Team:AFCM-Egypt/Model
Modeling of DREP-based vaccine replication vs traditional vaccine replication
Description
To simulate the efficacy of DREP-based Vaccine, we compared between plus-strand RNA molecules of traditional DNA vaccine replication vs plus-strand RNA molecules of DREP-based Vaccine within VMS. using populations of numbers (in the cytoplasm) of plus-strand viral RNA molecules (RPC), translation complexes (TC), viral polyprotein molecules (P), the enzyme NS5B and associated viral proteins needed for RNA synthesis (EC), the numbers of plus-strand RNA within the VMS ( after self-amplification) (RP), dsRNA within the VMS (RD), viral polymerase complexes within the VMS (E), the numbers of plus-strand RNA and dsRNA replicative intermediate complexes ( RIP and RID) respectively.
Parameter Estimates
Equation (1)
Plus-strand RNA, RPC, interacts with host cell ribosomes, (Ribo=10), to form a translation complex at an effective rate k1. RPC, by forming polysomes, disappears at rate k1 and reappears at rate k2 when translation is complete. Nucleases at the rate of MPC can degrade free plus-strand RNAs in the cytoplasm, lost from the cytoplasm by transport into VMS at the rate of kPin, and acquired by transport out of VMS at the rate of kPout.
Equation (2)
TC, which degrades at rate MT and Ribo represents a complex of 10 ribosomes to initiate translation concomitantly with RPC.
Equation (3)
Free viral polyprotein molecules, P, are produced by translation into separate viral proteins, including the enzymes responsible for viral RNA synthesis, at a rate of k2 per translation complex within the cytoplasm.
Equation (4)
Enzymes responsible for viral RNA synthesis, Ecyt, e.g., NS5B, at rate kc. Degraded before reaching the VMS at rate MEC, or transported into VMS at rate k8.
Equation (5-9)
In VMS, de novo development of RIPand RID complexes occurs with the rate constants k3 and k5, respectively, and degrades with the MP2 and MD2 rate constants. The nascent plus- and minus-strand RNAs are synthesised with rate constants of k4p and k4m , respectively. In VMS (RP and Rds), free plus-strand RNA and dsRNA degrade with MP and MD2 rate constants, respectively. Furthermore, the polymerase complex degrades or loses activity within VMS with a constant ME rate, which is probably lower than the MEC cytoplasmic degradation rate.
Simulation
1-Plus-strand RNA (Traditional Vaccine)
The graph shows the concentration of plus strand RNA molecules in the traditional vaccine relying on the traditional replicating abilities of traditional vaccines. It shows that the steady state is achieved after 75 days with a maximum concentration of 175 (population scale).
2-plus-strand RNA (based on self-replicating Replicons)
The graph shows the concentration of plus strand RNA molecules in our vaccine relying on self replicating viral abilities of replicons. It shows that the steady state is achieved after 75 days with a maximum concentration of 250 (population scale). which indicates that our design increases the efficiency of the vaccine by increasing the concentration of plus-strand RNA molecules.
Promoter optimization
Although, we have shown that replicon-based delivery outperform the traditional delivery, AFCM Egypt-2020 found that other factors could control replicon function such as SGPs. So, the team started by optimizing sets of SGPs for both EEV and SFV alpha viruses correlating their stability with experimentally reported expression efficacy. AFCM Egypt-2020 selected SGP30 and SGP15 because they have the highest expression rates as shown in the plot below.
And as shown in these graphs below, the number of +ve strand RNA is doubled by using SGP15 in comparison to SGP30. That’s why we chose it in the circuit.
Immune evasion system vs traditional degradation of replicon
We have been recommended by Dr noreen wauford from MIT to construct an immune evasion system to protect our replicon from immune attack So, we constructed it via addition of Gly/Ala repeats upstream to our 3 vaccine versions to be protected from CTls attacks We tested it via these differential equations.
Equations (1-11)
The designations for the concentrations are as follows. A, polyprotein; M, active replicase complexes; S, inactive replicase complexes; P, the form of inactive replicase complexes incapable of converting to active replicase complexes; F, cellular factor; R (E), the positive - (negative-) strand RNA; O (N), active replicase complexes on the positive- (negative-) strand RNA. where Q is the average concentration of the positive-strand RNA (R) with the free initiation site under the assumption that the active replicase complexes (O) are uniformly distributed along the strand length. And where V is the average concentration of the minus-strand RNA (E) with the free initiation site under the assumption that the active replicase complexes (N) are uniformly distributed along the strand length.
Results
The simulation showed a higher efficacy with using this system as it delays the time needed for degradation by about 30 days after addition of Gly/Ala repeats as illustrated in these graphs.
