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One of life's inevitable disappointmentsone felt often by scientists and artists, but not only by themcomes from expecting others to share the particularities of one's own sense of awe and wonder. This truth came home to me recently when I picked up Michael Guillen's fine book Five Equations That Changed the World (4) and discovered that my equationthe one that shaped my scientific careerwas not considered one of the five.

I met this equation in the winter of 1952-1953 when Emanuel Suter, the bacteriology and immunology instructor in the integrated Medical Sciences program at Harvard Medical School, brought three very young colleagues to help teach the instructional laboratory of this innovative course. In this way we 20 privileged students met Boris Magasanik, Marcus Brooke, and H. Edwin Umbarger and were plunged into bacterial physiology.

They had designed a laboratory experience to introduce us to contemporary issues and cutting-edge techniques in 1950s bacterial physiology. As I remember, one objective was to study diauxic growth by varying the limiting amount of glucose added to a minimal medium containing a secondary carbon source and inoculated with an enteric bacterium. A second objective was to construct the steps in a biosynthetic pathway by examining the abilities of various compounds to satisfy the nutritional needs of auxotrophic mutants. Both experiments required measuring the growth of bacteria, the former as a kinetic process.

For me, encountering the bacterial growth curve was a transforming experience. As my partner and I took samples of the culture at intervals to measure optical density and plotted the results on semilogarithmic paper, we saw, after the lag period, a straight line developing...beautiful in precision and remarkable in speed. As the line extended itself straight-edge true, I imagined what was happening in the flaskliving protoplasm being made from glucose and salts as the initial cells (Klebsiella aerogenes, they were called then) grew and divided. The liquid in the flask progressed from having a barely discernible haze to a milky whiteness thick with the stuff of life, all within a very brief Boston winter afternoon. Mutably specific autocatalysis, the physicist Erwin Schrödinger had declared a few years earlier (28), was the defining characteristic of living systems, and I had just witnessed the working out of the mathematical statement of that property, dN/dt = kN (where N is the number of cells or any extensive property thereof, t is time, and k is the first-order rate constant [in reciprocal time units]).

I had never before seen such a clear display of autocatalysis. Its mathematical elegance and simplicitybut more importantly, its invitation to exploreaffected me profoundly. The first-order rate constant k in the growth equation seemed to me the ideal tool by which to assess the state of a culture of cells, i.e., the rate at which they were performing life, as it were. I elected to pursue my Ph.D. studies with Boris Magasanik, studying the molecular basis of diauxic growth. Over the ensuing half-century, close analysis of growth curves was to be a central feature of my work, as I followed my intense curiosity (read obsession) about the processes that form living matter from salts and sugar. Catabolite repression, the growth rate-related regulation of stable RNA synthesis, the isolation and use of temperature-sensitive mutants in essential functions (particularly aminoacyl-tRNA synthetases), and the molecular responses of bacteria to heat and other stressesall these studies depended on inferences and deductions from the growth behavior of bacterial cultures.

For anyone interested in the synthesis of protoplasm, bacteria are the system to study (reviewed in reference 17). With four billion years of practice they have perfected the art of growing in many environments, and they outclass all other known forms of life in their rate of metabolism geared for autocatalysis. The first-order rate constant k is most conveniently expressed in minutes or hours for bacteria rather than in days, months, or years (as for most eucaryotes). Little matter that k is not a constant for long during batch cultivation of bacteria in the laboratory or fermentation vat or that its value may vary continuously in any given natural population. Suffice it that k for bacteria is very large, probably the largest for all Earth creatures.

