1
|
Biswas A, Choudhuri I, Arnold E, Lyumkis D, Haldane A, Levy RM. Kinetic coevolutionary models predict the temporal emergence of HIV-1 resistance mutations under drug selection pressure. Proc Natl Acad Sci U S A 2024; 121:e2316662121. [PMID: 38557187 PMCID: PMC11009627 DOI: 10.1073/pnas.2316662121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2023] [Accepted: 02/23/2024] [Indexed: 04/04/2024] Open
Abstract
Drug resistance in HIV type 1 (HIV-1) is a pervasive problem that affects the lives of millions of people worldwide. Although records of drug-resistant mutations (DRMs) have been extensively tabulated within public repositories, our understanding of the evolutionary kinetics of DRMs and how they evolve together remains limited. Epistasis, the interaction between a DRM and other residues in HIV-1 protein sequences, is key to the temporal evolution of drug resistance. We use a Potts sequence-covariation statistical-energy model of HIV-1 protein fitness under drug selection pressure, which captures epistatic interactions between all positions, combined with kinetic Monte-Carlo simulations of sequence evolutionary trajectories, to explore the acquisition of DRMs as they arise in an ensemble of drug-naive patient protein sequences. We follow the time course of 52 DRMs in the enzymes protease, RT, and integrase, the primary targets of antiretroviral therapy. The rates at which DRMs emerge are highly correlated with their observed acquisition rates reported in the literature when drug pressure is applied. This result highlights the central role of epistasis in determining the kinetics governing DRM emergence. Whereas rapidly acquired DRMs begin to accumulate as soon as drug pressure is applied, slowly acquired DRMs are contingent on accessory mutations that appear only after prolonged drug pressure. We provide a foundation for using computational methods to determine the temporal evolution of drug resistance using Potts statistical potentials, which can be used to gain mechanistic insights into drug resistance pathways in HIV-1 and other infectious agents.
Collapse
Affiliation(s)
- Avik Biswas
- Center for Biophysics and Computational Biology, College of Science and Technology, Temple University, Philadelphia, PA19122
- Laboratory of Genetics, The Salk Institute for Biological Studies, La Jolla, CA92037
- Department of Physics, University of California San Diego, La Jolla, CA92093
| | - Indrani Choudhuri
- Center for Biophysics and Computational Biology, College of Science and Technology, Temple University, Philadelphia, PA19122
- Department of Chemistry, Temple University, Philadelphia, PA19122
| | - Eddy Arnold
- Department of Chemistry and Chemical Biology, Center for Advanced Biotechnology and Medicine, Rutgers University, Piscataway, NJ08854
| | - Dmitry Lyumkis
- Laboratory of Genetics, The Salk Institute for Biological Studies, La Jolla, CA92037
- Graduate School of Biological Sciences, Department of Molecular Biology, University of California San Diego, La Jolla, CA92093
| | - Allan Haldane
- Center for Biophysics and Computational Biology, College of Science and Technology, Temple University, Philadelphia, PA19122
- Department of Physics, Temple University, Philadelphia, PA19122
| | - Ronald M. Levy
- Center for Biophysics and Computational Biology, College of Science and Technology, Temple University, Philadelphia, PA19122
- Department of Chemistry, Temple University, Philadelphia, PA19122
| |
Collapse
|
2
|
Boffi NM, Guo Y, Rycroft CH, Amir A. How microscopic epistasis and clonal interference shape the fitness trajectory in a spin glass model of microbial long-term evolution. eLife 2024; 12:RP87895. [PMID: 38376390 PMCID: PMC10942580 DOI: 10.7554/elife.87895] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/21/2024] Open
Abstract
The adaptive dynamics of evolving microbial populations takes place on a complex fitness landscape generated by epistatic interactions. The population generically consists of multiple competing strains, a phenomenon known as clonal interference. Microscopic epistasis and clonal interference are central aspects of evolution in microbes, but their combined effects on the functional form of the population's mean fitness are poorly understood. Here, we develop a computational method that resolves the full microscopic complexity of a simulated evolving population subject to a standard serial dilution protocol. Through extensive numerical experimentation, we find that stronger microscopic epistasis gives rise to fitness trajectories with slower growth independent of the number of competing strains, which we quantify with power-law fits and understand mechanistically via a random walk model that neglects dynamical correlations between genes. We show that increasing the level of clonal interference leads to fitness trajectories with faster growth (in functional form) without microscopic epistasis, but leaves the rate of growth invariant when epistasis is sufficiently strong, indicating that the role of clonal interference depends intimately on the underlying fitness landscape. The simulation package for this work may be found at https://github.com/nmboffi/spin_glass_evodyn.