Modeling of Immune Response in DREP-based vaccine vs Traditional DNA Vaccine
We have already simulated immune response against the three versions of multi-epitope vaccine, yet, we wanted to simulate variation in immune response against DREP based delivery vs traditional DNA vaccine delivery via T helper and DCs response. Vaccine cells (VC) are supposed to be recognized by Cytotoxic T cells (TC) and Antibodies (AB) that kill them. Killed VC releases both Interleukin-12 (IL12) and Tumor associated antigens (TAA). TAA are captured by antigen presenting cells (APC) and then presented to T helper cells (TH). IL12 stimulates both TH and TC actions. TH releases interleukin-2 (IL2) which boosts TH, TC, and B actions and stimulates B cells to differentiate into plasma B cells (B). B releases AB, and both AB and stimulated TC kill cancer cells (CC), which further release TAA.
Equations (1)
Vaccine cells (VC) with a predefined dose are inserted into the host. The vaccine cell inoculation is modelled by a kin(t, q) feature that adds q vaccine cells to the host cells at time t, if an injection was planned at that time. Since vaccine cells come from the outside, this concept is the only source of the equation.Cytotoxic T cells that recognise vaccine cells by their allogeneic MHC class II molecules (term -a19TCVC) or by particular antibodies that can specifically destroy vaccine cells by a complementary mechanism (term -a17ABVC) are blocked by vaccine cells that die from various causes, such as natural death (term -μ1VC).
Equations (2)
The dead or killed vaccine or cancer cells may release tumor-associated antigens (TAA). The number of released antigens is thought to be equal to both the number of vaccine cells and the number of suppressed cancer cells (VC and TAA respectively) (g21(a19TC+ a17AB+μ1)VC and g28 (a88+a89TC)VC). The root elements of the equation are represented by these two terms.Antigens, such as dendritic cells , macrophages and B cells, are exposed to normal degradation (term μ2TAA) and phagocytosis by antigen presenting cells (-a20APCTAA). In addition, antibodies can bind to free immune complexes producing antigens (term -a27ABTAA).
Equations (3)
The percentage of T helper activated cells is determined from the number of cells presenting antigen (APC) that occur in the system (g40APC term). Interleukins 12 and 2 (IL12 and IL2) tend to promote the priming and duplication of T helper cells (terms alp46 (IL2 IL2+s1)TH and alp45(IL12 IL12+s2)TH). It is worth noting that these cells are able to self-stimulate their activities because interleukin 2 is produced by T helper cells. The death factor is modelled on the word -μ4TH.
Equations (4)
A population of B cells (B) that has been triggered by positive feedback from T helper cells (TH) (g34TH term) and is therefore capable of releasing particular antibodies against cancer cells. In equation ( 10), we provide the B as an APC function. In promoting B cell replication, interleukin 2 (IL2) produced by T helper cells plays an adjuvant role (term alp36(IL2 IL2+s3)B). Death is modelled after the word -μ3B.
Equations (5)
Interleukin 12 (IL12) is mainly introduced through vaccine administrations, so it depends on the vaccine dosage. In previous in vivo experiments [24] interleukin 12 was introduced separately, but after transduction of IL2 genes inside vaccine cells [4], it is released by killed vaccine cells, so it is proportional to the number of killed vaccine cells (term g51(a19TC + a17AB + μ1)VC).
Equations (6)
The release of interleukin 2 is mainly by T helper cells (g64TH term). Interleukin 2 induces T helper priming, as previously mentioned, and primed T helper cells release more interleukin 2. It is prone to natural degradation (-μ6IL2) and is partly consumed by cytotoxic T cell priming (-a69TCIL2 term) and B cell replication (-a63BIL2 term) for mitotic and stimulus signals.
Equations (7)
The major outcome of the humoral immune response is antibodies. Plasma B(B) cells (term g73B) emit antibodies (AB) and are subject to natural degradation (term -μ7AB model). In addition, after performing their roles, they disappear: binding to particular targets, i.e. antigens (a72TAAAB), cancer and vaccine cells (a78CCAB and a71VCAB, respectively).
Equations (8)
Development of cancer cells (CC) is modelled by the expression [(1-(CCcm )*K-α88].The term -α88CC is used to take into account the killing of CC by other cells of the immune system that are known to be of minor significance to the mechanism and are thus not clearly modelled, such as Natural Killer cells that can destroy cancer cells that under express the main class I complex of histocompatibility. The word p models the continuous development of cancer cells from newborns.
Equations (9)
The priming of cytotoxic T cells (TC) relies primarily on vaccine cells (VC). In order to promote presentation (term γ91VC), vaccine cells are equipped with an allogeneic major histocompatibility class I complex. Via the release of interleukin 2 (term α96*(IL2IL2+S96)*TC)), replication is instead indirectly induced by T helper cells. The word -μ9TC is used to model natural death.
