Pattern formation during T-cell adhesion

T cells form intriguing patterns during adhesion to antigen-presenting cells. The patterns are composed of two types of domains, which either contain short TCR/MHCp receptor-ligand complexes or the longer LFA-1/ICAM-1 complexes. The final pattern consists of a central TCR/MHCp domain surrounded by a ring-shaped LFA-1/ICAM-1 domain, whereas the characteristic pattern formed at intermediate times is inverted with TCR/MHCp complexes at the periphery of the contact zone and LFA-1/ICAM-1 complexes in the center. Several mechanisms have been proposed to explain the T-cell pattern formation. Whereas biologists have emphasized the role of active cytoskeletal processes, previous theoretical studies suggest that the pattern evolution may be caused by spontaneous self-assembly processes alone. Some of these studies focus on circularly symmetric patterns and propose a pivot mechanism for the formation of the intermediate inverted pattern. Here, we present a statistical-mechanical model which includes thermal fluctuations and the full range of spatial patterns. We confirm the observation that the intermediate inverted pattern may be formed by spontaneous self-assembly. However, we find a different self-assembly mechanism in which numerous TCR/MHCp microdomains initially nucleate throughout the contact zone. The diffusion of free receptors and ligands into the contact zone subsequently leads to faster growth of peripheral TCR/MHCp microdomains and to a closed ring for sufficiently large TCR/MHCp concentrations. At smaller TCR/MHCp concentrations, we observe a second regime of pattern formation with characteristic multifocal intermediates, which resemble patterns observed during adhesion of immature T cells or thymozytes. In contrast to other theoretical models, we find that the final T-cell pattern with a central TCR/MHCp domain is only obtained in the presence of active cytoskeletal transport processes.     

Can optimal resource allocation models explain why ectotherms grow larger in cold?

Basically all organisms can be classified as determinate growers if their growth stops or almost stops at maturation, or indeterminate growers if growth is still intense after maturation. Adult size for determinate growers is relatively well defined, whereas in indeterminate growers usually two measures are used: size at maturation and asymptotic size. The latter term is in fact not a direct measure but a parameter of a specific growth equation, most often Bertalanffy's growth curve. At a given food level, the growth rate in determinate growers depends under given food level on physiological constraints as well as on investments in repair and other mechanisms that improve future survival. The growth rate in indeterminate growers consists of two phases: juvenile and adult. The mechanisms determining the juvenile growth rate are similar to those in determinate growers, whereas allocation to reproduction (dependent on external mortality rate) seems to be the main factor limiting adult growth. Optimal resource allocation models can explain the temperature-size rule (stating that usually ectotherms grow slower in cold but attain larger size) if the exponents of functions describing the size-dependence of the resource acquisition and metabolic rates change with temperature or mortality increases with temperature. Emerging data support both assumptions. The results obtained with the aid of optimization models represent just a rule and not a law: it is possible to find the ranges of production parameters and mortality rates for which the temperature-size rule does not hold.     

Enamel biomineralization defects result from alterations to amelogenin self-assembly

Enamel formation is a powerful model for the study of biomineralization. A key feature common to all biomineralizing systems is their dependency upon the biosynthesis of an extracellular organic matrix that is competent to direct the formation of the subsequent mineral phase. The major organic component of forming mouse enamel is the 180-amino-acid amelogenin protein (M180), whose ability to undergo self-assembly is believed to contribute to biomineralization of vertebrate enamel. Two recently defined domains (A and B) within amelogenin appear essential for this self-assembly. The significance of these two domains has been demonstrated previously by the yeast two-hybrid system, atomic force microscopy, and dynamic light scattering. Transgenic animals were used to test the hypothesis that the self-assembly domains identified with in vitro model systems also operate in vivo. Transgenic animals bearing either a domain-A-deleted or domain-B-deleted amelogenin transgene expressed the altered amelogenin exclusively in ameloblasts. This altered amelogenin participates in the formation an organic enamel extracellular matrix and, in turn, this matrix is defective in its ability to direct enamel mineralization. At the nanoscale level, the forming matrix adjacent to the secretory face of the ameloblast shows alteration in the size of the amelogenin nanospheres for either transgenic animal line. At the mesoscale level of enamel structural hierarchy, 6-week-old enamel exhibits defects in enamel rod organization due to perturbed organization of the precursor organic matrix. These studies reflect the critical dependency of amelogenin self-assembly in forming a competent enamel organic matrix and that alterations to the matrix are reflected as defects in the structural organization of enamel.     

