Logical operations Jesse Wu

Outline Logic review Logical operators Promoters Host conscious circuit design

Logical operators AND: true if all true OR: true if one true XOR: If both are different NOT: true -> false false -> true NAND: NOT(AND) NOR: NOT(OR)

Logic tables AND NAND OR NOR XOR x y | x&y !(x&y) x|y !(x|y) x^y 0 0 | | | | NOT x | !x | 0 | 1 | 1 | 0 |

XOR light off on light Watch the light

Result to operator lookup table 1100 – a 1010 – b 0000 – Always off 0001 – !(a|b) 0010 – !a|b 0011 – !a 0100 – a&!b 0101 – !b 0110 – a^b 0111 – !(a&b) 1100 – a 1010 – b 1000 – a&b 1001 – !(a^b) 1010 – b 1011 – !a&b 1100 – a 1101 – a|!b 1110 – a|b 1111 – Always on *Grayed out means only depends on a or b or neither.

Promoters Two kinds: Inducible Repressible Inducers and Repressors can be: Proteins Complexes Etc … Example: pLAC

Promoters - types Inducible Repressible

Promoters - pLAC Both an inducible and repressible promoter Only the inducible property can be used in E. coli experiments.

OR Simplest way: Use one inducible promoter and its inducer E.g. pRE and CII (from phage) PaPa XX PbPb X PXPX Output Xb a Inducible promoter Coding region of inducer

AND Simplest way: Use one inducible promoter and its two inducers which form a complex E.g. LuxI (BBa_C0061) + LuxR (BBa_C0062) forms a complex that can induce pLux (BBa_R0062) PaPa C1C1 C1C1 PbPb C2C2 PCPC Output C2C2 b a Inducible promoter Coding region of inducers C

AND - OR+inverters a 1 & a 2 & a 3 & … & a n =>!!(a 1 & a 2 & a 3 & … & a n ) Then by Demorgan’s law: =>!( !a 1 | !a 2 | !a 3 | … | !a n )

NAND, NOR NAND = AND + inverter NOR = OR + inverter One possible inverter: E.g. pTet (BBa_R0040) and Tet (BBa_C0040) P output NewOutput Output From AND/OR Repressible promoter

Sequential promoters (1/3) Two or more promoters in a row introduces ordering issues. Whether the circuit is on depends entirely on the second promoter since it may have an inducer or repressor bound to it, rendering the first promoter useless

Sequential promoters (2/3) a b 0 0 | | b 1 0 | | a+b a b 0 0 | a+b 0 1 | | b 1 1 | 0

Sequential promoters (3/3) a b 0 0 | b 0 1 | | a+b 1 1 | 0 a b 0 0 | | a+b 1 0 | | b

!!!Beware of host cell when selecting proteins!!! Beware of the proteins you use in your circuit. Since: The proteins used may affect the host cell E.g. if your protein is a protease, it might degrade other essential proteins within the cell The host cell might affect the proteins E.g. the proteins produced might not survive the environment within the host cell Example on next page

Reloxilator: System Detail P RE CII P RE HflB P RE LuxI P LUX CII HflB L AHL P LAC CIIIC The Oscillator The TunerThe Synchronizer P RE GFP The Reporter P LAC LuxR R R+AHL Host cell is E. coli DH5  HflB is a protease naturally occurring in E. coli. There are only 400 copies of the transmembrane HflB protein in E. coli. HflB is essential for E. coli survival. Circuit is doomed… -_-

Summary Logic: AND, OR, NOT, NAND, NOR, XOR Promoters: Inducible and/or repressible Inducers and repressors can be complexes Create circuits based on promoters and their inducers and repressors