Of course, these organisms are appropriately studied for properties other than growth. Bacteria have evolved a dazzling array of capabilities along with rapid growth. As a group, they utilize almost any chemical source to harness energy for growth and maintenance and have mastered photosynthesis as well. They assess their chemical and physical environment with great sensitivity. They move with purpose. They communicate with each other. They employ devilishly clever strategies for colonizing eucaryotic hosts, both plant and animal. (It is through this adeptness that most humans have come to know and respect bacteria.) The spore-formers in particular are famous for enduring long periods of nongrowth under conditions hostile to life (high or low temperature, dryness, and atmospheric pressures from a vacuum to many bars of hydrostatic pressure). Even non-spore-forming bacteria differentiate from a growing form to a form remarkably able to survive prolonged periods inimical to growth.

Each of these properties is the focus of contemporary studies, intensified in many cases by useful hints supplied by knowledge of a score or more of completely sequenced bacterial genomes. In particular, the quest to understand the molecular details of the conversion of bacterial cells from growth to stationary phase has attracted the attention of scores of bacterial physiologists, as Roberto Kolter has highlighted in his essay in this series of Guest Commentaries (8). The multiple, coordinated processes by which bacteria achieve a nongrowing state are proving a rich ground for molecular genetic, biochemical, and ultrastructural analyses.

There is no question, however, where emphasis was placed by bacterial physiologists during much of the past half century. Rapid growth and the ease with which it can be measured in bacteria provided both the subject matter and the background for most studies in bacterial physiology from 1950 onward. Many talented bacteriologists contributed to this interest, but it was probably Jacques Monod's seminal studies in the 1940s (e.g., references 12 and 13) that inspired modern studies on bacterial growth. Development of the theory of continuous culture by Aaron Novick and Leo Szilard (19), the stimulating musings of Arthur Koch (e.g., reference 6), and detailed studies by many others can be traced to Monod's precise mathematical formulation of the growth of bacterial cultures. Roberto Kolter (8) is correct when he credits Monod with fostering growth studies. There was no question about Monod's view. Hear him, for example, in 1949 (13): "The study of the growth of bacterial cultures does not constitute a specialized subject or branch of research: it is the basic method of Microbiology." (Emphasis supplied.) His own classic analysis had convinced him that "...the growth of bacterial cultures, despite the immense complexity of the phenomena to which it testifies, generally obeys relatively simple laws, which make it possible to define certain quantitative characteristics of the growth cycle...The accuracy, the ease, the reproducibility of bacterial growth constant determinations is remarkable and probably unparalleled, so far as quantitative biological characteristics are concerned."

If Monod founded what we might call the Paris school of growth physiology (with scores of postdoctoral and sabbatical fellows from the United States and around the world), the Danish microbiologist Ole Maaløe was not far behind in organizing a Copenhagen school, similarly peopled by many Americans and other foreigners (reviewed in reference 10). There are few outcomes of research on bacterial growth in the second half of the 20th century that do not derive directly or indirectly from the inspired leadership that flowed from these two cities.

Did Monod's views divert attention from the stationary phase and delay serious study of the developmental processes preparing cells for survival during nongrowth? I doubt it. I suggest the opposite is truethat the attention given by Monod to the usefulness of growth analysis in bacterial physiology and biochemistry hastened the day when nongrowth could be meaningfully studied. To recognize the right questions and pursue them required an understanding and an information base gained from growth studies. The physiology of nongrowth is not the absence of the physiology of growth. Understanding both the phenotypic and genotypic processes involved in stationary-phase physiology involves building on what we understand about growth physiology.

What do growth physiologists study, and what have they learned by peering into growth flasks and chemostats the past 50 years? Much of the work has been done with Escherichia coli and related enteric bacteria (summarized in reference 18), but many of the findings have been found to hold generally among procaryotes.