Generalized finite element solution to one-dimensional flux problems

A finite element numerical solution to the general one-dimensional flow equation is derived in a form that provides a convenient and general means to simulate a wide variety of one-dimensional flow techniques of interest to biological scientists, e.g., ultracentrifugation, electrophoresis, chromatography, etc. Diverse physical models defined in terms of column geometry, solute interactions, and the dependence of transport parameters on column position, time, or concentrations of one or more solutes, can be accommodated. A particularly useful aspect of the formulation is that a wide variety of boundary conditions can be simply applied to the end result, without rederivation of the solution for each new case. The numerical solution is expressed as matrix equations that are sufficiently general so that incorporation of particular models can be effected by substitution of appropriate quantities into the final result.     

Self-assembly of plant cell walls

The object of this paper is to define criteria for distinguishing between self-assembly and template-based assembly in plant cell walls. The example of cellulose shows that cell wall polymers biosynthesized at a membrane may retain parallel chain packing arrangements that are thermodynamically unstable and cannot be reproduced in vitro, making the experimental testing of the self-assembly hypothesis difficult. Also, natural cellulose is ordered on a number of scales of pattern, each of which may be constructed by either self- or template-based assembly independently of the rest. These conceptual problems apply equally to the self-assembly of complete cell walls and other cell wall polymers. It is suggested that the self-assembly concept should be applied only to one stage or level in the synthesis of a cell wall, and that an additional concept of parallel assembly may be useful for understanding the synthesis of some polysaccharides.     

Oogenesis and the spawning pattern in Greenland halibut from the North-west Atlantic

Gametogenesis in Greenland halibut Reinhardtius hippoglossoides from the North-west Atlantic is not synchronous between individuals of the same population suggesting that the spawning season is not well defined. Differences in oocyte size–frequency distributions in prespawning, spawning and spent conditions suggest that Greenland halibut are capable of de novo vitellogenesis prior to and during spawning, indicating that the spawning pattern is not determinate. Greenland halibut may be capable of fast-tracking oocytes to maturity, whereby during the spawning season oocyte batches may be brought quickly through vitellogenesis so as to increase the fish's yearly reproductive output. 1999 The Fisheries Society of the British Isles     

Fibrillins, fibulins, and matrix-associated glycoprotein modulate the kinetics and morphology of in vitro self-assembly of a recombinant elastin-like polypeptide

Elastin is the polymeric protein responsible for the properties of extensibility and elastic recoil of the extracellular matrix in a variety of tissues. Although proper assembly of the elastic matrix is crucial for its durability, the process by which this assembly takes place is not well-understood. Recent data suggest the complex interaction of tropoelastin, the monomeric form of elastin, with a number of other elastic matrix-associated proteins, including fibrillins, fibulins, and matrix-associated glycoprotein (MAGP), is important to achieve the proper architecture of the elastic matrix. At the same time, it is becoming clear that self-assembly properties intrinsic to tropoelastin itself, reflected in a temperature-induced phase separation known as coacervation, are also important in this assembly process. In this study, using a well-characterized elastin-like polypeptide that mimics the self-assembly properties of full-length tropoelastin, the process of self-assembly is deconstructed into "coacervation" and "maturation" stages that can be distinguished kinetically by different parameters. Members of the fibrillin, fibulin, and MAGP families of proteins are shown to profoundly affect both the kinetics of self-assembly and the morphology of the maturing coacervate, restricting the growth of coacervate droplets and, in some cases, causing clustering of droplets into fibrillar structures.     

Spatiotemporal control of PopZ localization through cell cycle–coupled multimerization

Bacterial cell poles constitute defined subcellular domains where numerous proteins localize, often at specific times, to affect various physiological processes. How pole recognition occurs and what governs the timing of protein localization are often unknown. In this paper, we investigate the mechanisms governing the localization of PopZ, a chromosome-anchoring protein whose unipolar to bipolar localization pattern is critical for cell cycle progression in Caulobacter crescentus. We provide evidence that polar localization of PopZ relied on its self-assembly into a higher-order structure (matrix) and that the unipolar to bipolar transition was coupled to the asymmetric distribution of ParA during the translocation of the origin-proximal ParB–parS partition complex. Collectively, our data suggest a model in which a local increase of ParA concentration promotes the assembly of a PopZ matrix precisely when and where this matrix is needed. Such coupling of protein assembly with a cell cycle–associated molecular asymmetry may represent a principle of cellular organization for controlling protein localization in both time and space.     

