Lentiviral Infections in Brain During Cart

LENTIVIRAL INFECTIONS IN BRAIN DURING CART A1 Appendix

Data conversion

The HIV-1 brain viral DNA was measured in units of log10 HIV DNA copies + 200 per gram of brain tissue, where 200 represents the approximate threshold concentration of the assay from human brain specimens [1].

These data were converted to HIV DNA copies per gram of brain tissue by exponentiation. The ratio of integrated proviral DNA to total viral DNA is 1:86 [2] and this ratio was used to infer the number of integrated HIV DNA copies per gram of brain tissue.

For the three SIV studies, the SIV brain viral DNA was measured in two different units [3-5]: log10

SIV DNA copy equivalents per 2 microgram of total DNA and log10 SIV DNA copy equivalents per 10,000 cells.

For the former unit, this data was converted to SIV DNA copy equivalents per 2 microgram of total

DNA by exponentiation. Using the conversion that each gram of brain tissue contains 4 micrograms of total host genomic DNA, the data was transformed to SIV DNA copy equivalents per gram of brain tissue. By using the ratio of integrated proviral DNA to total viral DNA (1:86) [2], the SIV DNA copy equivalents per gram of brain tissue were converted to integrated SIV DNA per gram of brain tissue.

For the latter unit, this data was converted to SIV DNA copy equivalents per 10,000 cells by exponentiation. Using the conversion that 150 000 cellular genomes contains 1 microgram of host genomic

DNA [6], the data was transformed to SIV DNA copy equivalents per 1 microgram of host genomic DNA.

By using the conversion that each gram of brain tissue contains 4 micrograms of host genomic DNA and the ratio of integrated proviral DNA to total viral DNA (1:86) [2], the SIV DNA copy equivalents per 1 microgram of host genomic DNA was converted to integrated SIV DNA per gram of brain tissue. Table 4 in this Appendix contains a full list of the converted data.

Model Fitting

The parameter for cART regimen efficacy in brain, ε, was set to zero during the model fitting for the untreated SIV-infected macaque data. The parameter for cART regimen efficacy in brain, ε, cannot be estimated from the literature for cART-treated HIV-infected patients. During the model fitting for the cART- treated HIV-infected patient data the parameter ε was set to where represented some unknown value in the 2

possible range 0-1. This allowed the model fitting to form parameter estimates for the three different cohorts

(Table 4): cART-treated HIV-infected patients without neurological disorders, cART-treated HIV-infected patients with neurological disorders, and untreated SIV-infected macaques.

Bayesian inference is used to fit the ODE model to the estimated number of infected brain macrophages at the time points in Table 1.

The ODE model was solved numerically by using the MATLAB function ode45 [10]. The function ode45 is based on an explicit Runge-Kutta (4,5) formula. The fitting was completed using a Markov Chain

Monte Carlo (MCMC) sampling program from the MATLAB Central File Exchange [11]. The MCMC program sampled from the natural logarithm of the following unnormalized posterior distribution, π(θ,p|D):

where θ is a vector of the unknowns x0, y0, and d, D = {(t1, k1),…,(tn, kn)} is the observed data from Table 4, p is an unknown hyperparameter from the negative binomial distribution, L(θ,p|D) is the likelihood function, and P(θ,p) is the prior distribution. The likelihood function is assumed to be a negative binomial distribution representing the probability of observing count data with over-dispersion (variance of the data is larger than the mean of the data):

where and μ(θ,ti) = y(θ,ti) and y(θ,ti) is the numerical solution to the ODE equation at ti, and 0 < p < 1 is the hyperparameter determining the most likely shape of the negative binomial distribution given the data.

The prior distributions for x0, y0, , d, and p are assumed to be uniform distributions:

where x0~U(a1,b1), y0~U(a2,d2), ~U(a3,d3), d~U(a4,b4), p~U(0,1) and ai, bi are constants for i = 1,…,4.

Convergence of the MCMC sampling to the estimated posterior distribution for each parameter was determined by using a general univariate comparison method [12]. The general univariate comparison method uses the distance of the empirical 100(1–α)% interval for the pooled samples, D, and divides this distance by the average of the distances of the empirical 100(1–α)% interval for each of the n chains, di, to receive the potential scale reduction factor, r [12]: A3 LENTIVIRAL INFECTIONS IN BRAIN DURING CART

For the general univariate comparison method the empirical 95% interval was used. The potential scale reduction factor, r, was close to 1 for all the estimated parameters and this indicates that the MCMC sampling converged to the estimated posterior distribution for each parameter.

The number of samples used by the MCMC sampler was 1,760,000 for each of the three datasets.

The 95% credible intervals of the fitted parameters obtained from Bayesian inference, using MCMC sampling, were used to measure sensitivity of model outcomes with respect to variations in these four parameters (the dark grey bands in Fig. 1 and Fig. 2). The 95% prediction intervals from the MCMC sampling is shown in Fig. 1 with the dashed light gray curves.

