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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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Thermodynamic equilibrium is a good predictor of yield for isothermal assembly after long assembly times for 1-dimensional complexes, but not 2- or 3-dimensional complexes.Assembly yields for a (a) 1×5 line complex, (b) 2×2, (c) 3×3, (d) 4×4 and (e) 5×5 square grid complex and (f) 2×2x2 cube complex as a function of the dimensionless temperature parameter, . Inset diagram depicts the complex. Numbers on the components in the complex indicate component identity (e.g. component “1” is different than component “2”). The dashed line indicates thermodynamic equilibrium. Dimensionless reaction time is defined as  where  is the macroscopic forward reaction rate constant and  is the initial concentration of components. Colored bars and boxes below figures represent the four different assembly regimes (Text S3). The assembly funnel regime is considered to be where the complex is thermodynamically favored (i.e.,) and assembly is rapid such that . Assembly “snapshots” (below graphs) are taken at  and  (top row), , , and  (bottom row) and comprised of ten random species drawn from the reaction mixture, weighted by concentration (Text S4). Error bars indicate the standard deviation of the reported quantity after 10 simulations and where omitted, are <1%. Here and elsewhere unless otherwise noted, there is no bond coupling ().
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pone-0111233-g002: Thermodynamic equilibrium is a good predictor of yield for isothermal assembly after long assembly times for 1-dimensional complexes, but not 2- or 3-dimensional complexes.Assembly yields for a (a) 1×5 line complex, (b) 2×2, (c) 3×3, (d) 4×4 and (e) 5×5 square grid complex and (f) 2×2x2 cube complex as a function of the dimensionless temperature parameter, . Inset diagram depicts the complex. Numbers on the components in the complex indicate component identity (e.g. component “1” is different than component “2”). The dashed line indicates thermodynamic equilibrium. Dimensionless reaction time is defined as where is the macroscopic forward reaction rate constant and is the initial concentration of components. Colored bars and boxes below figures represent the four different assembly regimes (Text S3). The assembly funnel regime is considered to be where the complex is thermodynamically favored (i.e.,) and assembly is rapid such that . Assembly “snapshots” (below graphs) are taken at and (top row), , , and (bottom row) and comprised of ten random species drawn from the reaction mixture, weighted by concentration (Text S4). Error bars indicate the standard deviation of the reported quantity after 10 simulations and where omitted, are <1%. Here and elsewhere unless otherwise noted, there is no bond coupling ().

Mentions: Estimating the yield of a complex by considering its free energy relative to the free energies of other potential products is a standard method of estimating the yield of a self-assembly reaction [36], but such estimates are relevant only when assembly reactions are close to equilibrium. To determine whether typical reactions approach equilibrium, we modeled the kinetics of assembly using component concentrations, reaction times and rates typical of experimental self-assembly reactions [29]–[32]. To understand the effects of temperature, we initially studied reactions that take place at a single temperature (a single value of ). Isothermal assembly of 1D line complexes quickly achieved yields near those predicted at thermodynamic equilibrium for all interaction energies considered (Fig. 2a and Figs. S3 and S4). The system as a whole also approached equilibrium, as demonstrated by the concentrations of both complexes and intermediates (Fig. S5). Yields of line complexes were highest when the interactions between components were strongest, in agreement with both thermodynamic predictions and similar studies of self-assembly kinetics [37].


An assembly funnel makes biomolecular complex assembly efficient.

Zenk J, Schulman R - PLoS ONE (2014)

Thermodynamic equilibrium is a good predictor of yield for isothermal assembly after long assembly times for 1-dimensional complexes, but not 2- or 3-dimensional complexes.Assembly yields for a (a) 1×5 line complex, (b) 2×2, (c) 3×3, (d) 4×4 and (e) 5×5 square grid complex and (f) 2×2x2 cube complex as a function of the dimensionless temperature parameter, . Inset diagram depicts the complex. Numbers on the components in the complex indicate component identity (e.g. component “1” is different than component “2”). The dashed line indicates thermodynamic equilibrium. Dimensionless reaction time is defined as  where  is the macroscopic forward reaction rate constant and  is the initial concentration of components. Colored bars and boxes below figures represent the four different assembly regimes (Text S3). The assembly funnel regime is considered to be where the complex is thermodynamically favored (i.e.,) and assembly is rapid such that . Assembly “snapshots” (below graphs) are taken at  and  (top row), , , and  (bottom row) and comprised of ten random species drawn from the reaction mixture, weighted by concentration (Text S4). Error bars indicate the standard deviation of the reported quantity after 10 simulations and where omitted, are <1%. Here and elsewhere unless otherwise noted, there is no bond coupling ().
© Copyright Policy
Related In: Results  -  Collection

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

pone-0111233-g002: Thermodynamic equilibrium is a good predictor of yield for isothermal assembly after long assembly times for 1-dimensional complexes, but not 2- or 3-dimensional complexes.Assembly yields for a (a) 1×5 line complex, (b) 2×2, (c) 3×3, (d) 4×4 and (e) 5×5 square grid complex and (f) 2×2x2 cube complex as a function of the dimensionless temperature parameter, . Inset diagram depicts the complex. Numbers on the components in the complex indicate component identity (e.g. component “1” is different than component “2”). The dashed line indicates thermodynamic equilibrium. Dimensionless reaction time is defined as where is the macroscopic forward reaction rate constant and is the initial concentration of components. Colored bars and boxes below figures represent the four different assembly regimes (Text S3). The assembly funnel regime is considered to be where the complex is thermodynamically favored (i.e.,) and assembly is rapid such that . Assembly “snapshots” (below graphs) are taken at and (top row), , , and (bottom row) and comprised of ten random species drawn from the reaction mixture, weighted by concentration (Text S4). Error bars indicate the standard deviation of the reported quantity after 10 simulations and where omitted, are <1%. Here and elsewhere unless otherwise noted, there is no bond coupling ().
Mentions: Estimating the yield of a complex by considering its free energy relative to the free energies of other potential products is a standard method of estimating the yield of a self-assembly reaction [36], but such estimates are relevant only when assembly reactions are close to equilibrium. To determine whether typical reactions approach equilibrium, we modeled the kinetics of assembly using component concentrations, reaction times and rates typical of experimental self-assembly reactions [29]–[32]. To understand the effects of temperature, we initially studied reactions that take place at a single temperature (a single value of ). Isothermal assembly of 1D line complexes quickly achieved yields near those predicted at thermodynamic equilibrium for all interaction energies considered (Fig. 2a and Figs. S3 and S4). The system as a whole also approached equilibrium, as demonstrated by the concentrations of both complexes and intermediates (Fig. S5). Yields of line complexes were highest when the interactions between components were strongest, in agreement with both thermodynamic predictions and similar studies of self-assembly kinetics [37].

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