The units and research projects covered on this page are:

• 1. What is meant by "steady state"?
• 2. Looking for the Realm of the Steady State:
     Exploring the log-phase or exponential growth phase of a culture of E. coli
• 3. Finding the Realm of the Steady State
• 4. Gross morphological aspects of E. coli and its steady state
• 5. The enzymological steady state in E. coli
• 6. Cell structures and the steady state in E. coli
• 7. Further projects, some perhaps worthy of doctoral research projects.

INTRODUCTION. What is meant by "steady state"? Let's start out by looking at this from a physicist's point of view. Suppose that in front of you is an "off" toaster. It is in steady state of one sort: over time it doesn't change. The filaments inside remain at the same cool temperature and it remains dark. Now you switch the toaster to "on", and what you will see for a few moments is that the filaments start glowing brighter and brighter and get hotter and hotter. This is NOT steady state as changes are taking place. However, within a few seconds, the hot filaments get no hotter, and no brighter as they have reached another sort of steady state, one that some might call dynamic equilibrium. This can be diagrammed as shown. The horizontal portions of the temperature curve indicate where "steady state" exists - where the temperature (and nothing else, for that matter) is changing. You thus see that there are two types of steady state - one in which the toaster sits equilibrated with room temperature and nothing is happening, and another in which current is flowing through and heating the toaster but the temperature has reached equilibrium and is unchanging.

Similarly in cells we can imagine various realms of the steady state. One such might be that the cell is dead, and disregarding decay the cell just sits there like a lump and doesn't change. Another realm might be dormancy, if the type of cell in front of us is one that can be dormant. Suppose it is a cell in a seed or in a bacterial spore. While the seed is almost in steady state (some very, very low levels of metabolism continue), the spore just sits there unchanged from minute to minute and day to day waiting for the right conditions to come along to induce germination.

Then there is the realm of hot toaster steady state in cells - that of dynamic equilibrium. This is that state when metabolism is on-going and yet the overall aspect of the cell remains unchanged - it sits there imbibing nutrients and putting out wastes - all at a constant rate.

However, cells that are in dynamic steady state, also are growing. So let us imagine a growing culture of E. coli. While all of the cells are metabolizing, some big ones are about to divide, others are in the process of dividing, and other small ones are new daughter cells ready to begin growing into big ones. This is obviously a very dynamic situation as lots of changes are going on. But let's now imagine that our culture is in a state of dynamic equilibrium. While the number of cells is changing (increasing), the statistically average cell remains unchanged. The average cell size is constant over time; the average respiration rate per cell is constant, the average amount of DNA per cell is constant; any and all aspects of the average cell remains constant. That is the realm of the dynamic steady state in a cell culture.

For more than a century, bacteriologists have looked at the population growth curves of their bacteria and have given names to various parts of those curves. Over these many decades they have generally assumed that the cells were in dynamic steady state during that portion called the "log phase" or "exponential phase." This assumption was important because it was the way to compare cells that were subjected to varying growth conditions. In the next section, you will see how wrong their assumption was! Those who do the following experiments should be forewarned that they will be labelled iconoclasts (dictionary anyone?) and considered very skeptically by most biologists, who have been raised on "log-phase" dynamic equilibrium doctrine.

It is amazing simple to overthrow the icon of the "log-phase" doctrine - so simple that it is a wonder why it hasn't been done long ago. Maybe because it is such a strong idol, a great deal of quantitative research in cell biology has not be done - because following that idol's dictum makes the work nearly impossible. And how easy is it? Look!

All you need to do is start a liquid culture of E. coli (or any other organism), and do what bacteriologists have been doing for decades - only while they followed one parameter of growth, you will follow TWO!

If the cells are truly in dynamic steady state, the slopes of the log-phase portions of the graph should be identical. So, over time, let's follow the two most common parameters - increasing absorbance (turbidity) of the culture and the number of cells. You will have three possible outcomes, and only the one shown in the middle below would indicate true steady state.

Thus, for your first project, you should run this experiment in your lab. It is very important that you do this because your teachers will most likely be very skeptical of this whole idea, and only experimental proof will convince them that this matter holds promise for further research. (It cannot be emphasized too strongly that the fact that the time-honored log-phase growth is NOT steady state will be taken skeptically. It has long been an icon of bacteriology. Remember the word 'iconoclast'? It might be further mentioned that it seems European bacteriologists hold more strongly to the concept that log-phase equals steady state, than do people elsewhere. The concept of "once you've seen one E. coli cell you've seen them all" is deeply imbedded in bacteriology - but without proof!)

