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An assembly funnel makes biomolecular complex assembly efficient.

Zenk J, Schulman R - PLoS ONE (2014)

Bottom Line: For typical complexes, an assembly funnel occurs in a narrow window of conditions whose location is highly complex specific.However, by redesigning the components this window can be drastically broadened, so that complexes can form quickly across many conditions.The generality of this approach suggests assembly funnel design as a foundational strategy for robust biomolecular complex synthesis.

View Article: PubMed Central - PubMed

Affiliation: Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, Maryland, United States of America.

ABSTRACT
Like protein folding and crystallization, the self-assembly of complexes is a fundamental form of biomolecular organization. While the number of methods for creating synthetic complexes is growing rapidly, most require empirical tuning of assembly conditions and/or produce low yields. We use coarse-grained simulations of the assembly kinetics of complexes to identify generic limitations on yields that arise because of the many simultaneous interactions allowed between the components and intermediates of a complex. Efficient assembly occurs when nucleation is fast and growth pathways are few, i.e. when there is an assembly "funnel". For typical complexes, an assembly funnel occurs in a narrow window of conditions whose location is highly complex specific. However, by redesigning the components this window can be drastically broadened, so that complexes can form quickly across many conditions. The generality of this approach suggests assembly funnel design as a foundational strategy for robust biomolecular complex synthesis.

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An assembly funnel means that complex assembly occurs via a small number of pathways.The possible set of reaction pathways govern assembly outcome under rearrangement-limited conditions, whereas thermodynamically favorable pathways govern assembly outcome in the assembly funnel regime. (a) Conformational entropy () of the system under different assembly conditions as a function of assembly time, . (b) Reference energy distributions of a 3×3 square grid complex based on thermodynamics and assembly configuration. Color spectrum indicates the number of bonds in an assembly. (c) Partition of energies at different times during self-assembly in the assembly funnel regime at  (green box), rearrangement-limited conditions at  (blue box), and during an anneal (black box). Over the course of an anneal,  transitions from -6 to 6, spending  at 100 different linearly decreasing isothermal conditions. Values at the top right are complex yields. Inset plots show detail. Error bars <1%.
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pone-0111233-g003: An assembly funnel means that complex assembly occurs via a small number of pathways.The possible set of reaction pathways govern assembly outcome under rearrangement-limited conditions, whereas thermodynamically favorable pathways govern assembly outcome in the assembly funnel regime. (a) Conformational entropy () of the system under different assembly conditions as a function of assembly time, . (b) Reference energy distributions of a 3×3 square grid complex based on thermodynamics and assembly configuration. Color spectrum indicates the number of bonds in an assembly. (c) Partition of energies at different times during self-assembly in the assembly funnel regime at (green box), rearrangement-limited conditions at (blue box), and during an anneal (black box). Over the course of an anneal, transitions from -6 to 6, spending at 100 different linearly decreasing isothermal conditions. Values at the top right are complex yields. Inset plots show detail. Error bars <1%.

Mentions: To further understand the influence of pathways on complex formation, we examined the kinds of intermediates that tend to arise and persist by measuring the conformational entropy, or distribution of species sizes and free energies, of the system. The conformational entropy is given by where is the fraction of species with energy and components. Higher values of conformational entropy correspond to broader distributions of assembly sizes and free energies. Under rearrangement-limited conditions, conformational entropy initially increases as many different intermediates form, and then plateaus (Fig. 3a). The species that form and remain are those that are most easily accessible via reaction pathways rather than those that are energetically favorable (Fig. 3b, c). In contrast, assembly in the assembly funnel regime favors the production of a relatively small number of intermediates, those lowest in free energy, so conformational entropy decreases with time as these low-energy intermediates and complexes form. Because complex size and geometry determine the possible reaction pathways and the types of assembly intermediates that can form [43], they also control the propensity of an assembly process to become “stuck” under a given set of reaction conditions.