Equations (10)
With the term antigen presenting cells we indicate a class of different types of cells, such as dendritic cells,, whose focal mission is to recognize, capture, and process antigens in order to present small antigenic sequences named peptides in conjunction with MHC class molecules to both cytotoxic and helper T cells. Antigen Presenting cells (APC) are then depending on the quantity of the antigens that have been released (term g02TAA), and can die (term -μ0APC).
simulation
1-Th response in DREP vs DNA vaccine
As shown in these graphs, T helper cell response is increased in DREP in comparison to traditional DNA vaccine which indicates eliciting higher immune response in DREP.
2-DCs response in DREP vs DNA vaccine
And for DC response, it showed significant difference due to increase in concentration of tumour associated antigen in DREP. Therefore, DCs act as a bridge between innate and adaptive immunity.
Mathematical Modeling of Anti-Cancer Response in DREP-based vaccine.
In order to simulate the anti-cancer response of our DREP-based vaccine, we performed this model to follow the dynamic of tumor size T (t) , TGF-β cocentration B(t), activated cytotoxic effector cells E(t), regulatory T cells R(t), vaccine-induced cytotoxic effector V(t). uninfected susceptible target cells (U), infected virus-producing cells (I), and the virus load (L). All are formulated by the following system of nonlinear ordinary differential equations (ODEs):
Table (1) shows Major used parameters.
Equation (1)
The tumor follows growth rate, a0, and carrying capacity, 1/c0. The second term describes the ability of immune cells to induce apoptosis of tumor cells. The last term defines the action of vaccine cells on tumor cells. Since vaccine cells are considered to be fully differentiated, they are assumed to be unaffected by the inhibitory effects of TGF-β. Vaccine cells induce the death of tumor cells at a rate δ0
Equation (2)
Maximum rate of TGF-β production is represented by the parameter a1; c2 is the critical tumor size at which the switch occurs; and the decay rate of the protein is d
Equation (3)
It describes the dynamics of the number of effector T cells . The first term represents immune recruitment. This term is divided by (1 + c3T B) for the negative effect of tumor growth and TGF-β production on immune recruitment a. r represents differentiation of effector cells into regulatory T cells . The fourth term models the removal of effector T cells from the system. These cells have both a natural death rate (δ1) ; and a death rate due to interaction with regulatory T cells (δ0).
Equation (4)
The first term represents that Tregs differentiate from effector T cells at a rate (r). The second term is the rate at which Tregs die.
Equation (5)
The first team is modeled as an influx of activated tumor-specific cytotoxic T cells. The second term represents the natural death rate.
Equation (6)
Uninfected target cells (U) are produced at a constant rate λ and die at rate d2
Equation (7)
By the interaction of virus (L) with uninfected target cells (U) at a constant infectivity rate k, the target cells become infected cells (I)
Equation (8)
Infected cells (I), which in turn produce infectious virus (L) with production rate p. Due to viral cytopathicity, immune elimination and/or apoptosis, infected cells (I) die at a rate δ2 . Virus is cleared at rate c from the cells.
Simulation
And in conclusion, it’s found that DREP-based vaccine elicits stronger anticancer response vs traditional DNA vaccine as shown in the graph above by decreasing tumor size.
Epitope-HLA Interaction Modeling
Utilising IMGT/HLA Allele Query Form, we could retrieve the protein sequence of the most common allele for HLA.
Then, using SWISS-MODEL which is a fully homology-modelling server, we could automate protein structure homology -modelling server, we could make protein modelling for HLA.
After that, through GalaxyWEB, we could predict protein interaction using GalaxyPepDock which is Protein-peptide docking based on interaction similarity. It is done by inserting both the protein and peptide sequence.
Figure: Molecular Docking Simulation between HLA-B*35:01 and predicted HPMSEYPTY peptide, represented by red sticks.
Figures: Showing how custommune anticipates the structural stability of our (HLA-epitope) complexes using Dfire-score.
Literature Cited
-
Dahari, H., Ribeiro, R. M., Rice, C. M., & Perelson, A. S. (2007). Mathematical modeling of subgenomic hepatitis C virus replication in Huh-7 cells. Journal of virology, 81(2), 750–760. https://doi.org/10.1128/JVI.01304-06
-
Ali, N., K. D. Tardif, and A. Siddiqui. 2002. Cell-free replication of the hepatitis C virus subgenomic replicon. J. Virol. 76:12001-12007.
-
Bartholomeusz, A. I., and P. J. Wright. 1993. Synthesis of dengue virus RNA in vitro: initiation and the involvement of proteins NS3 and NS5. Arch. Virol. 128:111-121.
-
Biebricher, C. K., M. Eigen, W. C. Gardiner, Y. Husim, H. C. Keweloh, and A. Obst. 1987. Complex chemical reaction systems, p. 17-38. In J. Warnatz and W. Jager (ed.), Mathematical modeling and simulation. Springer-Verlag, Berlin, Germany.
