Engineering Genetic Circuits (Chapman & Hall/CRC Mathematical and Computational Biology)

I find the many illustrations worked-out examples and ample number of figures and exercises at the end of each chapter quite useful and important. We provide complimentary e-inspection copies of primary textbooks to instructors considering our books for course adoption. Learn More about VitalSource Bookshelf. CPD consists of any educational activity which helps to maintain and develop knowledge, problem-solving, and technical skills with the aim to provide better health care through higher standards.

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His research interests include formal verification, asynchronous circuit design, and the analysis and design of genetic regulatory circuits. Would you like to tell us about a lower price? An Introduction to Systems Bioengineering Takes a Clear and Systematic Engineering Approach to Systems Biology Focusing on genetic regulatory networks, Engineering Genetic Circuits presents the modeling, analysis, and design methods for systems biology.

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Next, there is the cytoskeleton which is composed of microfilaments long thin fibers and microtubules hollow cylinders. The cytoskeleton gives a cell its shape and holds organelles in place. It also helps during endocytosis i. Lastly, there is the cytoplasm which is the large fluid-filled space inside the cell. While in prokaryotes, the cytoplasm does not have many compartments, in eukaryotes, it includes many organelles.

The cytoplasm is essential to a cell as it serves many functions including dissolving nutrients, breaking down waste products, and moving materials around the cell. For example, the nucleus of a human 12 Engineering Genetic Circuits cell has 23 chromosomes. In eukaryotes, the nucleus is the location where DNA replication and transcription takes place where as in prokaryotes, these functions occur in the cytoplasm. The nucleus has a spheroid shape and is enclosed by a double membrane called the nuclear membrane, which isolates and protects the genome from damage or interference from other molecules.

During transcription described in Section 1. Another important organelle is the ribosome, which is a protein and RNA complex used by both prokaryotes and eukaryotes to produce proteins from mRNA sequences. A ribosome is a large complex composed of structural RNA and about 80 different proteins.

During translation also described in Section 1. Due to the importance of protein synthesis, there are s or even s of ribosomes in a single cell. Ribosomes are found either floating freely in the cytoplasm or bound to the endoplasmic reticulum ER. The ER is a network of interconnected membranes that form channels within a cell. It is used to transport molecules that are either targeted for modifications or for specific destinations. There is a rough ER and a smooth ER. The rough ER is given its rough appearance by the ribosomes adhered to its surface. The mRNA for proteins that either stay in the ER or are exported from the cell are translated at these ribosomes.

The smooth ER receives the proteins synthesized at the rough ER. Proteins to be exported from the cell are passed to the Golgi apparatus to be processed further, packaged, and transported to other locations. Mitochondria and chloroplasts are organelles that generate energy. Mitochondria are self-replicating and appear in various shapes, sizes, and quantities. They have both an outer membrane that surrounds the organelle and an inner membrane with inward folds known as cristae that increase its surface area. Chloroplasts are similar, but they are only found in plants. They also have a double membrane and are involved in energy metabolism.

Mitochondria and chloroplasts have their own genome which is a circular DNA molecule. The mitochondrial genome is inherited from only the mother. It is believed that this DNA may have come from bacteria that lived within the cells of other organisms in a symbiotic fashion until it evolved to become incorporated within the cell. Although the mitochondrial genome is small, its genes code for some important proteins.

For example, the mitochondrial theory of aging suggests that mutations in mitochondria may drive the aging process. Lysosomes and peroxisomes are responsible for degrading waste products and food within a cell. They are spherical, bound by a membrane, and contain digestive enzymes, proteins that speed up biochemical processes. Since these enzymes are so destructive, they must be contained in a membrane-bound compartment. Peroxisomes and lysosomes are similar, but peroxisomes can replicate themselves while lysosomes are made in the Golgi apparatus.

Humans have between 20, and 25, genes while mustard grass has 25, known genes. Increased complexity can be achieved by the regulatory network that turns genes on and off. This network precisely controls the amount of production of a gene product, and it can also modify the product after it is made. Genes include not only coding sequences that specify the order of the amino acids in a protein, but also regulatory sequences that control the rate that a gene is transcribed. These regulatory sequences can bind to other proteins which in turn either activate i.

Transcription is also regulated through post-transcriptional modifications, DNA folding, and other feedback mechanisms.