(i) Differential gene expression in response to environmental signals leads to a cellular enzyme mélange unique to each particular environment. When growing at constant temperature with surplus nutrient, bacterial cells synthesize all of their protoplasmic constituents at near-constant differential rates and divide at a particular cell mass. Growth under constant conditions results in each cellular component increasing by the same proportion in each interval of timethe state called balanced growth (1). Often this state is maintained only transitorily because of rapid utilization of nutrients, accumulation of metabolic by-products, and increasingly inadequate rate of gas exchangeall of which induce changes in the differential rates of expression of many genes. In most instances, detrimental changes in the environment are met with changes in gene expression and hence, enzymic makeup, that permit continued growth, if only at a reduced rate. These adaptive patterns of unbalanced growth are responsible for the famous capacity of bacteria to grow under a variety of ambient conditions. It was only the advent of two-dimensional polyacrylamide gel electrophoresis that opened the eyes of bacteriologists to the magnitude of changes in the cell's protein complement (see references 5, 9, 21, 29, 30).

(ii) Certain major phenotypic characteristics are coordinated with the absolute growth rate and are completely independent of the chemical nature of the medium. Cell size and gross chemical composition (protein, RNA, DNA, carbohydrate, and lipid) are dramatically monotonic functions of the steady-state rate of growth at any given temperature. Except for the very lowest of growth rates, the faster the growth rate, the larger the cells, the richer they are in ribosomes and tRNA, and the greater their level of transcription and translation factors, including aminoacyl-tRNA synthetases (15, 17, 26). (Throughout the lower quarter of the growth rate range of E. coli, an irreducible minimum number of ribosomes is maintained [6]). No description of the average bacterial cell of a given species is possible unless one specifies the growth rate (17).

(iii) Over a range of growth rates at a given temperature, the rates of chain elongation of proteins, DNA, and RNA vary little, as does the time required between replication termination and cell division. From these observations, one can infer that the cell's enzymatic machinery for replication, transcription, and translation usually operate at near saturation (10, 20). Combined with the fact that the cellular levels of ribosomes and associated enzymes vary directly with growth rate, the somewhat constant rate of ribosome function makes great biological sense. Bacterial cells do not generally vary the rate of protein synthesis by changing how fast ribosomes work but by adjusting the number of ribosomes to the task at hand. Given the fact that the protein-synthesizing machinery makes up half or more of the cell's mass during fast growth, the economy of being able to reduce the rate of making this machinery during slow growth is quite evident (discussed in reference 17). At very low growth rates, the cells maintain a complement of nonfunctioning ribosomes that spring into action upon enrichment of the environment.

(iv) When environmental conditions change, forcing a reduction or permitting an increase in growth rate, the pattern of macromolecule synthesis follows a consistent pattern. On enrichment, the order of increase in rates of synthesis is RNA, then protein, and finally DNA. Frequency of cell division is the last parameter to increase. In this fashion, the cell rather quickly adopts the size and macromolecule composition characteristic of a rapidly growing cell. Upon nutrient restriction, the order of decrease in rates of synthesis is the same, with the net accumulation of RNA ceasing almost instantly, followed by declining rates of protein and DNA synthesis and of cell division. Again, the cell responds in such a way as to assume the phenotype of a small, slow-growing cell as rapidly as possible (14, 16, 24).

(v) Specific molecular mechanisms coordinate the expression of large sets of unlinked genes during growth. The number of these regulons (sets of unlinked operons controlled by a single regulator) and modulons (sets of operons and regulons controlled by a common regulator) is very large. Prominent among those related to growth rate per se are catabolite repression (23) and the stringent response (2), both of which contribute to the economy of metabolism during growth. Catabolite repression determines by a variety of mechanisms (including, but not restricted to, cyclic AMP and its regulatory protein, cyclic AMP receptor protein) the extent to which genes encoding catabolic enzymes are expressed in the presence of their inducing substrates. It is a device that in effect enables the cell to optimize use of available carbon and energy sources. The stringent responsethe granddaddy of global-control systemsdirectly or indirectly has dominion over a large portion of the cell's genome, restricting the synthesis of the entire translation machinery and other major cellular components during periods of limiting charged tRNA or constrained energy supply. The stringent response, whatever else it accomplishes, contributes to the ability of the cell to negotiate the transition between fast and slow growth.