Chapter 11. Chapter 11: Regulation of the lac Operon in Bacteria

Introduction

Unpacking the Problem
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You must read each slide, and complete any questions on the slide, in sequence.

The genes shown in the table below are from the lac operon system of E. coli. The symbols a, b, and c represent the repressor (I) gene, the operator (O) region, and the structural gene (Z) for β-galactosidase, although not necessarily in that order. Furthermore, the order in which the symbols are written in the genotypes is not necessarily the actual sequence in the lac operon.

  Activity (+) or inactivity (-) of the Z gene
Genotype Inducer absent Inducer present
a- b+ c+ + +
a+ b+ c- + +
a+ b- c- - -
a+ b- c+/a- b+ c- + +
a+ b+ c+/a- b- c- - +
a+ b+ c-/a- b- c+ - +
a- b+ c+/a+ b- c- + +

Based on the data in the table, deduce which symbol (a, b, and c) represents lac gene I, lac gene Z, and the operator region O. In the table, a superscript minus sign on a gene symbol merely indicates a mutant, but recall that some mutant behaviors in this system are given special mutant designations. After the symbols a, b, and c have been assigned to lac I, Z, and O, use the conventional gene symbols for the lac operon to designate some of the genotypes in the table.

(Data in this problem from J. Kuspira and G. W. Walker, Genetics: Questions and Problems. Copyright 1973 by McGraw-Hill.)

Unpack the Problem: Break this problem into several parts and arrive at a solution using this guided, step-by-step approach.

  • Part A (steps 1 and 2): Work with the haploid genotypes to make as many assignments as possible.
  • Part B (steps 3 and 4): Work with the diploid genotypes to make as many assignments as possible.
  • Part C (steps 5 and 6): Translate the abc symbols into conventional lac operon nomenclature.

Question

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1

The genes shown in the table below are from the lac operon system of E. coli. The symbols a, b, and c represent the repressor (I) gene, the operator (O) region, and the structural gene (Z) for β-galactosidase, although not necessarily in that order. Furthermore, the order in which the symbols are written in the genotypes is not necessarily the actual sequence in the lac operon.

  Activity (+) or inactivity (-) of the Z gene
Genotype Inducer absent Inducer present
a- b+ c+ + +
a+ b+ c- + +
a+ b- c- - -
a+ b- c+/a- b+ c- + +
a+ b+ c+/a- b- c- - +
a+ b+ c-/a- b- c+ - +
a- b+ c+/a+ b- c- + +

Based on the data in the table, deduce which symbol (a, b, and c) represents lac gene I, lac gene Z, and the operator region O. In the table, a superscript minus sign on a gene symbol merely indicates a mutant, but recall that some mutant behaviors in this system are given special mutant designations. After the symbols a, b, and c have been assigned to lac I, Z, and O, use the conventional gene symbols for the lac operon to designate some of the genotypes in the table.

(Data in this problem from J. Kuspira and G. W. Walker, Genetics: Questions and Problems. Copyright 1973 by McGraw-Hill.)

Unpack the Problem: Break this problem into several parts and arrive at a solution using this guided, step-by-step approach.

  • Part A (steps 1 and 2): Work with the haploid genotypes to make as many assignments as possible.
  • Part B (steps 3 and 4): Work with the diploid genotypes to make as many assignments as possible.
  • Part C (steps 5 and 6): Translate the abc symbols into conventional lac operon nomenclature.

