Team:LCG-UNAM-Mexico:KZM

KZM Simbiology ® diagram

As WTM, KZM is a stochastic molecular model of bacteriophage T7 life cycle, it was constructed to simulate the interplay between the kamikaze system and the phage T7 infection.
Both models, WTM and KZM, were constructed to monitor the evolution and abundance of molecular species in the systems.
For the purpose of this project we are particularly concerned in the abundance of phage T7 (burst size) at the end of the cycle (720 seconds) in each infection event.
Ensembles of runs of WTM and KZM will provide us with data to build Burst Size Distributions for each model. A Kamikaze BSD is next utilized by the population models to recreate the impact of our synthetic circuit in the infection at population level.

The following critical processes are accounted in this model:

• Insertion and translocation of T7 DNA at different times

Entry of T7 DNA into the host cell occurs in several distinct stages.
Phage's DNA is arranged in three classes of genes depending on their positions, it is translocated into the cell between 6 to 10 minutes after attachment, so this order and timing drives the phage's development. This phenomenon of DNA translocation is modeled here taking into account reported insertion speeds [REFERENCE].

• Transcription of different T7 DNA segments into polycistronic mRNAs

It has been shown that T7 genes are expressed in overlapped polycistronic mRNAs.
Transcription of T7 polycistronic mRNAs occurs if and only if its coding DNA segment is available in the cell. Transcription is dependent of the set of genes inserted at a time.
We define a set of transcription rates for every polycistronic mRNA taking into account constant bacterial or T7 RNA polymerase elongation rates and the length of the polycistronic mRNA, these transcription rates will be our rate limiting steps at the transcriptional level.

• Transcription of kamikaze system

Expression of kamikaze system occurs when T7 RNA polymerase is present in the cell, this protein activates transcription through a T7 RNA pol promoter.
Rate limiting step for this reaction is the elongation rate of T7 RNA polymerase, a translation rate for this polycistronic mRNA was constructed taking into account this limiting rate and the length of the produced messenger.
Kamikaze polycistronic mRNA codes for GFP, rRNAse domain of colicin E3(ColE3) and luxI.

• Degradation of phage mRNAs

We assume the same degradation rate for all T7 polycistronic mRNAs. Until now impact of this phenomenon had not been studied. It has been found that phage messengers are stabler than Bacterial mRNAs [REFERENCE].

• Translation of phage mRNAs into proteins

In this model, translation is simulated assuming an environment of unlimited amino acids
On the other hand, Quantity of ribosomes changes over time depending on the toxic action of ribosome-inactivating rRNAse domain of colicin E3.
We also assume that the elongation rate at which ribosomes incorporate amino acids is constant over all T7 mRNAs.
We define a set of initial translation rates and they are coupled to the ribosome decay so they change over time as well. Kamikaze system affect T7 cycle by reducing the number of bacteriophage proteins and therefore lowering the number of assembled T7 particles at the end of phage life cycle.

• Translation of kamikaze mRNA

Translation occurs as any other protein, its production decreases as a function the abundance of ribosomes and its translation rates.

• T7 DNA replication

DNA synthesis is simulated by taking elongation of T7 DNA polymerase as the rate-limiting step.
We assume an environment of limited free nucleotides so we can set a maximum number of T7 genomes produced in a single infection taking into account the size of the host genome (and this includes bacterial chromosomes, plasmids and other sources of free nucleotides).

• Procapsid Assembly

This phenomenon is simulated in almost the same way as Drew Endy et al. 1996 using mass action kinetics.

• DNA packaging and final assembly

Both processes are modeled using mass action kinetics as well. This last step requires complete procapsids, T7 DNA, and enough of each structural protein to complete the phage. The simulation assumes that packaging of DNA into the procapsid is the rate-limiting step for T7 progeny formation.

• Sabotage: Inactivation and decay of ribosomes

The main actor of this sabotage is rRNAse domain of colicin E3 (colE3), this toxin cleaves 16s rRNAs in active ribosomes rendering them useless to translate or inactive, it is expected a decay in the number of functional ribosomes and in the overall bacterial translation.

• Simulation, performance and BSD construction

This is a single simulation of the performance of WTM, with this algorithm we can study the evolution and behavior of molecular species in time.
For the purpose of our project we're particularly interested in the burst size an infected cell could produce in each infection process, as we said BSDs for WTM and KZM can be assembled with many runs of each model so we can compare the performance of our synthetic kamikaze system versus the wild-type at molecular and population levels.
Generated BSDs are next used by Cellular Automaton to choose the burst size an infected cell (with and without our kamikaze system) is going to release into the medium. BSDs are also use by the agent-based model, in both cases BZDs manage the fate of the population.
In this video there are plotted two molecular species, ABproteins or Major head proteins, this protein is the main component of T7 procapsids, it is evident the upper limit of molecules at which a procapsid assembly occurs. Production of this protein grows faster at late stages when polycistronic mRNAs responsible for them become more and more abundant in the cell.
T7 plotted in red grows until it reach a burst size of about 250 phages at the end of the cycle/simulation (lysis time 720 seconds).

References