some more routine and predictable than others (like cassette mechanisms), to more or less permanently alter its maximum doubling rate. The shortest term up and down regulation we probably never see in the lab, unless we produce microscale nutrient patches in a microfluidics device (see the work of F. Azam, J. Seymour, or R. Stocker). The medium scale is probably what we describe as lag phase, where the growth rate is less than we will see later in the culture. People who work on this know that max. growth rate is actually highly dependent not only on strain and media and temperature, but on inoculation size and observable population density. Anyway, you can create a system in which there is no limiting nutrient - every nutrient is in excess - and try to measure the growth rate, but this rate keeps changing as the organisms continue to adapt. Anyway, you do have periods of true log growth, with a fixed doubling time, to be sure. You just have to observe at the appropriate temporal and spatial scales. Bckirkup (talk) 15:26, 25 January 2008 (UTC)

I think "Bacterial Growth Curve" should redirect to this page. It doesn't seem to exist as a page on its own, but it would make sense for it to point here. No? —Preceding unsigned comment added by 24.47.186.143 (talk) 17:37, 2 April 2008 (UTC)

As I understand it, exponential growth refers to the population, which doubles at a constant rate. An alternative term is "logarithmic growth" and this is defined in the Oxford Dictionary of Biochemistry and Molecular Biology as "when the number of cells, or the cell mass, increases logarithmically (exponentially) with time. The rate of increase at any time is proportional to the number of cells, or cell mass, present." The diagram with the growth phases colored in various shades of blue is a little inaccurate, as the period between lag phase and the onset of exponential growth is marked as log phase, rather than lag phase. Log phase is only the portion of the semi-log graph that is a straight line. Tim Vickers (talk) 17:07, 14 September 2009 (UTC)
I think that the term "logarithmic growth" should not be used in a general encyclopedia like Wikipedia and I replaced it in some articles. No one but microbiologists will understand it because the log is the Inverse function of the exponential, and many processes with a very slow growth N(t)~log(t) are called logarithmic elsewhere (e.g. Binary search algorithm). No one would use "quadratic growth" and "square-root growth" synonymously, either. --Tinz (talk) 15:22, 30 May 2010 (UTC)
As a mathematician, I agree that the term "log phase" is an awful misuse. "exponential phase" makes a lot more sense. But we are not in a position to change the terms people use.
Another point I would make is that Michael Hardy's complaint that the growth cannot be maximal because it is increasing is merely a matter of choosing the right definition. The growth rate is best defined by something like the inverse of the time it takes the number of organisms to double. This growth rate remains constant in the ideal exponential growth.

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