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Chapter 84

Regulation Beyond the Operon

FREDERICK C. NEIDHARDT and MICHAEL A. SAVAGEAU

 

INTRODUCTION

In the first edition of this work appeared a chapter entitled "Multigene Systems and Regulons" (19). This chapter is worth a visit by anyone interested in the progress that has occurred since 1987 in the area of multigene systems.

Eight years ago the focus was on regulons and stimulons —terms already in widespread use to designate a group of operons controlled by a common regulator (a regulon), and a group of operons responding to a given environmental stimulus irrespective of regulatory mechanism (a stimulon). There was already an appreciation of the complex regulatory circuits that were beginning to emerge from studies on multigene networks in Escherichia coli. This complexity was fully acknowledged and treated with optimism and even some chauvinistic microbiological pride. The overall thrust of the 1987 chapter was the usefulness of considering multigene networks as stimulus-response systems, growing out of the fact that many global gene systems were first recognized as cellular responses to an environmental change. Viewed this way, the task for the investigator was one first of recognizing what genes are coregulated as part of a cellular response system, and then of discovering the elements of the system, including the attributes of the environment that are sensed by cells; the nature of the cellular sensor; the signals that are generated and the transducers that carry these signals; and finally the nature and mechanism of action of whatever (protein) is the ultimate regulator of gene expression. Finally, the cellular functions of the gene products forming the response were to be discovered, and the actions of modulators that feed back on the response system to assure a return to the prestimulus condition were to be sorted out.

This formalism was expected to be useful in guiding experimental studies and in providing a framework for the presentation and discussion of results. To some extent this has been the case. For example, many "two-component regulatory systems," which involve the autophosphorylation of a sensor kinase followed by phosphorylation of a response regulator, have been usefully analyzed as stimulus-response systems. These include osmoregulation (chapter 77), nitrogen regulation (chapter 86), phosphate regulation (chapter 87), and oxygen regulation (chapter 95). Likewise, for heat shock (chapter 88), the SOS response (chapter 89), and response to pH shift (chapter 96), the stimulus-response formalism has been useful. On the other hand, the notion of a stimulus-response system has limits; it does not carry one far toward understanding the diversity of regulons, their complex nature, their interactions, and their molecular control.

In this chapter we review the regulatory organization of genes into operons, regulons, and modulons and discuss the complex patterns of gene response to environmental stimuli involving these three regulatory units. We then describe how completing the "parts catalog" (genes and proteins) of E. coli will permit the possibility of global transcriptional and translational monitoring of gene expression in this organism. We encounter two questions of central interest in gene regulation: how the cell chooses particular modes of regulation for different operons and regulons, and how in situ function of regulons in the intact cell can be successfully modeled. Finally, we indicate the appropriateness at this time of employing techniques of systems analysis to approach these two questions.

 

OPERONS, REGULONS, AND MODULONS

 

Operons

The operon is a hallmark of the prokaryotic cell. This mode of gene organization achieves for bacteria a simple solution to the problem of coregulating genes of related function, such as those that encode the proteins of a metabolic pathway. On the other hand, this obviously successful strategy—most genes of enteric bacteria are clustered into multicistronic operons—has its limitations. First, some cellular processes involve too many genes to be accommodated in a single operon. The translation machinery of the cell, for example, consists of at least 150 gene products (the RNAs and proteins of ribosomes, tRNAs, aminoacyl-tRNA synthetases, and the translation initiation, elongation, and termination factors) directly involved in making protein from amino acids. Coordinating their synthesis is essential to the overall efficiency of growth, yet linking even the genes of those products needed in equal stoichiometry within a single operon would be awkward, if not impossible. Other examples abound, as in the processes of cell division (chapter 101), chemotaxis (chapter 73), adjustment to temperature shifts (chapters 88 and 98), energy transduction (chapters 17, 18, through 19), and differentiation into non-growth states (chapters 93 and 106).

A second limitation is that virtually every complex bacterial process involves a number of genes that must be subject both to independent regulation and to coordinated control. This situation arises commonly, e.g., in the ensemble of genes encoding catabolic enzymes of sugars, amino acids, and other nutrients that are potential sources of carbon and energy. These genes must be independently induced by the presence of their substrates in the medium, but must also be subject to global repression by a premium substrate such as glucose (chapter 85). Likewise, the branched and interlocking pathways of central metabolism contain many examples of enzymes whose levels must be responsive to individual signals, but which must also be coordinated with its metabolic neighbors.

For these two reasons, and others, levels of organization above the operon exist. In fact, the diverse physiological demands created by the wide-ranging environmental conditions under which bacteria can grow or survive would seem to dictate that regulation at levels beyond the operon must be a characteristic of virtually every bacterial gene. Increasingly, evidence supports this notion.

 

Regulons

Regulon organization presents a level of control above the operon and permits coordinated control of operons that each have their own unique controls. Nevertheless, induction of the individual operons of a regulon is not tightly coordinated; both the extent and time course of induction vary from operon to operon within a given regulon. This observation is easily made for large regulons—those with many operons—and is probably true for most. In the heat shock (HtpR) regulon, for example, there is a wide range in the induction ratio of the individual gene products. Thus, a given temperature shift brings about a 5- to 7-fold induction of some heat shock proteins and a 70-fold or greater induction of others (20). Likewise, in the Lrp (leucine response protein) regulon, metabolically and physiologically quite diverse genes are modulated in noncoordinate, parallel, and antiparallel fashion (chapter 94). Observations such as these indicate that for a given concentration of their shared active regulatory protein, the promoters of individual operons are poised at different degrees of saturation.

Regulons, it turns out, are extraordinarily diverse and exhibit as much diversity in the control of their expression as do independent operons. Some are controlled by regulatory proteins that stimulate transcription, e.g., PhoB (chapter 87). Some are controlled by regulatory proteins that inhibit transcription, e.g., LexA (chapter 89). Some are controlled by regulatory proteins that inhibit the transcription of some genes and stimulate the transcription of others, e.g., Lrp (chapter 94). Others are controlled by alternative sigma factors that program RNA polymerase to recognize promoters of genes of the particular regulon, e.g., sigma-32 (chapter 88).

