Quantitative study of the association thermodynamics and kinetics of DNA-coated particles for different functionalization schemes

The Role of Receptor Uniformity in Multivalent Binding

Multivalency is prevalent in various biological systems and applications due to the superselectivity that arises from the cooperativity of multivalent binding. Traditionally, it was thought that weaker individual binding would improve the selectivity in multivalent targeting. Here, using analytical mean field theory and Monte Carlo simulations, we discover that, for receptors that are highly uniformly distributed, the highest selectivity occurs at an intermediate binding energy and can be significantly greater than the weak binding limit. This is caused by an exponential relationship between the bound fraction and receptor concentration, which is influenced by both the strength and combinatorial entropy of binding. Our findings not only provide new guidelines for the rational design of biosensors using multivalent nanoparticles but also introduce a new perspective in understanding biological processes involving multivalency.

Self-Assembly of DNA-Grafted Colloids: A Review of Challenges

DNA-mediated self-assembly of colloids has emerged as a powerful tool to assemble the materials of prescribed structure and properties. The uniqueness of the approach lies in the sequence-specific, thermo-reversible hybridization of the DNA-strands based on Watson–Crick base pairing. Grafting particles with DNA strands, thus, results into building blocks that are fully programmable, and can, in principle, be assembled into any desired structure. There are, however, impediments that hinder the DNA-grafted particles from realizing their full potential, as building blocks, for programmable self-assembly. In this short review, we focus on these challenges and highlight the research around tackling these challenges.

On the interpretation of kinetics and thermodynamics probed by single-molecule experiments

Single-molecule pulling experiments are widely used to extract both thermodynamic and kinetic data on ligand-receptor pairs, typically by fitting different models to the probability distribution of rupture forces of the corresponding bond. Here, a theoretical model is presented that shows how a measurement of the number of binding and unbinding events as a function of the observation time can also give access to both the binding (kon) and the unbinding (koff) rates of bonds, which combined provide a well-defined bond free-energy ΔGbond. The connection between ΔGbond and the ligand-receptor binding constant measured by typical binding essays is critically discussed. The role played by the molecular construct used to tether ligands and receptors to a surface is considered, highlighting the various approximations necessary to derive general expressions that connect its structure to its contribution, termed ΔGcnf, to the bond free-energy. In this way, the validity and the assumptions underpinning widely employed formulas and experimental protocols used to extract binding constants from single-molecule experiments are assessed. Finally, the role of ΔGcnf in processes mediated by ligand-receptor binding is briefly considered, and an experiment to unambiguously measure this quantity proposed.

Kinetics of Nanoparticle-Membrane Adhesion Mediated by Multivalent Interactions

Multivalent adhesive interactions mediated by a large number of ligands and receptors underpin many biological processes, including cell adhesion and the uptake of particles, viruses, parasites, and nanomedical vectors. In materials science, multivalent interactions between colloidal particles have enabled unprecedented control over the phase behavior of self-assembled materials. Theoretical and experimental studies have pinpointed the relationship between equilibrium states and microscopic system parameters such as the ligand-receptor binding strength and their density. In regimes of strong interactions, however, kinetic factors are expected to slow down equilibration and lead to the emergence of long-lived out-of-equilibrium states that may significantly influence the outcome of self-assembly experiments and the adhesion of particles to biological membranes. Here we experimentally investigate the kinetics of adhesion of nanoparticles to biomimetic lipid membranes. Multivalent interactions are reproduced by strongly interacting DNA constructs, playing the role of both ligands and receptors. The rate of nanoparticle adhesion is investigated as a function of the surface density of membrane-anchored receptors and the bulk concentration of nanoparticles and is observed to decrease substantially in regimes where the number of available receptors is limited compared to the overall number of ligands. We attribute such peculiar behavior to the rapid sequestration of available receptors after initial nanoparticle adsorption. The experimental trends and the proposed interpretation are supported by numerical simulations.