There are some wise scientists who have realized that a strain of E. coli is not always the same under all conditions of growth. They have thus devised a tool to force their cultures into a prescribed steady state of growth. They use either a chemostat or a turbidostat. These are devices that slowly add sterile medium into the brew, and allow an equal amount of the culture to overflow into a drain. Thus the faster the rate of liquid flow-through, the faster the cells must grow and divide so that their numbers can keep up with the dilution rate. Thus if you adjust the flow-through rate to a half-time of 30 minutes, the culture's doubling time will become 30 minutes also. (Of course, once your flow-through rate exceeds the culture's maximum doubling speed, the culture cannot keep up and will slowly be diluted out and down the drain.) (A chemostat adjusts the culture so that the concentration of a specific chemical remains unchanged; the turbidostat keeps adding new medium so that the turbidity of the culture remains constant. Commercially available "fermenters" usually have all the capacities built in.)

Finding the Realm of the Steady State. Your data from the previous section will show you that log-phase cells are in fact changing over time. As to why, that can be left to subsequent experimentation. If turbid log-phase cultures are not in steady state, then where is that steady state, IF it exists at all? Conceptually, were you to have an ocean of aerated medium and you inoculate that ocean with just one E. coli cell, that cell should quickly attain a state in which it is growing and metabolizing as fast as it can. Soon it divides into two cells, and each of those should have essentially no impact on each other in that vast ocean of medium. Those two cells ought also grow and metabolize at a rate equal to that of the first cell. For many generations, the concentration of the cells should be so low that they have no impact on each other. All during that time they should - conceptually speaking - be in steady state growth. At some point they do start having an impact on each other and on the growth medium. Metabolic waste products build up to inhibitory levels, food sources are being noticeably depleted - and that includes the concentration of dissolved oxygen, which is at best about 10 parts per million (0.3 mM). That's a very low concentration! Compare it with the glucose you had added at 0.5% (28 mM). Perhaps this is a hint that the rising population of cells is being able to use the oxygen at a faster rate than new oxygen molecules can be dissolved into the medium. Or perhaps some other factor begins to impinge upon the cells causing them to go out of steady state.

Experiments: You might start with an E. coli culture at about 100 cfu/ml of well aerated medium. In the experience of this author, swirling is not the best oxygenator. Sparging (bubbling) with an aquarium bubbler is far superior - although foaming can be a problem. But you are an advanced young scientist, and such problems are mere hurdles for you to overcome by using your creativity. In such a sparged system, you might place an electronic oxygen probe and follow the [O₂] over time versus the turbidity. Of course, in the early stages you will have no detectible turbidity for your spectrophotometer to measure. (Another hurdle!) If you are not a lazy student, you might want to follow the cfu/ml also using plate counts, or you could follow the population density using a Coulter Counter, providing you have fitted the device with the proper size oriface. By either of these two ways, you can see how your culture is growing when it is below visible turbidity.

Gross morphological or intrinsic aspects of E. coli and its steady state. In this unit we shall be determining the values of various gross morphological parameters of the cells when they are in steady state, which you have derived in the previous unit. Those characteristics might be the average cell size, the average cell shape, the cells' specific gravity, etc.

If you have been fortunate enough to use a Coulter Counter, you may have also been able simultaneously to follow the average cell size. (These electronic devices often are set up to both count and size.) If you had done that, you will have been able to determine one morphological parameter and see when it was unchanging - an indicator that the cell was probably in steady state. (You may be interested to know that dormant E. coli are much smaller than ones that are growing rapidly. By 'much' let's just say that they have a volume of less than 10% that of the fast growing cells.

Another morphological determination might be doing an average cell length to average cell width study.

Probably one of the easier and rather inexpensive intrinsic properties you can measure is that of the overall specific gravity of E. coli. This is done by equilibrium density gradient centrifugation (isopycnography, for short!) using sodium bromide (NaBr) and your E. coli cells (ref 1). There are generally only two hurdles here to overcome: one is having to order and await the arrival of solid NaBr (you will need at least a pound of it!), and the other is being able to concentrate the cells from your "invisible" cultures. A minor hurdle to overcome in regard to concentrating your cells is that, unless you "stop" them, the cells will continue to grow, change and whatever while you are concentrating them. Once in the NaBr, they almost instantly die. It has been said that formalin is a good "stop" agent. (Formalin is formaldehyde gas dissolved in water and is what many people call "formaldehyde".) Make your sample to 0.01% formalin. Oh, there is a minor hurdle here also: when you measure out your sample from the culture, it might find itself going anaerobic as that sample is away from the sparging air - remember that a few seconds to an E. coli cell is like hours to a person. Perhaps it would be best to add the formalin to the graduated cylinder first, and then pour the sample into the cylinder so that the formalin will kill and "stop" the cells as they are poured in. (Along the way, you will have to show whether or not formalin changes the specific gravity of the cells, or makes them sticky and glop together.)

