The microtubule-nucleating factor MACERATOR tethers AUGMIN7 to microtubules and governs phragmoplast architecture.

The plant cytokinetic microtubule array, called the phragmoplast, exhibits higher microtubule dynamics in its center (midzone) than at the periphery (distal zone). This behavior is known as the axial asymmetry. Despite being a major characteristic of the phragmoplast, little is known about regulators of this phenomenon. Here we address the role of microtubule nucleation in axial asymmetry by characterizing MACERATOR (MACET) proteins in Arabidopsis thaliana and Nicotiana benthamiana with a combination of genetic, biochemical, and live-cell imaging assays, using photo-convertible microtubule probes, and modeling. MACET paralogs accumulate at the shrinking microtubule ends and decrease the tubulin OFF rate. Loss of MACET4 and MACET5 function abrogates axial asymmetry by suppressing microtubule dynamicity in the midzone. MACET4 also narrows the microtubule nucleation angle at the phragmoplast leading edge and functions as a microtubule tethering factor for AUGMIN COMPLEX SUBUNIT 7 (AUG7). The macet4 macet5 double mutant shows diminished clustering of AUG7 in the phragmoplast distal zone. Knockout of AUG7 does not affect MACET4 localization, axial asymmetry, or microtubule nucleation angle, but increases phragmoplast length and slows down phragmoplast expansion. The mce4-1 mce5 aug7-1 triple knockout is not viable. Experimental data and modeling demonstrate that microtubule nucleation factors regulate phragmoplast architecture and axial asymmetry directly by generating new microtubules and indirectly by modulating the abundance of free tubulin.

An ultra-stable gold-coordinated protein cage displaying reversible assembly.

Symmetrical protein cages have evolved to fulfil diverse roles in nature, including compartmentalization and cargo delivery1, and have inspired synthetic biologists to create novel protein assemblies via the precise manipulation of protein-protein interfaces. Despite the impressive array of protein cages produced in the laboratory, the design of inducible assemblies remains challenging2,3. Here we demonstrate an ultra-stable artificial protein cage, the assembly and disassembly of which can be controlled by metal coordination at the protein-protein interfaces. The addition of a gold (I)-triphenylphosphine compound to a cysteine-substituted, 11-mer protein ring triggers supramolecular self-assembly, which generates monodisperse cage structures with masses greater than 2 MDa. The geometry of these structures is based on the Archimedean snub cube and is, to our knowledge, unprecedented. Cryo-electron microscopy confirms that the assemblies are held together by 120 S-Aui-S staples between the protein oligomers, and exist in two chiral forms. The cage shows extreme chemical and thermal stability, yet it readily disassembles upon exposure to reducing agents. As well as gold, mercury(II) is also found to enable formation of the protein cage. This work establishes an approach for linking protein components into robust, higher-order structures, and expands the design space available for supramolecular assemblies to include previously unexplored geometries.

Artificial Protein Cage with Unusual Geometry and Regularly Embedded Gold Nanoparticles.

Artificial protein cages have great potential in a number of areas including cargo capture and delivery and as artificial vaccines. Here, we investigate an artificial protein cage whose assembly is triggered by gold nanoparticles. Using biochemical and biophysical methods we were able to determine both the mechanical properties and the gross compositional features of the cage which, combined with mathematical models and biophysical data, allowed the structure of the cage to be predicted. The accuracy of the overall geometrical prediction was confirmed by the cryo-EM structure determined to sub-5 Å resolution. This showed the cage to be nonregular but similar to a dodecahedron, being constructed from 12 11-membered rings. Surprisingly, the structure revealed that the cage also contained a single, small gold nanoparticle at each 3-fold axis meaning that each cage acts as a synthetic framework for regular arrangement of 20 gold nanoparticles in a three-dimensional lattice.

Reciprocal Nucleopeptides as the Ancestral Darwinian Self-Replicator.