Sox3 expression defines a common primordium for the epibranchial placodes in chick

The epibranchial placodes are ectodermal thickenings that generate sensory neurons of the distal ganglia of the branchial nerves. Although significant advances in our understanding of neurogenesis from the placodes have recently been made, the events prior to the onset of neurogenesis remain unclear. We found that chick Sox3 (cSox3) shows a highly dynamic pattern of expression before becoming confined to the final placodes: one pre-otic (geniculate) and three post-otic (one petrosal and two nodose) placodes. A fate-mapping study using lipophilic dyes revealed that all post-otic placodes arise within a single broad cSox3-positive domain, where cSox3 expression and epithelial thickness will be retained only in much smaller final neurogenic placodes. The data presented here suggest that post-otic placodes are remnants of a common primordium defined as a discrete domain of cSox3 expression.     

A flexible sigmoid function of determinate growth

A new empirical equation for the sigmoid pattern of determinate growth, 'the beta growth function', is presented. It calculates weight (w) in dependence of time, using the following three parameters: t(m), the time at which the maximum growth rate is obtained; t(e), the time at the end of growth; and w(max), the maximal value for w, which is achieved at t(e). The beta growth function was compared with four classical (logistic, Richards, Gompertz and Weibull) growth equations, and two expolinear equations. All equations described successfully the sigmoid dynamics of seed filling, plant growth and crop biomass production. However, differences were found in estimating w(max). Features of the beta function are: (1) like the Richards equation it is flexible in describing various asymmetrical sigmoid patterns (its symmetrical form is a cubic polynomial); (2) like the logistic and the Gompertz equations its parameters are numerically stable in statistical estimation; (3) like the Weibull function it predicts zero mass at time zero, but its extension to deal with various initial conditions can be easily obtained; (4) relative to the truncated expolinear equation it provides more reasonable estimates of final quantity and duration of a growth process. In addition, the new function predicts a zero growth rate at both the start and end of a precisely defined growth period. Therefore, it is unique for dealing with determinate growth, and is more suitable than other functions for embedding in process-based crop simulation models to describe the dynamics of organs as sinks to absorb assimilates. Because its parameters correspond to growth traits of interest to crop scientists, the beta growth function is suitable for characterization of environmental and genotypic influences on growth processes. However, it is not suitable for estimating maximum relative growth rate to characterize early growth that is expected to be close to exponential.     

Growth after maturity as a sub-optimal strategy

Patterns of optimal resource allocation to growth and reproduction were investigated using a numerical simulation. As in most previous analyses, cessation of growth when reproduction begins (the determinate strategy) appeared optimal. Here, it was additionally found that fitness was only slightly lower for individuals that continue to grow after maturation. Therefore, it is argued that selection for a determinate strategy may be too weak to overwhelm random processes like environmental stochasticity or genetic drift that shape patterns of growth, especially under low mortality. The consequences of an indeterminate strategy for optimal size at maturity and final size were investigated: prolonging the period in which growth and reproduction co-occurred decreased size at maturity only slightly but markedly increased the final size.     

Studies of Thermal Stability of Multivalent DNA Hybridization in a Nanostructured System

A fundamental understanding of molecular self-assembly processes is important for improving the design and construction of higher-order supramolecular structures. DNA tile based self-assembly has recently been used to generate periodic and aperiodic nanostructures of different geometries, but there have been very few studies that focus on the thermodynamic properties of the inter-tile interactions. Here we demonstrate that fluorescently-labeled multihelical DNA tiles can be used as a model platform to systematically investigate multivalent DNA hybridization. Real-time monitoring of DNA tile assembly using fluorescence resonance energy transfer revealed that both the number and the relative position of DNA sticky-ends play a significant role in the stability of the final assembly. As multivalent interactions are important factors in nature's delicate macromolecular systems, our quantitative analysis of the stability and cooperativity of a network of DNA sticky-end associations could lead to greater control over hierarchical nanostructure formation and algorithmic self-assembly.     