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Transcriptional regulation allows mRNA to be produced only when the product is needed. This behavior is quite analogous to electrical circuits in which multiple input signals are processed to determine multiple output signals. Thus, in this text, these regulatory networks are known as genetic circuits.

Eukaryotic cells have three different RNA polymerases. Transcription is initiated when a subunit of RNAP recognizes and binds to the promoter sequence found at the beginning of a gene. A promoter sequence is a unidirectional sequence that is found on one strand of the DNA. There are two promoter sequences upstream of each gene, and the location and base sequence of each promoter site varies for prokaryotes and eukaryotes, but both are recognized by RNAP. After binding to the promoter sequence, RNAP unwinds the double helix at that point and begins to synthesize a strand of mRNA in a unidirectional manner.

This strand is complementary to one of the strands of the DNA, and so it is known as the antisense or template strand. The other strand is known as the sense or coding strand. The transcription process terminates when the RNAP reaches a stop signal. Termination of transcription in eukaryotes is not fully understood.

The ability of RNAP to bind to the promoter site can be either enhanced or precluded by other proteins known as transcription factors. These proteins recognize portions of the DNA sequence near the promoter region known as operator sites. An overview of transcription and translation courtesy: In other words, an activator turns on or enhances gene expression while a repressor turns off or reduces gene expression. The effects of transcription factors can affect both adjacent genes known as cis-acting or distant genes known as trans-acting. Transcription can also be regulated by variations in the DNA structure and by chemical changes in the bases where the transcription factors bind.

For example, methylation is a chemical modification of the DNA in which a methyl group -CH3 is added. Methylation often occurs near promoter sites where there is cytosine preceded by guanine bases. The next step is protein synthesis from the mRNA by the translation process shown in Figure 1.

Translation is performed by the ribosomes using tRNA. Each tRNA has an anti-codon site that binds to a particular sequence of three nucleotides known as a codon. A tRNA also has an acceptor site that binds to the specific amino acid for the codon that is associated with the tRNA. Ribosomes are made up of a large subunit and a small subunit. Translation is initiated when a strand of mRNA meets the small subunit.

The large subunit has two sites to which tRNAs can bind. The A site binds to a new tRNA which comes bound to an amino acid. The translation process from mRNA into a polypeptide chain involves three steps: Next, a tRNA bound to methionine binds to this start signal beginning the elongation process. This process continues until translation comes to one of the three stop codons, that signals that translation should move into the termination step. There is no tRNA that binds to the stop codon which signals the ribosome to split into its two subunits and release the newly formed protein and the mRNA template.

At this point, the protein may undergo post-translational modifications while the mRNA is free to be translated again. A single mRNA transcript may code for many copies of a protein before it is degraded. It may even be transcribed by multiple ribosomes at the same time. Translation can be regulated by the binding of repressor proteins to the mRNA molecule. Translational regulation is heavily utilized during embryonic development and cell differentiation. Types of viruses courtesy: National Center for Biotechnology Information.

Their genomes include genes to produce their protein package and those required for reproduction during infection. Since viruses must utilize the machinery and metabolism of a host cell to reproduce, they are known as obligate intracellular parasites. Before entering the host, the virus is known as a virion, or package of genetic material.

A virion can enter a host through direct contact with an infected host or by a vector, or carrier. There are several types of viruses such as those shown in Figure 1. Bacteriophages are those that infect bacteria while animal viruses and retroviruses infect animals and humans. The main goal of a virus is to replicate its genetic material.

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There are five main stages to virus replication: During penetration, bacteriophages make a small hole in the cell wall and inject their genome into the cell leaving the virus capsid outside. Animal viruses and retroviruses, such as HIV, enter their host via endocytosis. During the replication stage, the virus begins the destructive process of taking over the cell and forcing it to produce new viruses. Retroviruses synthesize a complementary strand of DNA using the enzyme reverse transcriptase, which can then be replicated using the host cell machinery.

During this stage, the virus also instructs the host to construct a variety of proteins which are necessary for the virus to reproduce. First, early proteins are produced which are enzymes needed for nucleic acid replication. Next, late proteins are produced that are used to construct the virus capsid. Finally, lytic proteins are produced, if necessary, to open the cell wall for exit. During the assembly stage, the virus parts are assembled into new viruses simply by chance or perhaps assisted by additional proteins known as molecular chaperons. During the release stage, assembled viruses leave the cell either by exocytosis or by lysis.