Collapse
Affiliation(s)
- Nicholas M Boffi
- Courant Institute of Mathematical Sciences, New York UniversityNew YorkUnited States
| | - Yipei Guo
- Janelia Research CampusAshburnUnited States
| | - Chris H Rycroft
- Department of Mathematics, University of Wisconsin–MadisonMadisonUnited States
- Mathematics Group, Lawrence Berkeley National LaboratoryBerkeleyUnited States
| | - Ariel Amir
- Weizmann Institute of ScienceRehovotIsrael
- John A. Paulson School of Engineering and Applied Sciences, Harvard UniversityCambridgeUnited States
| |
Collapse
|
3
|
Mohanty V, Louis AA. Robustness and stability of spin-glass ground states to perturbed interactions. Phys Rev E 2023; 107:014126. [PMID: 36797942 DOI: 10.1103/physreve.107.014126] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2020] [Accepted: 12/16/2022] [Indexed: 06/18/2023]
Abstract
Across many problems in science and engineering, it is important to consider how much the output of a given system changes due to perturbations of the input. Here, we investigate the glassy phase of ±J spin glasses at zero temperature by calculating the robustness of the ground states to flips in the sign of single interactions. For random graphs and the Sherrington-Kirkpatrick model, we find relatively large sets of bond configurations that generate the same ground state. These sets can themselves be analyzed as subgraphs of the interaction domain, and we compute many of their topological properties. In particular, we find that the robustness, equivalent to the average degree, of these subgraphs is much higher than one would expect from a random model. Most notably, it scales in the same logarithmic way with the size of the subgraph as has been found in genotype-phenotype maps for RNA secondary structure folding, protein quaternary structure, gene regulatory networks, as well as for models for genetic programming. The similarity between these disparate systems suggests that this scaling may have a more universal origin.
Collapse
Affiliation(s)
- Vaibhav Mohanty
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford, OX1 3NP, United Kingdom
- MD-PhD Program and Program in Health Sciences and Technology, Harvard Medical School, Boston, Massachusetts 02125, USA and Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Ard A Louis
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford, OX1 3NP, United Kingdom
| |
Collapse
|
4
|
Getting higher on rugged landscapes: Inversion mutations open access to fitter adaptive peaks in NK fitness landscapes. PLoS Comput Biol 2022; 18:e1010647. [PMID: 36315581 PMCID: PMC9648849 DOI: 10.1371/journal.pcbi.1010647] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2022] [Revised: 11/10/2022] [Accepted: 10/09/2022] [Indexed: 11/12/2022] Open
Abstract
Molecular evolution is often conceptualised as adaptive walks on rugged fitness landscapes, driven by mutations and constrained by incremental fitness selection. It is well known that epistasis shapes the ruggedness of the landscape’s surface, outlining their topography (with high-fitness peaks separated by valleys of lower fitness genotypes). However, within the strong selection weak mutation (SSWM) limit, once an adaptive walk reaches a local peak, natural selection restricts passage through downstream paths and hampers any possibility of reaching higher fitness values. Here, in addition to the widely used point mutations, we introduce a minimal model of sequence inversions to simulate adaptive walks. We use the well known NK model to instantiate rugged landscapes. We show that adaptive walks can reach higher fitness values through inversion mutations, which, compared to point mutations, allows the evolutionary process to escape local fitness peaks. To elucidate the effects of this chromosomal rearrangement, we use a graph-theoretical representation of accessible mutants and show how new evolutionary paths are uncovered. The present model suggests a simple mechanistic rationale to analyse escapes from local fitness peaks in molecular evolution driven by (intragenic) structural inversions and reveals some consequences of the limits of point mutations for simulations of molecular evolution. Ninety years ago, Wright translated Darwin’s core idea of survival of the fittest into rugged landscapes—a highly influential metaphor—with peaks representing high values of fitness separated by valleys of lower fitness. In this picture, once a population has reached a local peak, the adaptive dynamics may stall as further adaptation requires crossing a valley. At the DNA level, adaptation is often modelled as a space of genotypes that is explored through point mutations. Therefore, once a local peak is reached, any genotype fitter than that of the peak will be away from the neighbourhood of genotypes accessible through point mutations. Here we present a simple computational model for inversion mutations, one of the most frequent structural variations, and show that adaptive processes in rugged landscapes can escape from local peaks through intragenic inversion mutations. This new escape mechanism reveals the innovative role of inversions at the DNA level and provides a step towards more realistic models of adaptive dynamics, beyond the dominance of point mutations in theories of molecular evolution.
