The role of multivalency in the association kinetics of patchy particle complexes

Intrinsic and effective rate constants have an important role in the theory of diffusion-limited reactions. In a previous paper, we provide detailed microscopic expressions for these intrinsic rates [A. Vijaykumar, P. G. Bolhuis, and P. R. ten Wolde, Faraday Discuss. 195, 421 (2016)], which are usually considered as abstract quantities and assumed to be implicitly known. Using these microscopic expressions, we investigate how the rate of association depends on the strength and the range of the isotropic potential and the strength of the non-specific attraction in case of the anisotropic potential. In addition, we determine the location of the interface where these expressions become valid for anisotropic potentials. In particular, by investigating the particles' orientational distributions, we verify whether the interface at which these distributions become isotropic agrees with the interface predicted by the effective association rate constant. Finally, we discuss how large the intrinsic association rate can become, and what are the consequences for the existence of the diffusion limited regime.

show abstract

“…This behavior was also found in Ref. 35. Moreover, beyond a limiting value of ns , the association rates reach a plateau.…”

Section: Rate Constants For the Anisotropic Potentialsupporting

confidence: 85%

The magnitude of the intrinsic rate constant: How deep can association reactions be in the diffusion limited regime?

Wolde

Bolhuis

2017

The Journal of Chemical Physics

Self Cite

View full text Add to dashboard Cite

show abstract

“…Control over multivalent interactions is essential in engineering various interactions between and with nanoparticles 1–5 . Multivalency—i.e.…”

Section: Introductionmentioning

confidence: 99%

A stochastic view on surface inhomogeneity of nanoparticles

et al. 2019

View full text Add to dashboard Cite

The interactions between and with nanostructures can only be fully understood when the functional group distribution on their surfaces can be quantified accurately. Here we apply a combination of direct stochastic optical reconstruction microscopy (dSTORM) imaging and probabilistic modelling to analyse molecular distributions on spherical nanoparticles. The properties of individual fluorophores are assessed and incorporated into a model for the dSTORM imaging process. Using this tailored model, overcounting artefacts are greatly reduced and the locations of dye labels can be accurately estimated, revealing their spatial distribution. We show that standard chemical protocols for dye attachment lead to inhomogeneous functionalization in the case of ubiquitous polystyrene nanoparticles. Moreover, we demonstrate that stochastic fluctuations result in large variability of the local group density between particles. These results cast doubt on the uniform surface coverage commonly assumed in the creation of amorphous functional nanoparticles and expose a striking difference between the average population and individual nanoparticle coverage.

show abstract

“…41,42 Knowledge of the association kinetics of such systems enables the understanding and improved design of complex colloidal self-assembly. 43,44 As the interaction potential is anisotropic, particles undergo both translational and orientational diffusion. We therefore also study the rate constants as a function of the orientational diffusion constant of the particles.…”

Section: Introductionmentioning

confidence: 99%

Rate constants for proteins binding to substrates with multiple binding sites using a generalized forward flux sampling expression

Wolde

Bolhuis

2018

The Journal of Chemical Physics

Self Cite

View full text Add to dashboard Cite

To predict the response of a biochemical system, knowledge of the intrinsic and effective rate constants of proteins is crucial. The experimentally accessible effective rate constant for association can be decomposed in a diffusion-limited rate at which proteins come into contact and an intrinsic association rate at which the proteins in contact truly bind. Reversely, when dissociating, bound proteins first separate into a contact pair with an intrinsic dissociation rate, before moving away by diffusion. While microscopic expressions exist that enable the calculation of the intrinsic and effective rate constants by conducting a single rare event simulation of the protein dissociation reaction, these expressions are only valid when the substrate has just one binding site. If the substrate has multiple binding sites, a bound enzyme can, besides dissociating into the bulk, also hop to another binding site. Calculating transition rate constants between multiple states with forward flux sampling requires a generalized rate expression. We present this expression here and use it to derive explicit expressions for all intrinsic and effective rate constants involving binding to multiple states, including rebinding. We illustrate our approach by computing the intrinsic and effective association, dissociation, and hopping rate constants for a system in which a patchy particle model enzyme binds to a substrate with two binding sites. We find that these rate constants increase as a function of the rotational diffusion constant of the particles. The hopping rate constant decreases as a function of the distance between the binding sites. Finally, we find that blocking one of the binding sites enhances both association and dissociation rate constants. Our approach and results are important for understanding and modeling association reactions in enzyme-substrate systems and other patchy particle systems and open the way for large multiscale simulations of such systems.

show abstract

The role of multivalency in the association kinetics of patchy particle complexes

Cited by 14 publications

References 51 publications

The magnitude of the intrinsic rate constant: How deep can association reactions be in the diffusion limited regime?

The magnitude of the intrinsic rate constant: How deep can association reactions be in the diffusion limited regime?

A stochastic view on surface inhomogeneity of nanoparticles

Rate constants for proteins binding to substrates with multiple binding sites using a generalized forward flux sampling expression

Contact Info

Product

Resources

About