Bacteriophages, on the other hand, typically must lyse, or break open, the cell to exit. These viruses have a gene that codes for the enzyme lysozyme that breaks down the cell wall causing it to swell and burst killing the host cell. The new viruses are then released into the environment. He also found that some of the newly infected E. It is a bacteriophage that infects E. The lysis strategy uses the machinery of the E. It then lyses the cell wall killing the cell and allowing the newly formed viruses to escape and infect other cells. The lysogeny strategy is a bit more subtle.

Its DNA is then replicated through the normal process of cell division. If after perhaps many generations it detects the eminent demise of its host, it can revert to the lysis strategy to produce new viruses that escape to infect other cells. Over the years, much has been learned about this simple genetic circuit. It serves to both illustrate the concepts involved in such genetic circuits as well as a running example to explain the analysis methods presented in later chapters. CI monomers are produced from the cI gene.

These operator sites are overlapped by two promoters. In this case, RNAP bound to this promoter transcribes to the right producing transcripts from the cro gene. These two promoters form a genetic switch since transcripts can typically only be produced in one direction at a time. A single molecule, or monomer, of CI is composed of a carboxyl C and amino N domain connected by a chain of 40 amino acids.

Two CI monomers react to form a dimer, CI2. This process is shown in Figure 1. Similarly, the cro gene codes for the Cro protein which also dimerizes in order to bind to OR operator sites as shown in Figure 1. Cro monomers are produced from the cro gene. Two Cro monomers form a Cro dimer which can bind to one of the OR operator sites. CI2 also serves as an activator when it is bound to OR 2. Although shown in black-and-white terms, things in biology are rarely so clear-cut. The rate of transcription in the scenario shown in Figure 1. It has no effect, however, on PR.

While the PRM promoter producing transcripts for the CI molecule is initially inactive, the PR promoter producing transcripts for the Cro molecule is initially active as shown in Figure 1. Its promoter has a stronger affinity for RNAP. Finally, if Cro2 happens to also bind to either operator sites OR 1 or OR 2, it represses its own production see Figure 1.

While CI2 and Cro2 can bind to any of the three operator sites at any time, they have a different affinity to each site. The Cro2 has the reverse affinity as shown in Figure 1. Namely, it is likely to first bind to OR 3 to turn off CI production. Finally, in very high concentration, Cro2 can be found bound to all three sites. The effect of CI2 and Cro2 bound to each operator site.

Likely position of Cro2 bound to OR versus Cro2 concentration. At moderate concentration, it is equally likely to be also bound to b OR 2 or c OR 1.

Cooperativity of CI2 binding. As mentioned above, the first dimer to bind to OR typically binds to OR 1. Next, this dimer helps attract another CI2 molecule onto the OR 2 site. It does this by bending over such that one carboxyl domain from each dimer touch as shown in Figure 1. This effect is known as cooperativity, and it is so strong that it appears almost as if the two dimers bind simultaneously. The two dimers bound in this way have a dual effect as shown in Figure 1.

Engineering Genetic Circuits - CRC Press Book

Namely, they repress production of Cro and they activate production of CI. While not often found in wild-type i. The effect of cooperativity is that the repression of Cro by CI becomes more switch like. The one without cooperativity is also controlled by CI monomers rather than dimers in that dimerization is also a form of cooperativity.

The cooperative switch is very stable to small perturbations around this value. Effect of cooperativity of CI2 molecules on repression of Cro production. However, when the concentration of CI drops significantly, the repression of Cro production is rapidly released. In the non-cooperative switch, repression drops off much more gradually, making the transition to lysis much less sharp.

Given the above discussion, at low to moderate concentrations of CI and Cro, there are three common configurations. First, there may be no molecules bound to OR. In this case, Cro is produced at its full rate of production while CI is only produced at its low basal rate. In this case, Cro production is repressed and CI production is activated. Third, a Cro2 molecule may be bound to OR 3.

In this case, CI cannot be produced even at its basal rate while Cro continues to be produced. Therefore, the feedback through the binding of the products as transcription factors coupled with the affinities described makes the OR operator behave as a genetic bistable switch. In one state, Cro is produced locking out production of CI. In this state, the cell follows the lysis pathway since genes downstream of Cro produce the proteins necessary to construct new viruses and lyse the cell.

