C10. Macromolecule Oligomer Formation and Symmetry - Biology

C10. Macromolecule Oligomer Formation and Symmetry - Biology

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Many proteins are found in aggregated states and have quaternary structure. What mechanism determines whether a monomeric protein forms a homooligomer? Why do they stop at a certain n value? Can proteins be engineered to do so? If mutation can induce oligomer formation, then fewer mutations would be required to produce a symmetric oligomer from subunits since fewer mutations would be required as a single mutation in a single monomer would be represented n times in a single oligomer of n monomers. Hence a basic knowledge of symmetry of protein oligomers is necessary.

In the study of small molecules, chemists describe symmetry through the use of mathematical symmetry operations and elements, which find great use in analysis of structure and in molecular spectroscopy. These concepts are usually first encountered in physical and inorganic chemistry classes. A symmetry operation is a movement of an object like a molecule that leads to an identical, superimposable molecule.. Each operation has a symmetry element (point, line, or plane) about which the motion occurs. Some examples are shown below:

Table: Symmetry Elements and Operations

Element (with Jmol link)Operation
inversion center (i)projection through center (point) of symmetry of point x,y,z to point -x,-y,-z
proper rotation axis (Cn)rotation around a Cn axis by 360o/n where C denotes Cyclic
horizontal (σh) and vertical (σv) symmetry planereflection across a horizontal or vertical plane
improper rotation axis (Sn)rotation around a Sn axis by 360o/n followed by reflection in plane perpendicular to the axis.

Luckily for students trying to apply these rules to protein oligomers, biomolecules made up of chiral monomers (such as the L-amino acids of proteins) can not be converted to identical structures using inversion or reflection since the chirality of monomer would change - for proteins this would entail and L to D amino acid change. That excludes all but proper rotation axes (Cn) from the list above.

A point group is a collection of symmetry operations that define the symmetry about a point. The 4 types of symmetries around a point are those described above: rotational symmetry, inversion symmetry, mirror symmetry, and improper rotation. The types of point groups around a point include:

  • cyclic (Cn) - contain one single Cn rotation axis. A biological example is the tobacco mosaic virus double disk (34 monomers, C17). In this point group note that the n in Cn is equal to the number of monomers and the angle of rotation is 360o/n.

Figure: C2 Symmetry

  • dihedral (Dn) - These have mutually perpendicular rotation axes. Specifically they contain at least 1 C2 axis perpendicular to a Cn axis (Canter and Schimmel. Biophysical Chemistry - Part 1). The minimal number of subunits is n. Most protein oligomers fall into this category. The packing (or asymmetric) unit does not have to be a single monomer but could be a heteodimer.

    1. A D2 point group has 1 C2 axis and 2 perpendicular C2 axes, and 4 monomers (like Hb). These proteins can dissociate into two dimers (such as two α/β dimers for Hb). Note that a different arrangment of 4 monomers could produce a oligomer with C4 symmetry instead of D2.

    2. A D4 point group has 1 C4 axis and 4 C2 axes, along with 2n=8 subunits. An example of a D4 point group is ribulose bisphosphate carboxylase/oxygenase (RuBisCO) which has 8 subunits (where a subunit, or more technically the assymetric subunit, is a dimer of a small and large molecular weight protein). This point group could arise from quaternary structure of two C4 tetramers or four C2 dimers.

Figure: D2 Symmetry

  • cubic - contain four C3 axes connecting opposite corners of a cube (so the lines are effectively diagonals) arranged as the four body diagonals (lines connecting opposite corners) of a cube. The tetrahedron (4 sides), cube (6), octahedron (8), and icosohedron (20), perfect Platonic solids (in which all faces, edges and angles are congruent) all have related 3 C3 axes (diagonals connecting opposite corners for cubes, diagonals from a vertex to the opposite face for tetrahedrons, line connecting two opposite faces for octahedron, etc ) so they all can be considered to be part of the cubic point group.

Cubes have a total of 13 symmetry axes comprising 3 types (three C4 axes passing through the centers of opposite faces, four C3 axes passing through opposite vertices, and six C2 axes passing through the the centers of opposite edges). On octahedron can be aligned with a cube and be shown to have the same symmetry axes.

  • Flash movie: Cube (red) and Octrahedron (blue) with 13 symmetry axes.