Even the simplest organisms are too complex to have spontaneously arisen fully formed, yet precursors to first life must have emerged ab initio from their environment. A watershed event was the appearance of the first entity capable of evolution: the Initial Darwinian Ancestor. Here, we suggest that nucleopeptide reciprocal replicators could have carried out this important role and contend that this is the simplest way to explain extant replication systems in a mathematically consistent way. We propose short nucleic acid templates on which amino-acylated adapters assembled. Spatial localization drives peptide ligation from activated precursors to generate phosphodiester-bond-catalytic peptides. Comprising autocatalytic protein and nucleic acid sequences, this dynamical system links and unifies several previous hypotheses and provides a plausible model for the emergence of DNA and the operational code.

An artificial protein cage made from a 12-membered ring.

Artificial protein cages have great potential in diverse fields including as vaccines and drug delivery vehicles. TRAP-cage is an artificial protein cage notable for the way in which the interface between its ring-shaped building blocks can be modified such that the conditions under which cages disassemble can be controlled. To date, TRAP-cages have been constructed from homo-11mer rings, i.e., hendecamers. This is interesting as convex polyhedra with identical regular faces cannot be formed from hendecamers. TRAP-cage overcomes this limitation due to intrinsic flexibility, allowing slight deformation to absorb any error. The resulting TRAP-cage made from 24 TRAP 11mer rings is very close to regular with only very small errors necessary to allow the cage to form. The question arises as to the limits of the error that can be absorbed by a protein structure in this way before the formation of an apparently regular convex polyhedral becomes impossible. Here we use a naturally occurring TRAP variant consisting of twelve identical monomers (i.e., a dodecamer) to probe these limits. We show that it is able to form an apparently regular protein cage consisting of twelve TRAP rings. Comparison of the cryo-EM structure of the new cage with theoretical models and related cages gives insight into the rules of cage formation and allows us to predict other cages that may be formed given TRAP-rings consisting of different numbers of monomers.

Characterization of near-miss connectivity-invariant homogeneous convex polyhedral cages.

Following the discovery of a nearly symmetric protein cage, we introduce the new mathematical concept of a near-miss polyhedral cage (p-cage) as an assembly of nearly regular polygons with holes between them. We then introduce the concept of the connectivity-invariant p-cage and show that they are related to the symmetry of uniform polyhedra. We use this relation, combined with a numerical optimization method, to characterize some classes of near-miss connectivity-invariant p-cages with a deformation below 10% and faces with up to 17 edges.

Shape-Morphing of an Artificial Protein Cage with Unusual Geometry Induced by a Single Amino Acid Change.

Artificial protein cages are constructed from multiple protein subunits. The interaction between the subunits, notably the angle formed between them, controls the geometry of the resulting cage. Here, using the artificial protein cage, "TRAP-cage", we show that a simple alteration in the position of a single amino acid responsible for Au(I)-mediated subunit-subunit interactions in the constituent ring-shaped building blocks results in a more acute dihedral angle between them. In turn, this causes a dramatic shift in the structure from a 24-ring cage with an octahedral symmetry to a 20-ring cage with a C2 symmetry. This symmetry change is accompanied by a decrease in the number of Au(I)-mediated bonds between cysteines and a concomitant change in biophysical properties of the cage.

A Peptide-Nucleic Acid Replicator Origin for Life.

Evolution requires self-replication. But, what was the very first self-replicator directly ancestral to all life? The currently favoured RNA World theory assigns this role to RNA alone but suffers from a number of seemingly intractable problems. Instead, we suggest that the self-replicator consisted of both peptides and nucleic acid strands. Such a nucleopeptide replicator is more feasible both in the light of the replication machinery currently found in cells and the complexity of the evolutionary path required to reach them. Recent theoretical and mathematical work supports this idea and provide a blueprint for future investigations.

Effects of periodic electromagnetic field on charge transport in macromolecules.

We study effects of periodic fields on charge transport in macromolecules and show that solitons acquire complex dynamics induced by the interplay between the periodic in time external field, energy dissipation, and depends on the molecule symmetry. Soliton dynamics is a superposition of the oscillations of the soliton c.m.c. with the frequency of the external field and directed current. Even unbiased periodic in time fields can cause drift of solitons (the ratchet effect) in the Peierls-Nabarro periodic potential. This effect has a threshold with respect to the intensity and frequency of the field. We calculate the dependence of the amplitude of soliton oscillations and the velocity of the drift on the intensity of the field, its frequency, and energy dissipation. Thus, we show that nonlinear charge transport processes in a field which is periodic in time acquire completely different dynamics than linear processes. This clearly plays a role in metabolism of biosystems.