In the other state, CI is produced locking out production of Cro. In this state, the cell follows the lysogeny pathway since proteins necessary to produce new viruses are not produced. In the lysogeny state, the cell develops an immunity to further infection.

The cleaved CI monomers are unable to dimerize and bind to OR 1 which reduces the concentration of CI2 molecules allowing Cro production to begin. Once a cell commits to lysogeny, it becomes very stable and does not easily change over to the lysis pathway. An induction event is necessary to cause the transition from lysogeny to lysis.

For example, as described earlier, lysogens i. UV light creates DNA damage that is potentially fatal to the cell. It also has the effect of cleaving the CI monomer into two parts as shown in Figure 1. This inactivates the CI molecule making it incapable of forming a dimer and binding to OR. As the concentration of complete CI molecules diminish, the cell is unable to maintain the lysogeny state.

Cro production begins again moving the cell into the lysis pathway. How do these proteins locate these sequences from amongst the millions within the bacteria? The second column of Table 1. The top line of each row is one strand of the DNA while the bottom line is the complementary strand. The base pair shown in lower case represents the midpoint of the sequence. Observing from this midpoint, one finds that a strand on one side of the midpoint is nearly symmetric with the complementary strand on the other side.

This may not, however, be readily obvious. The last row accumulates frequencies of each base pair in each position. The most likely entries form the following consensus sequence: For example, there is always an A in the 2nd and 16th position, a C in the 4th and 14th position, and nearly always a C in the 6th and 12th position. There are, however, some differences. It is these differences that cause the differences in affinity for CI2 and Cro2 for the different operators. Notice that the first half of the operator sites OR 1 and OR 3 agree perfectly with the consensus sequence.

The second half, however, has several differences which lead to different affinities for CI2 and Cro2. To see how CI2 and Cro2 recognize these operator sites differently, it is necessary to consider their structures in more detail. These figures also show the attractions between these amino acids and the bases within the second half of the sequences for OR 1 and OR 3 note that they are reversed and inverted from how they are shown in Table 1. Both CI2 and Cro2 begin with the amino acid glutamine gln which is attracted to the A-T base pair in the second position.

They also agree in the second amino acid serine ser which is drawn to the C-G base pair in the fourth position. This commonality shows why CI2 and Cro2 are both attracted to these operator sites. They differ, however, in the remaining amino acids. The case is the reverse for OR 1. Note that as shown in Figure 1. RNAP like transcription factors must locate a particular sequence associated with a promoter on which to bind.

There are many promoters each associated with one or more genes on a strand of DNA. Considering the sequences associated with these promoters, one can generate a consensus sequence indicating the most likely i. It turns out that the most important part of the sequence are the 6 base pairs located near the and positions where means 35 base pairs away from the start of the gene. Comparing these portions of the consensus sequence with the same portions of the PRM promoter and the PR promoter, it is found that the PR promoter is a better match to the consensus sequence than PRM differing in only two bases while PRM differs in four.

The first step is circularization. At each end of this strand is 12 bases of single stranded DNA known as cohesive, or sticky, ends which join to form a circular strand of DNA. The location marked cos is the location of the cohesive ends. Continuing in a clockwise direction, the next 22 genes encode proteins that construct the head and tail of the virus. The site labeled attp, or attachment site, is where the DNA is split when it in integrated within the E. Next, comes five individual genes labeled, cIII, N, cI, cro, and cII which are used to make the decision between lysis and lysogeny as described below.

The Q gene is used during the lysis pathway. Finally, the three genes labeled lysis are used to lyse, or open, the bacteria. Transcripts from PRM are always terminated immediately after transcribing the cI gene. Transcripts from PR , however, encounter a terminator switch after transcribing the cro gene and can continue to transcribe cII, O, P, and Q genes.

This potential transcription is indicated with a dashed line.

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The promoter PL begins transcription for the N gene. Transcripts beginning at PL also encounter a terminator switch and can potentially continue to transcribe cIII, xis, and int genes. The int gene can also be transcribed starting from the PI promoter. The PR0 promoter transcribes the genes for the proteins needed for the lysis pathway.

The Pantiq promoter produces reverse transcripts for the gene Q. Finally, the PRE promoter can produce transcripts of the cI gene as well as reverse transcripts for the cro gene. The remainder of this section describes this complete circuit in more detail. The N and cro genes are the only ones that are active very early.

