Viral Assembly
to fix
- References section needed
- Less wall of text, more bullets/bolding, etc.
We want a full network for assembly. Players include ungapped DNA, regular DNA, 35s transcript, 19s transcript, mutated DNA and transcripts (later on), P1 to P6. Need to describe how these all interact to lead to viable viral capsids.
Some discussion of a short-term stochastic model and a long-term mass-action ODE model.
Should also discuss other in-cell viral models here.
We plan to formulate models without cas9 effects to start.
Here we investigate published models of viral assembly so we may be able to produce our own.
The Turnip Mosaic Virus (TuMV) is a positive-sense ssRNA virus. Martínez et al. [3] presented a basic model of TuMV genome amplification within a protoplast during an infection cycle. Since the TuMV uses host machinery to replicate its genome, the model they present only considers various copies of the genome and how they increase over time without worrying about other viral dynamics. They do, however, account for the limited amount of viral genomes that may be present in the cell by assuming logistic growth.
From this paper we learned there are two essential methods of ssRNA genome amplification: Geometric and Stamping Machine replication. In pure geometric replication, the genome is duplicated and both the original and the newly-produced strand may be used as a template for further replication. Since TuMV lacks proofreading ability this leads to compounding errors in replication which may decrease viral fitness. In pure stamping machine replication, there are only a few original templates of the genome which are used to produce new strands. The new copies are not used to produce further strands in order to prevent errors from accumulating. In reality most viruses (including CaMV) use some combination of both types of replication. This allows for both rapid amplification (from geometric replication) and errors to be minimized (from stamping machine).
Specifically for TuMV, there are two different types of RNA strands that may encode the genome. These are the positive-sense and negative-sense RNA strands, which are complementary to one another. Ultimately it’s the positive-sense RNA which is packaged and infects cells, but negative-sense RNA is essential to amplification. The initial (+) sense strand is transcribed to produce a (-) sense strand which may itself be transcribed to form new (+) sense strands.
The model presented by Martínez et al. [3] initially considers three state variables: one is the concentration of negative-sense RNA and the other two are concentrations of positive-sense RNA separated by how the strands are synthesized. In order to simulate the initial infection by a few copies of the viral genome, the authors put the positive-sense RNA under the inducible 35S promoter from CaMV. This “initial” RNA is denoted by p_35S to indicate it’s origin and replication of the genomes directly from these copies is analogous of stamping machine replication (a few original copies used to produced many more). The negative-sense RNA is denoted by m. The concentration of positive-sense RNA synthesized from complementary negative-sense strands are denoted by p_repl and is analogous to geometric amplification.
They make the assumption that amplification is limited to logistic growth and get the system:
[ Eq’ns (1)-(4) in the paper ]
They perform further analysis on this first system, but it is fairly involved and mostly irrelevant to our system.
What we have learned from this model is that genome amplification is a combination of geometric and stamping machine replication. In our case it’s been confirmed that the newly-synthesized CaMV genomes may re-enter the plant nucleus and be used as templates [1], but most copies of 35S RNA are transcribed from a few initial templates. We also learned that it’s critical to track both the coding dsDNA as well as the complimentary 35S pregenomic RNA since they will be used to produce one another. The experimental methods may be useful for our lab team to help us determine parameter values for our model. Since the authors used the CaMV 35S promoter they already measured the transcription rate of 35S RNA. Finally, the authors later analysis may prove useful to us when trying to understand how mutation of our target sequence may alter effectiveness of our silencing system.
Viruses in the same group as TuMV include Tobacco Mosaic Virus (TMV), Tomato Mosaic Virus (ToMV), SARS-CoV, Rhinovirus, and lots of other famous human diseases. However, it is not too closely related to the CaMV so we will need to look into more closely related viruses as well.
The second model we summarize is the Hepatitis B model of intracellular replication presented by Nakabayashi and Sasaki [4]. Hepatitis B is a Group VII (dsDNA-RT) virus similar to the virus we are targeting so we expect their model to be similar to our own.
The HepB core particle consists of the viral genome (partially double stranded DNA - pdsDNA) which is packaged alongside viral polymerase inside a nucleocapsid (made of “core” protein - see the green hexagon in the image above). The core particle is itself packaged inside a capsid made of surface protein (the thick blue circle in the image above).