One of the wide open areas in microbiological biochemistry is that almost all of what is known is that either a gene is on or off - and not how much of the enzyme is present - just that it is present. This author and others cracked that door open with regard to lactase when they showed that only in highly dilute cultures was lactase constant per cell (ref 2). Previously, as told to us by two former graduate students working in the lab alongside a small group of Nobel laureates, these "wisemen" had tried to correlate the amount of lactase present in cultures of transposition mutants (their lac-operons were situated in different places on the E. coli chromosomes), but they could not make heads or tails out of their data. We finally came to the conclusion that they had erred in their thinking that the statistically average E. coli cell remained the same throughout what they considered was "log-phase" growth (start remembering the 'icon'!). Donache showed initially that they were very wrong even when gross morphology of the cells were inspected: the cells averaged smaller and smaller as the "straight" log-phase line continued (ref 2). That's when this author came on scene and was asked to see if some corroboration could be made of his findings - but on an enzymatic level. Within days, it was shown that as a culture proceeded up its log-phase growth curve, the amount of lactase per cell increased - their lac-operons were being turned more and more "on" (also ref 3). The log-phase icon was beginning to crack badly!

Using this as a starting point, you might wish to determine the steady state concentrations of other enzymes - such as alkaline phosphatase (AP), LDH, and others. Knowing this, you can then use this as a tool for detecting the effects of other factors on that enzyme's concentration. With AP, you might want to ascertain the effect of exogenous inorganic phosphate on intracellular AP concentrations, and/or the effect of exogenous glucose-6-phosphate, for example.

You now see that you are opening the door onto a whole new realm - the effect of changing environmental conditions (stresses) on gene expression. While some of this is known, what is known is only qualitatiive. You can now do quantitative studies.

Cell structures in steady state in E. coli. Starting with this unit, which should be only for very advanced students, only rough ideas for research projects will be given. In that vein, let's list some of the structures you might measure under various steady state conditions.

1. The amount of and/or the thickness of the various cell boundary components - walls and membranes.
2. The ribosome content of cells. In E. coli the percentage of rRNA varies between 10% and 30% of the dry weight of the cells. What influences the ribosome content? Is it strictly growth rate as has been suggested?
3. Quantify the flagella/cell. To this author's knowledge this has never been reported - and certainly not under various conditions of steady state.
4. The amount of and molecular weights of lipopolysaccharide (LPS) on wild strains of E. coli (do not attempt this with the usual laboratory strains - they are "rough" and have no LPS!). Your findings will have implications for immunologists, pathologists and vaccine makers.
5. Do the same with regard to the capsular polysaccharides of wild strains of E. coli.

Further possibilities for research. The name of one of the major "games" of life is called "CONTROL". The tool of using steady states in your quantifications of various cell parameters will suddenly allow much more precision to be made in seeing how various factors affect the cell - especially keeping mind on how genetic expression might be affected in a quantitative way.

For example, if the dormant steady state is always a constant, and the dynamic steady state is variable depending on the food supply, then this might tell us something more about the dormant state - what mechanisms have evolved to provide the dormant cell with "the right stuff" for long-term survival and revival (the fixed set of preparations for recovery that will be used to usher the cell into that dynamic, non-steady state of germination).

Along the lines of the cell's transitioning or ramping up and down between the static and dynamic steady states, the genome must be involved. As once shown, there seems to be a rationale for the layout of the genes on the E. coli chromosome in which the placement assists in making more or less of the various gene products (ref 4). But from the cell's perspective the placement of its genes is like having them written in stone as they have only the rarest of possibility of jumping to another position. Nevertheless, the genes do move and selective advantage quickly singles out the positions that work best. Thus, in a way, the current map of E. coli (and Shigella and Salmonella) is a sort of steady state condition that is a best fit for the current world. How fast can a transposed lac-operon, for example, move back to its "usual" position? Would it move there? This is a sort of in vitro/in vivo evolution experiment!

- - - R E F E R E N C E S - - -

Who are some of the authors, below? This is being mentioned because some of these authors were students at the time of doing this published work. Hopefully, your seeing what has happened to others will be inspirational to you. At the end of these references, the students' names are listed and what they were doing approximately 20 years later.

1. Vermeulen, Carl W. 1982. Equilibrium Density Gradient Centrifugation for Introductory Biochemistry. J. Chem. Ed. 59: 1079-1080. (Return to your reading site.)
2. Cho, Sung-Ae, Gail Gasparich, Darren Sledgeski, Carol Ezzell, and Carl Vermeulen. 1984. The realm of the steady state in Escherichia coli. Biochem. Biophys. Res. Commun. 124: 625-628. (Return to your reading site.)
3. Masters, Millicent, Peter Moir, Renata Spiegelberg, J. Howard Pringle, and Carl Vermeulen. 1985. Is the Chromosome of Escherichia coli Differentiated Along Its Length with Respect to Gene Density or Accessibility to Transscription? In "The Molecular Biology of Bacterial Growth" Schaechter, M., Neidhardt, F. Ingraham, J., and Kjeldgaard, N., eds. (In honor of Ole Maaløe.) Jones & Bartlett Publ, Inc. Boston. pp. 335-343. (Return to your reading site.)
4. Snellings, Karla, and Carl Vermeulen. 1982. Non-Random Layout of the Amino Acid Loci on the Genome of Escherichia coli. J. Molec. Biol. 157: 687-688.(Return to your reading site.)

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