Wobbles and other kink-breather solutions of the sine-Gordon model.

We study various solutions of the sine-Gordon model in (1+1) dimensions. We use the Hirota method to construct some of them and then show that the wobble, discussed in detail in a recent paper by Kälberman, is one of such solutions. We concentrate our attention on a kink and its bound states with one or two breathers. We study their stability and some aspects of their scattering properties on potential wells and on fixed boundary conditions.

The origin of phragmoplast asymmetry.

The phragmoplast coordinates cytokinesis in plants [1]. It directs vesicles to the midzone, the site where they coalesce to form the new cell plate. Failure in phragmoplast function results in aborted or incomplete cytokinesis leading to embryo lethality, morphological defects, or multinucleate cells [2, 3]. The asymmetry of vesicular traffic is regulated by microtubules [1, 4, 5, 6], and the current model suggests that this asymmetry is established and maintained through treadmilling of parallel microtubules. However, we have analyzed the behavior of microtubules in the phragmoplast using live-cell imaging coupled with mathematical modeling and dynamic simulations and report that microtubules initiate randomly in the phragmoplast and that the majority exhibit dynamic instability with higher turnover rates nearer to the midzone. The directional transport of vesicles is possible because the majority of the microtubules polymerize toward the midzone. Here, we propose the first inclusive model where microtubule dynamics and phragmoplast asymmetry are consistent with the localization and activity of proteins known to regulate microtubule assembly and disassembly.

A compartmental model analysis of integrative and self-regulatory ion dynamics in pollen tube growth.

Sexual reproduction in higher plants relies upon the polarised growth of pollen tubes. The growth-site at the pollen tube tip responds to signalling processes to successfully steer the tube to an ovule. Essential features of pollen tube growth are polarisation of ion fluxes, intracellular ion gradients, and oscillating dynamics. However, little is known about how these features are generated and how they are causally related. We propose that ion dynamics in biological systems should be studied in an integrative and self-regulatory way. Here we have developed a two-compartment model by integrating major ion transporters at both the tip and shank of pollen tubes. We demonstrate that the physiological features of polarised growth in the pollen tube can be explained by the localised distribution of transporters at the tip and shank. Model analysis reveals that the tip and shank compartments integrate into a self-regulatory dynamic system, however the oscillatory dynamics at the tip do not play an important role in maintaining ion gradients. Furthermore, an electric current travelling along the pollen tube contributes to the regulation of ion dynamics. Two candidate mechanisms for growth-induced oscillations are proposed: the transition of tip membrane into shank membrane, and growth-induced changes in kinetic parameters of ion transporters. The methodology and principles developed here are applicable to the study of ion dynamics and their interactions with other functional modules in any plant cellular system.

A thermodynamic model of microtubule assembly and disassembly.

Microtubules are self-assembling polymers whose dynamics are essential for the normal function of cellular processes including chromosome separation and cytokinesis. Therefore understanding what factors effect microtubule growth is fundamental to our understanding of the control of microtubule based processes. An important factor that determines the status of a microtubule, whether it is growing or shrinking, is the length of the GTP tubulin microtubule cap. Here, we derive a Monte Carlo model of the assembly and disassembly of microtubules. We use thermodynamic laws to reduce the number of parameters of our model and, in particular, we take into account the contribution of water to the entropy of the system. We fit all parameters of the model from published experimental data using the GTP tubulin dimer attachment rate and the lateral and longitudinal binding energies of GTP and GDP tubulin dimers at both ends. Also we calculate and incorporate the GTP hydrolysis rate. We have applied our model and can mimic published experimental data, which formerly suggested a single layer GTP tubulin dimer microtubule cap, to show that these data demonstrate that the GTP cap can fluctuate and can be several microns long.