Interaction Heterogeneity can Favorably Impact Colloidal Crystal Nucleation

Colloidal particles with short-ranged attractions, e.g., micron-scale spheres functionalized with single-stranded DNA oligomers, are susceptible to becoming trapped in disordered configurations even when a crystalline arrangement is the ground state. Moreover, for reasons that are not well understood, seemingly minor variations in the particle formulation can lead to dramatic changes in the crystallization outcome. We demonstrate, using a combination of equilibrium and nonequilibrium computer simulations, that interaction heterogeneity-variations in the energetic interactions among different particle pairs in the population-may favorably impact crystal nucleation. Specifically, interaction heterogeneity is found to lower the free energy barrier to nucleation via the formation of clusters comprised preferentially of strong-binding particle pairs. Moreover, gelation is inhibited by "spreading out over time" the nucleation process, resulting in a reduced density of stable nuclei, allowing each to grow unhindered and larger. Our results suggest a simple and robust approach for enhancing colloidal crystallization near the "sticky sphere" limit, and support the notion that differing extents of interaction heterogeneity arising from various particle functionalization protocols may contribute to the otherwise unexplained variations in crystallization outcomes reported in the literature.

Theory and simulation of DNA-coated colloids: a guide for rational design

By exploiting the exquisite selectivity of DNA hybridization, DNA-coated colloids (DNACCs) can be made to self-assemble in a wide variety of structures. The beauty of this system stems largely from its exceptional versatility and from the fact that a proper choice of the grafted DNA sequences yields fine control over the colloidal interactions. Theory and simulations have an important role to play in the optimal design of self assembling DNACCs. At present, the powerful model-based design tools are not widely used, because the theoretical literature is fragmented and the connection between different theories is often not evident. In this Perspective, we aim to discuss the similarities and differences between the different models that have been described in the literature, their underlying assumptions, their strengths and their weaknesses. Using the tools described in the present Review, it should be possible to move towards a more rational design of novel self-assembling structures of DNACCs and, more generally, of systems where ligand-receptor are used to control interactions.

Critical Undercooling in DNA-Mediated Nanoparticle Crystallization

The nucleation of DNA-functionalized nanoparticle superlattices is observed to exhibit a temperature hysteresis between melting (superlattice dissociation) and freezing (particle association) transitions that allows for the study of nucleation thermodynamics. Through detailed study of the assembly of these particles, which can be considered programmable atom equivalents (PAEs), we identify this hysteresis as critical undercooling-a phase transition phenomenon related to a thermodynamic barrier to nucleation. The separable nature of the DNA bonding elements and nanoparticle core enables the PAE platform to pose unique questions about the microscopic dependencies of critical undercooling and, ultimately, to control the nucleation pathway. Specifically, we find that the undercooling required to initiate nucleation increases as the nanoparticle coordination number increases (number of particles to which a single particle can bind).

The combination of gold nanorods and nanoparticles with DNA nanodevices for logic gates construction

In this work, two DNA nanodevices were constructed utilizing a DNA strand displacement reaction. With the assistance of gold nanoparticles (AuNPs) and gold nanorods (AuNRs), the autonomous reactions can be reflected from the aggregation states of nanoparticles. By sequence design and the two non-overlapping double hump-like UV-vis spectral peaks of AuNPs and AuNRs, two logic gates with multiple inputs and outputs were successfully run with expected outcomes. This method not only shows how to achieve computing with multiple logic calculations but also has great potential for multiple targets detection.

Solid colloids with surface-mobile linkers

In this report we review the possibilities of using colloids with surface mobile linkers for the study of colloidal self-assembly processes. A promising route to create systems with mobile linkers is the use of lipid (bi-)layers. These lipid layers can be either used in the form of vesicles or as coatings for hard colloids and emulsion droplets. Inside the lipid bilayers molecules can be inserted via membrane anchors. Due to the fluidity of the lipid bilayer, the anchored molecules remain mobile. The use of different lipid mixtures even allows creating Janus-like particles that exhibit directional bonding if linkers are used which have a preference for a certain lipid phase. In nature mobile linkers can be found e.g. as receptors in cells. Therefore, towards the end of the review, we also briefly address the possibility of using colloids with surface mobile linkers as model systems to mimic cell-cell interactions and cell adhesion processes.

Mobile linkers on DNA-coated colloids: valency without patches

Colloids coated with single-stranded DNA (ssDNA) can bind selectively to other colloids coated with complementary ssDNA. The fact that DNA-coated colloids (DNACCs) can bind to specific partners opens the prospect of making colloidal "molecules." However, in order to design DNACC-based molecules, we must be able to control the valency of the colloids, i.e., the number of partners to which a given DNACC can bind. One obvious, but not very simple approach is to decorate the colloidal surface with patches of single-stranded DNA that selectively bind those on other colloids. Here we propose a design principle that exploits many-body effects to control the valency of otherwise isotropic colloids. Using a combination of theory and simulation, we show that we can tune the valency of colloids coated with mobile ssDNA, simply by tuning the nonspecific repulsion between the particles. Our simulations show that the resulting effective interactions lead to low-valency colloids self-assembling in peculiar open structures, very different from those observed in DNACCs with immobile DNA linkers.