Upon infection, the viral polymerase fills gaps in the pdsDNA to form cccDNA (complete closed circular DNA). The cccDNA is then transcribed to produce 3.5kb pregenomic RNA as well as 2.4kb mRNA. The 3.5kb RNA is translated to make more viral polymerase and core protein. In order to make more core particles, the viral polymerase binds to the 3.5kb RNA to form a pregenome-polymerase complex. This complex is then coated by core protein and the pregenome is reverse transcribed to form a new core particle. The 2.4kb mRNA produces surface protein which then envelopes the core particle to make a complete viral particle.
This model is written as a system of ODEs: [ eq’n (1) from Nakabayashi ]
Where x = [ core particle ], y = [ cccDNA ], R_g = [ 3.5kb RNA ], c = [ core protein ], p = [ polymerase ], z = [ pregenome-polymerase complex ], R_s = [ 2.4kb mRNA ], s = [ surface protein ], and v = [ virion ].
The viral assembly dynamics are remarkably similar to CaMV assembly! They are similar in that they both have a dsDNA genome which is transcribed to pregenomic RNA (3.5kb RNA vs 35S RNA) and separate mRNA molecules produced (2.4kb mRNA vs 19S RNA) to aid in assembly. They both code for reverse transcriptase (viral polymerase vs P5) and surface protein which are used to produce new dsDNA and package particles respectively.
The primary differences are that the dsDNA in HBV must be processed to produce cccDNA, HBV has a core particle, and P6 is used as an activator of the other genes in CaMV. However, these differences may easily be accounted for to produce a model similar to Nakabayashi and Sasaki’s HepB model [4].
I might put a table here to summarize them. Also summarize everything we've learned about intracellular viral assembly modelling.
We first attempt a simple ODE model to describe viral assembly.
From the CaMV Life Cycle page, we conclude there are 10 state variables to consider: the concentration of dsDNA, the concentration of 35S RNA, the concentration of 19S RNA, the concentration of virions, and the concentrations of each of the six viral proteins [2].
We denote each as follows:
- x = [ dsDNA ]
- y = [ 35S RNA ]
- z = [ 19S RNA ]
- P1 = [ Protein 1 ]
- P2 = [ Protein 2 ]
- P3 = [ Protein 3 ]
- P4 = [ Protein 4 ]
- P5 = [ Protein 5 ]
- P6 = [ Protein 6 ]
- v = [ virion ]
- dsDNA is transcribed at a rate alpha_35S to produce 35S RNA
- dsDNA is transcribed at a rate alpha_19S to produce 19S RNA
- 19S is translated at a rate beta_P6 to produce P6
- P6 somehow activates production of P1-P5 from 35S RNA...this is unclear
- P5 reverse transcribes 35S RNA to produce dsDNA at a rate I will name later
- P4 packages the dsDNA at some other rate with no parameter yet
This section may be used to determine how many terms each ODE will have. We will determine the form of these terms when the interactions become more clear.
- dsDNA is produced in only one way (reverse transcription) and consumed two ways (packaging and degradation)
- 19S RNA is produced one way (transcription) and consumed one way (degradation)
- 35S RNA is produced one way (transcription) and consumed one way (degradation)
- Each protein (except P4) is produced one way (translation) and consumed one way (degradation)
- P4 is produced one way (translation) and consumed two ways (packaging and degradation)
- Virions are produced one way (packaging) and consumed one or two way (degradation and maybe emission from the cell)
From this I conclude the dsDNA and P4 ODEs will each have three terms, the RNA and non-P4 protein ODEs will each have two terms, and the viral particle will have either two or three. Most terms will be assumed to follow mass action kinetics.
[1] Bonneville, J. M., & Hohn, T. (1993). 16 A Reverse Transcriptase for Cauliflower Mosaic Virus State of the Art, 1992. Cold Spring Harbor Monograph Archive, 23, 357-390.
[2] Khelifa, M., Massé, D., Blanc, S., & Drucker, M. (2010). Evaluation of the minimal replication time of Cauliflower mosaic virus in different hosts. Virology, 396(2), 238-245.
[3] Martínez, F., Sardanyés, J., Elena, S. F., & Daròs, J. A. (2011). Dynamics of a plant RNA virus intracellular accumulation: stamping machine vs. geometric replication. Genetics, 188(3), 637-646.
[4] Nakabayashi, J., & Sasaki, A. (2011). A mathematical model of the intracellular replication and within host evolution of hepatitis type B virus: understanding the long time course of chronic hepatitis. Journal of theoretical biology, 269(1), 318-329.