Likewise, the modes of activation of these different sorts of regulators are diverse. Induction can occur by covalent modification (phosphorylation or dephosphorylation) of a positive or negative regulator, e.g., PhoB and NtrII (chapter 86), by destruction of a negative regulator (LexA), by elevating the cellular level of a regulator (sigma-32), or by changing its protein conformation by ligand binding, e.g., cyclic AMP-receptor protein (chapter 85). In one of the most intriguing regulons, the stringent response network, the regulatory protein (if there is one) has proven so elusive as to avoid discovery (chapter 92).

 

Modulons

It would have been naive to imagine that the approximately 1,000 operons of the enteric genome would turn out to be organized as some few hundred regulons, in the manner depicted in Fig. 1A. And, indeed, the true regulatory circuitry is far more complex; levels of organization above the regulon have been discerned for some time. The basic situation shown schematically in Fig. 1B, in which some or all of the genes of two different regulons are controlled by a second, overarching regulator, is quite common. The term modulon has been coined to designate a group of independent operons subject to a common regulator even though they may be members of different regulons. Modulons, thus, can be viewed as units of so-called global regulation.

Examples of modulons abound in the area of energy metabolism (see Table 1 in chapter 95). What may be considered the granddaddy of modulons is the set of genes encoding catabolic enzymes that are subject to control by the cyclic AMP-CAP regulatory complex. Many of these genes are organized as clusters (regulons) of a few operons subject to individual control by separate inducing ligands.

Astute observors will note that, as shown in Fig. 1B, not all members of a regulon have to be under the control of the same global regulator (R₃). The same figure also shows that an operon can be a member of a modulon without being a member of any regulon. This nomenclature is confusing to many, and can be avoided by using the general term "regulon" for any set of operons controlled by the same regulatory protein, whether or not subsets of these genes belong to other regulons. The concept of a modulon as a set of coregulated regulons is useful, however, in forcing general awareness that ultimately the regulation of each gene must be described by a complete circuit diagram rather than simply by a word.

 

STIMULONS

 

Multiple Elements of Stimulons

The term stimulon has been used for some time to denote an ensemble of genes responding to a defined stimulus, without regard to their regulatory organization or mechanism of induction (51). Raising the temperature activates the Htp (RpoH) regulon of E. coli (chapter 88) and restricting the supply of phosphate activates the Pho regulon (chapter 87), but many operons other than those under control of sigma-32 are induced by heat, and many dozens of genes other than those activated by PhoB (the Pho regulon regulator) are induced in cells starving for phosphate. In fact, in the latter example approximately 145 proteins are induced greater than threefold by phosphate starvation, while only about 38 genes are known members of the PhoB regulon (chapters 87 and 115; unpublished observations). Most responses of bacterial cells to even a simple environmental stimulus are complex, often involving multiple regulons and independent operons.

Stimulons, it should be emphasized, are defined operationally and not surprisingly are extremely heterogeneous in character. A fairly simple case would be the induction of two separate regulons following direct activation of their independent regulators by a single environmental agent. A more complex and probably more common stimulon is one in which one regulon is turned on by environmental activation of its regulator, and other regulons are turned on by secondary signals generated within the responding cell. Something of this sort must be the case when cells deplete the phosphorus in their medium; immediate induction of the PhoB regulon is accompanied almost simultaneously by induction of many other regulons and operons as the cells begin to differentiate into stationary phase. These include the heat shock (HtpR, sigma-32) regulon, the leucine response (Lrp) regulon, the LexA-controlled SOS regulon, and the OxyR-controlled regulon (chapter 115 and unpublished observations).

Appproximately as many proteins—137—are repressed threefold or greater during phosphate starvation as are induced. It has been easier to understand the induced proteins, because one is drawn to the notion that they equip the cell to scavenge phosphate and obtain it from organic sources. But what is the significance of the repressed proteins? Does their repression contribute directly to the cell’s ability to adapt to the new circumstance, or is the contribution indirect, simply making more of the cellular protein-forming capacity available to produce the induced emergency proteins? Whichever is the case, attention should be paid to the repressed proteins, and their repression should be regarded part of the stimulon.

 

Global Study of Stimulons

If one is to understand fully how cells respond to their environment, specific data on global gene expression will be needed. Fortunately, acquisition of such data is possible now and promises to be increasingly feasible in the near future. Two approaches to global measurements are being developed, one measuring translation and the other transcription. These approaches are complementary.

Global Translational Mapping.

The monitoring of global patterns of synthesis of individual proteins originated with the introduction in 1975 of two-dimensional polyacrylamide gel electrophoresis to resolve complex mixtures of proteins (25, 26). By presenting a more or less complete picture of the cell’s complement of proteins, two-dimensional gels encourage the construction of a protein inventory of the functional elements of model cells such as E. coli. It has not yet been sufficiently recognized, however, that two-dimensional gels are not simply an additional powerful tool for reductionist studies. By appropriate applications of radioactive labeling protocols, two-dimensional gel analysis permits exploration of the integrated operation of the intact cell and its changing patterns of gene expression. A unique feature of such studies is that they can provide detailed, provocative information about regulation of the ensemble of individual proteins of the cell, independent of knowledge of their biochemical or genetic identity.

The technology for global studies of this sort has continually improved since 1975. In the 1970s it took three months and a materials cost of $2,000 to do one global response experiment gathering the data for 200 protein spots. In the 1990s, a single person working for 1 month, at a materials cost of $100 per experiment, can gather the data for close to 1,000 protein spots.

Monitoring the integrated system behavior of genome expression during cellular adaptations can be accomplished by this approach, even if spot behavior is unsupplemented by other information. But making sense out of the collected spot behavioral data is aided greatly by knowledge of the biochemical identity and genetic origin of the individual protein spots. The value of identifying protein spots on two-dimensional gels has been so obvious that many person-years (part-time) have been devoted to making such identifications and providing them to the E. coli community. This was the birth of what was first called the E. coli gene-protein index, which was a referencing of the biochemical and/or genetic identity of individual protein spots. The 6th edition of what is now called the gene protein database appears as chapter 115 in this book. Most of the protein identifications derive from work aided by the community of E. coli investigators in the form of gifts of purified proteins, mutant strains, and cloned genes that have allowed identifications, one by one, of protein spots as known proteins or the products of known genes. Early progress was rapid, but rather soon the inventory of available purified proteins of E. coli became exhausted, and the analysis of defective or overproducing mutants proved tedious and sometimes gave ambiguous results. At the past rate of progress, many decades would be necessary to identify even the products of known genes, and with no hope of identifying all gene products by this approach.

