Takafumi Iwaki

Tooth germ invagination from cell-cell interaction: Working hypothesis on mechanical instability.

In the early stage of tooth germ development, the bud of the dental epithelium is invaginated by the underlying mesenchyme, resulting in the formation of a cap-like folded shape. This bud-to-cap transition plays a critical role in determining the steric design of the tooth. The epithelial-mesenchymal interaction within a tooth germ is essential for mediating the bud-to-cap transition. Here, we present a theoretical model to describe the autonomous process of the morphological transition, in which we introduce mechanical interactions among cells. Based on our observations, we assumed that peripheral cells of the dental epithelium bound tightly to each other to form an elastic sheet, and mesenchymal cells that covered the tooth germ would restrict its growth. By considering the time-dependent growth of cells, we were able to numerically show that the epithelium within the tooth germ buckled spontaneously, which is reminiscent of the cap-stage form. The difference in growth rates between the peripheral and interior parts of the dental epithelium, together with the steric size of the tooth germ, were determining factors for the number of invaginations. Our theoretical results provide a new hypothesis to explain the histological features of the tooth germ.

Folding transition of a single semiflexible polyelectrolyte chain through toroidal bundling of loop structures

We consider how the DNA coil-globule transition progresses via the formation of a toroidal ring structure. We formulate a theoretical model of this transition as a phenomenon in which an unstable single loop generated as a result of thermal fluctuation is stabilized through association with other loops along a polyelectrolyte chain. An essential property of the chain under consideration is that it follows a wormlike chain model. A toroidal bundle of loop structures is characterized by a radius and a winding number. The statistical properties of such a chain are discussed in terms of the free energy as a function of the fraction of unfolded segments. We also present an actual experimental observation of the coil-globule transition of single giant DNA molecules, T4 DNA (165.5 kbp), with spermidine (3+), where intrachain phase segregation appears at a NaCl concentration of more than 10 mM. Both the theory and experiments lead to two important points. First, the transition from a partially folded state to a completely folded state has the characteristics of a continuous transition, while the transition from an unfolded state to a folded state has the characteristics of a first-order phase transition. Second, the appearance of a partially folded structure requires a folded structure to be less densely packed than in the fully folded compact state.

Small Anion with Higher Valency Retards the Compaction of DNA in the Presence of Multivalent Cation

It has been established that, upon the addition of multivalent cations, long DNA chains in an aqueous solution exhibit a remarkable discrete transition from a coil state to a compact state at the level of a single chain. In this study, we investigated the polyelectrolyte nature of DNA with the experimental methodology of single-DNA observation, and provide a theoretical interpretation. We examined the effects of co-ions with different valencies (Cl(-), SO4(2-), PO4(3-)) on DNA compaction. As a result, we found that co-ions with a greater valency induce the coil state rather than the compact state. Based on a simple model with mean-field approximation that considered ion pairing, we show how the increase in entropy of small ions contributes to the stability of the compact state, by overcoming entropic penalties such as elastic confinement of the chain and a decrease in the translational freedom of counterions accompanied by charge neutralization.

Probability of double-strand breaks in genome-sized DNA by γ-ray decreases markedly as the DNA concentration increases.

By use of the single-molecule observation, we count the number of DNA double-strand breaks caused by γ-ray irradiation with genome-sized DNA molecules (166 kbp). We find that P1, the number of double-strand breaks (DSBs) per base pair per unit Gy, is nearly inversely proportional to the DNA concentration above a certain threshold DNA concentration. The inverse relationship implies that the total number of DSBs remains essentially constant. We give a theoretical interpretation of our experimental results in terms of attack of reactive species upon DNA molecules, indicating the significance of the characteristics of genome-sized giant DNA as semiflexible polymers for the efficiency of DSBs.

Association-dissociation equilibrium of loop structures in single-chain folding into a toroidal condensate.

Recently, it has been revealed that a semiflexible polyelectrolyte chain can form a partially folded conformation stably as a result of an electrostatic interaction. Interestingly, there are cases where the appearance of this structure requires a high-salt condition of a solution. In order to solve this problem, we consider the double equilibrium of the formation of loops and their aggregation on a single-chain polymer. First, an aggregate with a typical surface energy is examined as a test case. The basic nature of the folding transition is discussed with regard to the chemical potential of loop structures. Next, we consider a charged aggregate for which the interior is completely neutralized by counter ions. In this model, a partially folded chain appears with a high-salt condition. Based on this model, screened interactions between surface charges and a toroidal shape of a folded structure are considered essential factors bihind this phenomenon.