Tetrahedrons have a total of 7 symmetry axes comprising two types (four C3 axes of the cube and three C2 axes which are the same as the C4 axes of the cube. First note the relationship between a cube and an inscribed tetrahedron.

  • Flash movie: Tetrahedron with 7 symmetry axes.

A dodecahedron with 12 regular pentagon faces (green) and an icosohedron with 20 equilateral triangle sides (red) can be aligned with each other (as can cubes and octahedrons) and have 31 symmetry axes, as shown below. Note also the relations between a cube inside a dodecahedron and a octahedron inside of a dodecahedron that makes sharing of symmetry axes between these pairs more obvious.

  • Flash movie: dodecahedron and icosohedron with 31 symmetry axes.

vrml files for movies from

Examples of protein complexes with these point groups are:

  • aspartate-ß-decarboxylase, tetrahedral, 12 asymmetric units

  • dihydrolipoyl transsuccinylase, octahedral, 24 asymmetric subunits

  • many spherical viruses, icosahedral, 60 asymmetric units

Jmol: Updated Symmetry in Protein Oligomers (beta version with lots of work left to do) Jmol14 (Java) | JSMol (HTML5)

Proteins, especially those involved in cytoskeletal filaments, can form fibers which contain helical symmetry which differs from those described above since the monomers at the ends of helical fibers, although they have the same tertiary structures as those in the middle of the helical fibers, do not contact the same number of monomers as monomers internal in the oligomer and hence have different microenvironments.

A recent article by Grueninger et al. addresses the question of whether the process of oligomerization can be programmed into the genome. Can simple amino acid substitutions lead to oligomerization? Remember that oligomerization can be beneficial (formation of cytoskeleton filaments) or detrimental (formation of fibers in sickle cell anemia and mad cow disease). Oligomers with long half-lives (for example cytoskeletal filament such as actin and tubulin) and short half-lives (for example proteins causes transient activities are regulated by oligomer formation) are both necessary.

It has long been noted that if a protein chain forms oligomers, then a single amino acid change in the chain would be found n times in an oligomer of n chains. Mutations could either promote chain contact and oligomer formation or dissociation into monomeric or other asymmetric subunit composition if the mutation were in a region involved in subunit association (a contact region). Experimental work in this field of study is hampered by the fact that mutants made by site-specific mutagenesis to prefer the monomeric state often fail to fold (due to hydrophobic exposure and aggregation. Studies have shown that most contact areas between monomers or other asymmetric units are hydrophobic in nature and the contact regions must be complementary in shape. Obviously mutations that replace hydrophobic side chains involved in subunit contact with polar, polar charged, or bulkier hydrophobic side chains would inhibit oligomer formation.

Grueninger et al were able to successfully engineer dimer formation and oligomer formation as well. First consider the simplest case of a mutation in a monomer that can produce a dimer with C2 symmetry. This is illustrated below which also shows how a mutation that produces a weak interaction in a monomer could also produce a long helical aggregate (which can't be crystallized) without symmetry (as described above). A mutation at 2 could promote either oligomer helix formation or dimerization.

Figure: Mutations causing Dimer with C2 symmetry or Infinite Helix

(adapted from Grueninger et al. Science, 319, 206-209 (2008)

It should be noted that mutation could lead to dimer or oligomer formation by producing a more global conformational change in the monomer (not indicated in the example above) which leads to aggregate formation, as we have seen previously in the formation of dimers and aggregates of proteins associated with neurodegenerative diseases (like mad cow disease).

Grueninger produces mutants of two different proteins that showed dimer formation as analyzed by gel filtration chromatography (but did not crystallize so no 3D structures were determined). In addition the group modified urocanase, a C2 dimer, at 3 side chains to form a tetramer with D2 symmetry. Also, they modified L-rhamnulose-1-phosphae, a C4 tetramer, at a single position to form an octamer with D4 symmetry. The latter two were analyzed through x-ray crystallography. Their work suggests ways that complex symmetric protein structures arose in nature from simple mutation and evolutionary selection.