Fortunately, thanks to three new technical advances, the pace of identifications will be increased dramatically, with the real possibility that the protein products of all E. coli genes will ultimately be identified on two-dimensional gels. The new approach depends neither on purification of individual proteins nor on mutagenesis of individual genes; importantly, it is likewise independent of prior knowledge of the growth conditions needed for synthesis of a given protein (references are found in chapter 115 and reference 28). The new identification process begins by removing, one by one, the chromosomal inserts from the Kohara phage library and splicing them into one or another plasmid engineered to permit complete transcription of both strands of the chromosomal segment. These plasmids contain promoter sequences from phage T7 and phage T3 in opposite orientations. This transcription occurs in host cells that can be prevented from transcribing their own chromosomal genes and can be induced to form either the T7 or the T3 RNA polymerase. Proteins made from these transcripts can be radioactively labeled and thereby distinguished from the other cellular proteins. The labeled proteins expressed from the chromosomal fragment can then be resolved on two-dimensional gels and assigned coordinates on the reference gel image for this organism. Each expressed protein spot can then be matched to its encoding DNA on the segment by comparing the molecular weight and the isoelectric point of the protein (as measured by its gel location) with those predicted by the nucleotide sequence of the segment.

In this way a Genome Expression Map will gradually be produced that displays the two-dimensional gel location of every protein encoded by the genome and matches each protein spot to its gene. In addition, each protein of the cell will be sorted into general metabolic classes as they are identified. The Genome Expression Map and the annotated physiological information about the cellular proteins will be published periodically and maintained as a frequently updated, publicly accessible, electronic database (see chapter 115).

Global Transcriptional Mapping.

The monitoring of global patterns of gene transcription is of more recent origin. This technique was first described in 1993 (1) and grows directly out of the E. coli genome sequencing work of the Blattner laboratory—work, incidentally, that has been vital to the global translational mapping program as well. This technique employs hybridization to measure mRNA levels. Total RNA is extracted and purified from cultures growing in the condition of interest and in a reference condition. From the dried RNA pellet, ³²P-labeled total cDNA is made by using the random hexamer priming method. The labeled cDNA is then hybridized to an encyclopedia of DNA dot blots, using the same blots to probe the experimental and reference cDNA after an alkaline stripping procedure. The radioactivity hybridized is measured using a direct beta particle-measuring blot analyzer.

The key to the procedure is the encyclopedia of DNA dot blots. In work published so far, the test battery has consisted of DNA from hybrid lambda phage vectors containing overlapping chromosomal fragments ranging from 9 to 21 kilobases. Since these fragments may contain a dozen or so genes, induction of some genes may be masked by repression of others and therefore result in no net increase or decrease in the intensity of a particular blot. In spite of this limitation, impressive results have been obtained: many new heat shock genes have been disclosed, and many other environmental stimuli have been examined, including limitation for phosphate or ammonia, anaerobiosis, osmotic shock, entry into stationary phase, induction by isopropyl-β-d-thiogalactopyranoside (IPTG), and growth in the gnotobiotic mouse gut (1, 2). In the future the technique will be greatly improved by the construction of a larger and finer dot blot encyclopedia, one consisting of 4,000 to 6,000 ordered clones the size of a gene. In fact, PCR (polymerase chain reaction)-amplified gene fragments are a feasible alternative once the complete genome sequence is known.

A major feature of this approach is that the detection, cloning, and mapping of coregulated genes are achieved in a single step. This feature will not be fully available for the global translational mapping approach until the Genome Expression Map (described above) is available.

The global translational (two-dimensional protein gel) approach and the global transcriptional (cDNA dot blot) approach are complementary to each other. The information provided by each will be necessary, not just to provide confirmatory information, but to provide a combination of data about the regulation of gene expression through the distribution of the cell’s RNA polymerase molecules and the allocation of the cell’s protein-synthesizing capacity.

 

QUESTIONS RAISED BY DIVERSE GENE CIRCUITRY

 

Properties of Different Modes of Gene Regulation

The diversity of control mechanisms operating on regulons, and the diversity of the circuitry of regulons and modulons, bring the investigator face to face with one of the most perplexing questions of molecular physiology: are the different patterns of regulation of gene expression functionally meaningful; i.e., is each uniquely suited to the particular demands of the system it regulates? This question is as appropriately addressed to the control of regulons as it is to the control of operons. Important though it is, it is a question about which most contemporary studies remain silent.

The silence surrounding this issue is understandable. The traditional reductionist approach to the molecular physiology of the enteric bacterial cell has been enormously successful. In the past 8 years more regulons have been discovered and more of their regulatory genes have been cloned than in all previous years. The problem is that the information gained, interesting and necessary as it is, keeps high the preoccupation with elucidating further the molecular elements of each operon and regulon. This preoccupation is likely to continue for some time in the future, because there is a great deal to be learned.

Paradoxically, it is the success of this powerful reductionist paradigm that reveals its weaknesses. Through the genome sequencing project and the effort to identify all the gene products of this organism (chapter 115) we shall soon have a complete parts catalog for E. coli. An extensive inventory of the regulons of this organism and their mode of regulation will be added to the already impressive database on individual operons. Yet, none of this information will by itself contribute an answer to the question of the meaning of the diversity of gene circuitry.

 

Integration of Gene Regulation

The complexity of stimulons requires sorting out the different cellular components responding to an environmental stimulus as well as the mode of control of the constituent regulons. But a corollary to this situation is that no regulon operates in isolation: all participate in a cellular network that creates added demands and restrictions on the behavior of each regulon.

Examples of regulon interaction are abundant. Lowering the temperature not only induces the cold shock stimulon, it also represses the heat shock (HtpR) regulon and brings about a transient relaxed-like state of synthesis of transcription and translation proteins (12). Raising the temperature not only induces the heat shock regulon, it also represses the synthesis of proteins involved in the cold shock response (13) and brings about a transient stringent state (16). Limiting the phosphate supply, as we have noted, not only induces the Pho regulon, but also induces hundreds of other genes, including those of the heat shock regulon, beside repressing approximately 137 genes (defining repression arbitrarily as a threefold reduction in differential rate of synthesis). Only a few of these repressed proteins have been identified. Limitation for an amino acid can, under certain conditions, induce not only the stringent response, but also the heat shock regulon, along with the relevant amino acid biosynthetic pathways (9). Finally, complete starvation for any essential nutrient will eventually trigger all the regulons involved in preparing the cell for stationary-phase metabolism.

