A method for the characterization of foldings in protein ribbon models

The ribbon model of chain macromolecules is a useful tool for analyzing some of the targe-scale shape features of these complex systems. Up to now, the ribbon model has been used mostly to produce graphical displays, which are usually analyzed by visual inspection. In this work we suggest a computational method for characterizing automatically, in a concise and algebraic fashion, some of the important shape features of these ribbon models. The procedure is based on a graph-theoretical and knot-theoretical characterization of three well-defined projections of a space curve associated with the ribbon. The labeled graphs can be characterized by the handedness of the crossovers in the ribbon that are the vertices of the graph. The method can be used to provide a fully algebraic representation of the changes occurring when a molecule, such as a protein, undergoes conformational rearrangements (folding), as well as to provide a shape comparison for a pair of related molecular ribbons. This algebraic representation is well suited for easy storage, retrieval, and computer manipulation of the information on the ribbon's shape. Illustrative examples of the method are provided.     

Imaging cerebroside-rich domains for phase and shape characterization in binary and ternary mixtures

The objective of this paper is to review phase behavior and shape characterization of cerebroside-rich domains in binary and ternary lipid bilayers, as obtained by microscopy techniques. These lipid mixtures provide a format to examine molecular (e.g. headgroup, tail unsaturation, and tail hydroxylation) and thermodynamic (e.g. temperature and mole percentages) factors that determine phase behavior, molecular partitioning, crystal/atomic scale structure, and microstructure/shape (particularly of phase-separated domains). Microscopy can provide excellent spatial (often with high resolution) characterization of cerebroside-rich domains (and their surroundings) to identify, describe or infer with high certainty these characteristics. In the introduction to this review we review briefly the molecular structure, phase behavior, and intermolecular interactions of cerebrosides, in comparison to ceramides and sphingomyelins and in some binary and biological systems. The bulk of the review is then devoted to microscopy investigations of cerebroside-rich domain microstructure and shape dynamics in binary and ternary (one component is cholesterol) systems. Quantitative and/or high-resolution microscopy techniques have been used to interrogate cerebroside-rich domains such as freeze-fracture electron microscopy, atomic force microscopy, imaging elipsometry, two-photon fluorescence microscopy, and LAURDAN generalized polarization in addition to the laboratory workhorse technique of epifluorescence microscopy that allows a quick often qualitative assessment of microstructure and dynamics. We particularly focus on the information these microscopy investigations have revealed with respect to phase behavior, cholesterol partitioning, domain shape, and determinants of domain shape.     

Characterization of global molecular shape transitions between “open” and “closed” protein conformations

Induced-fit configurational transitions in proteins can take many forms. In cases, we find small “closures” of a loop onto the substrate. In other cases, the structural changes triggered by a ligand involve large rearrangements that affect entire domains. The nature of these transitions is normally assessed by a visual analysis or in terms of simple local geometrical parameters, such as interresidue distances, backbone dihedral angles, and relative displacements between domains. This approach is limited and rather undiscriminating. In this work, we apply recently introduced ideas from macromolecular shape analysis to characterize the global shape changes accompanying “open closed” transitions in proteins. Here, we monitor two distinct properties simultaneously: molecular size and self-entanglements. The method is applied to some proteins exhibiting pairs of structurally different conformations (adenylate kinase, hexokinase, citrate synthase, alcohol dehydrogenase, triosephosphate isomerase, thioredoxin, and aspartate amino-transferase). The conformational change associated with these proteins is classified according to an order parameter that considers various molecular shape features. The results allow one to recognize, in a nonvisual fashion, the likely occurrence of local or global structural rearrangements. In addition, the technique provides an insight into folding features that may remain invariant during the configurational transitions. © 1996 John Wiley & Sons, Inc.     

Size isn't everything

Much progress has been made recently towards uncovering the mechanisms that control the size to which organisms and their organs grow, and identifying some of the genes responsible. Size control, however, is only half of the equation. In growing to the right size, tissues must also grow to the right shape. A recent paper suggests that a hitherto overlooked cellular behaviour governs the size and shape of a growing tissue, and issues a challenge to developmental biologists to identify the molecular mechanisms involved.     

Control of growth and organ size in Drosophila.