Collapse
|
5
|
Teimouri H, Spaulding C, Kolomeisky AB. Optimal pathways control fixation of multiple mutations during cancer initiation. Biophys J 2022; 121:3698-3705. [PMID: 35568975 PMCID: PMC9617135 DOI: 10.1016/j.bpj.2022.05.011] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/06/2022] [Revised: 04/04/2022] [Accepted: 05/10/2022] [Indexed: 11/02/2022] Open
Abstract
Cancer starts after initially healthy tissue cells accumulate several specific mutations or other genetic alterations. The dynamics of tumor formation is a very complex phenomenon due to multiple involved biochemical and biophysical processes. It leads to a very large number of possible pathways on the road to final fixation of all mutations that marks the beginning of the cancer, complicating the understanding of microscopic mechanisms of tumor formation. We present a new theoretical framework of analyzing the cancer initiation dynamics by exploring the properties of effective free-energy landscape of the process. It is argued that although there are many possible pathways for the fixation of all mutations in the system, there are only a few dominating pathways on the road to tumor formation. The theoretical approach is explicitly tested in the system with only two mutations using analytical calculations and Monte Carlo computer simulations. Excellent agreement with theoretical predictions is found for a large range of parameters, supporting our hypothesis and allowing us to better understand the mechanisms of cancer initiation. Our theoretical approach clarifies some important aspects of microscopic processes that lead to tumor formation.
Collapse
Affiliation(s)
- Hamid Teimouri
- Department of Chemistry, Rice University, Houston, Texas; Center for Theoretical Biological Physics, Rice University, Houston, Texas
| | - Cade Spaulding
- Department of Chemistry, Rice University, Houston, Texas
| | - Anatoly B Kolomeisky
- Department of Chemistry, Rice University, Houston, Texas; Center for Theoretical Biological Physics, Rice University, Houston, Texas; Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas; Department of Physics and Astronomy, Rice University, Houston, Texas.
| |
Collapse
|
6
|
Cárdenas P, Corredor V, Santos-Vega M. Genomic epidemiological models describe pathogen evolution across fitness valleys. SCIENCE ADVANCES 2022; 8:eabo0173. [PMID: 35857510 PMCID: PMC9278859 DOI: 10.1126/sciadv.abo0173] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/07/2022] [Accepted: 05/26/2022] [Indexed: 06/15/2023]
Abstract
Genomics is fundamentally changing epidemiological research. However, systematically exploring hypotheses in pathogen evolution requires new modeling tools. Models intertwining pathogen epidemiology and genomic evolution can help understand processes such as the emergence of novel pathogen genotypes with higher transmissibility or resistance to treatment. In this work, we present Opqua, a flexible simulation framework that explicitly links epidemiology to sequence evolution and selection. We use Opqua to study determinants of evolution across fitness valleys. We confirm that competition can limit evolution in high-transmission environments and find that low transmission, host mobility, and complex pathogen life cycles facilitate reaching new adaptive peaks through population bottlenecks and decoupling of selective pressures. The results show the potential of genomic epidemiological modeling as a tool in infectious disease research.