These examples emphasize the fact already mentioned: no regulon operates in isolation. Therefore, analysis of the dynamic properties actually displayed by a given response system—a necessary measurement to approach a systems analysis of the regulon’s control—will have to be performed in vivo in concert with all interacting gene networks. The context is important.

Therefore, besides the question raised by the diversity of control mechanisms and the circuitry of regulons, there is a second, related, question: can one integrate the molecular information for individual operons and regulons into models of the living cell and make quantitative predictions regarding systemic behavior, i.e., predict accurately the stimulon response to any given environmental stress?

Neither of the two important questions raised in this section can be approached by the standard (reductionist) methods of molecular biology. Both require an analysis of system behavior, a task requiring ideas and methods that until recently have rarely been employed in molecular biology.

In the next three sections, we outline an approach to biochemical systems analysis that has successfully dealt with questions of integrative molecular biology.

 

USEFUL ABSTRACTION OF GENE REGULATION

To evaluate the functional significance of the many mechanisms and circuits of gene regulation, it is necessary first to pare each pattern down to its essentials and to ignore irrelevant detail that would otherwise obscure the theme. This is an art. At any given point in the development of our understanding, what is required may be more detail or more abstraction. The following sections represent abstractions of fundamental features of gene regulation that have proved significant in the elucidation of basic rules that govern their design.

 

Unit of Transcription

Figure 2A shows a stylized operon (39, 41). Gene sequences encode proteins having effector functions (enzymes, transporters, structural elements, etc.) or regulator functions (repressors, antiterminators, etc.) and in some cases both. Delineator sequences (promoters and terminators) mark the beginnings and ends of transcriptional units. Modulator sequences (operators, initiators, enhancers, silencers, etc.), which are associated with delineator sequences, provide recognition sites for specific molecules that are capable of modulating the rate of synthesis of mRNA. Regulators (repressors, activators, antiterminators, complementary RNAs, etc.) interact with modulator sequences, alone or in concert with other macromolecules and low-molecular-weight ligands, to control the rate of mRNA synthesis. Modifiers (inducers, corepressors, etc.) are low-molecular-weight metabolites whose increase in concentration represents a biochemical signal that causes gene expression to increase (induction) or decrease (repression).

Figure 2B is another stylized view of the unit of transcription (11, 31, 33). It focuses attention on processes that are important in manifesting expression: mRNA synthesis, mRNA degradation (and dilution within growing cells), protein synthesis, protein degradation (and dilution). The horizontal arrows indicate the flow of material. Each pool of material at this level is subject to the conservation of mass: the difference between the aggregate rate of appearance and the aggregate rate of disappearance of any molecule must equal the rate of change in its concentration (Kirchhoff’s node law). The vertical arrows that terminate on a horizontal arrow represent catalytic or modifier influences upon the indicated process. These vertical arrows represent the flow of information rather than the flow of material. Figure 2C represents a further simplification in which the individual names of molecular species have been replaced by a systematic symbolic nomenclature that facilitates mathematical representation and analysis.

 

Modes of Control

The mode of control used to govern any process can be manifested in one of two alternative forms, as illustrated in Fig. 3 (34, 41). In one (the negative mode), the process is spontaneously active and control is exercised by a restraining element (repressor, proterminator, etc.); in the other (the positive mode), the process is constitutionally inactive and control is exercised by an activating element (activator, antiterminator, etc.). In either case, the effectiveness of the regulatory element can be modulated by a low-molecular-weight modifier (inducer, corepressor, etc.). It is important to note that the two modes represent alternative mechanisms for realizing the same physiological function (induction or repression).

The bias (on or off) associated with a transcript delineator is intimately related to the mode of control. If control is to involve the positive mode, then the delineator must be biased off. The positive element acts to overcome this built-in bias and increase expression in a regulated fashion. If control is to involve the negative mode, then the delineator must be biased on. The negative element then acts to overcome this built-in bias and decrease expression in a regulated fashion.

 

Expression Characteristic

The physiological consequence of gene regulation is typically a sigmoidal curve representing different steady-state levels of expression (fraction of operators free, concentration of mRNA, concentration of protein, metabolic flux) as a function of stimulus intensity (concentration of inducer, concentration of corepressor). This is referred to as the expression characteristic of the transcriptional unit (11, 31, 33). It is most conveniently depicted as three asymptotic regions in a log-log plot (Fig. 4); at one extreme of stimulus intensity there is a basal level of expression, at the other extreme there is a maximal level of expression, and at intermediate intensities there is a region of regulatable expression.

Four features (Fig. 4) are sufficient to completely define the expression characteristic (11, 41). Capacity for regulation is defined as the ratio of maximal to basal level of expression (induction ratio). Logarithmic gain in expression is defined as the slope of the regulatable region. Threshold is defined as the stimulus intensity at the intersection of the two asymptotes that define the low-stimulus plateau and regulatable region. Basal expression is defined as the level of expression on the lower plateau.

Two other important concepts are defined in relation to the expression characteristic. The operating point of the system is defined as the point on the expression characteristic at which the system nominally resides in any given environment. The demand for gene expression is defined as high if, on average, the system operates at the high end of its regulatable region in the organism’s natural environment, or low if, on average, the system operates at the low end of its regulatable region.

 

Elemental Circuitry

Control of effector gene expression by a specific regulator involves the coupling of two operons and constitutes the simplest of gene circuits. Figure 5A shows the classical circuit (lacI-lacZ), in which regulator expression is constitutive and thus completely uncoupled from effector gene expression. Figure 5B shows the autogenous circuit (putA), in which the regulator and effector genes are located within the same transcriptional unit and hence have their expression perfectly coupled, increasing or decreasing in unison. The analysis of these circuits has been advanced over a period of several decades (11, 31, 33, 46). Figure 5C shows the generic circuit (metR-metE), in which both regulator and effector genes are regulated but not necessarily in a perfectly coupled fashion (11, 40). Coupling in the generic circuit can exhibit one of three distinct patterns. Direct coupling is exhibited when expression of both regulator and effector genes increases (induction) or decreases (repression), although not necessarily to the same degree. Uncoupling implies that expression of the regulator gene is unchanged while that of the effector genes increases (induction) or decreases (repression). Inverse coupling is exhibited when expression of the regulator gene increases while that of the effector genes decreases (repression), or when expression of the regulator gene decreases while that of the effector genes increases (induction).

