A new configurational bias scheme for sampling supramolecular structures

Abstract

We present a new simulation scheme which allows an efficient sampling of reconfigurable supramolecular structures made of polymeric constructs functionalized by reactive binding sites. The algorithm is based on the configurational bias scheme of Siepmann and Frenkel and is powered by the possibility of changing the topology of the supramolecular network by a non-local Monte Carlo algorithm. Such a plan is accomplished by a multi-scale modelling that merges coarse-grained simulations, describing the typical polymer conformations, with experimental results accounting for free energy terms involved in the reactions of the active sites. We test the new algorithm for a system of DNA coated colloids for which we compute the hybridisation free energy cost associated to the binding of tethered single stranded DNAs terminated by short sequences of complementary nucleotides. In order to demonstrate the versatility of our method, we also consider polymers functionalized by receptors that bind a surface decorated by ligands. In particular, we compute the density of states of adsorbed polymers as a function of the number of ligand-receptor complexes formed. Such a quantity can be used to study the conformational properties of adsorbed polymers useful when engineering adsorption with tailored properties. We successfully compare the results with the predictions of a mean field theory. We believe that the proposed method will be a useful tool to investigate supramolecular structures resulting from direct interactions between functionalized polymers for which efficient numerical methodologies of investigation are still lacking.

Programmable interactions with biomimetic DNA linkers at fluid membranes and interfaces

“…[12] reports the general expression of α(r, h), also considering cases in which the two linkers have different lengths. For non-ideal and flexible linkers, ∆G conf AB (r, h) is usually calculated using Monte Carlo methods [135,[150][151][152]. To derive an expression for ∆G conf AB (h) valid for the case in which linkers A and/or B are mobile, the corresponding fixed-linker expression (e.g.…”

“…Despite the fact that non-specific (e.g. electrostatic or steric) interaction between linkers are sometimes accounted for in the derivation of the linker-linker complexation free energy [135,151,152] (see Sec. 4.1), so far we have neglected non-specific interactions between linkers that do not belong to the same complex.…”

Melting transition in lipid vesicles functionalised by mobile DNA linkers

“…[57][58][59] To produce dashed curves ∆G 0 has been corrected with an attractive term (2 kJ mol been developed to calculate the free energy of multivalent interactions. 26,27,[29][30][31][32][33][34][35] Considering a set of interacting multivalent objects, these methods attempt to enumerate all possible configurations of the supramolecular network of linkers mediating the interactions. The success of these theories enabled the development of efficient simulation schemes for characterising the phase behaviour of multivalent objects, coarse-grained as simple particles with effective pair interactions.…”

“…20,25 Analytical methods capable of capturing the resulting entropic effects have been recently developed. [26][27][28][29][30][31][32][33][34][35] Such theories have been utilised to calculate effective potentials in DNA mediated interactions between solid [26][27][28][29][30][31] and deformable paricles, [35][36][37][38][39] as well as to design superselective probes. 20,25,[32][33][34][35]40 Analytical models have however limited applicability to those biologically and technologically relevant scenarios where non-specific contributions significantly affect the interactions.…”

Efficient sampling of reversible cross-linking polymers: Self-assembly of single-chain polymeric nanoparticles

“…Kinetic bottlenecks, limiting the number of binding/unbinding events between complexes, are overcome by dedicated Monte Carlo moves in which complexes tethered to backbones are bound/unbound in a single step of the algorithm. The methodology is based on configurational bias moves [26][27][28][29] powered by topological jumps as previously tested when studying hybridization of tethered single-stranded DNA carrying reactive sticky ends, and adsorption of ideal chains on functionalized interfaces 30 . We stress that the proposed methodology is general allowing the study of different types of supramolecular linkages (as specified by size, strength, or directionality) and how they influence large-scale properties of the aggregates.…”