Self-assembly of DNA-coded nanoclusters

We present a theoretical discussion of a self-assembly scheme which makes it possible to use DNA to uniquely encode the composition and structure of micro- and nanoparticle clusters. These anisotropic DNA-decorated clusters can be further used as building blocks for hierarchical self-assembly of larger structures. We address several important aspects of possible experimental implementation of the proposed scheme: the competition between different types of clusters in a solution, possible jamming in an unwanted configuration, and the degeneracy due to symmetry with respect to particle permutations.Comment: v2, 4 pages, 7 figures, added journal re

Loop realizations of quantum affine algebras

We give a simplified description of quantum affine algebras in their loop presentation. This description is related to Drinfeld's new realization via halves of vertex operators. We also define an idempotent version of the quantum affine algebra which is suitable for categorification.Comment: 19 page

Revealing the visually unknown in ancient manuscripts with a similarity measure for IR-imaged inks

One of the tasks facing historians and conservationists is the authentication or dating of medieval manuscripts. To this end it is important to them to verify whether writings on the same or different manuscripts are concurrent. In this work we explore this task by capturing images of manuscript pages in infrared (IR) and modelling and then comparing the ink appearance of segmented text. The modelling of the text appearance relies on the unsupervised multimodal clustering of ink descriptors and the derived probability density functions. The similarity measure is built around the distribution of cluster labels and their proportions. We demonstrate our method by using both model inks of known composition and authentic Byzantine manuscripts

An ink texture descriptor for nir-imaged medieval documents

In this work we explore the task of authenticating and dating ancient manuscripts by capturing images of pages in nearinfrared (NIR) and modelling and then comparing the ink appearance of segmented text. We present a texture feature descriptor to characterize and recognize semi-transparent materials such as the inks found in manuscripts. These textural patterns are different in nature from perceptual entities such as textons, tokens, frequency or repeatability of textural elements. Our ink texture descriptor relates a set of ink features from various first and second-order statistics to semi-liquid and viscous image-based properties of inks. In particular, we propose eigen features from the joint gray-level probabilities and off-diagonal sums of co-occurrence matrices. We test the qualities of the features with a classifier trained with the ink descriptor to show how well it recognizes eight different inks of known composition. Presented with the very same task the human visual system would fail to spot the ink composition difference given the inks inter-class and intra-class distances are extremely short

Colloids with key-lock interactions: non-exponential relaxation, aging and anomalous diffusion

The dynamics of particles interacting by key-lock binding of attached biomolecules are studied theoretically. Experimental realizations of such systems include colloids grafted with complementary single-stranded DNA (ssDNA), and particles grafted with antibodies to cell-membrane proteins. Depending on the coverage of the functional groups, we predict two distinct regimes. In the low coverage localized regime, there is an exponential distribution of departure times. As the coverage is increased the system enters a diffusive regime resulting from the interplay of particle desorption and diffusion. This interplay leads to much longer bound state lifetimes, a phenomenon qualitatively similar to aging in glassy systems. The diffusion behavior is analogous to dispersive transport in disordered semiconductors: depending on the interaction parameters it may range from a finite renormalization of the diffusion coefficient to anomalous, subdiffusive behavior. We make connections to recent experiments and discuss the implications for future studies.Comment: v2: substantially revised version, new treatment of localized regime, 19 pages, 10 figure

Kinetic limitations of cooperativity based drug delivery systems

We study theoretically a novel drug delivery system that utilizes the overexpression of certain proteins in cancerous cells for cell specific chemotherapy. The system consists of dendrimers conjugated with "keys" (ex: folic acid) which "key-lock" bind to particular cell membrane proteins (ex: folate receptor). The increased concentration of "locks" on the surface leads to a longer residence time for the dendrimer and greater incorporation into the cell. Cooperative binding of the nanocomplexes leads to an enhancement of cell specificity. However, both our theory and detailed analysis of in-vitro experiments indicate that the degree of cooperativity is kinetically limited. We demonstrate that cooperativity and hence the specificity to particular cell type can be increased by making the strength of individual bonds weaker, and suggest a particular implementation of this idea. The implications of the work for optimizing the design of drug delivery vehicles are discussed.Comment: 4 pages, 4 figures, v3: minor revision

Error-proof programmable self-assembly of DNA-nanoparticle clusters

We study theoretically a new generic scheme of programmable self-assembly of nanoparticles into clusters of desired geometry. The problem is motivated by the feasibility of highly selective DNA-mediated interactions between colloidal particles. By analyzing both a simple generic model and a more realistic description of a DNA-colloidal system, we demonstrate that it is possible to suppress the glassy behavior of the system, and to make the self-assembly nearly error-proof. This regime requires a combination of stretchable interparticle linkers (e.g. sufficiently long DNA), and a soft repulsive potential. The jamming phase diagram and the error probability are computed for several types of clusters. The prospects for the experimental implementation of our scheme are also discussed. PACS numbers: 81.16.Dn, 87.14.Gg, 36.40.EiComment: 6 pages, 4 figures, v2: substantially revised version, added journal re

Statistical Mechanics of DNA-Mediated Colloidal Aggregation

We present a statistical mechanical model of aggregation in colloidal systems with DNA mediated interactions. We obtain a general result for the two-particle binding energy in terms of the hybridization free energy $\Delta G$ of DNA and two model dependent properties: the average number of available DNA bridges \left and the effective DNA conccentration $c_{eff}$. We calculate these parameters for a particular DNA bridging scheme. The fraction of all the $n$-mers, including the infinite aggregate, are shown to be universal functions of a single parameter directly related to the two-particle binding energy. We explicitly take into account the partial ergodicity of the problem resulting from the slow DNA binding-unbinding dynamics, and introduce the concept of angular localization of DNA linkers. In this way, we obtain a direct link between DNA thermodynamics and the global aggregation and melting properties in DNA-colloidal systems. The results of the theory are shown to be in quantitative agreement with two recent experiments with particles of micron and nanometer size. PACS numbers: 81.16.Dn, 82.20.Db, 68.65.-k, 87.14.GgComment: 12 pages, 6 figures, v2: added reference, expanded conclusion, added journal re