Cis 112 Assignment Adam Isaacson

Viruses represent a serious public health threat, and millions of people die every year from viral diseases. Beyond baseline annual infection rates, periodic outbreaks arising from increased exposure or mutations that enhance transmissibility require emergency action to contain them. In an effort to prevent and combat viral infection, researchers worldwide are endeavoring to develop vaccines and drug-based treatments. Important biological targets for antiviral intervention include viral enzymes, such as the human immunodeficiency virus protease,(1) cellular host factors, which facilitate viral replication, such as cyclophilin-A(2) and Hsp70 chaperone,(3) glycoproteins on the surface of enveloped viruses, such as the neuraminidase of Influenza,(4) and virus capsids.(5)

Due to their essential structural and functional roles in housing, protecting, and ultimately delivering the viral genome, capsids are of great pharmacological interest as drug targets.

Capsids are specialized protein shells that encase the genetic material of viral pathogens. Due to their essential structural and functional roles in housing, protecting, and ultimately delivering the viral genome, capsids are of great pharmacological interest as drug targets. Assembly, the mechanism by which protein subunits associate to form capsids, can be targeted for disruption either in terms of timing or the geometry of formation, leading to the production of aberrant, nonviable capsids or alternative superstructures that do not suitably encapsulate the genetic material. Improperly formed capsids can interfere significantly with various stages of the viral life cycle, including RNA reverse transcription and cellular trafficking.(6) Conversely, disassembly can be targeted by locking the capsid or otherwise disrupting the uncoating process, preventing the release of genetic material and rendering the virus particle noninfective. Disassembly may also be triggered prematurely, such that genetic material is released at an inappropriate time or location. Many small-molecule drug compounds have been developed to inhibit appropriate viral assembly and uncoating, providing a means to thwart completion of both the replication and infection processes.

While vaccines are administered to promote acquired immunity against viruses, antibodies and drug compounds are dispensed primarily as postinfection therapeutics, providing emergency-response treatment and relief to patients. Small-molecule drugs (typically <900 Da) are of particular interest to the chemistry and pharmacology communities because they are less expensive to develop and have commercial potential to be synthesized cheaply and quickly once past clinical trials. Owing to their minimal size, small-molecule drugs can more easily pass through cellular membranes and penetrate into tissues and are, thus, more readily delivered to sites of infection within the body.

Examples of capsid-specific small-molecule drugs include HAP1, active against hepatitis B virus (HBV),(7) and PF74, active against human immunodeficiency virus type 1 (HIV-1).(8) Beyond extensive experimental studies aimed at characterizing capsid–drug interactions, computational methods, particularly molecular dynamics (MD) simulations, are emerging as an essential technique to investigate the effects of small-molecule drugs on capsid structure and dynamics.(9) MD simulations are beneficial both for application to known capsid–drug systems as well as for drug discovery.(10-15) For example, recent work on the interaction of V-073 with poliovirus capsid revealed the atomic basis of drug resistance.(16) Notably, the results of the poliovirus work, as well as research presented in the present Perspective applying MD simulations to study drug-bound HBV and HIV-1 capsids, underscore the importance of simulating not isolated capsid proteins but functional assemblies up to the level of complete capsids. Such studies demonstrate the necessity of employing all-atom models, as well as emulating native environmental conditions, to capture the subtle, yet significant effects of small-molecule drugs on dynamic capsid properties. In the present Perspective, the key steps of preparing a capsid–drug simulation are outlined, data describing drug-bound HBV and HIV-1 capsids are presented, and an outlook on the applicability of MD simulations of virus capsids to reveal novel drug targets is offered.

Virus Capsid Morphology. Virus capsids can be composed of one or more types of protein building blocks (protomers), arranged according to well-defined geometric relationships.(6) These relationships are leveraged both when solving experimental structures and when building full-scale atomic models for study with MD simulations. Capsid morphology can be governed by icosahedral (e.g., HBV, poliovirus) or helical (e.g., Ebola) symmetry rules or may exhibit a conical, polymorphic structure that lacks overall symmetry (e.g., HIV-1).

