Contiguous Lattice Research Articles

What we have learned and will learn from cell ultrastructure in embedment‐free section electron microscopy

The limitations inherent in conventional electron microscopy (EM) using epoxy ultrathin sections for a clear recognition of biological entities having electron densities similar to or lower than that of epoxy resin have led to the development of embedment-free sectioning for EM. Embedment-free section EM is reliably performed using water-soluble polyethylene glycol (PEG) as a transient embedding medium, with subsequent de-embedment of PEG by immersion into water, followed by critical point-drying (CPD) of the embedment-free section. The present author has stressed that this approach clearly discloses structures whose contours and/or appearance are accordingly vague and/or fuzzy in conventional EM, but does not reveal any new structures. Based on embedment-free electron microscopy (PEG-EM), this article presents five major findings regarding strand- or microtrabecular lattices which have been clearly revealed to occur in the cytoplasmic matrix-an impossibility with conventional EM. These are (1) the appearance of lattices of different compactness in various cells and in intracellular domains of a given cell; (2) the faithful reproduction from an albumin solution in vitro of strand-lattices with correspondingly increasing compactness following increasing concentrations; (3) the appearance of more compact lattices from gelated gelatin than from solated gelatin at a given concentration in vitro; (4) the appearance of either greater or less lattice-compactness by hyper- or hypotonic pretreatments of cells; and (5) the appearance of certain intracellular proteins confined to the centripetal demilune-domain of centrifuged ganglion cells which is occupied with strand-lattices of a substantial compactness. From these findings, questions now arise as to the biological significance of the individual strand itself in the microtrabecular lattices in PEG-EM. In addition, it may be that the appearance of strand-lattices in a given biological domain represents the presence of soluble proteins; the lattice-compactness indicates the concentration of soluble proteins in the domain, and the aqueous cytoplasm is equivalent to the aqueous solution. Further, the appearance of two contiguous lattice domains exhibiting differing degrees of compactness in a given cell indicates that cytoplasmic proteins are solated in a domain with less compact lattices, whereas they are gelated in the other domain. These proposed interpretations need to be confirmed by further studies. If confirmed, the control mechanisms of the localization and movement of intracellular organelles could then be understood on the basis not only of information about the cytoskeletons but also of cell ultrastructure-related information on the concentration and sol-gel states of intracellular proteins. In addition, possible interpretations of the significance of strand-lattices in PEG-EM are also applicable to the nucleoplasm, especially extra-heterochromatin (euchromatin) areas. Finally, several potential uses/advantages of PEG-EM in the cell-ultrastructure have also been demonstrated, especially in three-dimensional reconstructions of nonmembranous structures including stereo-viewing using a pair of EM images with appropriate tilting as well as electron microscopic tomography.

Stability Differentials for Proximal vs Distal Fusion of Total Hip Arthroplasty Femoral Impaction Grafts

In impaction grafting for revision joint arthroplasty, the morselized cancellous bone ideally remodels into a new contiguous lattice. However, the use of biologically active factors may sometimes be indicated to enhance fusion. The purpose of this study was to determine the stability of femoral impaction-graft constructs for which either only the proximal or distal half of the morselized cancellous bone volume was modeled as fused. Fusing the proximal half of the impaction-graft volume resulted in a higher femoral stem stability than did fusing the distal half. This proximal graft fusion also resulted in a stem stability that was similar to that of fusing the entire graft. These results emphasize the importance of proximal fixation of an impaction-grafted femoral stem.