The other genes such as cI do produce transcripts, but only at a low basal rate initially. Recall that a buildup of Cro can trigger the lysis pathway to be taken. The protein N is known as an anti-terminator, and its role is illustrated in Figure 1. RNAP that binds to the promoter PL known as the left promoter since transcripts move from the left of the gene cI transcribes the gene N, and it then hits a terminator switch as shown in Figure 1. This action blocks transcription about 80 percent of the time such that all genes downstream of the switch do not get transcribed, and the proteins that they code for do not get produced.

The result is that the RNAP now passes over the terminator switch and continues to transcribe the remaining genes as shown in Figure 1. As mentioned above, there is another terminator switch that blocks transcripts to the right, and it is also controlled by the N protein. The transition from the very early to the early stage is marked by a buildup of the protein N. As just described, the protein N closes the terminator switches allowing transcripts from the PR and PL promoters to transcribe additional genes see the dashed arrows in Figure 1.

Transcripts beginning from the PL promoter now proceed past its terminator switch to transcribe the cIII, xis, and int genes. These transcripts also continue on to transcribe an important non-genetic portion of the DNA known as sib. The sib portion of the mRNA forms a hairpin as shown in Figure 1. Since the Int portion is destroyed before the Xis portion, more of the Xis protein is allowed to be synthesized than Int as shown in Figure 1.

An excess of Xis prevents the DNA from being integrated, so it prevents lysogeny. There are two potential sets of late genes depending on whether lysis or lysogeny has been chosen. The key to this decision is the activity of the protein CII. This protein activates the PRE promoter which gives a jump-start to the production of the protein CI. With it, positive feedback in PRM further increases CI production and locks out further Cro production driving the virus down the lysogeny pathway. The activity of CII is determined by environmental factors.

Bacterial proteases enzymes that degrade proteins attack and destroy CII readily, making it very unstable. Growth in a nutrient rich medium activates these proteases whereas starvation has the opposite effect. For this reason, well-fed cells tend towards lysis. The production of CIII is limited by the terminator switch. Therefore, higher multiplicities of infection lead to a higher probability of lysogeny. The late genes active for the lysis case are shown in Figure 1.

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The protein Q that also built up during the early stage activates the PR0 promoter. As a result, genes are transcribed that code for proteins to construct the heads and tails of new viral capsids as well as those necessary to lyse the cell. The late genes for the lysogeny case are shown in Figure 1. The mRNA transcripts produced from the Pantiq promoter are complementary to the transcripts for the gene Q.

Therefore, these transcripts can bind to the transcripts for the gene Q preventing them from being translated into Q proteins and helping to prevent the activation of PR0 that is needed by the lysis pathway. The promoter PRE produces transcripts of the gene cI. The promoter PI is located in the middle of the xis gene, so the transcripts that it produces do not produce the Xis protein. Finally, this process can be reversed during induction.

Induction requires both the proteins Int and Xis. This time, however, it does not transcribe the sib region as it is located on the other side of the attP site and ends up on the other side of the integrated genome as shown in Figure 1. This portion of this genetic circuit is shown in Figure 1. Finally, after CI degrades, the system has returned to the initial state. This genetic circuit can be represented graphically as shown in Figure 1. While there are a variety of different ways to model a genetic circuit using chemical reactions, the following procedure is systematic and produces a fairly reasonable model.

Create a species for RNAP as well as for each promoter and protein. Create degradation reactions for each protein. Create open complex formation reactions for each promoter. Create dimerization reactions, if needed. Create repression reactions for each repressor. Create activation reactions for each activator. This procedure is illustrated using the simple genetic circuit shown in Figure 1. As shown in Figure 1. Step 3 creates a reversible reaction denoted by a double arrow in the diagram for each promoter which models the binding of RNAP to the promoter to form a complex with default equilibrium constant of Ko.

For each of the resulting complexes, another reaction is added with this complex as a modifier that models transcription and translation. The result of step 3 for this example is shown in Figure 1. Finally, the value np indicates the average number of proteins produced per mRNA transcript. Step 4 creates a reversible reaction to form dimers for each species that must first dimerize to act as a transcription factor, as is the case for the CI molecule in this example see Figure 1.

Step 5 creates a reversible reaction that binds each repressor species to the promoter that it represses preventing it from being able to bind to RNAP. Note that the value nc specifies the number of molecules that must bind to cause repression. Finally, Step 6 adds a reversible reaction that binds each activator species with RNAP to the promoter that is activated.

