Difference between revisions of "Team:OUC-China/polycistron"

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</div>  
 
</div>  
 
<br />(3)Activation:
 
<br />(3)Activation:
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<div align="center">         </div>  
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<div align="center">     <math>
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<mrow>
 +
  <msubsup>
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  <mi>O</mi>
 +
  <mi>n</mi>
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  <mi>R</mi>
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  </msubsup>
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  <mover>
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  <mo>&#x2192;</mo>
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  <mrow>
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    <msub>
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    <mi>k</mi>
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    <mrow>
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      <mi>t</mi><mi>r</mi><mi>a</mi><mi>n</mi><mi>s</mi><mo stretchy='false'>[</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo stretchy='false'>]</mo></mrow>
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    </msub>
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  <mi>A</mi>
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  <mi>n</mi>
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  <mi>R</mi>
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  </msubsup>
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  </mrow>
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</math>
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    </div>  
 
<br />(4)Back-translocation:
 
<br />(4)Back-translocation:
−
<div align="center">         </div>  
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<div align="center">     <math>
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<mrow>
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  <msubsup>
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  <mi>O</mi>
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  <mrow>
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    <mi>n</mi><mo>&#x2212;</mo><mn>1</mn></mrow>
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  <mi>R</mi>
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  </msubsup>
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  <mtext>+</mtext><msup>
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  <mi>U</mi>
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  <mi>R</mi>
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  </msup>
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  <msub>
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  <mrow></mrow>
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  <mrow>
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    <mo stretchy='false'>[</mo><mi>n</mi><mo>+</mo><mo>&#x25B3;</mo><mi>R</mi><mi>i</mi><mi>b</mi><mo>&#x2212;</mo><mn>2</mn><mo>,</mo><mi>n</mi><mo>&#x2212;</mo><mo>&#x25B3;</mo><mi>R</mi><mi>i</mi><mi>b</mi><mo stretchy='false'>]</mo></mrow>
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  </msub>
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  <mover>
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  <mo>&#x2192;</mo>
 +
  <mrow>
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    <msub>
 +
    <mi>k</mi>
 +
    <mrow>
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      <mi>b</mi><mi>t</mi></mrow>
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    </msub>
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    </mrow>
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  </mover>
 +
  <msubsup>
 +
  <mi>A</mi>
 +
  <mrow>
 +
    <mi>n</mi><mo>&#x2212;</mo><mn>3</mn></mrow>
 +
  <mi>R</mi>
 +
  </msubsup>
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  <mtext>+</mtext><msup>
 +
  <mi>U</mi>
 +
  <mi>R</mi>
 +
  </msup>
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  <msub>
 +
  <mrow></mrow>
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  <mrow>
 +
    <mo stretchy='false'>[</mo><mi>n</mi><mo>+</mo><mo>&#x25B3;</mo><mi>R</mi><mi>i</mi><mi>b</mi><mo>&#x2212;</mo><mn>3</mn><mo>,</mo><mi>n</mi><mo>+</mo><mo>&#x25B3;</mo><mi>R</mi><mi>i</mi><mi>b</mi><mo>&#x2212;</mo><mn>1</mn><mo stretchy='false'>]</mo></mrow>
 +
  </msub>
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  </mrow>
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</math>
 +
    </div>  
 
<br />(5)Drop-off:
 
<br />(5)Drop-off:
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<div align="center">         </div>  
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<div align="center">   <math>
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<mrow>
 +
  <msubsup>
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  <mi>O</mi>
 +
  <mi>n</mi>
 +
  <mi>R</mi>
 +
  </msubsup>
 +
  <mover>
 +
  <mo>&#x2192;</mo>
 +
  <mrow>
 +
    <msub>
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    <mi>k</mi>
 +
    <mrow>
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      <mi>d</mi><mi>r</mi><mi>o</mi><mi>p</mi></mrow>
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    </msub>
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    </mrow>
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  </mover>
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  <mtext>Rib+</mtext><msup>
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  <mi>U</mi>
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  <mi>R</mi>
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  </msup>
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  <msub>
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  <mrow></mrow>
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  <mrow>
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    <mo stretchy='false'>[</mo><mi>n</mi><mo>&#x2212;</mo><mo>&#x25B3;</mo><mi>R</mi><mi>i</mi><mi>b</mi><mo>,</mo><mi>n</mi><mo>+</mo><mo>&#x25B3;</mo><mi>R</mi><mi>i</mi><mi>b</mi><mo stretchy='false'>]</mo></mrow>
 +
  </msub>
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  </mrow>
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</math>
 +
    </div>  
 
<br />(6)Trans-translation:
 