The capsids of icosahedral viruses comprise 20 identical triangular faces, adjoined by 12 vertices and 30 edges. As such, their structures can be partitioned into n-fold rotational symmetry axes, around which a 360/n rotation produces n equivalent views of the polyhedron. The center of each triangular face denotes a three-fold symmetry axis; each vertex, representing the interface of five triangular faces, denotes a five-fold symmetry axis; edges each denote a two-fold (quasi-six-fold) symmetry axis (Figure 1A). The number of constituent protomers and their organization onto the icosahedral lattice is described by a triangulation number, the primary metric by which such capsids are classified.

Figure 1. Morphological relationships shared by icosahedral and cone-shaped virus capsids. (A) Schematic illustration of the capsid of an icosahedral virus, delineated according to symmetry operators: three-fold symmetry axes (blue) lie at the center of each triangular face, five-fold symmetry axes (red) lie at each vertex, and two-fold (quasi-six-fold) symmetry axes (beige) lie along each edge. Each kite shape represents an asymmetric unit comprising T protomers. A given icosahedral capsid has three asymmetric units, or 3T protomers, per face and is constructed of 60T protomers total. (B) Schematic illustration of the capsid of an icosahedral virus, specifically HBV, delineated according to its pentameric (red) and hexameric (beige) capsomeres: pentamers represent an association of five protomers, while hexamers represent an association of six protomers. A given icosahedral capsid contains exactly 12 pentamers, which impart sufficient curvature to close the 60T protomer lattice. (C) Schematic illustration of the capsid of a cone-shaped virus, specifically HIV-1, which is similarly constructed of pentamers (red) and hexamers (beige). Although HIV-1 capsids are polymorphic by nature, they nevertheless require (just as icosahedral capsids do) exactly 12 pentamers to achieve lattice closure in their mature form.

The key steps of preparing a capsid–drug simulation are outlined, data describing drug-bound HBV and HIV-1 capsids are presented, and an outlook on the applicability of MD simulations of virus capsids to reveal novel drug targets is offered.

Triangulation number T, defined according to Caspar and Klug’s mathematical formulation(17)(1)where H and K are 0 or positive integers, takes on discrete values in the sequence 1, 3, 4, 7, 9, 13, 16, ... . Practically, T corresponds to the possible subdivisions of one-third of the equilateral triangular faces of an icosahedron that produce smaller geometric units of equal dimension. As such, it determines the number of protomers that constitute an asymmetric unit (T), the number required to form a given icosahedral face (3T, three asymmetric units related by three-fold symmetry), and the number encompassed by the entire capsid assembly (60T, twenty 3T faces). For example, the HBV capsid, which exists primarily as a T = 4 structure, has 3T = 12 protomers per face and comprises 60T = 240 total proteins. In many icosahedral viruses, as with HBV, 60T copies of a single identical protomer, which occupy quasi-equivalent positions according to their placement along the rotational symmetry axes, make up the full capsid.

Alternative to the asymmetric unit, the protomers of icosahedral capsids can also be grouped into subunits of five or six protomers, centered on five-fold or quasi-six-fold symmetry axes, respectively (Figure 1B). These pentameric and hexameric capsomeres, as they are called, impart unique geometric characteristics to the capsid surface; while associations centered on hexamers lie essentially flat, those centered on pentamers adopt a convex shape. According to Eberhard’s theorem,(18) a closed polyhedron, or convex polytope, satisfies the condition(2)where pk indicates the number of k-gonal faces. It follows then that in the absence of triangles (p3), squares (p4), and higher-order polygonal faces (k ≥ 7), a closed capsid requires exactly 12 pentagons and an undetermined number of hexagons. For example, a T = 4 capsid, like HBV, is composed of 12 pentamers and 30 hexamers, or 240 protomers. However, virus capsids are not limited to icosahedral symmetries, as conical or coffin-shaped cages also satisfy eq 2. For example, an HIV-1 capsid may contain 216 hexagons and 12 pentagons(19) (Figure 1C), with the latter distributed as five at the apex and seven at the base.

