Modeling the Time Evolution of Drug Resistance in HIV using Kinetic Monte-Carlo Simulations

In specific sequence backgrounds with specific associated mutations (called accessory) mutations a primaryDRM (affecting drug-susceptibility strongly) can become highly favorable or entrenched due to drug pressure.

The entrenchment of primary DRMs in specific backgrounds has strong implications for the clinical outcomeof HIV drug therapy.

The use of Kinetic Monte Carlo Simulation helps to understand the kinetic pathways of different distributionof the drug susceptibility of a protein called drug-resistance mutations in drug experienced and drug naïvepatients.

Introduction

Conclusion KMC simulations help to understand the kinetic routes to drug resistance in HIV-1 starting from the drug-naïve state.

The influence of specific sequence backgrounds on the favorability of primary DRMs through the time evolution from the drug-naïveto the drug-experienced state shows the effects of “contingency” and “entrenchment” of a mutation.

Evolutionary coupling between drug resistance sites leads to a much larger dispersion compare to polymorphic mutations.

Difference in average waiting time between independent and coupled model for the DRMs are significantly larger (by two-fold)compare to polymorphic mutation.

Acknowledgement & References

Kinetic Monte Carlo Simulation

Results & Discussions

Indrani Choudhuri1, Avik Biswas1,2, Allan Haldane1,2, Ronald M. Levy1,2,3

1Center for Biophysics and Computational Biology, 2Department of Physics, 3Department of Chemistry, Temple University, Philadelphia, PA

How does the drug-naïve distribution (orange) evolve to the wider distribution in drug-experiencedpatients (green)?

How long does it take to acquire drug resistance at different sites on HIV proteins? Do some proteinsacquire resistance more readily than others?

Are entrenching sequences already present in the drug naïve population? How does the evolution of drug resistance within an individual differ from that of the population of

individuals?

Dynamics and Background Influences on the Mutation

Waiting Time Distribution

The sample size of the MSA plays a critical role in determining the quality and effectiveness of the model3 and we confirm that the models are fit using sufficient data with minimal overfitting.

• Time Evolution towards drug resistance primarily expressed as: 𝑑𝑑𝑑𝑑(𝑆𝑆)𝑑𝑑𝑑𝑑

= 𝜅𝜅𝑃𝑃(𝑆𝑆)where 𝜅𝜅 is a rate matrix, 𝑃𝑃(𝑆𝑆) is the probability of a sequence 𝑆𝑆.

This work has been supported by the NIH grants U54-GM103368 to the HIV Interaction and Viral Evolution Center (HIVE), R01-GM030580, and S10OD020095 (to R.M.L). References:[1] Biswas, A., Haldane, A.; Arnold, E.; Levy, RM. eLife, 8, (2019), 50524.[2] Mora T, Bialek W. J. Stat. Phys. 144, (2011), 268–302.[3] Haldane A, Levy RM. Phys. Rev. E 99, (2019), 032405.[4] DePristo M. A., Weinreich D. M., Hartl D. L., Nat Rev Genet 6, (2005), 678.[5] Shah P.; McCandlish D. M., Plotkin J. B., Proc. Natl. Acad. Sci. U.S.A., (2015), 112, E3226.

The Hamming distance distribution with respect to the wild-type sequence for drug-naïve and drug-experienced HIV-1 Protease sequences.1

Project Goals

Distribution of Hamming Distances from wild-type in HIV-1 Protease The Potts model is a probabilistic model of sequence co-variation built on the single and pairwise site amino-acid frequencies of a protein MSA.2

The maximum entropy model takes the form of an exponential distribution is given by the following equations;

Dynamics and Background Influences on the Mutation

• The Kinetic Monte Carlo simulation is started with protease Consensus (NL4-3) sequence and the simulation is performed under drug experienced Hamiltonian.

• As the the favorability of the mutation measured by the change in the Potts energy difference (∆E) increases, the frequency of the mutation also increases.4

• Different protein in different position acquired drug resistance faster than other

• The favorability of the mutation of a single trajectory is measured by ∆E indicates that the primary mutations leading to drug resistance can become highly favored (or entrenched) by the complex mutation patterns arising in response to drug pressure.

• The effect of the mutation at a particular position is considered when the substitution occurs (time = 0) and extending it backward or forwards in time.

• As the background becomes more conducive towards acquiring a primary resistance mutation (contingency),5 the substitution occurs, and over time, the mutation becomes entrenched in its background.

Mutation Type

Position Wild Type

MutantAverage Waiting Time Index of Dispersion

Independent Model

Coupled Model

Independent Model

Coupled Model

DRM 54 I V 2.92 7.00 1.00 1.7090 L M 3.93 8.73 1.00 3.01

Polymorphic

71 A T 1.75 2.04 1.00 1.1077 V I 3.90 4.10 1.00 1.20

• Difference in average waiting time between independent and coupled model for the drug resistance mutations (DRMs) are significantly larger (by two-fold) compare to polymorphic mutation.

• Evolutionary coupling between drug resistance sites leads to a much larger index of dispersion .