Collapse
Affiliation(s)
- Pablo Cárdenas
- Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Vladimir Corredor
- Departamento de Salud Pública, Facultad de Medicina, Universidad Nacional de Colombia, Bogotá, D.C., Colombia
| | - Mauricio Santos-Vega
- Grupo Biología Matemática y Computacional, Departamento Ingeniería Biomédica, Universidad de los Andes, Bogotá, D.C., Colombia
| |
Collapse
|
7
|
Guo Y, Amir A. The effect of weak clonal interference on average fitness trajectories in the presence of macroscopic epistasis. Genetics 2022; 220:6529545. [PMID: 35171996 PMCID: PMC8982035 DOI: 10.1093/genetics/iyac028] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2021] [Accepted: 01/28/2022] [Indexed: 11/13/2022] Open
Abstract
Adaptation dynamics on fitness landscapes is often studied theoretically in the strong-selection, weak-mutation regime. However, in a large population, multiple beneficial mutants can emerge before any of them fixes in the population. Competition between mutants is known as clonal interference, and while it is known to slow down the rate of adaptation (when compared to the strong-selection, weak-mutation model with the same parameters), how it affects the shape of long-term fitness trajectories in the presence of epistasis is an open question. Here, by considering how changes in fixation probabilities arising from weak clonal interference affect the dynamics of adaptation on fitness-parameterized landscapes, we find that the change in the shape of fitness trajectory arises only through changes in the supply of beneficial mutations (or equivalently, the beneficial mutation rate). Furthermore, a depletion of beneficial mutations as a population climbs up the fitness landscape can speed up the rescaled fitness trajectory (where adaptation speed is measured relative to its value at the start of the experiment), while an enhancement of the beneficial mutation rate does the opposite of slowing it down. Our findings suggest that by carrying out evolution experiments in both regimes (with and without clonal interference), one could potentially distinguish the different sources of macroscopic epistasis (fitness effect of mutations vs change in fraction of beneficial mutations).
Collapse
Affiliation(s)
- Yipei Guo
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA,Program in Biophysics, Harvard University, Boston, MA 02115, USA,Janelia Research Campus, Virginia, VA 20147, USA
| | - Ariel Amir
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA,Corresponding author: John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA.
| |
Collapse
|
8
|
Schwarcz D, Burov S. Self-assembly of two-dimensional, amorphous materials on a liquid substrate. Phys Rev E 2022; 105:L022601. [PMID: 35291111 DOI: 10.1103/physreve.105.l022601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2021] [Accepted: 01/26/2022] [Indexed: 06/14/2023]
Abstract
Recent experimental utilization of liquid substrate in the production of two-dimensional crystals, such as graphene, together with a general interest in amorphous materials, raises the following question: is it beneficial to use a liquid substrate to optimize amorphous material production? Inspired by epitaxial growth, we use a two-dimensional coarse-grained model of interacting particles to show that introducing a motion for the substrate atoms improves the self-assembly process of particles that move on top of the substrate. We find that a specific amount of substrate liquidity (for a given sample temperature) is needed to achieve optimal self-assembly. Our results illustrate the opportunities that the combination of different degrees of freedom provides to the self-assembly processes.
Collapse
Affiliation(s)
- Deborah Schwarcz
- Physics Department, Bar-Ilan University, Ramat Gan 5290002, Israel
| | - Stanislav Burov
- Physics Department, Bar-Ilan University, Ramat Gan 5290002, Israel
| |
Collapse
|
9
|
Bhattacharya S, Mohanty A, Achuthan S, Kotnala S, Jolly MK, Kulkarni P, Salgia R. Group Behavior and Emergence of Cancer Drug Resistance. Trends Cancer 2021; 7:323-334. [PMID: 33622644 PMCID: PMC8500356 DOI: 10.1016/j.trecan.2021.01.009] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2020] [Revised: 01/25/2021] [Accepted: 01/26/2021] [Indexed: 02/06/2023]
Abstract
Drug resistance is a major impediment in cancer. Although it is generally thought that acquired drug resistance is due to genetic mutations, emerging evidence indicates that nongenetic mechanisms also play an important role. Resistance emerges through a complex interplay of clonal groups within a heterogeneous tumor and the surrounding microenvironment. Traits such as phenotypic plasticity, intercellular communication, and adaptive stress response, act in concert to ensure survival of intermediate reversible phenotypes, until permanent, resistant clones can emerge. Understanding the role of group behavior, and the underlying nongenetic mechanisms, can lead to more efficacious treatment designs and minimize or delay emergence of resistance.