Table 5 contains the parameter estimates including the outliers in Table 4. The 95% credible interval for the transmission coefficient is 0.824-1.07 times greater with outliers in comparison to without outliers in the data for cART-treated HIV-infected patients without neurological disorders. The 95% credible interval for the transmission coefficient is 1.02-1.42 times greater with outliers in comparison to without outliers in the data for cART-treated HIV-infected patients with neurological disorders. The outliers drag up the mean and 95% credible interval for the number of HIV-infected brain macrophages per gram of brain tissue at 10 years from 18.23 (18.16-18.73) to 600 (582-674) for cART-treated HIV-infected patients without neurological disorders, and from 1.11e4 (9.42×103-1.24×104) to 6.19e4 (5.35-6.76×104) for cART-treated

HIV-infected patients with neurological disorders.

Appendix References

1. Gelman BB, Lisinicchia JG, Morgello S, Masliah E, Commins D, Achim CL, et al. Neurovirological correlation with HIV-associated neurocognitive disorders and encephalitis in a HAART-era cohort. J Acquir

Immune Defic Syndr 2013; 62(5):487-495. 4

2. Suspène R, Meyerhans. Quantification of unintegrated HIV-1 DNA at the single cell level in vivo. PLoS

One 2012; 7(5):e36246.

3. Zink MC, Brice AK, Kelly KM, Queen SE, Gama L, Li M, et al. Simian immunodeficiency virus-infected macaques treated with highly active antiretroviral therapy have reduced central nervous system viral replication and inflammation but persistence of viral DNA. J Infect Dis 2010; 202(1):161-170.

4. Clements JE, Babas T, Mankowski JL, Suryanarayana K, Piatak M Jr., Tarwater PM, et al. The central nervous system as a reservoir for simian immunodeficiency virus (SIV): steady-state levels of SIV DNA in brain from acute through asymptomatic infection. J Infect Dis 2002; 186:905-913.

5. Graham DR, Gama L, Queen SE, Li M, Brice AK, Kelly KM, et al. Initiation of HAART during acute simian immunodeficiency virus infection rapidly controls virus replication in the CNS by enhancing immune activity and preserving protective immune responses. J Neurovirol 2011; 17:120-130

6. Fujimura RK, Shapshak P, Feaster D, Epler M, Goodkin K. A rapid method for comparative quantitative polymerase chain reaction of HIV-1 proviral DNA extracted from cryopreserved brain tissues. J Virol

Methods 1997; 67:177-187.

7. Davis LE, Hjelle BL, Miller VE, Palmer DL, Llewellyn AL, Merlin TL, et al. Early viral brain invasion in iatrogenic human immunodeficiency virus infection. Neurology 1992; 42:1736-1739.

8. Matlab version 8.3.0.532 Natick, Massachusetts. The MathWorks Inc., 2014.

9. Grinsted, Aslak (2015). Markov Chain Monte Carlo sampling of posterior distribution

(http://www.mathworks.com/matlabcentral/fileexchange/49820-grinsted-gwmcmc). MATLAB Central File

Exchange. Received June 2, 2015.

10. Gelman A, Brooks SP. General methods for monitoring convergence of iterative simulations. J Comp

Graph Stat 1998; 7(4):434-455.

Table 4 Conversion of HIV-1 and SIV DNA to the estimated number of infected brain macrophages per gram of brain tissue at different times from primary infection

Virus Neurological Estimated Viral DNA Estimated integrated Estimated infected Ref Disorders Years infected copies/g viral DNA copies/g brain macrophages/g HIV-1 - 0.04 9-172 α 0.1-2 α 0.1-2α [7] A5 LENTIVIRAL INFECTIONS IN BRAIN DURING CART

