Chemical Reactions and Reaction Efficiency in Compartmentalized Systems. In: Prigogine I, Rice SA, editors. Advances in Chemical Physics. Hoboken: John Wiley & Sons, Inc.; 2000. pp. 245-406. [DOI: 10.1002/9780470141748.ch4]

Controlling the Kinetics of Self-Reproducing Micelles by Catalyst Compartmentalization in a Biphasic System

Compartmentalization of reactions is ubiquitous in biochemistry. Self-reproducing lipids are widely studied as chemical models of compartmentalized biological systems. Here, we explore the effect of catalyst location on copper-catalyzed azide-alkyne cycloadditions which drive the self-reproduction of micelles from phase-separated components. Tuning the hydrophilicity of the copper-ligand complex, so that hydro-phobic or -philic catalysts are used in combination with hydro-philic and -phobic coupling partners, provides a wide range of reactivity patterns. Analysis of the kinetic data shows that reactions with a hydrophobic catalyst are faster than with a hydrophilic catalyst. Diffusion-ordered spectroscopy experiments suggest compartmentalization of the hydrophobic catalyst inside micelles while the hydrophilic catalyst remains in the bulk aqueous phase. The autocatalytic effects observed can be tuned by varying reactant structure and coupling a hydrophilic alkyne and hydrophobic azide results in a more pronounced autocatalytic effect. We propose and test a model that rationalizes the observations in terms of the phase behavior of the reaction components and catalysts.

Spectrum of walk matrix for Koch network and its application

Various structural and dynamical properties of a network are encoded in the eigenvalues of walk matrix describing random walks on the network. In this paper, we study the spectra of walk matrix of the Koch network, which displays the prominent scale-free and small-world features. Utilizing the particular architecture of the network, we obtain all the eigenvalues and their corresponding multiplicities. Based on the link between the eigenvalues of walk matrix and random target access time defined as the expected time for a walker going from an arbitrary node to another one selected randomly according to the steady-state distribution, we then derive an explicit solution to the random target access time for random walks on the Koch network. Finally, we corroborate our computation for the eigenvalues by enumerating spanning trees in the Koch network, using the connection governing eigenvalues and spanning trees, where a spanning tree of a network is a subgraph of the network, that is, a tree containing all the nodes.

Random walks on deterministic scale-free networks: exact results

We study the random walk problem on a class of deterministic scale-free networks displaying a degree sequence for hubs scaling as a power law with an exponent gamma=log 3/log 2. We find exact results concerning different first-passage phenomena and, in particular, we calculate the probability of first return to the main hub. These results allow to derive the exact analytic expression for the mean time to first reach the main hub, whose leading behavior is given by tau approximately V1-1/gamma, where V denotes the size of the structure, and the mean is over a set of starting points distributed uniformly over all the other sites of the graph. Interestingly, the process turns out to be particularly efficient. We also discuss the thermodynamic limit of the structure and some local topological properties.

Reaction efficiency of diffusion-controlled processes on finite, planar arrays. II. Crystal surfaces

We consider 36 planar nets identified by O'Keeffe and Hyde and calculate for each, using the theory of finite Markovian processes, the overall mean walk length n (first passage time) of a reactant diffusing randomly on a finite platelet before being trapped at a reaction center; the results are analyzed in terms of the total number N of lattice sites, the number N(b) of boundary sites, the average valence nu, and the bond orientation function Psi. We establish that crystalline platelets that are members of the same compatible class are characterized by very comparable catalytic efficiencies. The results obtained are also linked to an analysis of the kinetics of docking in postnucleation stages of protein self-assembly and to a recent conjecture on the symmetries of planar nets and the hard disk freezing transition.

Exact mean first-passage time on the T-graph

We consider a simple random walk on the T-fractal and we calculate the exact mean time taug to first reach the central node i0. The mean is performed over the set of possible walks from a given origin and over the set of starting points uniformly distributed throughout the sites of the graph, except i0. By means of analytic techniques based on decimation procedures, we find the explicit expression for taug as a function of the generation g and of the volume V of the underlying fractal. Our results agree with the asymptotic ones already known for diffusion on the T-fractal and, more generally, they are consistent with the standard laws describing diffusion on low-dimensional structures.

Modeling the early stages of self-assembly in nanophase materials

The early stages of self-assembly of the elementary building blocks of nanophase materials are studied. The relative roles of entropic and energetic factors in determining the relative abundance of the final products present is analyzed using both a kinetic mean field model and a mesoscopic approach in which self-assembly is viewed as an encounter-controlled process on a discrete lattice. The relevance of the results in zeolite synthesis in connection with the ordered liquid phases recently discovered in these materials is discussed.

Aggregation of dipolar colloidal particles: geometric effects

To understand the importance of confinement and the influence of translational degrees of freedom on aggregation of dipolar colloidal particles, we calculate numerically-exact values for the mean encounter time for two nonspherically symmetric molecules to form a two-molecule cluster, regarded here as a precursor to aggregation. A lattice model is formulated in which the asymmetry of the molecules is accounted for by representing each as a "dimer" in the sense that each molecule is specified to occupy two adjacent lattice sites. The two dimers undergo simultaneous translation, and the mean times for their encounter are determined. Exact numerical results are obtained via application of the theory of finite Markov processes. The results allow one to examine in a detailed way the interplay among such factors as geometrical confinement, system size, translational motion, and specific orientational effects in influencing the aggregation event. The results are compared with previously reported theoretical predictions and experiments on the behavior of dipolar colloidal particles in the presence of an applied magnetic field.