Statistical mechanics of dimerizations and its consequences for small systems

Zangi, Ronen

doi:10.1039/d2cp04450a

Cited by 5 publications

(18 citation statements)

References 55 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Previously, we showed that for homo- and hetero-dimerizations, the average number of bound particles is related to relative fluctuations in the system. , Accordingly, for the two-body reaction described in eq 8, we can write the average number of a cluster of size ( i + j ) as ⟨ N A i + j ⟩ = 1 l ( N A i + j , N A i + j ) − l [ N A i + j , N A i false( N A j − δ italicij false) ] where the relative fluctuations between two variables ζ and η are defined by l (ζ, η) = ⟨ζη⟩/(⟨ζ⟩⟨η⟩) – 1. In Figure a, we test this equality on R2 series for systems with N A total ≥ 5, 6, and 8 for dimer, trimer, and tetramer, respectively.…”

Section: Resultsmentioning

confidence: 99%

“…Previously, we showed that for homo-and hetero-dimerizations, the average number of bound particles is related to relative fluctuations in the system. 34,35 Accordingly, for the two-body reaction described in eq 8, we can write the average number of a cluster of size (i + j) as…”

Section: Journal Of Chemicalmentioning

confidence: 99%

“…is considered. It is found that K is not given by the expression widely applied in the literature, 24−33 ⟨c AB ⟩c ⌀ /(⟨c A ⟩⟨c B ⟩), but must include cross-correlations in reactants' concentrations, yielding the expression 34,35…”

Section: ■ Introductionmentioning

confidence: 99%

“…To this end, a simple, elementary, two-body reaction A + B ⇌ italicAB is considered. It is found that K is not given by the expression widely applied in the literature, − ⟨ c AB ⟩ c ⌀ /(⟨ c A ⟩⟨ c B ⟩), but must include cross-correlations in reactants’ concentrations, yielding the expression , K = false⟨ c italicAB false⟩ false⟨ c A ( c B − δ AB / V ) false⟩ c ⌀ where δ AB equals zero for hetero-dimerizations ( A and B are distinct components) and equals one for homo-dimerizations ( A and B are the same components, i.e., A ≡ B ). The subtraction of the reciprocal of volume term, 1/ V , in homo-dimerizations, excludes self-correlations in particle number.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Multimerizations, Aggregation, and Transfer Reactions of Small Numbers of Molecules

Zangi

2023

J. Chem. Inf. Model.

Self Cite

View full text Add to dashboard Cite

Chemical equilibria of multimerizations in systems with small numbers of particles exhibit a behavior seemingly at odds with that observed macroscopically. In this paper, we apply the recently proposed expression of equilibrium constant for binding, which includes cross-correlations in reactants’ concentrations, to write an equilibrium constant for the formation of clusters larger than two (e.g., trimer, tetramer, and pentamer) as series of two-body reactions. Results obtained by molecular dynamics simulations demonstrate that the value of this expression is constant for all concentrations and system sizes, as well as at an onset of a phase transition to an aggregated state, where densities in the system change discontinuously. In contrast, the value of the commonly utilized expression of equilibrium constant, which ignores correlations, is not constant and its variations can reach few orders of magnitude. Considering different paths for the same multimer formation, with elementary reactions of any order, yields different expressions for the equilibrium constant, yet, with exactly the same value. This is also true for routes with essentially zero probability to occur. Existence of different expressions for the same equilibrium constant imposes equalities between averages of correlated, along with uncorrelated, concentrations of participating species. Moreover, a relation between an average particle number and relative fluctuations derived for two-body reactions is found to be obeyed here as well despite couplings to additional equilibrium reactions in the system. Analyses of transfer reactions, where association and dissociation events take place on both sides of the chemical equation, further indicate the necessity to include cross-correlations in the expression of the equilibrium constant. However, in this case, the magnitudes of discrepancies of the uncorrelated expression are smaller, likely because of partial cancellation of correlations, which exist on both the reactant and product sides.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Journal Of Chemicalmentioning

confidence: 99%

Section: ■ Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Multimerizations, Aggregation, and Transfer Reactions of Small Numbers of Molecules