Question

N757z4sz25iZkmO7DfpgTJqwOSr6TRM7z2tWxKkD/zVSmnu4FYDcs5RoS7EUgKm0PF8sGAC4/oBpAZJxK//qhRwyRKSLjIRMcGMHdRGMGLcpX+j4dD7kxtT7Y2UNZDPG0GrEhJYiTDFnN6RovDlYVjZJaMv2g4LxYOf19a1Cv4i/F0N8HuEFe8vnaOEfPo2bi99E9gxgGczgfzfbFSgpHcWP5b6+V5MD+4JsOG7mHwCsiOYtJD0/C2g7WLP2iKAGAK7t0CwGXKKhC0/wJOf8+26b21ccm4AbV7C+Z/0iSREIdCK+d/bu0oZGM4L9AaN9kwHXv6zbLeFnzhlsddLIoZslnI9pb3HMNYluWGytNFFteLyuX0K3TSvNHFABTVdmokhNZq8GoFhFvZox3fFDlEoXicPYlVOsplaC0x47oVB9f5UiXW3+iJJI4hOW2ylAMZpUvNtmLJftQhx4MrlKVFiVKTWVDv6dLwGud0sxbirQ6v/+uvPDKAugaeWfbKHccGwrwqgTMYjI4SdyZyAJ6pxCpsZMMFmstTJ7JPtOhG2kCQG+wnUK+5pwTu8kg9SqPmmINABN1dZmHnbdaD83o3g+HJG3LX+d2UimNKVHHD4aY3RpTc6qWesDTSYYTz14SD1IEHxRtVMjsuU40dErlX+Q47mndQQIVZac/o8VUt91f+L+NokKltg+Iq5YUs6biYVmbDXKyXuoinE5klSj72D0GkgMOnmUb7JashuH+/Q15WgLSdhZmfUEwTsLDmEF8U6sHDTIlE+6HnrE20lFUBLWI/fZak9REGJzknzcxEH5Q9Ybzbg4gaDlOJVMtpXxGl3IFGtzwOvTqKtbbavnIVMZ61NI5ULJ88JhFutYVr7yKz60S73IudFx/2NbG/Hj8VuiKxlmDodmofxL/YmFEtO0Yw7z/OidlbQfMOk0m/jAIonD75KAXJn2iIIsYssubBDethG+fSACCAJRb88TWxS7kYu3iEqh4GVW8+sfG3rgS8vCdpHE7Zkjvnbrr/Fj+l5IR1ZWg5kdgqEZ5pBEY/yR/+Q9beE0edTb2GJDhI8cKa8tkTW+Cn9J8DiocV6NV8yEVJvnXw0xoteub9hjIQz1MR+NGy+oWW4G/0sfVlVMm8ZZiODDSkL3xgtNHr4jdvvdSeHLV5K2QYABmKJkAPLp3NbJeP5bpTQH9O8g/+DXRchJJ7Xp9PLLNG44RTRiL1k8MbSu0CLGcf0rSAy3p9Opyq/fufTZqvfStrh6Zkhzchjja4JegniD1bQR17G0XpNCt/63+Bz/8+D+MbwitQ3Yz0tPEl+5YgYI0OgXkFhZYcaDlLXUsycMvhrbs3/iun6tcvUAxOBGCdMc507aXMD84S8DdOe1jBneskMhu+jpv2/MKACgIvbgeL9hd6wDICD8zmni0VraFoUYzYTtHHCvWq9nKR4v7fN75NGsrSwLq3Rc5GhuJbs8nfw3GUDmswPaBcExNElkRdZAqp0H6SaZCjzU3vAyPHAIQEQP4jyukMENpag8NBggnYl3Tm2buJsFyPzasCowQbs7ygwEx6+MA0PampGH+xdN/nNonCg76W98T/knqvAounVv9gSkZJaYYqzH9SdWOyBMuRcGa4hrKX/LjuUz4OlwXVjz4mwVlQkPxtSoE/+gGXBhl27JjEwEJUHGchdAFdUXunPNKmc40D0p7f9NuPavBFmlRJTVmFX7wQ57U+eFjZO+cXAVb83XP6+LDGAaypxXjC0xYUBjK0X7n/rW09jVDeAoK0b8bG49xu+1ikZUNlAjMfTbcuhKqwiQS+FU33IPeJzdFH7XETrf+5KcpVnkQ4Iuv2cwrXrGm6b0NIUuHg1KPzvTlb/NkDgQlEd03RpCrKlqlYlFywq0jLCC+67fy4HX7z/55JrK00+tOmE6EqSJWzcyg/X+FuZWJhlsShamu0dK9AMhATa5zAwZnC1tw3LxGOfTFdq/xQQNLr3a6zjO5lAXDI2mp2mpqM3rOj3ESIltkx3ZW1p8jdD5vDjqwfSZF16mCqH93PwdAVG+0TiThyPwfbsqM1OdjCzPiZgFDNicg2QAymQZC/KOUomhxVKjQzTCOFe5OK93E3XUWsPR8tuRI4Qpb/a6TCUVf2SozbZlYjHEJR498WIh0bEtRubKkGozRJfVClEQMlsH4R6tmgcEPC86SF/a7o/Pnp5I1KFzQtQgTTMTtpycT1EU00QXmsfDdTTyWk9dyy01FPZUvFfPtiwsVEC6Iyie6W1uzn8nzm6l0VwZm+/+EsAqfZ92Ohjg6lt1/bUugUmR3fh3THxg11R1Mfs/H9HGQsxrHlNrGzoWf48vNirjw+zEiyuGyiL7/7LKYP659cmtdOFAYlEIqg94KByUJBOGlhDQRXfZY7xUfDJWh8n6RqUZIoin+oQ2ss3Dw+LCBagMcQUBuiQ3Y8/YbY0gGjm7PuFwSPgXdb9Nhcm6dU6aLzipftAwXj6pfI9oWKwBk0H08pRcZT/dKNxDXzylXV0S4I4CQ7ZFHykvxK5f53HQSb/jAJSBrCzXzpyshKb02Lm1M/8qM1kGriD3zFJ0I+Y4HoQZxTymoADjqtQ=
1