Capsid–Drug Complex Preparation for All-Atom Simulation. Using the geometric relationships and symmetry rules described above, atomic models of protomer associations up to complete, fully assembled capsids can be constructed for computational study with MD simulations. All-atom structures for elementary subunits, such as asymmetric units or capsomeres, are typically based on experimentally derived coordinates, obtained by either X-ray crystallography or nuclear magnetic resonance (NMR) spectroscopy. In the event that inherently flexible regions of the protomers, particularly loops and chain termini, are not resolved in the experimental structures, these missing features may be modeled based on homology or in silico prediction routines, using software such as Modeler(20) or Rosetta.(21) Complete elementary subunits are assembled into capsids either by applying icosahedral symmetry operations, facilitated by programs like VIPERdb,(22) by ordering them onto polyhedral cages with the CageBuilder feature of Chimera,(23) or by fitting them to density maps obtained from cryoelectron microscopy (cryo-EM) or small-angle X-ray scattering (SAXS) experiments with programs such as Situs(24) and molecular dynamics flexible fitting (MDFF).(25)

Conical capsids, such as HIV-1, lack overall symmetry, which poses a tremendous challenge to resolving their chemical structure. In these cases, MDFF(25) can be essential to obtaining all-atom models. For example, the structure of the helical lattice of HIV-1 (PDB 3J34) was revealed by MDFF, combining the crystal structure of the flat, isolated hexamer,(26) the NMR structure of the truncated dimer,(27) which provides information regarding the interhexameric contacts, and the cryo-EM-obtained density of cylindrical assemblies containing solely hexamers.(19) On the basis of additional data from cryo-EM and the crystal structure of the hexamer,(28) the structure of the entire HIV-1 capsid(19) (PDB 3J3Y), consisting of 12 pentamers and 216 hexamers, was computationally derived by analogy to fullerenes. A key step in the derivation was the construction of a pentamer of hexamers (POH; see Figure 4B) from the experimentally-computationally obtained structure of a hexamer surrounded by six hexamers.(19)

Simulating virus capsids in interaction with small-molecule drug compounds involves an extra layer of complexity. First and foremost, an accurate all-atom structure of the whole capsid must be made available to describe drug binding. Second, coordinates and parameters describing the drug and its properties must be obtained. If an experimental structure of the capsid–drug complex is not available, a model structure may be produced by docking the drug molecule into the known binding pocket or interface with programs like AutoDock.(29) While the capsid itself can be parametrized readily by application of established biomolecular force fields, compatible parameters dictating the dynamic properties of the nonstandard drug compound must be compiled or otherwise derived ab initio. Fortunately, generalized versions of most popular force fields are available, such as the Charmm General Force Field (CGenFF)(30) and the Generalized AMBER Force Field (GAFF),(31) for the specific purpose of addressing drug-like molecules. Generalized force fields provide parameter coverage for common chemical substructures and functional groups and further define a consistent approach for the development of any additional necessary parameters. Following the stated approach, any parameters not supplied by the generalized force field must be derived in a compatible manner. Specialized tools have been developed to facilitate parametrization, either by analogy to molecules for which parameters are known (e.g., the CGenFF Program(32, 33) and MATCH(34)) or by computing the parameters from first-principles (e.g., employing ffTK(35) and Force Balance(36)).