Cryo-electron microscopy imaging of Alzheimer’s amyloid-beta 42 oligomer displayed on a functionally and structurally relevant scaffold

Amyloid-β peptide (Aβ) oligomers are pathogenic species of amyloid aggregates in Alzheimer’s disease. Like certain protein toxins, Aβ oligomers permeabilize cellular membranes, presumably through a pore formation mechanism. Due to their structural and stoichiometric heterogeneity, the structure of these pores remains to be characterized. We studied a functional Aβ42-pore equivalent, created by fusing Aβ42 to the oligomerizing, soluble domain of the α-hemolysin (αHL) toxin. Our data reveal Aβ42-αHL oligomers to share major structural, functional and biological properties with wild-type Aβ42-pores. Single-particle cryo-EM analysis of Aβ42-αHL oligomers (with an overall resolution of 3.3 Å) reveals the Aβ42-pore region to be intrinsically flexible. We anticipate that the Aβ42-αHL oligomers will allow studying many of the features of the wild type amyloid oligomers that cannot be studied otherwise, and may represent a highly specific antigen for the development of immuno-base diagnostics and therapies.

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Single molecule localization microscopy (SMLM) is one of the most widely applied types of optical super-resolution microscopy. The image resolution is ultimately limited by the density of the fluorescent labels on the structure of interest and the finite precision of each localization 1,2 . Recently, methods for obtaining higher precision localizations have been reported, which work by either increasing the number of collected photons per molecule via e.g. cryogenic imaging 3,4 , or by introducing patterned illumination 5,6 . The first limitation remains, however, and one approach to boosting the apparent degree of labeling (DOL) and filling in missing labels can be applied when the sample consists of many identical copies of the structure of interest (e.g. a macromolecule). In this case, combining many structures into a single “super-particle” increases the effective labeling density and improves the signal-to-noise ratio (SNR) and resolution significantly. Besides these improvements, structural features of the data such as symmetry give insight into the morphology and functional properties of subcellular structures. In SMLM, this has been limited so far to the detection of rather simple morphologies 7 , but no algorithms have been introduced that can find arbitrary symmetry group(s) needed to characterize 3D structures.

Existing approaches to particle averaging in SMLM can be classified as either template-based or as adaptations of single particle analysis (SPA) algorithms for cryo-electron microscopy (EM) images. Template-based methods 8,9 are computationally efficient, but are susceptible to template bias artefacts. Methods derived from SPA for cryo-EM 10,11 have been employed to generate 3D reconstructions from 10 4 to 10 6 2D projections of random viewing angles of a structure. However, there are two major problems with the adaptation of these algorithms to 3D SMLM data. Firstly, the image formation in cryo-EM 9 differs from SMLM where in the first the electron-specimen interaction potential is imaged (a continuous function) and in the latter (repeated) localizations of a fluorescently (under) labeled structure are imaged. Secondly, the inherent 2D nature of the input data. While the first problem can be ignored in favorable experimental conditions such as high labeling density, high localization precision, and abundant number of localizations, the latter problem remains. The three-dimensional data of 3D SMLM (x, y, z coordinates) is not compatible with 2D processing even if you render the localizations into a voxelated representation. Of course projecting the data to 2D would unnecessarily throw away information and increase the problem of pose estimation. Sub-tomogram averaging 12 utilizes the 3D tomographic reconstruction primarily to identify the particle locations but the actual averaging and final reconstruction is again done on the 2D projections as in SPA to avoid missing wedge reconstruction artifacts present in the tomogram. Recently, Shi et. al. 13 also described a structure-specific method for 3D fusion, although they implicitly assume cylindrical particles and projected the volume onto top views only.

Here, we introduce a 3D particle fusion approach for SMLM which does not require, but can incorporate, a priori knowledge of the target structure such as the symmetry group. It works directly on 3D volume of localization data, rather than 2D projections, and accounts for anisotropic localization uncertainties. In addition, we propose a method for detecting the full rotational symmetry group of the structure from the data itself, which can subsequently be used in order to improve the fusion outcome. We report 3D reconstructions of the Nuclear Pore Complex (NPC) obtained from three different SMLM techniques. The results demonstrate a two orders of magnitude SNR amplification, and Fourier shell correlation (FSC) resolution values as low as 14–16 nm, which enables the structural identification of distinct proteins within a large macromolecular complex such as the NPC. We further retrieve the 8-fold rotational symmetry of the NPC assembly and the full tetragonal symmetry of a 3D tetrahedron DNA-origami nanostructure, without any prior knowledge imposed on the data.