The genes shown in the table below are from the lac operon system of E. coli. The symbols a, b, and c represent the repressor (I) gene, the operator (O) region, and the structural gene (Z) for β-galactosidase, although not necessarily in that order. Furthermore, the order in which the symbols are written in the genotypes is not necessarily the actual sequence in the lac operon.

  Activity (+) or inactivity (-) of the Z gene
Genotype Inducer absent Inducer present
a- b+ c+ + +
a+ b+ c- + +
a+ b- c- - -
a+ b- c+/a- b+ c- + +
a+ b+ c+/a- b- c- - +
a+ b+ c-/a- b- c+ - +
a- b+ c+/a+ b- c- + +

Based on the data in the table, deduce which symbol (a, b, and c) represents lac gene I, lac gene Z, and the operator region O. In the table, a superscript minus sign on a gene symbol merely indicates a mutant, but recall that some mutant behaviors in this system are given special mutant designations. After the symbols a, b, and c have been assigned to lac I, Z, and O, use the conventional gene symbols for the lac operon to designate some of the genotypes in the table.

(Data in this problem from J. Kuspira and G. W. Walker, Genetics: Questions and Problems. Copyright 1973 by McGraw-Hill.)

Unpack the Problem: Break this problem into several parts and arrive at a solution using this guided, step-by-step approach.

  • Part A (steps 1 and 2): Work with the haploid genotypes to make as many assignments as possible.
  • Part B (steps 3 and 4): Work with the diploid genotypes to make as many assignments as possible.
  • Part C (steps 5 and 6): Translate the abc symbols into conventional lac operon nomenclature.

Question 11.1

As determined previously, the b symbol represents the Z gene. Which of the partial diploids can be used to assign the a and c genes to parts of the lac operon? To answer the question, complete the following table by selecting yes or no from each pull-down menu.
Partial diploid genotype Can be used to assign symbols to lac operon components?
a+ b- c+/a- b+ c- sjkhLuRCQ4SijoxQ
a+ b+ c+/a- b- c- sjkhLuRCQ4SijoxQ
a+ b+ c-/a- b- c+ PcjeiwlDuBLi5zTg
a- b+ c+/a+ b- c- PcjeiwlDuBLi5zTg
Correct. Each partial diploid genotype has to be evaluated for its ability to unambiguously provide information about assigning the a and c symbols to the lac operator site and repressor gene. To do this, assume that the a symbol, for example, represents the lac I gene. Then ask if the β-galactosidase activity results are consistent with the assumption and could not be the result of an alternative assumption. Using this type of analysis, the a+ b- c+/a- b+ c- and a+ b+ c+/ a- b- c- genotypes fail, but the a+ b+ c-/ a- b- c+ and a- b+ c+/ a+ b- c- allow for assigning the a and c symbols.
Incorrect. Each partial diploid genotype has to be evaluated for its ability to unambiguously provide information about assigning the a and c symbols to the lac operator site and repressor gene. To do this, assume that the a symbol, for example, represents the lac I gene. Then ask if the β-galactosidase activity results are consistent with the assumption and could not be the result of an alternative assumption. Using this type of analysis, the a+ b- c+/a- b+ c- and a+ b+ c+/ a- b- c- genotypes fail, but the a+ b+ c-/ a- b- c+ and a- b+ c+/ a+ b- c- allow for assigning the a and c symbols.

The genes shown in the table below are from the lac operon system of E. coli. The symbols a, b, and c represent the repressor (I) gene, the operator (O) region, and the structural gene (Z) for β-galactosidase, although not necessarily in that order. Furthermore, the order in which the symbols are written in the genotypes is not necessarily the actual sequence in the lac operon.

  Activity (+) or inactivity (-) of the Z gene
Genotype Inducer absent Inducer present
a- b+ c+ + +
a+ b+ c- + +
a+ b- c- - -
a+ b- c+/a- b+ c- + +
a+ b+ c+/a- b- c- - +
a+ b+ c-/a- b- c+ - +
a- b+ c+/a+ b- c- + +

Based on the data in the table, deduce which symbol (a, b, and c) represents lac gene I, lac gene Z, and the operator region O. In the table, a superscript minus sign on a gene symbol merely indicates a mutant, but recall that some mutant behaviors in this system are given special mutant designations. After the symbols a, b, and c have been assigned to lac I, Z, and O, use the conventional gene symbols for the lac operon to designate some of the genotypes in the table.