Aggregation dynamics, structure, and mechanical properties of bigels

Recently we have introduced bigels, inter-penetrating gels made of two different colloidal species. Even if particles with simple short-range isotropic potential are employed, the selective interactions enable the tunability of the self-assembly, leading to the formation of complex structures. In the present paper, we explore the non-equilibrium dynamics and the phenomenology underlying the kinetic arrest under quench and the formation of bigels. We demonstrate that the peculiar bigel kinetics can be described through an arrested spinodal decomposition driven by demixing of the colloidal species. The role played by the presence of a second colloidal species on the phase diagram, as expanded to account for the increased number of parameters, is clarified both via extensive numerical simulations and experiments. We provide details on the realisation of bigels, by means of DNA-coated colloids (DNACCs), and the consequent imaging techniques. Moreover we evidence, by comparison with the usual one-component gel formation, the emergence of controllable timescales in the aggregation of the bigels, whose final stages are also experimentally studied to provide morphological details. Finally, we use numerical models to simulate the bigel response to mechanical strain, highlighting how such a new material can bear significantly higher stress compared to the usual one-component gel. We conclude by discussing possible technological uses and by providing insights on the viable research steps to undertake for more complex and yet tuneable multi-component colloidal systems.

Designing stimulus-sensitive colloidal walkers

Colloidal particles with DNA "legs" that can bind reversibly to receptors on a surface can be made to 'walk' if there is a gradient in receptor concentration. We use a combination of theory and Monte Carlo simulations to explore how controllable parameters, e.g. coating density and binding strength, affect the dynamics of such colloids. We find that competition between thermodynamic and kinetic trends imply that there is an optimal value for both the binding strength and the number of "legs" for which transport is the fastest. Using available thermodynamic data on DNA binding, we indicate how directionally reversible, temperature-controlled transport of colloidal walkers can be achieved. In particular, the present results should make it possible to design a chromatographic technique that can be used to separate colloids with different DNA functionalizations.

Influence of dsDNA fragment length on particle binding in an evanescent field biosensing system

Particle labels are widely used in affinity-based biosensing due to the high detection signal per label, the high stability, and the convenient biofunctionalization of particles. In this paper we address the question how the time-course of particle binding and the resulting signals depend on the length of captured target molecules. As a model system we used fragments of dsDNA with lengths of 105 bp (36 nm), 290 bp (99 nm) and 590 bp (201 nm), detected in an evanescent-field optomagnetic biosensing system. On both ends the fragments were provided with small-molecule tags to allow binding of the fragments to protein-coated particles and to the capture molecules at the sensor surface. For isolated single particles bound to the surface, we observe that the optical scattering signal per particle depends only weakly on the fragment length, which we attribute to the pivoting motion that allows the particles to get closer to the surface. Our data show a strong influence of the fragment length on the particle binding: the binding rate of particles to the sensor surface is an order of magnitude higher for the longest dsDNA fragments compared to the smallest fragment studied in this paper. We attribute the enhanced binding rate to the length and motional freedom of the fragments. These results generate a new dimension for the design of assays and systems in particle-based biosensing.

Hydrodynamics selects the pathway for displacive transformations in DNA-linked colloidal crystallites

The degree to which DNA-linked particle crystals, particularly those composed of micrometer-scale colloids, are able to dynamically evolve or whether they are kinetically arrested after formation remains poorly understood. Here, we study a recently observed displacive transformation in colloidal binary superlattice crystals, whereby a body-centered cubic to face-centered cubic transformation is found to proceed spontaneously under some annealing conditions. Using a comprehensive suite of computer simulation tools, we develop a framework for analyzing the many displacive transformation pathways corresponding to distinct, but energetically degenerate, random hexagonal close-packed end states. Due to the short-ranged, spherically symmetric nature of the particle interactions the pathways are all barrierless, suggesting that all end states should be equally likely. Instead, we find that hydrodynamic correlations between particles result in anisotropic mobility along the various possible displacive pathways, strongly selecting for pathways that lead to the fcc-CuAu-I configuration, explaining recent experimental observations. This finding may provide clues for discovering new approaches for controlling structure in this emerging class of materials.