<br />(6)Trans-translation:
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<div align="center">         </div>  
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<div align="center">     <math>
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<mrow>
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  <mi>R</mi><mover>
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  <mo>&#x2192;</mo>
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  <mrow>
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    <msub>
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    <mi>k</mi>
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    <mi>u</mi>
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    </msub>
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    </mrow>
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  </mover>
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  <mo stretchy='false'>[</mo><mi>R</mi><mi>i</mi><msup>
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  <mi>b</mi>
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  <mi>R</mi>
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  </msup>
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  <mo stretchy='false'>]</mo><mi>R</mi><mi>i</mi><mi>b</mi></mrow>
 +
</math>
 +
    </div>  
 
<br />(7)Elongation completion
 
<br />(7)Elongation completion
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<div align="center">         </div>  
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<div align="center">   <math>
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<mrow>
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  <msup>
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  <mi>A</mi>
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  <mi>R</mi>
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  </msup>
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  <msub>
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  <mrow></mrow>
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  <mrow>
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    <msub>
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    <mi>n</mi>
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    <mrow>
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      <mi>l</mi><mi>a</mi><mi>s</mi><mi>t</mi></mrow>
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    </msub>
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    </mrow>
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  </msub>
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  <mover>
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  <mo>&#x2192;</mo>
 +
  <mrow>
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    <msub>
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    <mi>k</mi>
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    <mi>u</mi>
 +
    </msub>
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    </mrow>
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  </mover>
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  <mo stretchy='false'>[</mo><mi>R</mi><mi>i</mi><msup>
 +
  <mi>b</mi>
 +
  <mi>R</mi>
 +
  </msup>
 +
  <mo stretchy='false'>]</mo><mi>R</mi><mi>i</mi><mi>b</mi><mo>+</mo><msubsup>
 +
  <mi>U</mi>
 +
  <mrow>
 +
    <mo stretchy='false'>[</mo><msub>
 +
    <mi>n</mi>
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    <mrow>
 +
      <mi>l</mi><mi>a</mi><mi>s</mi><mi>t</mi></mrow>
 +
    </msub>
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    <mo>,</mo><msub>
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    <mi>n</mi>
 +
    <mrow>
 +
      <mi>l</mi><mi>a</mi><mi>s</mi><mi>t</mi></mrow>
 +
    </msub>
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    <mo>&#x2212;</mo><mo>&#x25B3;</mo><mi>R</mi><mi>i</mi><mi>b</mi><mo stretchy='false'>]</mo></mrow>
 +
  <mi>R</mi>
 +
  </msubsup>
 +
  <mo>+</mo><msub>
 +
  <mi>P</mi>
 +
  <mrow>
 +
    <mtext>prem</mtext></mrow>
 +
  </msub>
 +
  </mrow>
 +
</math>
 +
    </div>  
 
<br />(8)Folding and activation:
 
<br />(8)Folding and activation:
−
<div align="center">         </div>  
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<div align="center">   <math>
 +
<mrow>
 +
  <msub>
 +
  <mi>P</mi>
 +
  <mrow>
 +
    <mtext>prem</mtext></mrow>
 +
  </msub>
 +
  <mover>
 +
  <mo>&#x2192;</mo>
 +
  <mrow>
 +
    <msub>
 +
    <mi>k</mi>
 +
    <mrow>
 +
      <mi>f</mi><mi>o</mi><mi>l</mi><mi>d</mi></mrow>
 +
    </msub>
 +
    </mrow>
 +
  </mover>
 +
  <mi>P</mi></mrow>
 +
</math>
 +
    </div>  
 
<br />(9)Protein degradation
 
<br />(9)Protein degradation
−
<div align="center">         </div>  
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<div align="center">     <math>
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<mrow>
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  <mi>P</mi><mover>
 +
  <mo>&#x2192;</mo>
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  <mrow>
 +
    <msub>
 +
    <mi>k</mi>
 +
    <mrow>
 +
      <mi>d</mi><mi>e</mi><mi>c</mi></mrow>
 +
    </msub>
 +
    </mrow>
 +
  </mover>
 +
  <mi>&#x03D5;</mi></mrow>
 +
</math>
 +
    </div>  
 +
 +
  In the 8 reaction equations above, the Rib stands for the free ribosome while the RibR represents to the ribosome which is binding to the RNA chain. <math>
 +
<mrow>
 +
  <mo>&#x25B3;</mo><mi>R</mi><mi>N</mi><mi>A</mi><mi>p</mi></mrow>
 +
</math>
 +
represents to the footprint of ribosome. Every ribosome will occupied about (<math>
 +
<mrow>
 +
  <mn>2</mn><mo>&#x25B3;</mo><mi>R</mi><mtext>ib+1</mtext></mrow>
 +
</math>
 +
) nucleotides. URN ,Orn and Arn are the ribonucleic equivalent fo Un, On and An in transcriptional part, which has similarity meaning.
 