Transplantation experiments have shown that developing metazoan organs carry intrinsic information about their size and shape. Organ and body size are also sensitive to extrinsic cues provided by the environment, such as the availability of nutrients. The genetic and molecular pathways that contribute to animal size and shape are numerous, yet how they cooperate to control growth is mysterious. The recent identification and characterization of several mutations affecting growth in Drosophila melanogaster promises to provide insights. Many of these mutations affect the extrinsic control of animal size; others affect the organ-intrinsic control of pattern and size. In this review, we summarize the characteristics of some of these mutations and their roles in growth and size control. In addition, we speculate about possible connections between the extrinsic and intrinsic pathways controlling growth and pattern.     

Shape group studies of molecular similarity: relative shapes of Van der Waals and electrostatic potential surfaces of nicotinic agonists

In drug design, the usual strategy involves characterizing and comparing the shapes of molecules. We apply a simple method to accomplish this goal: determining the symmetry-independent shape groups (homology groups of algebraic topology) of a molecular surface.In this paper, we have adapted the method to describing the interrelation between Van der Waals and electrostatic potential surfaces. We describe rigorously the shape features in a series of molecules by using specific ranges of electrostatic potential over a Van der Waals surface. We consider a series of four nicotinic agonists as an example and discuss their expected activities as potential drugs on the basis of the shape similarities found.     

Morphological vs. molecular evolution: ecology and phylogeny both shape the mandible of rodents

What actually is the expected pattern relating to molecular and morphological divergence? A phylogenetic correlation is expected; however, natural selection may force morphological evolution away from this expected correlation. To assess this relationship and the way it is modulated by selection, we investigated the radiation of the murine rodents, also called as Old World rats and mice. Regarding their diet, they are diversified as they include many omnivorous as well as specialist taxa. The size and shape of the mandible, a morphological character involved in the feeding process, was quantified and compared with an estimate of molecular divergence based on interphotoreceptor retinoid binding protein (IRBP) sequences. Size and shape of the mandible appeared to be related by an allometric relationship whatever the ecology of the taxa. Small size characterizes most murines, causing a dominance of low size distances; still, the frequency of important size differentiation increases with molecular distances. Regarding shape changes, the pattern is much contrasted between omnivores and specialists. A pattern of phenotypic drift characterizes the mandible evolution of taxa sharing an omnivorous diet. Little saturation occurs over more than 10 million years with regard to the shape of the mandible that appears as a valuable marker of phylogenetic history in this context. In contrast, important morphological distances can occur when specialist taxa are involved, even when the molecular divergence is small. Ecological specialization thus triggers an uncoupling of molecular and phenotypic evolution, and the departure from a phenotypic drift pattern.     

Multiple molecular recognition mechanisms. Cytochrome P450--a case study

Biomolecular recognition is complex. The balance between the different molecular properties that contribute to molecular recognition, such as shape, electrostatics, dynamics and entropy, varies from case to case. This, along with the extent of experimental characterization, influences the choice of appropriate computational approaches to study biomolecular interactions. Here, we present computational studies of cytochrome P450 enzymes and their interactions with small molecules and with other proteins. These interactions exemplify some of the diversity of molecular determinants of binding affinity and specificity observed for proteins and we discuss some of the challenges that they pose for molecular modelling and simulation.     

Nuclear matrix of HeLa S3 cells. Polypeptide composition during adenovirus infection and in phases of the cell cycle

A subnuclear fraction has been isolated from HeLa S3 nuclei after treatment with high salt buffer, deoxyribonuclease, and dithiothreitol. This fraction retains the approximate size and shape of nuclei and resembles the nuclear matrix recently isolated from rat liver nuclei. Ultrastructural and biochemical analyses indicate that this structure consists of nonmembranous elements as well as some membranous elements. Its chemical composition is 87% protein, 12% phospholipid, 1% DNA, and 0.1% RNA by weight. The protein constituents are resolved in SDS- polyacrylamide slab gels into 30-35 distinguishable bands in the apparent molecular weight range of 14,000 - 200,000 with major peptides at 14,000 - 18,000 and 45,000 - 75,000. Analysis of newly synthesized polypeptides by cylindrical gel electrophoresis reveals another cluster in the 90,000-130,000 molecular weight range. Infection with adenovirus results in an altered polypeptide profile. Additional polypeptides with apparent molecular weights of 21,000, 23,000, and 92,000 become major components by 22 h after infection. Concomitantly, some peptides in the 45,000-75,000 mol wt range become less prominent. In synchronized cells the relative staining capacity of the six bands in the 45,000-75,000 mol wt range changes during the cell cycle. Synthesis of at least some matrix polypeptides occures in all phases of the cell cycle, although there is decreased synthesis in late S/G2. In the absence of protein synthesis after cell division, at least some polypeptides in the 45,000- 75,000 mol wt range survive nuclear dispersal and subsequent reformation during mitosis. The possible significance of this subnuclear structure with regard to structure-function relationships within the nucleus during virus replication and during the life cycle of the cell is discussed.     