 

PREDICTION OF BASIC RULES FOR GENE REGULATION

With the terms and concepts defined in the previous section we are in a position to summarize some of the general rules that have been predicted to characterize the regulation of gene expression. The first is concerned with the mode of control for an operon, while the second and third are concerned with the coupling of regulator and effector gene expression in elementary circuits.

 

Demand Theory

The development of demand theory is based on a selectionist argument. Models with either the positive or the negative mode of control, but otherwise equivalent, have been analyzed exhaustively to identify their functional differences (33). The results show that these models are funtionally equivalent in nearly all aspects; however, they respond in diametrically opposed ways to mutations in the regulatory mechanism itself. When mutants generated in response to the natural mutational tendency (entropy) compete with the wild type in different environments, the outcome predicted is the natural selection of alternative modes of control in environments requiring either high- or low-level expression of the effector genes (34, 41).

The rule governing the mode of control is simply stated in terms of demand for gene expression (Table 1). It says that one can predict a positive mode of control for genes whose expression is at the high end of their regulatable region (i.e., that are in high demand) in the organism’s natural environment, or a negative mode for genes whose expression is at the low end of their regulatable region (i.e., that are in low demand). For example, arginine is among the most abundant amino acids in the colon of warm-blooded animals (3, 24). The E. coli residing in this environment can utilize the preformed arginine and repress the genes encoding the arginine biosynthetic pathway. Thus, there is a low demand for expression of these genes, and demand theory allows us to predict a negative mode for their control. Indeed, expression of the arginine biosynthetic system is subject to repressor control (15). The correlation uncovered by demand theory also can be used to make predictions in the opposite sense. For example, the maltose catabolic system in E. coli has a positive mode of control involving an activator protein (5), and hence we can predict a high demand for expression, which in this case means an abundance of maltose in the colon. Indeed, the disaccharide maltose is among the most abundant sugars in the colon (32). Tests of this nature have been conducted successfully in dozens of cases. The rule appears to have a high predictive value.

As is evident from these examples, application of demand theory requires that we know something of the physiological function of the genes and the natural environment of the organism. Thus, it links many different levels of biological understanding from the molecular mechanisms of gene expression to cellular physiology to population ecology, and we should expect a number of further implications to follow from this simple rule. Two examples of the internally consistent interlocking relationships that follow from demand theory are given below.

Histidine is among the amino acids that are least abundant in the colon (3, 24). This has logically related consequences for the modes of control for both the histidine biosynthetic system and the histidine catabolic system of enteric bacteria (40, 41). The biosynthetic system will be in high demand because the bacteria must make their own histidine, while the catabolic system will be in low demand because there is little preformed histidine in their environment that can be taken up. Thus, according to demand theory, one can predict a positive mode of control for biosynthesis and a negative mode for catabolism (Table 2). In strains of Salmonella that are able to synthesize and catabolize histidine, the his operon has a positive mode involving attenuation control and the hut operons have a negative mode involving repressor control. (The low abundance of this amino acid in the organism’s natural environment implies weak selective pressure for the maintenance of the histidine catabolic function, which is in keeping with the highly variable character of this function among enteric bacteria.)

The regulation of differentiated cell-specific functions provides a rigorous test of demand theory because several interlocking predictions of mode must fit and the mode for a given function must switch in the predicted fashion during differentiation (39, 41). The simplest model consists of two cell types each expressing a unique or cell-specific protein. Tryptophan biosynthesis in E. coli provides an example of a cell-specific function if one considers the organism in its different environments expressing different sets of genes as a simple model system of differentiation (Table 3). Free tryptophan is relatively abundant in the colon of warm-blooded animals (34). As a consequence, trp expression in the environment of the colon is in low demand because tryptophan need not be synthesized endogenously, whereas trp expression in the environment of lakes and streams is in high demand because tryptophan is relatively scarce in this environment (37) and must be synthesized by the organism (Fig. 6). Differential expression of other genes occurs as well in these two environments, and we can consider E. coli expressing different sets of genes in these two environments as exhibiting two differentiated cell types: colon-type E. coli and aquatic-type E. coli (37, 39, 41). In colon-type E. coli, trp expression is in low demand and is predicted to be under negative control (repression by trpR); in aquatic-type E. coli, trp expression is in high demand and is predicted to be under positive control (attenuation by a tryptophan-stalled ribosome). Note that the regulatory mechanism has the predicted mode in each cell type and that during differentiation from one cell type to the other (say aquatic-type to colon-type) the mode of control for this cell-specific function (trp) switches from one mode (positive) to the opposite (negative). This pattern (positive mode/high demand, negative mode/low demand) is one of four logical possibilities for the modes and their switching in this case. The other three (positive mode/high demand, positive mode/low demand; negative mode/high demand, positive mode/low demand; negative mode/high demand, negative mode/low demand), although capable of realizing the same regulatory behavior, are not consistent with demand theory and are not selected for in the case of trp expression in E. coli.

Other examples of specific predictions, interlocking predictions, and the switching of modes are described elsewhere (36-41), but the above examples are sufficient to exhibit the simplicity of demand theory and its power to unify conceptually what otherwise would be a set of disparate observations. As we shall see in the next section, demand theory also plays a role in predicting the circuitry that couples regulator and effector gene expression.

 

Elementary Circuit Theory

Unlike the development of demand theory, which is based primarily on qualitative arguments, the development of elementary circuit theory requires a more quantitative analysis based on several criteria for functional effectiveness, the most important being robustness and physiological response time.

Organisms in nature are continually subjected to a variety of perturbations including temperature fluctuations, errors in transcription and translation, and minor mutations. The robustness of a design is determined by calculating the deviation in the normal behavior caused by a perturbation in the value of the various parameters that define the system (11, 30, 33, 49). If the system with design "A" is less sensitive to these perturbations than the system with design "B," then design "A" is considered more robust. Robust designs have selective value, whereas those whose normal behavior is drastically altered by small perturbations tend to be selected against.