 
 
 

Revision as of 21:31, 17 October 2018

Team OUC-China: Main
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polycistron

In our miniToe polycistron system, we build a coupled transcription-translation model considering several events in prokaryotes to get a deep understanding of polycistron. Then we simplify this model into a more flexible model to predict how the miniToe structure changes the relative expression level in polycistron.

1.Current model for polycistron expression system


Before we modeling our system, we firstly give a short review on model of polycistron expression system. For the common model, they believe that the mRNA of different cistrons in different positions has the same abundance and if they have the same translation rate, the protein which produced by different cistrons is equal. But in the truth, the natural polycistron has many strategies in regulate the protein abundance such as the overleap or hairpin in 3’. And for the synthetic polycistron, many things just like the transcription polarity and translation coupling paly an important roles. Many of them control the protein by control the mRNA abundance. So a more precise model for polycistron is needed.

2.The coupled transcription-translation model for monocistron


In this part we will present a coupled transcription-translation model for the polycistron in prokaryotes. The model is based on the Andre S Riberio’s work, he presents a coupled transcription-translation model for monocistron. We have done some works to extend the model to use in the polycistron.

2.1 The origin model for monocistron


The origin model build by Andre S Riberio is a stochastic delayed differential equation model in sequence-level, and it can be divided into two mian part: the transcriptional part and the translational part. The transcriptional part can be described by the following events:
(1)Initiation and promoter complex formation:
Pro+RNAp → RNAp·Pro( τ OC )

(2)Promoter clearance:
RNAp·Pro+ U [1,△RNAp+1] → O 1 +Pro

(3)Elongation:
A n + U n+△RNAp+1 → O n+1 + U n−△RNAp + U R n−△RNAp

(4)Activation:
O n → A n

(5)Pausing:
O n → k p O n p O n ← 1/ τ p O n p

(6)Pause release due to collision:
O n p + A n−2△RNAp−1 → 0.8 k m O n + A n−2△RNAp−1 i

(7) Pause release by collision
O n p + A n−2△RNAp−1 → 0.2 k m O n + A n−2△RNAp− 1 p

(8)Arrest:
O n → k ar O n ar O n ← 1/ τ ar O n ar

(9)Editing:
O n → k ec O n correcting O n ← 1/ τ c O n correcting

(10)Premature termination:
O n → k pre RNAp+ U [n−△RNAp,n+△RNAp]

(11)Pyrophosporolysis:
O n + U n−△RNAp−1 + U R n−△RNAp−1 → k pyro O n−1 + U n+△RNAp−1

(12)Completion:
A n last → k f RNAp+ U [ n last , n last −△RNAp]

(13) mRNA degradation:
A n last → k dr ϕ

In the 13 reaction equations above, the Pro stands for the promoter region, the RNAp is RNA polymerase while the Pro-RNAp stands for the promoter which is occupied by the RNA polymerase. An, On and Un are standing for the nth nucleotides in the stage of activated, occupied and unoccupied. U[strat,end] stands for the nucleotides in the range from start number to end number in index. Onp, Onar and Oncorrecting represents the a paused, arrested and error correcting at position n. And due to the temporal steric, the RNAp will occupied about () nucleotides. denotes transcribed ribonucleotides which are free.

The translation part can be described by the following events:
(1)Initiation:
Rib+ U R [1,n+△Rib+1] → k trans_init O 1 R +Ri b R

(2)Stepwise translocation:
A n−3 R + U R [n+△Rib−3,n+△Rib−1] → k tm O n−2 R

O n−2 R → k tm O n−1 R

O n−1 R → k tm O n R + U R [n+△Rib−2,n+△Rib]

(3)Activation:
O n R → k trans[A,B,C] A n R

(4)Back-translocation:
O n−1 R + U R [n+△Rib−2,n−△Rib] → k bt A n−3 R + U R [n+△Rib−3,n+△Rib−1]

(5)Drop-off:
O n R → k drop Rib+ U R [n−△Rib,n+△Rib]

(6)Trans-translation:
R → k u [Ri b R ]Rib

(7)Elongation completion
A R n last → k u [Ri b R ]Rib+ U [ n last , n last −△Rib] R + P prem

(8)Folding and activation:
P prem → k fold P

(9)Protein degradation
P → k dec ϕ
In the 8 reaction equations above, the Rib stands for the free ribosome while the RibR represents to the ribosome which is binding to the RNA chain. △RNAp represents to the footprint of ribosome. Every ribosome will occupied about ( 2△Rib+1 ) nucleotides. URN ,Orn and Arn are the ribonucleic equivalent fo Un, On and An in transcriptional part, which has similarity meaning.

Fig.1-1 The working process of miniToe system

All the reactions happened in our first system, miniToe, can be described chronologically by following five main steps[1]:

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