Regeneration of roots from callus reveals stability of the developmental program for determinate root growth in Sonoran Desert Cactaceae

In some Sonoran Desert Cactaceae the primary root has a determinate root growth: the cells of the root apical meristem undergo only a few cell division cycles and then differentiate. The determinate growth of primary roots in Cactaceae was found in plants cultivated under various growth conditions, and could not be reverted by any treatment tested. The mechanisms involved in root meristem maintenance and determinate root growth in plants remain poorly understood. In this study, we have shown that roots regenerated from the callus of two Cactaceae species, Stenocereus gummosus and Ferocactus peninsulae, have a determinate growth pattern, similar to that of the primary root. To demonstrate this, a protocol for root regeneration from callus was established. The determinate growth pattern of roots regenerated from callus suggests that the program of root development is very stable in these species. These findings will permit future analysis of the role of certain Cactaceae genes in the determinate pattern of root growth via the regeneration of transgenic roots from transformed calli.     

Regulation of axis determinacy by the Arabidopsis PINHEAD gene

Plants produce proximal-distal growth axes with two types of growth potential: they can be indeterminate, in which case growth continues indefinitely, or they can be determinate, in which case growth is limited to the production of a single organ or a discrete set of organs. The indeterminate shoot axes of Arabidopsis pinhead/zwille mutants frequently are transformed to a determinate state. PINHEAD (PNH) is expressed in the central domain of the developing plant: the provascular tissue, the shoot apical meristem, and the adaxial (upper) sides of lateral organ primordia. Here, we show that ectopic expression of PNH on the abaxial (lower) sides of lateral organs results in upward curling of leaf blades. This phenotype correlates with a loss of cell number coordination between the two surfaces of the blade, indicating that ectopic PNH can cause changes in cell division rates. More strikingly, moving PNH expression from the central to the peripheral domain of the embryo causes transformation of the determinate cotyledon axis to an indeterminate state. We propose that growth axes are specified as determinate versus indeterminate in a PNH-mediated step. Our results add to a growing body of evidence that radial positional information is important in meristem formation. These results also indicate that genes regulating cell division and axis determinacy are likely to be among PNH targets.     

Probabilistic Analysis of Pattern Formation in Monotonic Self-Assembly

Inspired by biological systems, self-assembly aims to construct complex structures. It functions through piece-wise, local interactions among component parts and has the potential to produce novel materials and devices at the nanoscale. Algorithmic self-assembly models the product of self-assembly as the output of some computational process, and attempts to control the process of assembly algorithmically. Though providing fundamental insights, these computational models have yet to fully account for the randomness that is inherent in experimental realizations, which tend to be based on trial and error methods. In order to develop a method of analysis that addresses experimental parameters, such as error and yield, this work focuses on the capability of assembly systems to produce a pre-determined set of target patterns, either accurately or perhaps only approximately. Self-assembly systems that assemble patterns that are similar to the targets in a significant percentage are “strong” assemblers. In addition, assemblers should predominantly produce target patterns, with a small percentage of errors or junk. These definitions approximate notions of yield and purity in chemistry and manufacturing. By combining these definitions, a criterion for efficient assembly is developed that can be used to compare the ability of different assembly systems to produce a given target set. Efficiency is a composite measure of the accuracy and purity of an assembler. Typical examples in algorithmic assembly are assessed in the context of these metrics. In addition to validating the method, they also provide some insight that might be used to guide experimentation. Finally, some general results are established that, for efficient assembly, imply that every target pattern is guaranteed to be assembled with a minimum common positive probability, regardless of its size, and that a trichotomy exists to characterize the global behavior of typical efficient, monotonic self-assembly systems in the literature.     

The epithelial mitogen keratinocyte growth factor binds to collagens via the consensus sequence glycine-proline-hydroxyproline

The binding of certain growth factors and cytokines to components of the extracellular matrix can regulate their local availability and modulate their biological activities. We show that mesenchymal cell-derived keratinocyte growth factor (KGF), a key stimulator of epithelial cell proliferation during wound healing, preferentially binds to collagens I, III, and VI. Binding is inhibited in a dose-dependent manner by denatured single collagen chains and collagen cyanogen bromide peptides. This interaction is saturable with dissociation constants of approximately 10(-8) to 10(-9) m and estimated molar ratios of up to three molecules of KGF bound to one molecule of triple helical collagen. Furthermore, collagen-bound KGF stimulated the proliferation of transformed keratinocyte or HaCaT cells. Ligand blotting of collagen-derived peptides points to a limited set of collagenous consensus sequences that bind KGF. By using synthetic collagen peptides, we defined the consensus sequence (Gly-Pro-Hyp)(n) as the collagen binding motif. We conclude that the preferential binding of KGF to the abundant collagens leads to a spatial pattern of bioavailable KGF that is dictated by the local organization of the collagenous extracellular matrix. The defined collagenous consensus peptide or its analogue may be useful in wound healing by increasing KGF bioactivity and thus modulating local epithelial remodeling and regeneration.     