An investigation of the structural and dynamic properties of the C-terminal fragment of the human protein VASP (VASP 336−380) has been performed. Full length VASP has been shown to be tetrameric in solution, and the C-terminal 45 residues of the protein have been suggested to be responsible for the oligomerization. We have expressed and purified a C-terminal fragment of the human VASP protein from residue 336−380. It was found to form a stable domain in its own right. The fragment was shown by CD spectroscopy to form a helical structure, stable under a wide range of temperature and pH conditions. A 15 N-HSQC-experiment exhibits only one set of peaks, suggesting a high degree of symmetry for a putative oligomer. Measurements of the rotational correlation time τC of the molecule and analytical ultracentrifugation data show VASP (336−380) to be entirely tetrameric in solution. The secondary structure was confirmed from a 15 N-NOESY-HSQC experiment and is completely α-helical. We conclude that VASP (336−380) forms a tetramer in solution via a coiled coil arrangement and is solely responsible for tetramerization of full-length VASP.


Two-dimensional molecular assemblies on surfaces have opened a way to design and control chirality, featuring promising electronic and chemical properties that depend on the local handedness of the layer. Yet, the mechanisms leading to spontaneous chiral resolution are not fully understood at every reaction stage. Here, starting from achiral 10-bromoanthracene-9-boronic acid as a molecular precursor, we demonstrate enantiomeric induction in products during the stage of covalent bonding, stemming from the competing point symmetries of the Ag(001)-supporting surface and the reaction products. Upon dehalogenation and dehydration of precursors, hexagonal boroxine rings linked by organometallic anthracene dimers are formed, which undergo a strong interaction with a fourfold symmetric substrate. The prochiral structural character of the resulting oligomer and its impact over the spatial distribution of the electronic molecular states are revealed by high-resolution scanning tunneling microscopy and spectroscopy.

Rapamycin-induced oligomer formation system of FRB–FKBP fusion proteins

Fusion proteins containing FRB and FKBP formed oligomers on adding rapamycin.

Various oligomers were generated by adjusting the configuration of fusion proteins.

FRB–FKBP fusion protein without a linker (FR–FK) specifically formed a tetramer.

Proteins fused to FR–FK also formed a tetramer.

Most proteins form larger protein complexes and perform multiple functions in the cell. Thus, artificial regulation of protein complex formation controls the cellular functions that involve protein complexes. Although several artificial dimerization systems have already been used for numerous applications in biomedical research, cellular protein complexes form not only simple dimers but also larger oligomers. In this study, we showed that fusion proteins comprising the induced heterodimer formation proteins FRB and FKBP formed various oligomers upon addition of rapamycin. By adjusting the configuration of fusion proteins, we succeeded in generating an inducible tetramer formation system. Proteins of interest also formed tetramers by fusing to the inducible tetramer formation system, which exhibits its utility in a broad range of biological applications.


Sevigny J, Chiao P, Bussière T, Weinreb PH, Williams L, Maier M, Dunstan R, Salloway S, Chen T, Ling Y, O'Gorman J, Qian F, Arastu M, Li M, Chollate S, Brennan MS, Quintero-Monzon O, Scannevin RH, Arnold HM, Engber T, Rhodes K, Ferrero J, Hang Y, Mikulskis A, Grimm J, Hock C, Nitsch RM, Sandrock A. The antibody aducanumab reduces Aβ plaques in Alzheimer's disease. Nature . 2016 Aug 31537(7618):50-6. PubMed.

Silverman JM, Gibbs E, Peng X, Martens KM, Balducci C, Wang J, Yousefi M, Cowan CM, Lamour G, Louadi S, Ban Y, Robert J, Stukas S, Forloni G, Hsiung GR, Plotkin SS, Wellington CL, Cashman NR. A Rational Structured Epitope Defines a Distinct Subclass of Toxic Amyloid-beta Oligomers. ACS Chem Neurosci . 2018 Jul 189(7):1591-1606. Epub 2018 Apr 16 PubMed.

Gibbs E, Silverman JM, Zhao B, Peng X, Wang J, Wellington CL, Mackenzie IR, Plotkin SS, Kaplan JM, Cashman NR. A Rationally Designed Humanized Antibody Selective for Amyloid Beta Oligomers in Alzheimer's Disease. Sci Rep . 2019 Jul 89(1):9870. PubMed.

