Machine learning aided multiscale modelling of the HIV-1 infection in the presence of NRTI therapy

Abstract

Human Immunodeficiency Virus (HIV) is one of the most common chronic infectious diseases in humans. Extending the expected lifetime of patients depends on the use of optimal antiretroviral therapies. Emergence of the drug-resistant strains can reduce the effectiveness of treatments and lead to Acquired Immunodeficiency Syndrome (AIDS), even with antiretroviral therapy. Investigating the genotype-phenotype relationship is a crucial process for optimizing the therapy protocols of the patients. Here, a mathematical modelling framework is proposed to address the impact of existing mutations, timing of initiation, and adherence levels of nucleotide reverse transcriptase inhibitors (NRTIs) on the evolutionary dynamics of the virus strains. For the first time, the existing Stanford HIV drug resistance data have been combined with a multi-strain within-host ordinary differential equation (ODE) model to track the dynamics of the most common NRTI-resistant strains. Overall, the D4T-3TC, D4T-AZT and TDF-D4T drug combinations have been shown to provide higher success rates in preventing treatment failure and further drug resistance. The results are in line with the genotype-phenotype data and pharmacokinetic parameters of the NRTI inhibitors. Moreover, we show that the undetectable mutant strains at the diagnosis have a significant effect on the success/failure rates of the NRTI treatments. Predictions on undetectable strains through our multi-strain within-host model yielded the possible role of viral evolution on the treatment outcomes. It has been recognized that the improvement of multi-scale models can contribute to the understanding of the evolutionary dynamics, and treatment options, and potentially increase the reliability of genotype-phenotype models.

Keywords: AIDS; HIV infection; Machine learning; Mathematical models; NRTI therapy.

Figure 1. Regression performance of the six ANN models for each NRTI to predict logarithmic fold change values (log(FC)) of the mutant strains existing in the data.

The x-axis of the figures denotes logarithmic fold change value, which is mathematically equivalent to $log\left(\frac{{\left(I{C}_{50}\right)}_{mutant}}{{\left(I{C}_{50}\right)}_{wild-type}}\right)$, for all existing mutant strains in the data and y-axis denotes corresponding predictions of the ANN models. For each ANN model, linear correlation coefficient (R) and mean square error (MSE) metrics are specified to measure the ability of these models to fit the existing real data.

Figure 2. Illustration of the core parts of multi-strain within-host model (5) with NRTI therapy.

Model (5) assumes the healthy CD4 + T cells $\left(T\left(t\right)\right)$ and macrophage cells $\left(M\left(t\right)\right)$ as the main targets of the viral strains $\left(V_i\left(t\right)\right).$ $T\left(t\right)$ and $M\left(t\right)$ increase with both homeostatic cell proliferation and cell proliferation due to the increasing viral load. Viral strains infect both CD4 + T cells and macrophage cells and then those healthy cells become infected CD4 + T cells $\left(T_i^{\ast }\left(t\right)\right)$ and macrophage cells $\left(M_i^{\ast }\left(t\right)\right).$ $T_i^{\ast }\left(t\right)$ and $M_i^{\ast }\left(t\right)$ compartments produce mature viral strains $V_i\left(t\right)$ with some constant rates. All compartments have natural death or clearance with some constant rates. NRTIs block the infection mechanism of the viral strains in healthy cells. The efficiency of the NRTIs is estimated through pharmacokinetic Eq. (3) and the pre-trained artificial neural network models that map the genotype data to fold-change values of the IC₅₀’s with respect to the wild type virion.

Figure 3. Probability distributions of infection rate (β_i) values of various viral strains in the presence of NRTI therapy combinations.

(β_i) values are calculated with Eqs. (7)–(8) depending on the drug pairs. (β_i) values are effected by pharmacokinetic parameters, IC₅₀ values for the viral strains, baseline infection rate k_T = 4.5714 × 10⁸ and the fixed viral fitness value (c_i = 0.3015) of the viral strains.

Figure 4. Illustration of possible mono and dual NRTI therapy outcomes carried out using 512 random α,τ pairs in the current multi-strain within-host model (5).

The initial strain has been selected as $G_{51}=\left\{65N,69D,70R,115F,215Y\right\}$. Blue circles represent the failure after 20 years of simulation, i.e., the AIDS phase occurs when the patients start the therapy τ after infection and take the therapy with an adherence rate α. Purple squares mean that the therapy succeeds under the conditions mentioned above. SR values represent the success rate defined as SR = # of purple squares/# of all data points.

Figure 5. The effect of initiation timing is illustrated with healthy cell and virion counts.

The initial strain is taken as $G_{51}=\left\{65N,69D,70R,115F,215Y\right\}$ and the common adherence level α = 0.5 is considered. (A) Dynamics of T(t) and M(t) when τ = 50, (B) dynamics of viral strains when τ = 50,  (C) dynamics of T(t) and M(t) when τ = 360, (D) dynamics of viral strains when τ = 360. Black dashed vertical lines in parts c and d denote the HIV detection limit in blood as 200 copies/ml (Barletta, Edelman & Constantine, 2004).

Figure 6. SR values of various NRTI combinations obtained by simulating multi-strain within-host model (5) with initial viral strain G_ij for randomly scattered 512 α,τ∈0,1×0,365 pairs.

Figure 7. Prediction process of SR values from the infection rates of the detected and possible mutant strains.

The models G_i are constructed by considering i generation of mutant strains and the detected strain itself. For each generation, mean and maximum values of the infection rates are assigned to the input of possible ANN and MLR models. SR_ANN and SR_MLR denote the SR prediction of the ANN and MLR models from the given infection rate input.

Figure 8. Regression and classification performances of models G_i having the ANN architectures on predicting the SR values of the therapies.

Models G_i assume the infection rates of the detected strain and its first i mutant generations and have 2i + 1 input values. Mean square error (MSE), linear correlation coefficient (R), and area under the curve (AUC) metrics are presented for both training and test data.

Figure 9. Regression and classification performances of models G_i having the MLR architectures on predicting the SR values of the therapies.

Models G_i assume the infection rates of the detected strain and its first i mutant generations and have 2i + 1 input values. Mean square error (MSE), linear correlation coefficient (R), and area under the curve (AUC) metrics are presented for both training and test data.