Cyclic Mixture Mutagenesis \\ for DNA-Based Computing -- Gradual Transformation Version<A NAME="2"> </A><A NAME="sec:gradTM"> </A>

Go backward to Large Tape Head Version
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Gradual Transformation Version

Next, we have the same simple Turing machine implemented using the idea of gradual transformation of a given source substring to a result substring.

        :q0 TCAGTCATG
        #   XXX
        :L1 GATGTCATG
        #      XXX
        :L2 GATCCGATG
        #         XXX
        :0  GATCCGCGA
 
        #0  GATCCGCGA
        #   XXX
        :R1 TCACCGCGA
        #      XXX
        :R2 TCAGTCCGA
        #         XXX
        #q0 TCAGTCATG
 
        3'- !0 !0 !q0 !0 !0 -5'
 
        0  L1 R1  0
        0  L2 R2  0
        0  0  q0  0

(In reality, we would not have the mismatches close together like this, because our model of the thermodynamics, which is based on data for isolated mismatches, might no longer be valid. However, this is easily fixed by simply reordering the bases in the symbol encodings.)

Below is a sample run of this machine. We skip the steps on which no change occurs. Note that by step 7 the tape head has moved forwards one step, and on step 29 it has moved forwards 2 steps. This is as far as it can go, since we have not provided here for a "1" as a flanking symbol to the right. Thereafter the tape head simply continues random-walking. It hits the limit again on cycle 77.

----------------------------------------------------------------------
sim tur1.olig -T 30 -n -s 4 -p 1000
Parameters: file = tur1.olig, T = 303.15, c = 1e-07, t = 240,
            p = 1000, s = 4
 
Cycle = 1, time = 4:00, temp =  30.00.
[0      ][L1     ][R1     ][0      ]                  
GATCCGCGAGATGTCATGTCACCGCGAGATCCGCGA                  
:::::::::XXX::::::XXX:::::::::::::::                  
CTAGGCGCTAGTCAGTACCTAGGCGCTCTAGGCGCTCTAGGCGCTGCCACTAGA
[!0     ][!q0    ][!0     ][!0     ][!0     ][!1     ]
 
Cycle = 5, time = 4:00, temp =  30.00.
[0      ][L2     ][R2     ][0      ]                  
GATCCGCGAGATCCGATGTCAGTCCGAGATCCGCGA                  
::::::::::::XXX::::::XXX::::::::::::                  
CTAGGCGCTCTACAGTACAGTGGCGCTCTAGGCGCTCTAGGCGCTGCCACTAGA
[!0     ][!L1    ][!R1    ][!0     ][!0     ][!1     ]
 
Cycle = 7, time = 4:00, temp =  30.00.
[0      ][0      ][q0     ][0      ]                  
GATCCGCGAGATCCGCGATCAGTCATGGATCCGCGA                  
:::::::::::::::XXX::::::XXX:::::::::                  
CTAGGCGCTCTAGGCTACAGTCAGGCTCTAGGCGCTCTAGGCGCTGCCACTAGA
[!0     ][!L2    ][!R2    ][!0     ][!0     ][!1     ]
 
Cycle = 11, time = 4:00, temp =  30.00.
[0      ][L2     ][R2     ][0      ]                  
GATCCGCGAGATCCGATGTCAGTCCGAGATCCGCGA                  
:::::::::::::::XXX::::::XXX:::::::::                  
CTAGGCGCTCTAGGCGCTAGTCAGTACCTAGGCGCTCTAGGCGCTGCCACTAGA
[!0     ][!0     ][!q0    ][!0     ][!0     ][!1     ]
 
Cycle = 13, time = 4:00, temp =  30.00.
[0      ][L1     ][R1     ][0      ]                  
GATCCGCGAGATGTCATGTCACCGCGAGATCCGCGA                  
::::::::::::XXX::::::XXX::::::::::::                  
CTAGGCGCTCTAGGCTACAGTCAGGCTCTAGGCGCTCTAGGCGCTGCCACTAGA
[!0     ][!L2    ][!R2    ][!0     ][!0     ][!1     ]
 
