Henrik Flyvbjerg

Modeling elastic properties of microtubule tips and walls

Abstract Electron micrographs of tips of growing and shrinking microtubules are analyzed and interpreted. The many shapes observed are all consistent with a simple mechanical model, a flexible tube with competing intrinsic curvatures. Observations are also consistent with growing and shrinking microtubules having the same intrinsic curvature for protofilaments, the one observed in oligomers peeling off shrinking microtubules. If this is so, the lateral bonds between protofilaments are responsible for the difference between shapes of tips on growing and shrinking microtubules.

Limited flexibility of the inter-protofilament bonds in microtubules assembled from pure tubulin

Abstract The superposition of the regular arrangement of tubulin subunits in microtubules gives rise to moiré patterns in cryo-electron micrographs. The moiré period can be predicted from the dimensions of the tubulin subunits and their arrangement in the surface lattice. Although the average experimental moiré period is usually in good agreement with the theoretical one, there is variation both within and between microtubules. In this study, we addressed the origin of this variability. We examined different possibilities, including artefacts induced by the preparation of the vitrified samples, and variations of the parameters that describe the microtubule surface lattice. We show that neither flattening nor bending of the microtubules, nor changes in the subunit dimensions, can account for the moiré period variations observed in 12 and 14 protofilament microtubules. These can be interpreted as slight variations, in the range –0.5 Å to +0.9 Å, of the lateral interactions between tubulin subunits in adjacent protofilaments. These results indicate that the inter-protofilament bonds are precisely maintained in microtubules assembled in vitro from pure tubulin. The fact that the moiré period is not affected by bending indicates that the local interactions between tubulin subunits are sufficiently stiff to accommodate large deformations of the microtubule wall.

'T Hooft's non-Abelian magnetic flux has zero classical energy

Abstract We prove that for a given non-Abelian flux in SU (N) Z (N) as defined by t Hooft it is possible to find a field configuration having this flux but zero classical energy. In fact one can construct solutions to the Yang-Mills equations with arbitrary classical energy and a given magnetic flux. This is due to an interplay between the group properties of SU (N) Z (N) and the boundary conditions imposed by t Hooft (compatification to a torus). We show this by comparing a SU (N) Z (N) gauge theory on the torus with a SU (N) Z (N) gauge theory on a sphere and a U(1) gauge theory on the torus.

1N-expansion of the non-linear σ-model: The first three orders

Abstract The two-point function of the O( N )-symmetric non-linear σ-model is expanded in 1 N , keeping terms of three leading orders. The mass gap and the magnetic susceptibility are obtained from the two-point function. They are evaluated on square lattices for N = 3 and N = 4. The systematic errors of the 1 N series truncated after the first, second, or third term are found by using recent high-precision Monte Carlo results as bench marks. For all three truncations, we find systematic errors which are smaller than the expected magnitude of neglected terms, both for the mass gap and for the susceptibility. This result is uniform in the inverse coupling β, and valid for N as small as 3. We conclude that the 1 N series approach the exact results as rapidly as one could ever hope for.

1N-expansion of the non-linear σ-model

Abstract The two-point function of the O( N )-symmetric non-linear σ-model is expanded in 1/ N , keeping both the leading term and the first correction term. From this function the mass gap and the magnetic susceptibility are obtained. After mass renormalization, the Feynman diagrams giving these quantities are evaluated on two-dimensional, square lattices. The results compare very favorably with Monte Carlo results for all values of the inverse coupling β. The first non-vanishing term in 1 N - expansion of the four-point function is also obtained.

Physics of Biological Systems: From Molecules to Species

From the contents: Indroduction: Physics - and the Physics of Biological Systems DNA Proteins Motors, Membranes, Microtubules Neurons, Brains, and Sensory Signal Processing. Evolution, Micro- and Macro-Scale.

Improved QCD vacuum for gauge groups SU(3) and SU(4)

Abstract The effective energy for a covariantly constant background field in a pure Yang-Mills theory is calculated to loop order one. For gauge group SU(3) [SU(4)] it is found that the “vacuum” configuration consists of two [three] constant color magnetic fields of equal non-zero magnitude orthogonal to each other in color as well as physical space. We conclude that the structure of the Copenhagen vacuum is more complex than previously expected.

Mass gap of O (N) σ-models in 2D. Support for exact results from 1 N-expansion

Abstract The mass gaps of the non-linear σ-models in 2D are given to three leading orders in 1/N as functions of the bare coupling up to correlation lengths 150. Within the small systematic error introduced by truncating the 1 N -expansion, our results agree with available Monte Carlo results for N⩾3. At weak coupling, our results agree with recent exact results for the mass gaps based on the Bethe ansatz and the S-matrices of the models, the two sets of results thus lending support to each other. Our calculation features “Fourier accelerated” numerical evaluation of Feynman diagrams, and the use of finite size scaling to obtain infinite volume results from finite volume results.

Some exact results for the O(N)-symmetric non-linear σ-model to O(1/N)

With the non-linear σ-model on the lattice in view, we study its continuum version with a finite, sharp momentum cut-off. We find exact analytical results for its mass gap and magnetic susceptibility to two leading orders in 1/N. Asymptotically, at weak coupling, our results converge to those of renormalization group improved weak coupling perturbation theory to two-loop order, and give the ratio of the mass to the Λ-parameter analytically. Thus our results provide an opportunity to study the rate at which asymptotic scaling is approached. Since this approach is slow for low values of N, we find a region of intermediate coupling strenghts, where our results describe non-asymptotic scaling of a well-defined and universally valid kind.

Magnetic susceptibility of O(N) σ-models in 2D. Weak coupling results from 1 N expansion

Abstract The magnetic susceptibilities of the non-linear σ-models in 2D are given to three leading orders in 1 N as functions of the inverse bare coupling β and up to correlation lengths 150. Within the systematic error introduced by truncating the 1 N expansion, our results agree with Monte Carlo results for N⩾3. We argue that the 1/N series is convergent with a β-dependent radius of convergence approaching 1 2 at weak coupling, and use this to predict the value for the magnetic susceptibility at asymptotically weak coupling. Our calculation features “Fourier accelerated” numerical evaluation of Feynman diagrams, and extrapolation of finite volume results to infinite volume by phenomenological scaling.