Schemmert S, Schartmann E, Zafiu C, Kass B, Hartwig S, Lehr S, Bannach O, Langen KJ, Shah NJ, Kutzsche J, Willuweit A, Willbold D. Aβ Oligomer Elimination Restores Cognition in Transgenic Alzheimer's Mice with Full-blown Pathology. Mol Neurobiol . 2018 Jul 12 PubMed.

Sperling R, Salloway S, Brooks DJ, Tampieri D, Barakos J, Fox NC, Raskind M, Sabbagh M, Honig LS, Porsteinsson AP, Lieberburg I, Arrighi HM, Morris KA, Lu Y, Liu E, Gregg KM, Brashear HR, Kinney GG, Black R, Grundman M. Amyloid-related imaging abnormalities in patients with Alzheimer's disease treated with bapineuzumab: a retrospective analysis. Lancet Neurol . 2012 Mar11(3):241-9. PubMed.

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A comprehensive study has been undertaken to establish the primary factors that control transport of oxygen and nitrogen in polymer-derived carbogenic molecular sieves (CMS). Characterization of the nanostructure of CMS derived from poly(furfuryl alcohol) (PFA) indicates that significant physical and chemical reorganization occurs as a function of synthesis temperature. Spectroscopic measurements show a drastic decrease in oxygen and hydrogen functionality with increasing pyrolysis temperature. Structural reorganization and elimination of these heteroatoms lead to a measurable increase in the unpaired electron density in these materials. High-resolution transmission electron microscopy and powder neutron diffraction are used to probe the corresponding changes in the physical structural features in the CMS. These indicate that as the pyrolysis temperature is increased, the structure of the CMS transforms from one that is disordered and therefore highly symmetric to one that is more ordered on a length scale of 15 Å and hence less symmetric. This structural transformation process, one of symmetry breaking and pattern formation, is often observed in other nonlinear dissipative systems, but not in solids. Symmetry breaking provides the driving force for these high-temperature reorganizations, but unlike most dissipative systems, these less-symmetric structures remain frozen in place when energy is no longer applied. The impact of these nanostructural reorganizations on the molecular sieving character of the CMS is studied in terms of the physical separation of oxygen and nitrogen. These results show that the effective diffusivities of oxygen and nitrogen in the CMS vary by more than an order of magnitude across the range of synthesis temperatures studied. Although the electronic nature of the CMS leads to higher equilibrium capacity for oxygen, it is the physical nanostructure which governs the separation of these two molecules. It is concluded that the primary separation mechanism is steric and configurational in nature, a conclusion in good agreement with the general features of the kinetic hypothesis conjectured by earlier workers.


This study investigated Janus and strawberry-like particles composed of azo molecular glass and polydimethylsiloxane (PDMS) oligomer, focusing on controllable fabrication and formation mechanism of these unique structures and morphologies. Two materials, the azo molecular glass (IA-Chol) and PDMS oligomer (H2pdca-PDMS), were prepared for this purpose. The Janus and strawberry-like particles were obtained from the droplets of a dichloromethane (DCM) solution containing both IA-Chol and H2pdca-PDMS, dispersed in water and stabilized by poly(vinyl alcohol). Results show that the structured particles are formed through segregation between the two components induced by gradual evaporation of DCM from the droplets, which is controlled by adding ethylene glycol (EG) into the above dispersion. Without the addition of EG, Janus particles are formed through the full segregation of the two components in the droplets. On the other hand, with the existence of EG in the dispersion, strawberry-like particles instead of Janus particles are formed in the phase separation process. The diffusion of EG molecules from the dispersion medium into the droplets causes the PDMS phase deswelling in the interfacial area due to the poor solvent effect. Caused by the surface coagulation, the coalescence of the isolated IA-Chol domains is jammed in the shell region, which results in the formation of the strawberry-like particles. For the particles separated from the dispersion and dried, the PDMS oligomer phase of the Janus particles can adhere and spread on the substrate to form unique “particle-on-pad” morphology due to its low surface energy and swelling ability, while the strawberry-like particles exist as “standstill” objects on the substrates. Upon irradiation with a linearly polarized laser beam at 488 nm, the azo molecular glass parts in the particles are significantly deformed along the light polarization direction, which show unique and distinct morphologies for these two types of the particles.

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