Once a complete capsid or capsid–drug complex model is constructed, its environment must be adjusted to mimic native conditions. As many viruses are sensitive to pH, a crucial step of structure preparation involves assignment of appropriate protonation states to polar and charged protein residues. Programs such as propKa(37) or H++(38) can be used to predict protonation states based on local pKa values; however, pKa calculations must be performed on subunits only after they have been assembled into a complete capsid (with drug bound, if applicable) to account for the local pKa values of all relevant molecular interfaces. Counter ions should then be placed around the capsid system to achieve charge neutrality. The CIonize (short for “Coulombic Ionize”) plugin in VMD(39) can be used to compute the Coulomb potential of the capsid system and position cations and anions at suitable points of minimum energy. Deliberate placement of counterions during structure preparation serves to reduce the computational time required for equilibration during the simulation phase of the project. Finally, the capsid system is immersed in a solvent box containing bulk water molecules and sufficient ions to produce the desired salt concentration, typically biological salinity of 150 mM NaCl. A summary of the general workflow for preparing an MD simulation of a small-molecule drug-bound icosahedral virus capsid can be found in Chart 1. To illustrate how simulations of capsids and capsid–protein assemblies are currently being used to investigate the dynamic and allosteric effects of small-molecule drug compounds, the following presents data describing drug-bound HBV (Figure 2C) and HIV-1 (Figure 2F) virus capsids.

Figure 2. Structures of drug-bound virus capsids. (A) The small-molecule drug HAP1 binds into (B) a closed pocket at the interface between the C (cyan) and D (blue) protomer chains of each asymmetric unit, (C) deep within the surface of the HBV capsid. (D) The small-molecule drug PF74 binds at (E) a surface-exposed interface between the N- and C-terminal domains of adjacent capsid proteins within (F) the pentamers or hexamers of the mature HIV-1 capsid.

Chart 1. Standard Workflow of Setting up a Simulation of a Drug-Bound Icosahedral Capsid

Drug-Induced Quaternary Rearrangements in the HBV Capsid. HBV is a leading cause of liver disease, cirrhosis, and heptocellular cancer worldwide. Although a vaccine to prevent viral infection has been available since 1982, there is currently no cure for the more than 240 million people the World Health Organization estimates are chronically infected. HBV is found primarily as a T = 4 icosahedral structure, whose capsid comprises 120 copies of homodimeric core protein (Cp). Because the HBV capsid plays an essential role in multiple stages of the viral life cycle and the core assembly domain of its Cp constituents has no human homologue that could interfere with drug selectivity in vivo,(40) it represents a promising therapeutic target.

HAP1 (Figure 2A) is a small-molecule drug that affects assembly of the HBV capsid in vitro. Particularly, HAP1 enhances capsid assembly kinetics and, at high concentrations, misdirects assembly to produce aberrant, noncapsid particles(41) that manifest as sheets of hexameric capsomeres.(42) A number of experimental studies have investigated the effects of HAP1 on HBV structure, including cocrystallization of the drug with a preformed capsid.(7)

The design and implementation of a heterogeneous computer networking laboratory

Authors: Guillermo A. Francia, IIIJacksonville State University, Mathematics, Computing and Information Sciences Department, 700 Pelham Rd North, Jacksonville, AL
Randy K. SmithJacksonville State University, Mathematics, Computing and Information Sciences Department, 700 Pelham Rd North, Jacksonville, AL
Published in:
· Proceeding
CCSC '00 Proceedings of the fourteenth annual consortium on Small Colleges Southeastern conference
Pages 231-238

Roanoke College, Salem, Virginia, USA
Consortium for Computing Sciences in Colleges, USA ©2000
table of contents
· Proceeding
Proceedings of the second annual CCSC on Computing in Small Colleges Northwestern conference
Pages 231-238

Oregon Graduate Institute, Beaverton, Oregon, USA
Consortium for Computing Sciences in Colleges, USA ©2000
table of contents
· Journal
Journal of Computing Sciences in Colleges
Volume 16 Issue 2, Jan. 2001
Pages 231-238
Consortium for Computing Sciences in Colleges, USA
table of contents
2000 Article
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