Self-replication in colloids with asymmetric interactions

Self-replication is a ubiquitous process in organisms. Understanding the key ingredients of self-replication is critical for developing self-sustaining systems in the laboratory. Moreover, finding the optimal conditions to generate accurate replicas and adequate output can accelerate industrial processes enormously. Here, we propose a scheme for self-replication where asymmetric interactions in colloids are used to find optimal self-replication conditions by controlling the input of energy. We generalize a recently developed kinetic Monte Carlo algorithm to treat both translational and rotational motions of Brownian anisotropic colloids. We report two main findings from our simulations: first, by fine tuning the particle interactions, highly accurate self-replication is achievable with a moderate sacrifice of reaction speed. Second, with the introduction of energy cycling to enable periodic assembly/disassembly of the system's components the replicator population grows exponentially. The exponential growth constant is a non-monotonic function of the period of the pulsed energy delivery.

Probing the relative orientation of molecules bound to DNA through controlled interference using second-harmonic generation

A method is described in which the interference of radiated second-harmonic electric fields generated by a pair of oriented molecules intercalated into double-stranded DNA is controlled and measured. The results show that the relative molecular orientation of the two molecules significantly changes the magnitude of the observed second-harmonic generation intensity, which is described by a simple model that accounts for the interferences of the radiated fields. The technique presented shows promise for future experiments investigating structural changes induced by the formation of a DNA-biomolecule complex.

Entropy-driven collective interactions in DNA brushes on a biochip

Cell-free gene expression in localized DNA brushes on a biochip has been shown to depend on gene density and orientation, suggesting that brushes form compartments with partitioned conditions. At high density, the interplay of DNA entropic elasticity, electrostatics, and excluded volume interactions leads to collective conformations that affect the function of DNA-associated proteins. Hence, measuring the collective interactions in dense DNA, free of proteins, is essential for understanding crowded cellular environments and for the design of cell-free synthetic biochips. Here, we assembled dense DNA polymer brushes on a biochip along a density gradient and directly measured the collective extension of DNA using evanescent fluorescence. DNA of 1 kbp in a brush undergoes major conformational changes, from a relaxed random coil to a stretched configuration, following a universal function of density to ionic strength ratio with scaling exponent of 1/3. DNA extends because of the swelling force induced by the osmotic pressure of ions, which are trapped in the brush to maintain local charge neutrality, in competition with the restoring force of DNA entropic elasticity. The measurements reveal in DNA crossover between regimes of osmotic, salted, mushroom, and quasineutral brush. It is surprising to note that, at physiological ionic strength, DNA density does not induce collective stretch despite significant chain overlap, which implies that excluded volume interactions in DNA are weak.

Efficient self-assembly of DNA-functionalized fluorophores and gold nanoparticles with DNA functionalized silicon surfaces: the effect of oligomer spacers

Although strategies for the immobilization of DNA oligonucleotides onto surfaces for bioanalytical and top-down bio-inspired nanobiofabrication approaches are well developed, the effect of introducing spacer molecules between the surface and the DNA oligonucleotide for the hybridization of nanoparticle–DNA conjugates has not been previously assessed in a quantitative manner. The hybridization efficiency of DNA oligonucleotides end-labelled with gold nanoparticles (1.4 or 10 nm diameter) with DNA sequences conjugated to silicon surfaces via hexaethylene glycol phosphate diester oligomer spacers (0, 1, 2, 6 oligomers) was found to be independent of spacer length. To quantify both the density of DNA strands attached to the surfaces and hybridization with the surface-attached DNA, new methodologies have been developed. Firstly, a simple approach based on fluorescence has been developed for determination of the immobilization density of DNA oligonucleotides. Secondly, an approach using mass spectrometry has been created to establish (i) the mean number of DNA oligonucleotides attached to the gold nanoparticles and (ii) the hybridization density of nanoparticle–oligonucleotide conjugates with the silicon surface–attached complementary sequence. These methods and results will be useful for application with nanosensors, the self-assembly of nanoelectronic devices and the attachment of nanoparticles to biomolecules for single-molecule biophysical studies.

