Team:NYU Abu Dhabi/Model

Mathematical Modelling

The following species were used

Species Name	Symbol Used
Recombinase	$R$
Primer	$Pr$
DNA	$D$
DNA Polymerase	$P$
Single Strand Binding Protein (SSB)	$S$
A specific binding of recombinase to a primer to form a closed complex	$R:Pr$
A specific binding of recombinase and primer to the DNA to form a closed complex	$R:Pr:D$
A specific binding of recombinase, primer, SSB protein to the DNA to form a closed complex	$R:Pr:D:S$
A specific binding of recombinase, primer, SSB protein, DNA Polymerase to the DNA to form a closed complex	$R:Pr:D:S:P$
A specific binding of primer, SSB protein, DNA Polymerase to the DNA to form a closed complex	$Pr:D:S:P$

The following parameters were used

Parameter	Variable Name
Forward rate constant for the binding of Recombinase and Primer	$k1f$
Reverse rate constant for the binding of Recombinase and Primer	$k1r$
Forward rate constant for the binding of Recombinase, Primer to DNA	$k2f$
Reverse rate constant for the binding of Recombinase, Primer to DNA	$k2r$
Forward rate constant for the binding of Recombinase, Primer, DNA to SSB protein	$k3f$
Reverse rate constant for the binding of Recombinase, Primer, DNA to SSB protein	$k3r$
Forward rate constant for the binding of Recombinase, Primer, DNA, SSB protein to DNA Polymerase	$k4f$
Reverse rate constant for the binding of Recombinase, Primer, DNA, SSB protein to DNA Polymerase	$k4r$
Forward rate constant for the unbinding of Recombinase from the Recombinase, Primer, DNA, SSB protein, DNA Polymerase complex	$k5f$
Reverse rate constant for the unbinding of Recombinase from the Recombinase, Primer, DNA, SSB protein, DNA Polymerase complex	$k5r$
Rate constant for the replication of DNA with the complex consists of Primer, DNA, SSB Protein, DNA Polymerase	$kf$

$$ 1. R + Pr \leftrightharpoons R:Pr $$ $$ 2. R:Pr + D \leftrightharpoons R:Pr:D $$ $$ 3. R:Pr:D + S \leftrightharpoons R:Pr:D:S $$ $$ 4. R:Pr:D:S + P \leftrightharpoons R:Pr:D:S:P $$ $$ 5. R:Pr:D:S:P \leftrightharpoons R + Pr:D:S:P $$ $$ 6. Pr:D:S:P \to 2D + S + P + Pr + D $$

Species Name	Symbol Used
Recombinase	\(R\)
Primer	\(Pr\)
DNA	\(D\)
DNA Polymerase	\(P\)
Single Strand Binding Protein (SSB)	\(S\)
A specific binding of recombinase to a primer to form a closed complex	\(R:Pr\)
A specific binding of recombinase and primer to the DNA to form a closed complex	\(R:Pr:D\)
A specific binding of recombinase, primer, SSB protein to the DNA to form a closed complex	\(R:Pr:D:S\)
A specific binding of recombinase, primer, SSB protein, DNA Polymerase to the DNA to form a closed complex	\(R:Pr:D:S:P\)
A specific binding of primer, SSB protein, DNA Polymerase to the DNA to form a closed complex	\(Pr:D:S:P\)

Parameter	Variable Name
Forward rate constant for the binding of Recombinase and Primer	\(k1f\)
Reverse rate constant for the binding of Recombinase and Primer	\(k1r\)
Forward rate constant for the binding of Recombinase, Primer to DNA	\(k2f\)
Reverse rate constant for the binding of Recombinase, Primer to DNA	\(k2r\)
Forward rate constant for the binding of Recombinase, Primer, DNA to SSB protein	\(k3f\)
Reverse rate constant for the binding of Recombinase, Primer, DNA to SSB protein	\(k3r\)
Forward rate constant for the binding of Recombinase, Primer, DNA, SSB protein to DNA Polymerase	\(k4f\)
Reverse rate constant for the binding of Recombinase, Primer, DNA, SSB protein to DNA Polymerase	\(k4r\)
Forward rate constant for the unbinding of Recombinase from the Recombinase, Primer, DNA, SSB protein, DNA Polymerase complex	\(k5f\)
Reverse rate constant for the unbinding of Recombinase from the Recombinase, Primer, DNA, SSB protein, DNA Polymerase complex	\(k5r\)
Rate constant for the replication of DNA with the complex consists of Primer, DNA, SSB Protein, DNA Polymerase	\(kf\)

Team:NYU Abu Dhabi/Model

Mathematical Modelling

The following species were used

Species Name

Symbol Used

Recombinase

\(R\)

Primer

\(Pr\)

DNA

\(D\)

DNA Polymerase

\(P\)

Single Strand Binding Protein (SSB)

\(S\)

A specific binding of recombinase to a primer to form a closed complex

\(R:Pr\)

A specific binding of recombinase and primer to the DNA to form a closed complex

\(R:Pr:D\)

A specific binding of recombinase, primer, SSB protein to the DNA to form a closed complex

\(R:Pr:D:S\)

A specific binding of recombinase, primer, SSB protein, DNA Polymerase to the DNA to form a closed complex

\(R:Pr:D:S:P\)

A specific binding of primer, SSB protein, DNA Polymerase to the DNA to form a closed complex

\(Pr:D:S:P\)

The following parameters were used

Parameter

Variable Name

Forward rate constant for the binding of Recombinase and Primer

\(k1f\)

Reverse rate constant for the binding of Recombinase and Primer

\(k1r\)

Forward rate constant for the binding of Recombinase, Primer to DNA

\(k2f\)

Reverse rate constant for the binding of Recombinase, Primer to DNA

\(k2r\)

Forward rate constant for the binding of Recombinase, Primer, DNA to SSB protein

\(k3f\)

Reverse rate constant for the binding of Recombinase, Primer, DNA to SSB protein

\(k3r\)

Forward rate constant for the binding of Recombinase, Primer, DNA, SSB protein to DNA Polymerase

\(k4f\)

Reverse rate constant for the binding of Recombinase, Primer, DNA, SSB protein to DNA Polymerase

\(k4r\)

Forward rate constant for the unbinding of Recombinase from the Recombinase, Primer, DNA, SSB protein, DNA Polymerase complex

\(k5f\)

Reverse rate constant for the unbinding of Recombinase from the Recombinase, Primer, DNA, SSB protein, DNA Polymerase complex

\(k5r\)

Rate constant for the replication of DNA with the complex consists of Primer, DNA, SSB Protein, DNA Polymerase

\(kf\)

Based on the reaction model above, the following equations could be deduced: