Research ArticleChemistry

Allosteric pathway selection in templated assembly

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Science Advances  11 Oct 2019:
Vol. 5, no. 10, eaaw3353
DOI: 10.1126/sciadv.aaw3353
  • Fig. 1 Overview of our template-assembling system and kinetic model.

    (A) Structure of assembler units and template as proposed in our model and used in the simulations. Assemblers consist of a part responsible for template binding, the docking domain (D), an assembly domain (A) capable of providing lateral attractions between assemblers, and a purely repulsive stability domain (S). We use a template consisting of 90 beads, T90, and assemblers made from one docking domain, five assembly domains, and four stability domains (D1A5S4). (B) Schematic overview of all pair interactions used in our simulations. Note that the remaining repulsive WCA potentials besides USS are not shown. (C) Suggested assembly states and pathways, including the rate constants defined in the kinetic model. Gray arrows indicate transitions that were ignored in our model.

  • Fig. 2 Monitoring templated self-assembly over time.

    (A) Typical kinetic diagram showing the evolution of the fraction of assemblers, f, in each of the four states over time. Simulation performed at EAA = 1.0 kBT and EDT = 17 kBT. (B to D) The general picture of simulations of the assembly process starts with a homogeneous field of assembler units and a single template (purple beads) (B); after some time, there appear free-assembled assembler species in solution, and there are clumps of assemblers on the template—the changes in template morphology as a direct result of assembled assemblers is visible (C). At the end of the simulation, most assemblers will have attached to the template and fully cover a highly deformed template (D). All simulations are performed in a box with periodic boundary conditions.

  • Fig. 3 Tuning interaction strength steers the assembly kinetics.

    Kinetic diagrams are shown for a series of simulations with varying assembler-template attraction strengths (EDT) (A to D) and varying assembly-assembly (lateral associative) attraction (EAA) (E to H). We show the evolution of the fraction of assemblers f in each of the four assembly states over time tB. Black lines represent the optimal solutions found for the kinetic model. Plotted for EDT = 5, 10, 15, and 20 kBT (A to D) and EAA = 0.4, 0.8, 1.2, and 1.8 kBT (E to H).

  • Fig. 4 Evolution of rate constants over varying interaction strengths.

    Rate constants found for the kinetic model are shown over a series of simulations with increasing assembler-template interaction strength (EDT) (A to D) and increasing assembly-assembly attraction strength (EAA) (E to H). Data points are the average value of the 10 best fits found by the simulated annealing optimization algorithm. We performed each simulation five times and have plotted results for all replicates as an indicator of the spread between identical simulations. The gray shaded area in (E) to (H) represents the values for EAA ( ≥ 1.2 kBT), where we find substantial aggregates in bulk and our model starts to loose accuracy.

  • Fig. 5 Allosteric switching accelerates templated self-assembly.

    (A) Mechanism of allostery defined in the simulations. (B) Kinetic diagrams showing the fraction of assemblers (f) in the docked-assembled (DA) state over time, with allostery both turned on (green) and off (red) for the three values of EAA. Simulations were carried out at EDT = 17 kBT.

  • Fig. 6 Two observed assembly mechanisms.

    (A) Simulation snapshot of a recruitment event of an individual assembler by one already docked on to the template. (B) Snapshot of a collective docking event of an aggregate of assemblers. These simulations have been performed on a static and stretched template as an aid to visual clarity. All other data in this paper use a fully flexible template as described in Materials and Methods.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/10/eaaw3353/DC1

    Section S1. Assumptions made in the kinetic model

    Section S2. Cooperativity without allostery

    Section S3. Overview of all kinetic diagrams

    Section S4. Differentiating between aggregates and recruited assemblers

    Section S5. Residuals obtained for the simulated annealing fit algorithm

    Fig. S1. Determining the reaction order of free assembly.

    Fig. S2. Template occupancy profiles for simulations with a rigid template.

    Fig. S3. Overview of kinetic diagrams at varying assembler-template interaction strengths without allostery.

    Fig. S4. Overview of kinetic diagrams at varying assembler-assembler interaction strengths without allostery.

    Fig. S5. Overview of kinetic diagrams at varying assembler-assembler interaction strengths including allostery.

    Fig. S6. Schematic representation of two free-assembled (FA) states.

    Fig. S7. Overview of kinetic diagrams at varying assembler-assembler interaction strengths without allostery, differentiating between two FA states.

    Fig. S8. Overview of kinetic diagrams at varying assembler-assembler interaction strengths including allostery, differentiating between two FA states.

    Fig. S9. Histograms of fit residuals at varying assembler-template interaction strength.

    Fig. S10. Histograms of fit residuals at varying assembler-assembler interaction strength.

    Movie S1. Time lapse of a simulation in the absence of allostery.

    Movie S2. Time lapse of a simulation including allostery.

    References (4046)

  • Supplementary Materials

    The PDF file includes:

    • Section S1. Assumptions made in the kinetic model
    • Section S2. Cooperativity without allostery
    • Section S3. Overview of all kinetic diagrams
    • Section S4. Differentiating between aggregates and recruited assemblers
    • Section S5. Residuals obtained for the simulated annealing fit algorithm
    • Fig. S1. Determining the reaction order of free assembly.
    • Fig. S2. Template occupancy profiles for simulations with a rigid template.
    • Fig. S3. Overview of kinetic diagrams at varying assembler-template interaction strengths without allostery.
    • Fig. S4. Overview of kinetic diagrams at varying assembler-assembler interaction strengths without allostery.
    • Fig. S5. Overview of kinetic diagrams at varying assembler-assembler interaction strengths including allostery.
    • Fig. S6. Schematic representation of two free-assembled (FA) states.
    • Fig. S7. Overview of kinetic diagrams at varying assembler-assembler interaction strengths without allostery, differentiating between two FA states.
    • Fig. S8. Overview of kinetic diagrams at varying assembler-assembler interaction strengths including allostery, differentiating between two FA states.
    • Fig. S9. Histograms of fit residuals at varying assembler-template interaction strength.
    • Fig. S10. Histograms of fit residuals at varying assembler-assembler interaction strength.
    • References (4046)

    Download PDF

    Other Supplementary Material for this manuscript includes the following:

    • Movie S1 (.mp4 format). Time lapse of a simulation in the absence of allostery.
    • Movie S2 (.mp4 format). Time lapse of a simulation including allostery.

    Files in this Data Supplement:

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