Note that the value na specifies the number of molecules that must bind to cause activation. The resulting complex is then used as a modifier in a reaction to produce a species at an activated rate of production. Putting this all together results in the complete reaction-based model for this example shown in Figure 1. This model has 10 species and 10 reactions of which 5 are reversible. It is one of, if not the best, understood genetic circuit. Constant V alue Kd 0. Activation reactions for PRE.

There are numerous systems to which parallels can be drawn. These range from other phages with similar mechanics to bacteria with circuits that must respond properly to various forms of stress to even circuits involved in development and cell differentiation.

This text, therefore, also uses it as a running example. For the engineer or computer scientist who would like to learn about cellular biology, the textbook by Tozeren and Byers provides a detailed yet approachable description of the field. A remarkably useful and humorous introduction to genetics can be found in the book by Gonick and Wheelis When learning a new field, one of the most important tasks is to learn the terms used in that field. There are numerous dictionaries of biological and genetic terms, including one by King and Stansfield Another excellent resource for finding definitions of terms is at http: Finally, for the person who wants to really dig into the subject matter, there are several excellent textbooks Berg et al.

This discovery marked the beginning of extensive studies of this virus and lysogeny. An excellent history of this work is presented in Gottesman and Weisberg An important step in this work was the discovery that induction could be activated by UV light Lwoff and Gutmann, The contents of Section 1.

Is the forward or reverse reaction favored?

Using trial-and-error find the point the concentrations of [E], [S], and [ES] in which this reaction reaches a steady-state hint: Use the parameter values provided and assume that CI dimerizes before acting as a transcription factor. Use the parameter values provided and assume that CI and Cro dimerize before acting as a transcription factor.

There are a variety of different ways this system can be modeled using chemical reactions, so this is just one possible model. A schematic diagram of this model is shown in Figure 1. In this diagram, the solid boxes are genes, the hollow boxes are operator sites, the bent arrows are promoters, the diamonds are NUT sites, and the breaks are terminator switches. This model also includes the biochemical reactions involved in dimerization of CI and Cro as well as those involved in the degradation of each protein.

The reactions shown in Figure 1. This reaction is reversible, and it has an equilibrium constant ratio of the forward over the reverse rate constant KP RE2 with a value of 0. Note that equilibrium constants are shown with capital letters, and rate constants with lower-case letters. The value np is the number of proteins produced on average from an mRNA transcript before it is degraded. The rate for this reaction is kP REb with a value of 0. This complex does not result in transcription. The protein CII is an activator meaning that this complex leads to an increased rate of transcription.

This can be seen in the fifth reaction which produces CI via transcription and translation. In this case, however, the activated rate is 0. Of these 40 configurations, 13 result in transcription with one resulting in transcription in both directions. This results in a model with 52 reactions. The first group of reactions shown in Figure 1. There are three potential reactions in which CI2 could bind to each of the three possible operator sites.

In this model, this is collapsed into one reaction that indicates that one molecule of CI2 has bound somewhere to OR. Similarly, the three reactions for Cro2 are collapsed into one. The second group of reactions shown in Figure 1. Even using the simplification just described results in nine distinct configurations and 16 reactions for this case. Note that the equilibrium constants for each group are roughly related to the likelihood of each configuration.

Engineering Genetic Circuits

Equilibrium constants across groups though are incomparable. Two of the most common configurations have either two molecules of CI2 or one molecule each of CI2 and Cro2 bound to OR which do not lead to transcription. The most common configuration in this group though is to have a molecule of Cro2 bound to OR 3 and RNAP bound to the other two sites leading to production of Cro. The final set of reactions shown in Figure 1. There are only two common configurations. The proteins CI and Cro must dimerize before they can act as transcription factors.

The CI and Cro monomers can also degrade. The dimerization and degradation reactions for CI and Cro are shown in Figure 1. Constant V alue KP R30 0. The model for the promoter PL is very similar to the ones for the other promoters. This promoter is repressed by either CI2 or Cro2. Some transcripts, however, are terminated before they reach the cIII gene resulting in a rate of production that is only 20 percent of the full rate. This behavior is modeled with the reactions shown in Figure 1. The production of the protein CII is modeled in a similar way in Figure 1.