Cycle = 15, time = 4:00, temp =  30.00.
[0      ][L2     ][R2     ][0      ]                  
GATCCGCGAGATCCGATGTCAGTCCGAGATCCGCGA                  
::::::::::::XXX::::::XXX::::::::::::                  
CTAGGCGCTCTACAGTACAGTGGCGCTCTAGGCGCTCTAGGCGCTGCCACTAGA
[!0     ][!L1    ][!R1    ][!0     ][!0     ][!1     ]
 
Cycle = 19, time = 4:00, temp =  30.00.
[0      ][0      ][q0     ][0      ]                  
GATCCGCGAGATCCGCGATCAGTCATGGATCCGCGA                  
:::::::::::::::XXX::::::XXX:::::::::                  
CTAGGCGCTCTAGGCTACAGTCAGGCTCTAGGCGCTCTAGGCGCTGCCACTAGA
[!0     ][!L2    ][!R2    ][!0     ][!0     ][!1     ]
 
Cycle = 23, time = 4:00, temp =  30.00.
         [0      ][L1     ][R1     ][0      ]         
         GATCCGCGAGATGTCATGTCACCGCGAGATCCGCGA         
         :::::::::XXX::::::XXX:::::::::::::::         
CTAGGCGCTCTAGGCGCTAGTCAGTACCTAGGCGCTCTAGGCGCTGCCACTAGA
[!0     ][!0     ][!q0    ][!0     ][!0     ][!1     ]
 
Cycle = 27, time = 4:00, temp =  30.00.
         [0      ][L2     ][R2     ][0      ]         
         GATCCGCGAGATCCGATGTCAGTCCGAGATCCGCGA         
         ::::::::::::XXX::::::XXX::::::::::::         
CTAGGCGCTCTAGGCGCTCTACAGTACAGTGGCGCTCTAGGCGCTGCCACTAGA
[!0     ][!0     ][!L1    ][!R1    ][!0     ][!1     ]
 
Cycle = 29, time = 4:00, temp =  30.00.
         [0      ][0      ][q0     ][0      ]         
         GATCCGCGAGATCCGCGATCAGTCATGGATCCGCGA         
         :::::::::::::::XXX::::::XXX:::::::::         
CTAGGCGCTCTAGGCGCTCTAGGCTACAGTCAGGCTCTAGGCGCTGCCACTAGA
[!0     ][!0     ][!L2    ][!R2    ][!0     ][!1     ]
 
Cycle = 33, time = 4:00, temp =  30.00.
         [0      ][L2     ][R2     ][0      ]         
         GATCCGCGAGATCCGATGTCAGTCCGAGATCCGCGA         
         :::::::::::::::XXX::::::XXX:::::::::         
CTAGGCGCTCTAGGCGCTCTAGGCGCTAGTCAGTACCTAGGCGCTGCCACTAGA
[!0     ][!0     ][!0     ][!q0    ][!0     ][!1     ]
 
Cycle = 37, time = 4:00, temp =  30.00.
         [0      ][L1     ][R1     ][0      ]         
         GATCCGCGAGATGTCATGTCACCGCGAGATCCGCGA         
         ::::::::::::XXX::::::XXX::::::::::::         
CTAGGCGCTCTAGGCGCTCTAGGCTACAGTCAGGCTCTAGGCGCTGCCACTAGA
[!0     ][!0     ][!L2    ][!R2    ][!0     ][!1     ]
 
Cycle = 41, time = 4:00, temp =  30.00.
[0      ][0      ][q0     ][0      ]                  
GATCCGCGAGATCCGCGATCAGTCATGGATCCGCGA                  
::::::::::::::::::XXX::::::XXX::::::                  
CTAGGCGCTCTAGGCGCTCTACAGTACAGTGGCGCTCTAGGCGCTGCCACTAGA
[!0     ][!0     ][!L1    ][!R1    ][!0     ][!1     ]
 
Cycle = 43, time = 4:00, temp =  30.00.
[0      ][L2     ][R2     ][0      ]                  
GATCCGCGAGATCCGATGTCAGTCCGAGATCCGCGA                  
:::::::::::::::XXX::::::XXX:::::::::                  
CTAGGCGCTCTAGGCGCTAGTCAGTACCTAGGCGCTCTAGGCGCTGCCACTAGA
[!0     ][!0     ][!q0    ][!0     ][!0     ][!1     ]
 