-
Chu, P. W., and E. G. Westaway. 1985. Replication strategy of Kunjin virus: evidence for recycling role of replicative form RNA as template in semiconservative and asymmetric replication. Virology140:68-79.
-
Mishchenko, E. L., Bezmaternykh, K. D., Likhoshvai, V. A., Ratushny, A. V., Khlebodarova, T. M., YU. SOURNINA, N. A. T. A. L. I. A., ... & Kolchanov, N. A. (2007). Mathematical model for suppression of subgenomic hepatitis C virus RNA replication in cell culture. Journal of bioinformatics and computational biology, 5(02b), 593-609
-
Tsantrizos YS, Bolger G, Bonneau P, Cameron DR, Goudreau N, Kikolj G, LaPlante SR, Llinds-Brunet M, Macrocyclic inhibitors of the NS3 protease as potential therapeutic agents of hepatitis c Virus infection, Angew Chem 42:1355–1360, 2003.
-
Johnston VK, Maley D, Gagnon RC, Grassmann CW, Behrens SE, Sarisky RT, Kinetic profile of a heterocyclic HCV replicon RNA synthesis inhibitor, Biochem Biophys Res Commun 311:672–677, 2003.
-
Bianca, C., Chiacchio, F., Pappalardo, F., & Pennisi, M. (2012). Mathematical modeling of the immune system recognition to mammary carcinoma antigen. BMC bioinformatics, 13 Suppl 17(Suppl 17), S21. https://doi.org/10.1186/1471-2105-13-S17-S21
-
appalardo F, Castiglione F, Lollini PL, Motta S. Modelling and Simulation of Cancer Immunoprevention vaccine. Bioinformatics. 2005;21(12):2891–2897. doi: 10.1093/bioinformatics/bti426.
-
appalardo F, Halling-Brown MD, Rapin N, Zhang P, Alemani D, Emerson A, Paci P, Duroux P, Pennisi M, Palladini A, Miotto O, Churchill D, Rossi E, Shepherd AJ, Moss DS, Castiglione F, Bernaschi M, Lefranc MP, Brunak S, Motta S, Lollini PL, Basford KE, Brusic V. ImmunoGrid, an integrative environment for large-scale simulation of the immune system for vaccine discovery, design, and optimization. Briefings in Bioinformatics. 2009;10(3):330–340.
-
Bianca C, Pennisi M, Motta S, Ragusa MA. Immune System Network and Cancer Vaccine. AIP Conference Proceedings. 2011;1389:945–948.
-
Pappalardo F, Mastriani E, Lollini PL, Motta S. Genetic Algorithm against Cancer. Lecture Notes in Computer Science. 2006;3849:223–228. doi: 10.1007/11676935_27.
-
Wilson, S., & Levy, D. (2012). A mathematical model of the enhancement of tumor vaccine efficacy by immunotherapy. Bulletin of mathematical biology, 74(7), 1485-1500
-
Byrne, H., & Gourley, S. (1997). The role of growth factors in avascular tumour growth. Math. Comput. Model., 26(4), 35–55.
-
Cappuccio, A., Elishmereni, M., & Agur, Z. (2006). Cancer immunotherapy by interleukin-21: potential treatment strategies evaluated in a mathematical model. Cancer Res., 66(14), 7293–7300.
-
de Pillis, L. G., Radunskaya, A., & Wiseman, C. L. (2005). A validated mathematical model of cellmediated immune response to tumor growth. Cancer Res., 65(17), 7950–7958
-
Dermime, S., Armstrong, A., Hawkins, R. E., & Stern, P. L. (2002). Cancer vaccines and immunotherapy. Br. Med. Bull., 62, 149–162.
-
Robinson, J., Halliwell, J., Hayhurst, J., Flicek, P., Parham, P., & Marsh, S. (2015, January). The IPD and IMGT/HLA database: Allele variant databases. Retrieved October 26, 2020, from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4383959/
-
Waterhouse, A., Bertoni, M., Bienert, S., Studer, G., Tauriello, G., Gumienny, R., . . . Schwede, T. (2018, July 2). SWISS-MODEL: Homology modelling of protein structures and complexes. Retrieved October 26, 2020, from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6030848/
-
C;, L. (n.d.). GalaxyPepDock: A protein-peptide docking tool based on interaction similarity and energy optimization. Retrieved October 26, 2020, from https://pubmed.ncbi.nlm.nih.gov/25969449/
-
Tarek, M., Elhefnawi, M., Maricato, J., Diaz, R., Shytaj, I., & Savarino, A. (2020, January 01). Custommune: A web tool to design personalized and population-targeted vaccine epitopes. Retrieved October 26, 2020, from