(Data in this problem from J. Kuspira and G. W. Walker, Genetics: Questions and Problems. Copyright 1973 by McGraw-Hill.)

Unpack the Problem: Break this problem into several parts and arrive at a solution using this guided, step-by-step approach.

  • Part A (steps 1 and 2): Work with the haploid genotypes to make as many assignments as possible.
  • Part B (steps 3 and 4): Work with the diploid genotypes to make as many assignments as possible.
  • Part C (steps 5 and 6): Translate the abc symbols into conventional lac operon nomenclature.

Question

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1

The genes shown in the table below are from the lac operon system of E. coli. The symbols a, b, and c represent the repressor (I) gene, the operator (O) region, and the structural gene (Z) for β-galactosidase, although not necessarily in that order. Furthermore, the order in which the symbols are written in the genotypes is not necessarily the actual sequence in the lac operon.

  Activity (+) or inactivity (-) of the Z gene
Genotype Inducer absent Inducer present
a- b+ c+ + +
a+ b+ c- + +
a+ b- c- - -
a+ b- c+/a- b+ c- + +
a+ b+ c+/a- b- c- - +
a+ b+ c-/a- b- c+ - +
a- b+ c+/a+ b- c- + +

Based on the data in the table, deduce which symbol (a, b, and c) represents lac gene I, lac gene Z, and the operator region O. In the table, a superscript minus sign on a gene symbol merely indicates a mutant, but recall that some mutant behaviors in this system are given special mutant designations. After the symbols a, b, and c have been assigned to lac I, Z, and O, use the conventional gene symbols for the lac operon to designate some of the genotypes in the table.

(Data in this problem from J. Kuspira and G. W. Walker, Genetics: Questions and Problems. Copyright 1973 by McGraw-Hill.)

Unpack the Problem: Break this problem into several parts and arrive at a solution using this guided, step-by-step approach.

  • Part A (steps 1 and 2): Work with the haploid genotypes to make as many assignments as possible.
  • Part B (steps 3 and 4): Work with the diploid genotypes to make as many assignments as possible.
  • Part C (steps 5 and 6): Translate the abc symbols into conventional lac operon nomenclature.

Question

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
1

The genes shown in the table below are from the lac operon system of E. coli. The symbols a, b, and c represent the repressor (I) gene, the operator (O) region, and the structural gene (Z) for β-galactosidase, although not necessarily in that order. Furthermore, the order in which the symbols are written in the genotypes is not necessarily the actual sequence in the lac operon.

  Activity (+) or inactivity (-) of the Z gene
Genotype Inducer absent Inducer present
a- b+ c+ + +
a+ b+ c- + +
a+ b- c- - -
a+ b- c+/a- b+ c- + +
a+ b+ c+/a- b- c- - +
a+ b+ c-/a- b- c+ - +
a- b+ c+/a+ b- c- + +

Based on the data in the table, deduce which symbol (a, b, and c) represents lac gene I, lac gene Z, and the operator region O. In the table, a superscript minus sign on a gene symbol merely indicates a mutant, but recall that some mutant behaviors in this system are given special mutant designations. After the symbols a, b, and c have been assigned to lac I, Z, and O, use the conventional gene symbols for the lac operon to designate some of the genotypes in the table.

(Data in this problem from J. Kuspira and G. W. Walker, Genetics: Questions and Problems. Copyright 1973 by McGraw-Hill.)

Unpack the Problem: Break this problem into several parts and arrive at a solution using this guided, step-by-step approach.

  • Part A (steps 1 and 2): Work with the haploid genotypes to make as many assignments as possible.
  • Part B (steps 3 and 4): Work with the diploid genotypes to make as many assignments as possible.
  • Part C (steps 5 and 6): Translate the abc symbols into conventional lac operon nomenclature.

Question

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
1

Conclusion

The correct assignments are a = lac O
  b = lac Z
  c = lac I

The convention is to write the lac genotype so that the symbols are in the same order as they appear in the lac operon. All wild-type lac operon components are written with a superscript + sign. The symbol Oc is that of a mutant operator region. It has impaired binding of the repressor product of the I gene, and, therefore, the lac operon associated with the Oc operator cannot be turned off. This type of mutation acts in cis and acts in a dominant fashion. The symbol I- represents a repressor gene that cannot make functional repressor. The result is an operon that constitutively expresses the lac Z gene and makes β-galactosidase whether inducer is present or absent.