Forcing by rare species and intransitive loops creates distinct bouts of extinction events conditioned by spatial pattern in competition communities

Using a spatially explicit multiple species competition framework, the pattern of extinction for an effect/response competition cellular automata model is presented. It is found that, for a particular matrix with a negative row/column sum covariance, (1) there are two phases of transient behavior, presented in the framework of graph partitioning, and (2) the ultimate behavior of the system in space can be understood as mainly the operation of three distinct intransitive competitive loops. Of particular interest is the effect that a set of initially excluded species have on the final outcome of spatial pattern formation. Even though initial exclusion happens quite rapidly, and it would seem that species excluded early could not have an effect on the eventual outcomes of competition, there is a clear statistical effect, contributing to the extant literature suggesting that rare or seemingly inconsequential species can effect the behavior of the common and obvious ones.     

Collagen self-assembly and the development of tendon mechanical properties

The development of the musculoskeleton and the ability to locomote requires controlled cell division as well as spatial control over deposition of extracellular matrix. Self-assembly of procollagen and its final processing into collagen fibrils occurs extracellularly. The formation of crosslinked collagen fibers results in the conversion of weak liquid-like embryonic tissues to tough elastic solids that can store energy and do work. Collagen fibers in the form of fascicles are the major structural units found in tendon. The purpose of this paper is to review the literature on collagen self-assembly and tendon development and to relate this information to the development of elastic energy storage in non-mineralizing and mineralizing tendons. Of particular interest is the mechanism by which energy is stored in tendons during locomotion. In vivo, collagen self-assembly occurs by the deposition of thin fibrils in recesses within the cell membrane. These thin fibrils later grow in length and width by lateral fusion of intermediates. In vitro, collagen self-assembly occurs by both linear and lateral growth steps with parallel events seen in vivo; however, in the absence of cellular control and enzymatic cleavage of the propeptides, the growth mechanism is altered, and the fibrils are irregular in cross section. Results of mechanical studies suggest that prior to locomotion the mechanical response of tendon to loading is dominated by the viscous sliding of collagen fibrils. In contrast, after birth when locomotion begins, the mechanical response is dominated by elastic stretching of crosslinked collagen molecules.     

Emergence of novel enzyme quasi-species depends on the substrate matrix

Current research on enzyme evolution has shown that many enzymes are promiscuous and have activities with alternative substrates. Mutagenesis tends to relax substrate selectivity, and evolving enzymes can be regarded (summed over evolutionary time) as clusters of enzyme variants, or “quasi-species,” tested against a “substrate matrix” defined by all chemical substances to which the evolvants are exposed.In this investigation, the importance of the substrate matrix for identification of evolvable clusters of enzymes was evaluated by random sampling of variants from a library of glutathione transferase (GST) mutants. The variant GSTs were created by DNA shuffling of homologous Alpha class sequences. The substrate matrix was an array of alternative substrates used under defined experimental conditions. The measured enzyme activities produced a rectangular matrix, in which the rows can be projected as enzyme vectors in substrate-activity space and, reciprocally, the columns can be projected as alternative substrate vectors in enzyme-activity space. Multivariate analysis of the catalytic activities demonstrated that the enzyme vectors formed two primary clusters or functional “molecular quasi-species.” These quasi-species serve as the raw material from which more specialized enzymes eventually could evolve. The substrate vectors similarly formed two major groups. Identification of separate quasi-species of GSTs in a mutant library was critically dependent on the nature of the substrate matrix. When substrates from just one of the two groups were used, only one cluster of enzymes could be recognized. On the other hand, expansion of the substrate matrix to include additional substrates showed the presence of a third quasi-species among the GST variants already analyzed. Thus, the portrayal of the functional quasi-species is intimately linked to the effective substrate matrix. In natural evolution, the substrates actually encountered therefore play a pivotal role in determining whether latent catalytic abilities become manifest in novel enzymes.