HIV-1 No 5-15 2.09×103 24 24 [1] HIV-1 No 5-15 540 6 6 [1] HIV-1 No 5-15 340 4 4 [1] HIV-1 No 5-15 1.65×103 19 19 [1] HIV-1 No 5-15 794 9 9 [1] HIV-1 No 5-15 2.85×103 33 33 [1] HIV-1 No 5-15 344 4 4 [1] HIV-1 No 5-15 2.07×103 24 24 [1] HIV-1 No 5-15 1.01×103 12 12 [1] HIV-1 No 5-15 674 8 8 [1] HIV-1 No 5-15 1.16×103 14 14 [1] HIV-1 No 5-15 3.26×104 379β 379β [1] HIV-1 No 5-15 3.56×103 41 41 [1] HIV-1 No 5-15 1.98×103 23 23 [1] HIV-1 No 5-15 428 5 5 [1] HIV-1 No 5-15 7.53×103 88 88 [1] HIV-1 No 5-15 1.54×103 18 18 [1] HIV-1 No 5-15 2.78×103 32 32 [1] HIV-1 No 5-15 8.86×103 103β 103β [1] HIV-1 No 5-15 1.04×103 12 12 [1] HIV-1 No 5-15 3.48×103 40 40 [1] HIV-1 No 5-15 200 2 2 [1] HIV-1 No 5-15 2.50×104 291β 291β [1] HIV-1 No 5-15 383 4 4 [1] HIV-1 No 5-15 813 9 9 [1] HIV-1 No 5-15 575 7 7 [1] HIV-1 No 5-15 1.08×104 125 β 125 β [1] HIV-1 No 5-15 8.00×103 93β 93β [1] HIV-1 No 5-15 1.72×103 20 20 [1] HIV-1 No 5-15 1.50×103 17 17 [1] HIV-1 No 5-15 1.75×106 20394β 20394β [1] HIV-1 No 5-15 514 6 6 [1] HIV-1 No 5-15 3.52×103 41 41 [1] HIV-1 No 5-15 377 4 4 [1] HIV-1 No 5-15 733 9 9 [1] HIV-1 Yes 5-15 7.96×106 92577 β 92577 β [1] HIV-1 Yes 5-15 1.23×104 143 143 [1] HIV-1 Yes 5-15 1.03×106 11954 11954 [1] HIV-1 Yes 5-15 1.49×104 173 173 [1] HIV-1 Yes 5-15 8.28×105 9627 9627 [1] HIV-1 Yes 5-15 3.08×107 358510 β 358510 β [1] HIV-1 Yes 5-15 2.30×104 268 268 [1] HIV-1 Yes 5-15 2.62×103 31 31 [1] HIV-1 Yes 5-15 3.46×104 402 402 [1] HIV-1 Yes 5-15 899 10 10 [1] HIV-1 Yes 5-15 1.15×106 13412 13412 [1] HIV-1 Yes 5-15 3.74×103 44 44 [1] HIV-1 Yes 5-15 9.08×103 106 106 [1] HIV-1 Yes 5-15 1.35×103 16 16 [1] HIV-1 Yes 5-15 5.71×107 664510 β 664510 β [1] HIV-1 Yes 5-15 1.69×104 197 197 [1] HIV-1 Yes 5-15 1.06×103 12 12 [1] HIV-1 Yes 5-15 6.19×106 72028 72028 [1] HIV-1 Yes 5-15 2.28×103 27 27 [1] HIV-1 Yes 5-15 2.67×106 31010 31010 [1] HIV-1 Yes 5-15 9.48×104 1103 1103 [1] HIV-1 Yes 5-15 5.55×106 64491 64491 [1] SIV - 0.027 258 3 3 [4] SIV - 0.027 688 8 8 [4] SIV - 0.027 3.35×103 39 39 [4] SIV - 0.027 344 4 4 [4] SIV - 0.027 2.58×103 30 30 [4] SIV - 0.027 1.03×103 12 12 [4] 6

SIV - 0.058 1.89×103 22 22 [4] SIV - 0.058 430 5 5 [4] SIV - 0.058 860 10 10 [4] SIV - 0.058 946 11 11 [4] SIV - 0.058 2.24×103 26 26 [4] SIV - 0.058 1.03×103 12 12 [4] SIV - 0.058 430 5 5 [5] SIV - 0.058 1.20×103 14 14 [5] SIV - 0.058 1.63×103 19 19 [5] SIV - 0.058 2.58×103 30 30 [5] SIV - 0.058 7.92×103 89 89 [5] SIV - 0.058 2.47×104 287 287 [5] SIV - 0.153 344 4 4 [4] SIV - 0.153 172 2 2 [4] SIV - 0.153 1.12×103 13 13 [4] SIV with encephalitis 0.153 6.11×103 71 71 [4] SIV - 0.153 430 5 5 [4] SIV - 0.153 2.75×103 32 32 [4] SIV - 0.230 7.55×103 3 3 [3] SIV with encephalitis 0.230 1.03×103 12 12 [3] SIV with encephalitis 0.230 1.12×103 13 13 [3] SIV with encephalitis 0.230 1.26×104 146 146 [3] SIV with encephalitis 0.230 7.23×104 841 841 [3] SIV with encephalitis 0.230 1.06×105 1235 1235 [3] αThis study detected proviral DNA in the brain by PCR. The number of viral DNA copies was not reported. It is assumed that the level of positive detection was approximately 100 copies Viral DNA per gram. The range of 9-172 copies Viral DNA per gram was chosen as the data from this study.

βThese observations were considered outliers since the observations were greater than 1.5 times the interquartile range for the respective cohort.

Table 5 Fitted parameter estimates and 95% credible intervals for the model fit to three datasets including the outliers

Datasets Symbol Parameter Estimate Unit (95% Credible Interval) 2.10×106 x0 Initial value for x per gm HIV-1 without 2.07×106-3.93×106 1.07 neurological y0 Initial value for y per gm 0.0058-2.00 disorders 7.77×10-7 (fit at 5, 10, 15 Transmission coefficient per year 2.39×10-7-5.23×10-6 years) 0.996 d Death rate brain macrophages per year 0.500-10.2 HIV-1 with 2.26×106 x0 Initial value for x per gm neurological 2.07×106-3.93×106

y0 Initial value for y 1.45 per gm A7 LENTIVIRAL INFECTIONS IN BRAIN DURING CART

0.0337-9.48 4.39×10-6 Transmission coefficient per year -7 -6 disorders 3.91×10 -5.74×10 8.80 (fit at 5, 10, 15 d Death rate brain macrophages per year 0.502-10.2 years)