Cycle = 53, time = 4:00, temp =  30.00.
[0      ][0      ][q0     ][0      ]                  
GATCCGCGAGATCCGCGATCAGTCATGGATCCGCGA                  
:::::::::::::::XXX::::::XXX:::::::::                  
CTAGGCGCTCTAGGCTACAGTCAGGCTCTAGGCGCTCTAGGCGCTGCCACTAGA
[!0     ][!L2    ][!R2    ][!0     ][!0     ][!1     ]
 
Cycle = 59, time = 4:00, temp =  30.00.
         [0      ][L1     ][R1     ][0      ]         
         GATCCGCGAGATGTCATGTCACCGCGAGATCCGCGA         
         :::::::::XXX::::::XXX:::::::::::::::         
CTAGGCGCTCTAGGCGCTAGTCAGTACCTAGGCGCTCTAGGCGCTGCCACTAGA
[!0     ][!0     ][!q0    ][!0     ][!0     ][!1     ]
 
Cycle = 65, time = 4:00, temp =  30.00.
[0      ][0      ][q0     ][0      ]                  
GATCCGCGAGATCCGCGATCAGTCATGGATCCGCGA                  
::::::::::::::::::XXX::::::XXX::::::                  
CTAGGCGCTCTAGGCGCTCTACAGTACAGTGGCGCTCTAGGCGCTGCCACTAGA
[!0     ][!0     ][!L1    ][!R1    ][!0     ][!1     ]
 
Cycle = 67, time = 4:00, temp =  30.00.
[0      ][L2     ][R2     ][0      ]                  
GATCCGCGAGATCCGATGTCAGTCCGAGATCCGCGA                  
:::::::::::::::XXX::::::XXX:::::::::                  
CTAGGCGCTCTAGGCGCTAGTCAGTACCTAGGCGCTCTAGGCGCTGCCACTAGA
[!0     ][!0     ][!q0    ][!0     ][!0     ][!1     ]
 
Cycle = 71, time = 4:00, temp =  30.00.
[0      ][0      ][q0     ][0      ]                  
GATCCGCGAGATCCGCGATCAGTCATGGATCCGCGA                  
:::::::::::::::XXX::::::XXX:::::::::                  
CTAGGCGCTCTAGGCTACAGTCAGGCTCTAGGCGCTCTAGGCGCTGCCACTAGA
[!0     ][!L2    ][!R2    ][!0     ][!0     ][!1     ]
 
Cycle = 73, time = 4:00, temp =  30.00.
         [0      ][L1     ][R1     ][0      ]         
         GATCCGCGAGATGTCATGTCACCGCGAGATCCGCGA         
         :::::::::XXX::::::XXX:::::::::::::::         
CTAGGCGCTCTAGGCGCTAGTCAGTACCTAGGCGCTCTAGGCGCTGCCACTAGA
[!0     ][!0     ][!q0    ][!0     ][!0     ][!1     ]
 
Cycle = 75, time = 4:00, temp =  30.00.
         [0      ][L2     ][R2     ][0      ]         
         GATCCGCGAGATCCGATGTCAGTCCGAGATCCGCGA         
         ::::::::::::XXX::::::XXX::::::::::::         
CTAGGCGCTCTAGGCGCTCTACAGTACAGTGGCGCTCTAGGCGCTGCCACTAGA
[!0     ][!0     ][!L1    ][!R1    ][!0     ][!1     ]
 
Cycle = 77, time = 4:00, temp =  30.00.
         [0      ][0      ][q0     ][0      ]         
         GATCCGCGAGATCCGCGATCAGTCATGGATCCGCGA         
         :::::::::::::::XXX::::::XXX:::::::::         
CTAGGCGCTCTAGGCGCTCTAGGCTACAGTCAGGCTCTAGGCGCTGCCACTAGA
[!0     ][!0     ][!L2    ][!R2    ][!0     ][!1     ]
----------------------------------------------------------------------

- Michael P. Frank, September 12, 1995. Formatted using HyperLaTeX-1.3.