Difference between revisions of "Team:UFMG Brazil/Modeling"

Modeling

Overview

Modeling is a powerful tool in Synthetic Biology and Engineering. In the LeishMANIA project, it has provided us with an important engineering approach to predict the Leishmania phagocytosis by macrophages, the subsequent IFN-β synthesis and the treatment efficacy. Thus, it helped us with modifying and testing our project design.

In order to check if our IFN-β delivery system would be effective, we have developed a scheme that represents in a simplified way its operation (Figure 1). After that, we searched for equations that represented the change amount of Leishmania cells, immune cells (monocytes and tissue macrophages) and the amount of IFN-β synthesized and distributed.

Figure 1 - Simplified scheme representing our system. (1) Skin macrophage kinetics during inflammation. (2) Tissue monocytes transformation in inflammatory tissue macrophages (ITM). (3) The ratio of promastigotes Leishmania cells (pL) successfully phagocytosed by macrophages and transformed in amastigotes (aL). (4) IFN-β mass of produced by the Anti Inflammatory Tissue Macrophages (ATM) hosting Leishmania amastigotes. (5) Number of ITM that will be converted to ATM considering the IFN-β mass and (6) IFN-β clearance.

MATHEMATICAL MODELING

Based on a literature search, we tried to define the best parameters for our mathematical modeling. Then we wrote a Perl script that simulates the transfection using our Leishmania chassis for 144 hours in a 250 g male Swiss mouse. The parameters used, as well as a brief explanation for how they were defined, are detailed below:

Phagocytosis rate: 80% - For the optimal ratio of ten Leishmania per macrophage, the literature suggest that 80% of the parasites are successful in the macrophages infection (Chang & Dwyer, 1978);

Macrophages Half-life: 20 hours - Literature sources indicates that the LY6C^hiCCR2⁺ CD62L⁺CX₃CR1^mid macrophage subpopulation (which is our subpopulation of interest) has a half-life of 20 hours (Ginhoux & Jung, 2014);

Leishmania Half-life: 108 hours. This value was optimized using the data found on the literature (Chang & Dwyer, 1978), nevertheless we still need a nexperimental verification;

Monocyte migration kinetics (6.2 x 10⁴ cells for each joint tissue cm²) versus time (hours):

f(x) = 1999.26 * x^3.55

Developed by us using the literature data (Furth et al., 1985), it represents the acute inflammatory state kinetics, but when considering that our approach is used in a chronic inflammatory state, the only the constant rate used is approximately of 1999 monocytes;

Leishmania ratio for each macrophage cell:

f(x) = ln (x) * 126.92 + 401.65

The Leishmania infectivity, its half-life and consequently IFN-β synthesis depend on their proportion on each host cell. We have improved this function using some literature data (Dortay & Mueller, 2010), where x represents the average time in hours that a wild Leishmania population culture leads to begin to decline in number of individuals. In our program, the x value was set to 360 hours (15 days). After these 360 hours, this numerical ratio stability is lost, but our work is safeguarded of this problem since our modified Leishmania chassis cannot reproduce and has a half-life of 108 hours.

IFN-β rate synthesis : 4.63 * 10^-11 ㎍ / Leishmania* hour (Dortay & Mueller, 2010);

IFN-β clearance in mice: 0.457 ml/min for each 20 g mouse (Abraham et al. 2010; Castello Branco et al., 2011);

Mouse joints total area: 0.998 mm² – 1.368mm² (Shi et al., 2014);

SOLUTION

We simulated the time of survival of amastigotes from L. donovani Cen^-/- (Figure 2) and the production of IFN-β (Figure 3) after injection of three different quantity of promastigotes. Regardless of promastigote inoculum, we predicted that the Cen^-/- amastigotes could be survive and produce recombinant proteins up to 22 days. Furthermore, the production of IFN-β increases in the same proportion that the number of promastigote injected. Only concentration of 1.5 and 2.8 * 10⁸ parasite reached the therapeutic levels of 10 ug described in the literature (Tak, 2004; Cor et. al, 2009). However, the number of induced anti-inflammatory macrophages by IFN-β is constant probably due to saturation of receptor and/or total number of macrophage in the inflammatory site (Figure 4). Since the concentration of 1.5 * 10⁸ was the minimal quantity of IFN-β that reached therapeutic levels and induced the optimized number of anti-inflammatory macrophages, it should be tested in wet lab experiments.

Figure 2 - Simulated amastigote number after injection of different quantity of promastigotes.

Figure 3 - Accumulated production of IFN-β after injection of different quantity of promastigotes.

Figure 4 - Number of anti-inflammatory macrophages induced by IFN-β after injection of different quantity of promastigotes.

REFERENCES

van Furth R, Nibbering PH, van Dissel JT, Diesselhoff-den Dulk MM. The characterization, origin, and kinetics of skin macrophages during inflammation. J Invest Dermatol. 1985 Nov;85(5):398-402.

Chang KP, Dwyer DM. Leishmania donovani. Hamster macrophage interactions in vitro: cell entry, intracellular survival, and multiplication of amastigotes. J Exp Med. 1978 Feb 1;147(2):515-30.

Corr M, Boyle DL, Ronacher L, Flores N, Firestein GS. Synergistic benefit in inflammatory arthritis by targeting I kappaB kinase epsilon and interferon β. Ann Rheum Dis. 2009 Feb;68(2):257-63. doi: 10.1136/ard.2008.095356. Epub 2008 Jul 24.

Dortay H, Mueller-Roeber B. A highly efficient pipeline for protein expression in Leishmania tarentolae using infrared fluorescence protein as marker. Microb Cell Fact. 2010 May 10;9:29. doi: 10.1186/1475-2859-9-29.

Abraham AK, Kagan L, Kumar S, Mager DE. Type I interferon receptor is a primary regulator of target-mediated drug disposition of interferon-β in mice. J Pharmacol Exp Ther. 2010 Jul;334(1):327-32.

Castello-Branco ACS, Diniz MFFM, Almeida RN, Santos HB, Oliveira KM, Ramalho JA, Dantas JG. 2011. Biochemical and hematological parameters of Wistar rat and Swiss mice in the Professor Thomas George Animal Laboratory. Revta Bras. Ciênc. Saúde 15:209-214.

Ginhoux, F., & Jung, S. (2014). Monocytes and macrophages: developmental pathways and tissue homeostasis. Nature Reviews. Immunology, 14(6), 392–404.

Shi, J., Liang, Q., Zuscik, M., Shen, J., Chen, D., Xu, H., Xing, L. (2014). Distribution and alteration of lymphatic vessels in knee joints of normal and osteoarthritic mice. Arthritis & Rheumatology (Hoboken, N.J.), 66(3), 657–66.

Tak, P. IFN-β in rheumatoid arthritis. Front Biosci. 2004 Sep 1;9:3242-7.