Arrested demixing opens route to bigels

Understanding and, ultimately, controlling the properties of amorphous materials is one of the key goals of material science. Among the different amorphous structures, a very important role is played by colloidal gels. It has been only recently understood that colloidal gels are the result of the interplay between phase separation and arrest. When short-ranged attractive colloids are quenched into the phase-separating region, density fluctuations are arrested and this results in ramified amorphous space-spanning structures that are capable of sustaining mechanical stress. We present a mechanism of aggregation through arrested demixing in binary colloidal mixtures, which leads to the formation of a yet unexplored class of materials--bigels. This material is obtained by tuning interspecies interactions. Using a computer model, we investigate the phase behavior and the structural properties of these bigels. We show the topological similarities and the geometrical differences between these binary, interpenetrating, arrested structures and their well-known monodisperse counterparts, colloidal gels. Our findings are supported by confocal microscopy experiments performed on mixtures of DNA-coated colloids. The mechanism of bigel formation is a generalization of arrested phase separation and is therefore universal.

Re-entrant melting as a design principle for DNA-coated colloids

Colloids functionalized with DNA hold great promise as building blocks for complex self-assembling structures. However, the practical use of DNA-coated colloids (DNACCs) has been limited by the narrowness of the temperature window where the target structures are both thermodynamically stable and kinetically accessible. Here we propose a strategy to design DNACCs, whereby the colloidal suspensions crystallize on cooling and then melt on further cooling. In a phase diagram with such a re-entrant melting, kinetic trapping of the system in non-target structures should be strongly suppressed. We present model calculations and simulations that show that real DNA sequences exist that should bestow this unusual phase behaviour on suitably functionalized colloidal suspensions. We present our results for binary systems, but the concepts that we develop apply to multicomponent systems and should therefore open the way towards the design of truly complex self-assembling colloidal structures.

DNA architectonics: towards the next generation of bio-inspired materials

The use of DNA in nanobiotechnology has advanced to a stage at which almost any two or three dimensional architecture can be designed with high precision. The choice of the DNA sequences is essential for successful self-assembly, and opens new ways of making nanosized monomolecular assemblies with predictable structure and size. The inclusion of designer nucleoside analogues further adds functionality with addressable groups, which have an influence on the function of the DNA nano-objects. This article highlights the recent achievements in this emerging field and gives an outlook on future perspectives and applications.

Binding and cleavage of DNA with the restriction enzyme EcoR1 using time-resolved second harmonic generation

The binding of EcoR1 to a 90-bp DNA duplex attached to colloidal microparticles and the subsequent cleavage by the enzyme was observed in real time and label-free with time-resolved second harmonic (SH) spectroscopy. This method provides a unique way to investigate biomolecular interactions based on its sensitivity to changes in structure and electrical charge on formation of a complex and subsequent dynamics. The binding of EcoR1 to the recognition sequence in DNA appears as a rapid increase in the SH signal, which is attributed to the enzyme-induced change in the DNA conformation, going from a rod-like to a bent shape. In the presence of the cofactor Mg(2+), the subsequent decay in the SH signal was monitored in real time as the following processes occurred: cleavage of DNA, dissociation of the enzyme from the DNA, and diffusion of the 74-bp fragment into the bulk solution leaving the 16-bp fragment attached to the microparticle. The observed decay was dependent on the concentration of Mg(2+), which functions as a cofactor and as an electrolyte. With SH spectroscopy the rehybridization dynamics between the rehybridized microparticle bound and free cleaved DNA fragments was observed in real time and label-free following the cleavage of DNA. Collectively, the experiments reported here establish SH spectroscopy as a powerful method to investigate equilibrium and time-dependent biological processes in a noninvasive and label-free way.

Direct measurements of DNA-mediated colloidal interactions and their quantitative modeling

DNA bridging can be used to induce specific attractions between small particles, providing a highly versatile approach to creating unique particle-based materials having a variety of periodic structures. Surprisingly, given the fact that the thermodynamics of DNA strands in solution are completely understood, existing models for DNA-induced particle interactions are typically in error by more than an order of magnitude in strength and a factor of two in their temperature dependence. This discrepancy has stymied efforts to design the complex temperature, sequence and time-dependent interactions needed for the most interesting applications, such as materials having highly complex or multicomponent microstructures or the ability to reconfigure or self-replicate. Here we report high-spatial resolution measurements of DNA-induced interactions between pairs of polystyrene microspheres at binding strengths comparable to those used in self-assembly experiments, up to 6 k(B)T. We also describe a conceptually straightforward and numerically tractable model that quantitatively captures the separation dependence and temperature-dependent strength of these DNA-induced interactions, without empirical corrections. This model was equally successful when describing the more complex and practically relevant case of grafted DNA brushes with self-interactions that compete with interparticle bridge formation. Together, our findings motivate a nanomaterial design approach where unique functional structures can be found computationally and then reliably realized in experiment.