The response time for a system is defined as the time that it takes to move from a pre-disturbance steady state to achieve and remain within ±5% of the new steady state that is established following the imposition of a sustained change in the environment. The response time for a system with a given design can be determined by solving the differential equations that describe the system and taking the appropriate measurements from the simulated response (11, 33, 50). When the results are quantitatively compared, one finds that the circuitry has a dramatic influence on response time. Designs with a fast response time are considered to have a selective advantage over designs with a more sluggish response to change.

Models with alternative circuits, but otherwise having equivalent designs, have been carefully constructed, characterized by detailed mathematical analysis, and quantitatively compared on the basis of the criteria for functional effectiveness. The results reveal predictable patterns relating the mode and logarithmic gain of the expression characteristic to the type of circuitry.

The rules governing circuits with extreme forms of coupling —the classical circuit, in which expression of regulator and effector genes is completely uncoupled, or the autogenous circuit, in which expression of regulator and effector genes is perfectly coupled (Fig. 7)—are shown in Table 4 (11). The autogenous circuit is predicted for systems with a negative mode (low demand) and a low logarithmic gain for their expression characteristic and for systems with a positive mode (high demand) and a high logarithmic gain. The classical circuit is predicted for systems with a negative mode and a high logarithmic gain and for systems with a positive mode and low logarithmic gain. For example, the lac and put operons are in low demand (negative mode), but the logarithmic gain for lac (classical circuit) is high whereas that for put (autogenous circuit) is low. Conversely, the mal and eut operons are in high demand (positive mode), but the logarithmic gain for mal (classical circuit) is low whereas that for eut (autogenous circuit) is high. Although there are experimental systems with extreme forms of coupling that fit these predictions, the majority exhibit more general forms of coupling between regulator and effector gene expression.

The rules governing circuits with more general forms of coupling (Fig. 8) are shown in Table 5 (W. S. Hlavacek and M. A. Savageau, J. Mol. Biol., in press). Expression of regulator and effector genes is predicted to be directly coupled for systems with a negative mode (low demand) and a low logarithmic gain for their expression characteristic and for systems with a positive mode (high demand) and a high logarithmic gain. Expression is predicted to be inversely coupled for systems with a negative mode and a high logarithmic gain for their expression characteristic and for systems with a positive mode and a low logarithmic gain. It should be noted that the extent of inverse coupling is predicted to be small: about a 70% reduction in expression of regulator as the effector genes are induced 30- to 100-fold. Expression is predicted to be uncoupled for both modes when there is an intermediate logarithmic gain for the expression characteristic. Several examples can be given of the application of these predictions to specific systems. For example, the metR-metE system is a positive-mode, low-gain circuit that exhibits inverse coupling, whereas the dsdC-dsdA system is a positive-mode, high-gain circuit that exhibits direct coupling. Conversely, the hutC-hutU system is a negative-mode, low-gain circuit that exhibits direct coupling. We are not aware of any circuits with a negative mode and inverse coupling that have been observed to date. The lacI-lacZ system has one of the highest logarithmic gains among the negatively controlled systems, and it appears to exhibit uncoupled circuitry. There are other examples of circuits that appear to be uncoupled. However, as noted above, the degree of inverse coupling is expected to be small, and, if not measured carefully, such small variations in expression might be mistaken for uncoupled expression.

These simple rules demonstrate that general themes apply to broad classes of operons despite their differences in molecular detail. The diversity of designs that is apparent in the survey of gene circuitry and mechanism given at the beginning of this chapter suggests that there are undoubtedly other rules to be discovered. However, we must expect that some differences in design will turn out to be functionally neutral or to be the result of a comparatively recent accident and hence defy any rule-like understanding.

 

Global Patterns of Gene Circuitry

Even though the complete diagram of gene circuitry for the cell is unknown, the survey at the beginning of this chapter makes it clear that elementary circuits can be combined in a large number of ways to realize a variety of physiological functions. Figure 9 depicts in very schematic form five of these that represent well-established organizational themes.

Operon circuitry (Fig. 9A) is characterized by a single specific regulator circuit controlling a single transcription unit whose polycistronic message encodes several protein products that function as a coordinated entity, e.g., a metabolic pathway as in this example. The lac operon is the classic case.

Regulon circuitry (Fig. 9B) is characterized by a single specific regulator circuit controlling several separate transcription units whose protein products function as a coordinated entity, again as a metabolic pathway in this example. Think of the arginine biosynthetic system here.

Hierarchical circuitry is depicted in Fig. 9C. Each of the specific regulators is coupled in a generic fashion to its cognate effector circuit. These specific effector circuits also are governed by a more general regulator circuit. In this example, expression of the general regulator is influenced by a common metabolic signal that is a downstream product of the two effector circuits.

Combinatorial circuitry allows a relatively small number of genes to generate a much larger number of cell types, each expressing a unique complement of proteins (Fig. 9D). Ten genes coupled in a combinatorial fashion could generate over 1,000 unique protein patterns. Combinatorial circuitry appears to be common, particularly in multicellular organisms that contain hundreds of different cell types. With this organizational pattern, specific genes must respond to more than one signal in a combinatorial fashion, which is consistent with finding upstream regulatory sequences composed of binding sites for multiple regulators.

Stimulons are operationally defined and may include a wide variety of circuitry. In the hypothetical example of Fig. 9E, a specific signal influences three distinct regulator circuits. Each of these in turn modulates the expression of two circuits. Most are effector circuits, but one is a secondary regulator circuit that is modulated in a combinatorial fashion by two of the primary regulators. The secondary regulator modulates a single effector circuit whose product is a signal that influences the expression of the third primary regulator.

 

INTEGRATIVE MOLECULAR BIOLOGY OF THE CELL

Can one integrate the molecular information for individual operons into models of the intact system and make quantitative predictions regarding systemic behavior? This was the second question raised by the survey of gene circuitry given above. As we begin to contemplate an integrated understanding of the cell, it is important to state more precisely what the goals are and to ascertain what will be necessary to achieve them.

One goal is to predict the dynamic (as well as steady-state) responses of the intact cell to novel changes in its environment. Moreover, we would like to relate the systemic behavior to the underlying molecular determinants of the cell. This would allow us to predict the systemic behavior in response to novel changes in the organism’s genome or to alter the genome specifically to achieve a desired systemic response.