Collapse
Affiliation(s)
- Supriyo Bhattacharya
- Translational Bioinformatics, Center for Informatics, Department of Computational and Quantitative Medicine, City of Hope National Medical Center, Duarte, CA 91010, USA
| | - Atish Mohanty
- Department of Medical Oncology and Therapeutics Research, City of Hope National Medical Center, Duarte, CA 91010, USA
| | - Srisairam Achuthan
- Center for Informatics, Division of Research Informatics, City of Hope National Medical Center, Duarte, CA 91010, USA
| | - Sourabh Kotnala
- Department of Medical Oncology and Therapeutics Research, City of Hope National Medical Center, Duarte, CA 91010, USA
| | - Mohit Kumar Jolly
- Center for BioSystems Science and Engineering, Indian Institute of Science, Bangalore 560012, India
| | - Prakash Kulkarni
- Department of Medical Oncology and Therapeutics Research, City of Hope National Medical Center, Duarte, CA 91010, USA
| | - Ravi Salgia
- Department of Medical Oncology and Therapeutics Research, City of Hope National Medical Center, Duarte, CA 91010, USA.
| |
Collapse
|
10
|
Abstract
Selection of mutants in a microbial population depends on multiple cellular traits. In serial-dilution evolution experiments, three key traits are the lag time when transitioning from starvation to growth, the exponential growth rate, and the yield (number of cells per unit resource). Here, we investigate how these traits evolve in laboratory evolution experiments using a minimal model of population dynamics, where the only interaction between cells is competition for a single limiting resource. We find that the fixation probability of a beneficial mutation depends on a linear combination of its growth rate and lag time relative to its immediate ancestor, even under clonal interference. The relative selective pressure on growth rate and lag time is set by the dilution factor; a larger dilution factor favors the adaptation of growth rate over the adaptation of lag time. The model shows that yield, however, is under no direct selection. We also show how the adaptation speeds of growth and lag depend on experimental parameters and the underlying supply of mutations. Finally, we investigate the evolution of covariation between these traits across populations, which reveals that the population growth rate and lag time can evolve a nonzero correlation even if mutations have uncorrelated effects on the two traits. Altogether these results provide useful guidance to future experiments on microbial evolution.
Collapse
|
11
|
Evolution Rapidly Optimizes Stability and Aggregation in Lattice Proteins Despite Pervasive Landscape Valleys and Mazes. Genetics 2020; 214:1047-1057. [PMID: 32107278 DOI: 10.1534/genetics.120.302815] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2019] [Accepted: 02/18/2020] [Indexed: 11/18/2022] Open
Abstract
The "fitness" landscapes of genetic sequences are characterized by high dimensionality and "ruggedness" due to sign epistasis. Ascending from low to high fitness on such landscapes can be difficult because adaptive trajectories get stuck at low-fitness local peaks. Compounding matters, recent theoretical arguments have proposed that extremely long, winding adaptive paths may be required to reach even local peaks: a "maze-like" landscape topography. The extent to which peaks and mazes shape the mode and tempo of evolution is poorly understood, due to empirical limitations and the abstractness of many landscape models. We explore the prevalence, scale, and evolutionary consequences of landscape mazes in a biophysically grounded computational model of protein evolution that captures the "frustration" between "stability" and aggregation propensity. Our stability-aggregation landscape exhibits extensive sign epistasis and local peaks galore. Although this frequently obstructs adaptive ascent to high fitness and virtually eliminates reproducibility of evolutionary outcomes, many adaptive paths do successfully complete the ascent from low to high fitness, with hydrophobicity a critical mediator of success. These successful paths exhibit maze-like properties on a global landscape scale, in which taking an indirect path helps to avoid low-fitness local peaks. This delicate balance of "hard but possible" adaptation could occur more broadly in other biological settings where competing interactions and frustration are important.
Collapse
|