Design rule for colloidal crystals of DNA-functionalized particles

We report a Monte Carlo simulation study of the phase behavior of colloids coated with long, flexible DNA chains. We find that an important change occurs in the phase diagram when the number of DNAs per colloid is decreased below a critical value. In this case, the triple point disappears and the condensed phase that coexists with the vapor is always liquid. Our simulations thus explain why, in the dilute solutions typically used in experiments, colloids coated with a small number of DNA strands cannot crystallize. We understand this behavior in terms of the discrete nature of DNA binding.

Site-selective binding of nanoparticles to double-stranded DNA via peptide nucleic acid "invasion"

We demonstrate a novel method for by-design placement of nano-objects along double-stranded (ds) DNA. A molecular intercalator, designed as a peptide nucleic acid (PNA)-DNA chimera, is able to invade dsDNA at the PNA-side due to the hybridization specificity between PNA and one of the duplex strands. At the same time, the single-stranded (ss) DNA tail of the chimera, allows for anchoring of nano-objects that have been functionalized with complementary ssDNA. The developed method is applied for interparticle attachment and for the fabrication of particle clusters using a dsDNA template. This method significantly broadens the molecular toolbox for constructing nanoscale systems by including the most conventional not yet utilized DNA motif, double helix DNA.

DNA-based soft phases

This chapter reviews the state-of-the-art in the study of molecular or colloidal systems whose mutual interactions are mediated by DNA molecules. In the last decade, the robust current knowledge of DNA interactions has enabled an impressive growth of self-assembled DNA-based structures that depend crucially on the properties of DNA-DNA interactions. In many cases, structures are built on design by exploiting the programmable selectivity of DNA interactions and the modularity of their strength. The study of DNA-based materials is definitely an emerging field in condensed matter physics, nanotechnology, and material science. This chapter will consider both systems that are entirely constructed by DNA and hybrid systems in which latex or metal colloidal particles are coated by DNA strands. We will confine our discussion to systems in which DNA-mediated interactions promote the formation of "phases," that is structures extending on length scales much larger than the building blocks. Their self-assembly typically involves a large number of interacting particles and often features hierarchical stages of structuring. Because of the possibility of fine-tuning the geometry and strength of the DNA-mediated interactions, these systems are characterized by a wide variety of patterns of self-assembly, ranging from amorphous, to liquid crystalline, to crystalline in one, two, or three dimensions.

Effect of oligonucleotide length on the assembly of DNA materials: molecular dynamics simulations of layer-by-layer DNA films

DNA strand length has been found to be an important factor in many DNA-based nanoscale systems. Here, we apply molecular dynamics simulations in a synergistic effort with layer-by-layer experimental data to understand the effect of DNA strand length on the assembly of DNA films. The results indicate that short (less than 10 bases) and long (more than 30 bases) single-stranded DNAs do not exhibit optimal film growth, and this can be associated with the limited accessibility of the bases on the surface due to formation of self-protected interactions that prevent efficient hybridization. Interestingly, the presence of a duplex attached to a single strand significantly alters the persistence length of the polyT strands. Our study suggests that restrained polyT, compared to labile suspensions of free polyT, are more capable of hybridization and hence DNA-based assembly.

Aggregation-disaggregation transition of DNA-coated colloids: experiments and theory

Colloids coated with complementary single-stranded DNA "sticky ends" associate and dissociate upon heating. Recently, microscopy experiments have been carried out where this association-dissociation transition has been investigated for different types of DNA and different DNA coverages [R. Dreyfus, M. E. Leunissen, R. Sha, A. V. Tkachenko, N. C. Seeman, D. J. Pine, and P. M. Chaikin, Phys. Rev. Lett. 102, 048301 (2009)]. It has been shown that this transition can be described by a simple quantitative model which takes into account the features of the tethered DNA on the particles and unravels the importance of an entropy cost due to DNA confinement between the surfaces. In this paper, we first present an extensive description of the experiments that were carried out. A step-by-step model is then developed starting from the level of statistical mechanics of tethered DNA to that of colloidal aggregates. This model is shown to describe the experiments with excellent agreement for the temperature and width of the transition, which are both essential properties for complex self-assembly processes.