The conceptual framework for this enterprise includes four areas in which focused effort will be required to achieve these goals: elements, interactions, measurements, and models.

 

Elements

We need to know the "players in the system," i.e., its basic molecular elements. This is the foundation for all else. The sustained activity in molecular biology over the past 50 years has gone a long way toward meeting this need. Perhaps 80% of E. coli‘s metabolic pathways have been discovered, and half of its genome has been defined genetically. Clearly, it is important to complete the systematic identification, characterization, and cataloging of the molecular elements for a strategically relevant organism like E. coli. This involves genome sequencing and protein identification along the lines that are currently being pursued.

 

Interactions

We need to know the network of interactions among the molecular elements; we need to know "who is talking to whom." Again, the efforts of molecular biologists have identified many relevant interactions within the cell. However, there have been no systematic approaches to identifying all the significant interactions in a manner that would be analogous to the systematic approaches that exist to identify the genes and proteins of the cell. The regular discovery of novel functions associated with old familiar molecules suggests that many important interactions among the molecular elements are still unknown.

Computer analysis of molecular networks (22) has provided further evidence that we are missing important interactions among the molecular elements; it also has provided a means to find these interactions. When mathematical models are constructed from known molecular elements and interactions, their behavior invariably differs, often radically, from the observed behavior of the intact cell. Yet, because such models embody so many basic physical constraints, they can be used as a guide in the systematic search for putative interactions that might have the ability to rectify the inconsistencies. For example, a model involving 33 metabolites and 41 enzymes was found to be unstable when the corresponding cell was stable. Something was obviously amiss, but how to find what it might be? If one considers each metabolite to be a potential signal and each enzyme to be a potential target, and subtracts the known interactions (127 in this case), then there are 1,226 putative interactions that remain to be examined—not something one would do experimentally. A computer algorithm was developed to look at the stabilizing influence of each putative interaction. The results showed that of the 1,226 possible interactions only 26 were actually capable of stabilizing the model. One can contemplate an experimental study involving a dozen or so putative interactions. In this case, a thorough search of the experimental literature was enough to reveal evidence for one of the 26 potential interactions, and when these data were incorporated into the model it exhibited a stable steady state that agreed with that of the intact cell. These results suggest that once a sufficient number of relevant interactions have been identified, mathematical models can be used as an heuristic guide in identifying those that remain to be characterized experimentally. As the size of the model increases to deal with the intact cell, the number of potential interactions increases enormously. If the 47-fold reduction in number of putative interactions that we have observed is typical, then computer scanning methods will prove to be a valuable component of any systematic strategy aimed at identifying and characterizing the molecular interactions of the cell.

New experimental technologies also provide avenues to a systematic identification of molecular interactions. The "two-hybrid system" (6) developed in Saccharomyces cerevisiae has revealed many protein-protein interactions previously unsuspected. Such a system needs to be developed for E. coli and used to systematically identify this class of molecular interactions. Combinatorial approaches involving nucleic acid binding (8) have similarly revealed a number of surprising molecular interactions among nucleic acids and proteins and have been proposed as a method to systematically identify all the molecules that interact with the genome. These methods may not work for all molecules, and one still has to assess the physiological relevance of the interactions that are found. Nevertheless, each of these methods has advantages that should be incorporated into an overall strategy to identify all the relevant molecular interactions in the cell. They also are important as indicators of the types of methodologies that need to be developed if we are to achieve this goal.

 

Measurements

We need the ability to monitor the molecular conversations occurring within the cell; i.e., we need to measure important biochemical signals dynamically, in situ. This represents a serious bottleneck to our study of the intact cell. Methods that are capable of monitoring the synthesis of mRNA and proteins in the living cell (see above) address critical needs in this area. These methods can be used to characterize important classes of cellular variables in various steady states; they also can be used to characterize the behavior of these molecules during a dynamic cellular response because the time scale for changes in the concentrations of these molecules is usually slow enough to allow for appropriate sampling.

Noninvasive methods like nuclear magnetic resonance spectroscopy (7, 10) come to mind for other molecular species in the cell, but the resolution of spectroscopy is currently limited. The destructive nature of most other approaches limits our ability to characterize the intracellular milieu. The absence of good information about the local environments within the cell limits our ability to simulate these in vitro. The appeal of in vitro methods is the convenience and power of studying a reaction in isolation from the complex natural milieu that makes measurement so difficult. In principle this approach can yield accurate results if one can make measurements in vitro under the conditions that actually exist in situ. There is a need to explore fundamental physical approaches that have the potential to resolve these issues if we are to make significant headway in measuring small-molecular-weight molecules in situ on a rapid time scale.

 

Models

We need the ability to represent the cell in an accurate and efficient manner in order to achieve understanding, prediction, and control. The familiar kinetic languages that have been used for models in biology since the turn of the century are inadequate for dealing with the emerging picture of the cell as a very nonhomogeneous, richly structured system in which many elements are interacting in a highly nonlinear fashion. The linear formalism is perhaps the simplest of these approaches. The mathematical tools that are available for the representation and analysis of linear systems are among the most highly developed and powerful. This approach has long been used in biology, and there are important problems for which this is the appropriate formalism. Nevertheless, this formalism itself can be used to rigorously demonstrate that it is incapable of representing behaviors typically associated with biological systems that derive from their inherent nonlinear character. The other familiar approach, the Michaelis-Menten formalism, has been used for models in biology since the turn of the century. It provides a nonlinear approach that has come to dominate our thinking about kinetics. It has been eminently useful for the characterization of enzyme-catalyzed reactions in the test tube. However, it is becoming clear that many of its fundamental assumptions, which have made it so useful in vitro, may not be appropriate for the conditions that exist within cells (42). Other indications of the inadequacy of the Michaelis-Menten formalism derive from attempts to construct models of integrated biochemical systems using kinetic data obtained in vitro (22). These models have exhibited a number of problems, including the failure to yield a steady state, the failure to yield a stable steady state, a lack of robustness, and the need to make ad hoc adjustments in order to rectify data obtained in vitro and in vivo. All of this evidence suggests that alternative formalisms must be considered for the representation and analysis of intact cellular systems. The power-law formalism introduced in the 1960s is the most promising alternative, as judged by a number of criteria (42, 45, 48, 56).