Zangi

2023

J. Chem. Inf. Model.

Self Cite

View full text Add to dashboard Cite

show abstract

“…In contrast, due to translation, the single-particle partition function of A gas particle depends on the volume of the gas. If we approximate the discrete sum of quantum translational energy states by an integral, the dependency of this single-particle partition function (both of the reference and the arbitrary systems) on volume can be shown to be linear and the following equality exists q S A ⊖ q A ⊖ / V ⊖ · q S ⊖ = q S A q A / V · q S …”

Section: Resultsmentioning

confidence: 99%

Breakdown of Langmuir Adsorption Isotherm in Small Closed Systems

Zangi

2024

Langmuir

Self Cite

View full text Add to dashboard Cite

For more than a century, monolayer adsorptions in which adsorbate molecules and adsorbing sites behave ideally have been successfully described by Langmuir's adsorption isotherm. For example, the amount of adsorbed material, as a function of concentration of the material which is not adsorbed, obeys Langmuir's equation. In this paper, we argue that this relation is valid only for macroscopic systems. However, when particle numbers of adsorbate molecules and/or adsorbing sites are small, Langmuir's model fails to describe the chemical equilibrium of the system. This is because the kinetics of forming, or the probability of observing, occupied sites arises from two-body interactions, and as such, ought to include cross-correlations between particle numbers of the adsorbate and adsorbing sites. The effect of these correlations, as reflected by deviations in predicting composition when correlations are ignored, increases with decreasing particle numbers and becomes substantial when only few adsorbate molecules, or adsorbing sites, are present in the system. In addition, any change that augments the fraction of occupied sites at equilibrium (e.g., smaller volume, lower temperature, or stronger adsorption energy) further increases the discrepancy between observed properties of small systems and those predicted by Langmuir's theory. In contrast, for large systems, these cross-correlations become negligible, and therefore when expressing properties involving two-body processes, it is possible to consider independently the concentration of each component. By applying statistical mechanics concepts, we derive a general expression of the equilibrium constant for adsorption. It is also demonstrated that in ensembles in which total numbers of particles are fixed, the magnitudes of fluctuations in particle numbers alone can predict the average chemical composition of the system. Moreover, an alternative adsorption equation, predicting the average fraction of occupied sites from the value of the equilibrium constant, is proposed. All derived relations were tested against results obtained by Monte Carlo simulations.

show abstract

Predicting Rubisco-Linker Condensation from Titration in the Dilute Phase

Payne-Dwyer,

Kumar,

Barrett

et al. 2024

Phys. Rev. Lett.

View full text Add to dashboard Cite

The condensation of Rubisco holoenzymes and linker proteins into “pyrenoids,” a crucial supercharger of photosynthesis in algae, is qualitatively understood in terms of “sticker-and-spacer” theory. We derive semianalytical partition sums for small Rubisco-linker aggregates, which enable the calculation of both dilute-phase titration curves and dimerization diagrams. By fitting the titration curves to surface plasmon resonance and single-molecule fluorescence microscopy data, we extract the molecular properties needed to predict dimerization diagrams. We use these to estimate typical concentrations for condensation, and successfully compare these to microscopy observations. Published by the American Physical Society 2024

show abstract

Statistical mechanics of dimerizations and its consequences for small systems

Abstract: Utilizing a statistical mechanics framework, we derive the expression of the equilibrium constant for dimerization reactions. An important feature arising from the derivation is the necessity to include two-body correlations...

Cited by 5 publications

References 55 publications

Multimerizations, Aggregation, and Transfer Reactions of Small Numbers of Molecules

Multimerizations, Aggregation, and Transfer Reactions of Small Numbers of Molecules

Breakdown of Langmuir Adsorption Isotherm in Small Closed Systems

Predicting Rubisco-Linker Condensation from Titration in the Dilute Phase

Contact Info

Product

Resources

About