An assembly funnel makes biomolecular complex assembly efficient.

Zenk J, Schulman R - PLoS ONE (2014)

An assembly funnel means that complex assembly occurs via a small number of pathways.The possible set of reaction pathways govern assembly outcome under rearrangement-limited conditions, whereas thermodynamically favorable pathways govern assembly outcome in the assembly funnel regime. (a) Conformational entropy () of the system under different assembly conditions as a function of assembly time, . (b) Reference energy distributions of a 3×3 square grid complex based on thermodynamics and assembly configuration. Color spectrum indicates the number of bonds in an assembly. (c) Partition of energies at different times during self-assembly in the assembly funnel regime at  (green box), rearrangement-limited conditions at  (blue box), and during an anneal (black box). Over the course of an anneal,  transitions from -6 to 6, spending  at 100 different linearly decreasing isothermal conditions. Values at the top right are complex yields. Inset plots show detail. Error bars <1%.
© Copyright Policy
Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC4215988&req=5

pone-0111233-g003: An assembly funnel means that complex assembly occurs via a small number of pathways.The possible set of reaction pathways govern assembly outcome under rearrangement-limited conditions, whereas thermodynamically favorable pathways govern assembly outcome in the assembly funnel regime. (a) Conformational entropy () of the system under different assembly conditions as a function of assembly time, . (b) Reference energy distributions of a 3×3 square grid complex based on thermodynamics and assembly configuration. Color spectrum indicates the number of bonds in an assembly. (c) Partition of energies at different times during self-assembly in the assembly funnel regime at (green box), rearrangement-limited conditions at (blue box), and during an anneal (black box). Over the course of an anneal, transitions from -6 to 6, spending at 100 different linearly decreasing isothermal conditions. Values at the top right are complex yields. Inset plots show detail. Error bars <1%.
Mentions: To further understand the influence of pathways on complex formation, we examined the kinds of intermediates that tend to arise and persist by measuring the conformational entropy, or distribution of species sizes and free energies, of the system. The conformational entropy is given by where is the fraction of species with energy and components. Higher values of conformational entropy correspond to broader distributions of assembly sizes and free energies. Under rearrangement-limited conditions, conformational entropy initially increases as many different intermediates form, and then plateaus (Fig. 3a). The species that form and remain are those that are most easily accessible via reaction pathways rather than those that are energetically favorable (Fig. 3b, c). In contrast, assembly in the assembly funnel regime favors the production of a relatively small number of intermediates, those lowest in free energy, so conformational entropy decreases with time as these low-energy intermediates and complexes form. Because complex size and geometry determine the possible reaction pathways and the types of assembly intermediates that can form [43], they also control the propensity of an assembly process to become “stuck” under a given set of reaction conditions.

Bottom Line: For typical complexes, an assembly funnel occurs in a narrow window of conditions whose location is highly complex specific.However, by redesigning the components this window can be drastically broadened, so that complexes can form quickly across many conditions.The generality of this approach suggests assembly funnel design as a foundational strategy for robust biomolecular complex synthesis.

View Article: PubMed Central - PubMed

Affiliation: Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, Maryland, United States of America.

ABSTRACT
Like protein folding and crystallization, the self-assembly of complexes is a fundamental form of biomolecular organization. While the number of methods for creating synthetic complexes is growing rapidly, most require empirical tuning of assembly conditions and/or produce low yields. We use coarse-grained simulations of the assembly kinetics of complexes to identify generic limitations on yields that arise because of the many simultaneous interactions allowed between the components and intermediates of a complex. Efficient assembly occurs when nucleation is fast and growth pathways are few, i.e. when there is an assembly "funnel". For typical complexes, an assembly funnel occurs in a narrow window of conditions whose location is highly complex specific. However, by redesigning the components this window can be drastically broadened, so that complexes can form quickly across many conditions. The generality of this approach suggests assembly funnel design as a foundational strategy for robust biomolecular complex synthesis.

Show MeSH