The power-law formalism is a mathematical language or representation with a structure consisting of ordinary nonlinear differential equations whose elements are products of power-law functions. The generalized-mass-action representation within the power-law formalism can be written in conventional notation as follows:

Each elemental process is represented by a product of power-law functions, one for each reactant or modifier that influences the process. The variables X_i and multiplicative parameters α _ik and β _ik are non-negative real numbers, while the exponential parameters g_ijk and h_ijk are real numbers that can be positive, negative, or zero. Basic definitions, fundamental concepts, methods of analysis, and applications to various classes of systems can be found elaborated elsewhere (e.g., see references 11, 22, 33, 48, 52, 53, 55, and 56).

The degree to which actual systems in nature conform to the power-law formalism has been examined from three different perspectives (45). The power-law formalism was first developed as a local representation for the kinetics of reactions exhibiting small variations about a nominal operating point in vivo (29). The theoretical basis for this development guarantees the accuracy of the local representation for a limited range of variations. It was subsequently recognized that essentially any nonlinear function could be systematically recast into an exact equivalent in the power-law formalism, which as a recast representation is accurate over global rather than merely local variations. Finally, it was shown that the power-law formalism can be considered a fundamental representation that includes as more limited special cases other representations such as Michaelis-Menten, mass-action, and linear, that are considered fundamental in various disciplines.

Power-law behavior is found at all hierarchical levels of organization from the molecular level of elementary chemical reactions (14, 21) to the organismal level of growth and allometric morphogenesis (23, 27, 35). This recurrence of the power law at different levels of organization is reminiscent of fractal phenomena, which exhibit the same behavior regardless of scale (17). In the case of fractal phenomena, it has been shown that this self-similar property is intimately associated with the power-law expression (47). Hence, it is not surprising that one of the most promising alternatives to the Michaelis-Menten formalism is provided by the power-law formalism.

What are some of the implications of power-law kinetics? Recent studies have shown that the intracellular milieu is crowded, that there are abundant interactions among different enzymes, and that reactions are often confined to two-dimensional membranes and one-dimensional channels (4, 18, 42, 54). Results based on kinetic theory, computer simulation, and experiment have demonstrated that reactions occurring in these dimensionally restricted spaces follow not mass-action kinetics but power-law kinetics (14, 21). This difference has important consequences for the kinetic behavior of individual enzymes. Power-law kinetics give rise to thresholds in molecular recognition and amplified discrimination of supra-threshold signals (43). The kinetic behavior differs in a number of other respects from that expected of a classical Michaelis-Menten rate law (44): First, the effective K_m decreases as the concentration of enzyme increases, whereas it is traditionally independent of enzyme concentration. Second, a plot of rate versus substrate concentration shows sigmoid kinetics and not the traditional hyperbolic kinetics. It is as if there were cooperativity among different binding sites for substrate, when in fact there is but a single binding site. Third, the kinetic order of the overall reaction with respect to total enzyme is greater than unity, whereas overall reaction rate is traditionally proportional to total enzyme, i.e., the kinetic order is unity. In this case, it is as if there were cooperativity of interaction among enzyme molecules, when in fact there is only a single molecule of enzyme participating in the reaction.

There also are important implications when it comes to predicting the integrated behavior of cellular systems. As noted in the previous section, the characterization of reaction kinetics under conditions that reflect their environment in vivo rather than in vitro will be important for the construction of accurate models of integrated systems. Differences in the kinetic behavior of individual enzymes in vitro and in vivo could have profound consequences. First, measurements made in vitro under dilute homogeneous conditions in order to characterize the affinity of an enzyme for its substrate would underestimate the true affinity in vivo. Such measurements often are used in conjunction with estimates of substrate concentration in vivo to make judgments about the potential significance of a reaction in vivo, and an underestimate could lead one to discount a reaction with physiological significance. Second, an erroneous estimate of kinetic order for a reaction could have major consequences for the predicted behavior of the intact system in which the reaction resides. This conclusion follows from the demonstration that the local behavior of the intact system is well represented within the power-law formalism, and that kinetic orders are the sole determinants for important aspects of systemic behavior such as logarithmic-gain factors in signal propagation, sensitivity to variation in rate-constant parameters, and system stability (through one of the two critical conditions for local stability).

The need for mathematical and computer-based methodologies aimed at effective representation, analysis, and prediction of integrated behavior will only increase with the scope of the systems being considered. A model of the intact E. coli cell represents a formidable challenge in this regard. It will undoubtedly be one of the first cells to be so characterized, and, as it has in the past, it will serve as a paradigm for the understanding of more complex organisms. The familiar kinetic languages are inadequate for this task; canonical nonlinear methods for large, spatially structured, nonhomogeneous, fractal kinetic systems are required. The power-law formalism provides the appropriate framework to address these issues.

We are close to completing the molecular inventory of the E. coli cell. We must become equally dedicated to cataloging the molecular interactions, measuring the cellular variables in situ, and integrating this information into appropriate models. If we do, then we can look forward to the day when these methods of integrative molecular biology can be applied to higher organisms with a view toward improved therapy and more effective biotechnology.

 

SUMMARY AND CONCLUSIONS

Beyond the particular controls unique to individual operons are additional mechanisms that serve to coordinate the expression of sets of operons. These controls create families of operons (regulons), frequently with memberships overlapping in such a way that complex patterns of expression result. Sets of regulons (modulons) are also united by common regulatory elements. The molecular mechanisms operating on different regulons are fully as diverse as the operon-specific mechanisms. In addition to continued discovery and reductive analysis of new regulons and modulons, related challenges for the future are (i) learning the biological logic of different regulatory circuits and (ii) integrating the molecular information on regulon control into appropriate, predictive models of the cell. Experimental studies can be expected to benefit from global monitoring of regulons and modulons. Theoretical advances should come from the application of different techniques of integrative systems analysis leading to predictive models of the intact cell.

ACKNOWLEDGMENTS

Preparation of this chapter was supported by Public Health Service research grant GM17892 from the National Institute of General Medical Sciences and grant MCB9417897 from the National Science Foundation (to F.C.N.), and by Public Health Service research grant GM30054 from the National Institute of General Medical Sciences (to M.A.S.).