The effect of salt concentration on the optical modes of charged cylindrical nanotubes

We have conducted calculations of the collective plasmon excitations for an electron gas confined to the surface of a charged single-walled cylindrical nanotube in salt solutions. Both positively and negatively charged nanotubes are investigated. At high salt concentration, the surface potential approaches zero, and the spectrum is close to that of a neutral nanotube. The highest-frequency branch of the plasmon excitation spectrum exhibits a redshift and a blueshift for negatively and positively charged nanotubes, respectively. Such a result can be attributed to the change of the number of eigenstates around the Fermi energy. As salt concentration is increased, the surface potential is screened out, and the spectral line shift diminishes. Our results also show that the negatively charged nanotube can be more sensitive to the ambient salt concentration than the positively charged one. The optimal sensor device occurs when the nanotube carries a linear charge density close to that of DNA. The theoretical pr...

Integral equation theory for hard spheres confined on a cylindrical surface: Anisotropic packing entropically driven

The structure of two-dimensional (2D) hard-sphere fluids on a cylindrical surface is investigated by means of the Ornstein-Zernike integral equation with the Percus-Yevick and the hypernetted-chain approximation. The 2D cylindrical coordinate breaks the spherical symmetry. Hence, the pair-correlation function is reformulated as a two-variable function to account for the packing along and around the cylinder. Detailed pair-correlation function calculations based on the two integral equation theories are compared with Monte Carlo simulations. In general, the Percus-Yevick theory is more accurate than the hypernetted-chain theory, but exceptions are observed for smaller cylinders. Moreover, analysis of the angular-dependent contact values shows that particles are preferentially packed anisotropically. The origin of such an anisotropic packing is driven by the entropic effect because the energy of all the possible system configurations of a dense hard-sphere fluid is the same. In addition, the anisotropic packing observed in our model studies serves as a basis for linking the close packing with the morphology of an ordered structure for particles adsorbed onto a cylindrical nanotube.

Preferential positioning of a nanoparticle bound to a polymer: Exact enumeration of a self-avoiding walk chain model

A lattice chain model is extended to investigate the preferential position of a sticky sphere bound to a polymer chain, motivated by wrapping one nanosize core-histone with DNA to form a nucleosome structure. It was shown that the single bound histone is populated in DNA chain ends from the experiment by T. Sakaue et al. [Phys. Rev. Lett. 87, 078105 (2001)]. Here, the possible mechanisms are examined to elucidate such behavior. For neutral chains or ionic chains in high salt concentrations, spheres bound on the middle of chain may trigger conformational constraints to reduce conformational entropy. For ionic chains, the bound sphere can be driven to chain ends if its effective charge and the charge of chain monomers are of like charge. The two-dimensional chain is further studied to mimic the chromosome strongly adsorbed onto surfaces, of which behavior is similar to the three-dimensional case with minor difference due to surface confinement.

Modelling of the inhomogeneous interior of polymer gels

A simple model has been investigated to elucidate the mean squared displacement (MSD) of probe molecules in cross-linked polymer gels. In the model, we assume that numerous cavities distribute in the inhomogeneous interior of a gel, and probe molecules are confined within these cavities. The individual probe molecules trapped in a gel are treated as Brownian particles confined to a spherical harmonic potential. The harmonic potential is chosen to model the effective potential experienced by the probe particle in the cavity of a gel. Each field strength is corresponding to the characteristic of one type of effective cavity. Since the statistical distribution of different effective cavity sizes is unknown, several distribution functions are examined. Meanwhile, the calculated averaged MSDs are compared to the experimental data by Nisato et al (2000 Phys. Rev. E 61 2879). We find that the theoretical results of the MSD are sensitive to the shape of the distribution function. For low cross-linked gels, the best fit is obtained when the interior cavities of a gel follow a bimodal distribution. Such a result may be attributed to the presence of at least two distinct classes of cavity in gels. For high cross-linked gels, the cavities in the gel can be depicted by a single-modal uniform distribution function, suggesting that the range of cavity sizes becomes smaller. These results manifest the voids inside a gel, and the shape of distribution functions may provide the insight into the inhomogeneous interior of a gel.