Axonal branch patterning and neuronal shape diversity: roles in developmental circuit assembly: Axonal branch patterning and neuronal shape diversity in developmental circuit assembly

Recent progress in human genetics and single cell sequencing rapidly expands the list of molecular factors that offer important new contributions to our understanding of brain wiring. Yet many new molecular factors are being discovered that have never been studied in the context of neuronal circuit development. This is clearly asking for increased efforts to better understand the developmental mechanisms of circuit assembly [1]. Moreover, recent studies characterizing the developmental causes of some psychiatric diseases show impressive progress in reaching cellular resolution in their analysis. They provide concrete support emphasizing the importance of axonal branching and synapse formation as a hotspot for potential defects. Inspired by these new studies we will discuss progress but also challenges in understanding how neurite branching and neuronal shape diversity itself impacts on specificity of neuronal circuit assembly. We discuss the idea that neuronal shape acquisition itself is a key specificity factor in neuronal circuit assembly.     

Mechanical model for a collagen fibril pair in extracellular matrix

In this paper, we model the mechanics of a collagen pair in the connective tissue extracellular matrix that exists in abundance throughout animals, including the human body. This connective tissue comprises repeated units of two main structures, namely collagens as well as axial, parallel and regular anionic glycosaminoglycan between collagens. The collagen fibril can be modeled by Hooke’s law whereas anionic glycosaminoglycan behaves more like a rubber-band rod and as such can be better modeled by the worm-like chain model. While both computer simulations and continuum mechanics models have been investigated for the behavior of this connective tissue typically, authors either assume a simple form of the molecular potential energy or entirely ignore the microscopic structure of the connective tissue. Here, we apply basic physical methodologies and simple applied mathematical modeling techniques to describe the collagen pair quantitatively. We found that the growth of fibrils was intimately related to the maximum length of the anionic glycosaminoglycan and the relative displacement of two adjacent fibrils, which in return was closely related to the effectiveness of anionic glycosaminoglycan in transmitting forces between fibrils. These reveal the importance of the anionic glycosaminoglycan in maintaining the structural shape of the connective tissue extracellular matrix and eventually the shape modulus of human tissues. We also found that some macroscopic properties, like the maximum molecular energy and the breaking fraction of the collagen, were also related to the microscopic characteristics of the anionic glycosaminoglycan.     

Epithelial morphogenesis in embryos: asymmetries, motors and brakes

Epithelial cells play a central role in many embryonic morphogenetic processes, during which they undergo highly coordinated cell shape changes. Here, we review some common principles that have recently emerged through genetic and cellular analyses performed mainly with invertebrate genetic models, focusing on morphogenetic processes involving epithelial sheets. All available data argue that myosin II is the main motor that induces cell shape changes during morphogenesis. We discuss the control of myosin II activity during epithelial morphogenesis, as well as the recently described involvement of microtubules in this process. Finally, we examine how forces unleashed by myosin II can be measured, how embryos use specific brakes to control molecular motors and the potential input of mechano-sensation in morphogenesis.     

Cyclosporin synthetase is a 1.4 MDa multienzyme polypeptide. Re-evaluation of the molecular mass of various peptide synthetases.

The earlier determined molecular mass of 0.8 MDa for the multifunctional polypeptide, cyclosporin synthetase, was re-evaluated by SDS-PAGE and CsCl density gradient centrifugation. In SDS-PAGE, new molecular mass values as standards were available from sequencing data. In the CsCl density gradient extremely low protein concentrations, such as 10-50 nM could be analysed due to the fluorescence detection system of the analytical ultracentrifuge. Both methods yielded approximately the same value of about 1.4 MDa. Using this molecular mass of cyclosporin synthetase as a reference the molecular masses of various related enzymes could be re-evaluated in SDS-PAGE. The sedimentation coefficient of 26.3 S for cyclosporin synthetase indicates an oblate overall shape of the enzyme.