Embedment-free section electron microscopy

Because of potential hindrance of clear viewing in epoxy sections of biological entities having an electron density similar to and lower than that of epoxy resin, the author has stressed that the embedment-free section electron microscopy is necessary for re-examination and/or clarification of biological specimen structures, and that the embedment-free electron microscopy is reliably done by using water-soluble polyethylene glycol (PEG) as a transient embedding media and by critical point-drying of embedment-free sections after de-embedment of PEG by immersion of semithin sections into water. With the embedment-free electron microscopy, the author has presented five major findings: the appearance of microtrabecular lattices with different compactnesses in various cells and in intracellular domains of a given cell, the faithful reproduction of microtrabecula-like strand lattices in vitro with increasing compactnesses from artificial protein solutions at correspondingly increasing concentrations, the appearance of more compact lattices from gelated gelatin than from solated gelatin at a given concentration in vitro, the changeability in compactnesses of the microtrabecular lattices by hyper- or hypotonic shock treatments of cells, and the confined appearance of an intracellular protein in the centripetal demilune of centrifuged ganglion cells which is occupied with the microtrabecular lattices of a substantial compactness. From these findings, several conclusions are drawn: individual strands themselves of the microtrabeculae are meaningless, the appearance of microtrabeculae represents the presence of proteins at a certain concentration, and it is therefore likely that the aqueous cytoplasm is equivalent to the aqueous solution. In addition, it is possible that the appearance of two contiguous lattice domains exhibiting different compactnesses in a given cell may represent the occurrence of a contiguity of sol to gel states of cytoplasmic domains. It is thus proposed that the localization and movement of intracellular organelles are controlled not only by the cytoskeletons but also by the concentration and sol/gel states of intracellular proteins. In addition, several potential usefulness of the embedment-free electron microscopy has also been demonstrated.

Branch counting probability approach to random sequential adsorption

In a previous Letter we derived analytic expressions to describe the adsorption kinetics of trimers on two-dimensional arrays. As a prerequisite to find the average saturation coverage at the jamming limit (〈 θ JL〉) we had to solve first the kinetic rate equation, which is a lengthy and troublesome task. This motivated us to derive a faster and easier procedure to determine 〈 θ JL〉. The method allows the exact determination of 〈 θ JL〉 when a small two-dimensional lattice is bombarded by objects that occupy β ⩾ 2 contiguous lattice sites, and is applied on a 3 × 5 lattice ceaselessly bombarded by linear trimers.

Nonlinear reactive systems on a lattice viewed as Boolean dynamical systems

We present a stochastic, time-discrete Boolean model that mimics the mesoscopic dynamics of the desorption reactions A+A-->A+S and A+A-->S+S in a one-dimensional lattice. In the continuous-time limit, we derive a hierarchy of dynamical equations for the subset of moments involving contiguous lattice sites. The solution of the hierarchy allows to compute the exact dynamics of the mean coverage for both microscopic and coarse-grained initial conditions, which turn out to be different from the mean field predictions. The evolution equations for the mean coverage and the second-order moments are shown to be equivalent to those provided by a time-continuous master equation. The important role of higher-order fluctuations is brought out by the failure of a truncation scheme retaining only two-particle fluctuation correlations.

A multitype random sequential process

A random sequential process (RSP) can be formulated in two different ways: (I) A linear array of n identical compartments is ceaselessly bombarded by particles which occupy β( β≥2) contiguous lattice sites. These so-called β-bell particles are assumed to make contact in a spatially random manner and to stick only if striking β (adjacent) vacant compartments. (II) A linear array of n identical compartments is sequentially filled by β-bell particles, the occupation process being ‘‘selective,’’ i.e., always being directed to vacant sequences of compartments of lengths at least β. Dynamics of RSP’s has always been formulated in either way and in the case of lattice spaces all the efforts have been addressed so far to allow in the space filling process just one kind of particle. The aim of this paper is to remove that restriction and to consider a lattice space filling problem with various kinds of particles involved. The situations of the two above-described models, making no difference in the one-type case, become distinct in the multitype case. In this paper we will be concerned with the generalization of model II.

Average saturation coverage for one-dimensional arrays of β-bell particles

When β-bell particles (particles occupying β contiguous lattice sites) are placed in a random manner on a one-dimensional array of N compartments, we are simultaneously creating sequences of 1, 2, 3, …, β − 1, vacant compartments. Clearly, after a long period of time a saturation situation arises in which the probability of placing a β-bell particle on such an array becomes zero even though the coverage has not attained the value of one. It is shown that v( β, N), the average fraction of vacant compartments when β-bell particles are placed in a random manner on a linear array of N compartments is exactly described by the recursion relation: v(β, N)= N − β N(N − β + 1 [(N − 1) v(β, N − 1) + 2v(β, N − β)] .

Exact parastatistics for one-dimensional lattice space

Exact parastatistics are developed which describe the occupation of a one-dimensional lattice space by any arbitrary distribution of particles {gλ}, (λ=1,2,3,…,), where λ is the particle correlation distance, i.e., the number of contiguous lattice sites occupied by a particle.