Kevin Cahill

On the kinematics of protein folding

We offer simple solutions to three kinematic problems that occur in the folding of proteins. We show how to construct suitably local elementary Monte Carlo moves, how to close a loop, and how to fold a loop without breaking the bond that closes it.

Molecular electroporation and the transduction of oligoarginines

Certain short polycations, such as TAT and polyarginine, rapidly pass through the plasma membranes of mammalian cells by an unknown mechanism called transduction as well as by endocytosis and macropinocytosis. These cell-penetrating peptides (CPPs) promise to be medically useful when fused to biologically active peptides. I offer a simple model in which one or more CPPs and the phosphatidylserines of the inner leaflet form a kind of capacitor with a voltage in excess of about 200 mV, high enough to create a molecular electropore. The model is consistent with an empirical upper limit on the cargo peptide of 40-60 amino acids and with experimental data on how the transduction of a polyarginine-fluorophore into mouse C(2)C(12) myoblasts depends on the number of arginines in the CPP and on the CPP concentration. The model makes three testable predictions.

Riemannian gauge theory and charge quantization

In a traditional gauge theory, the matter fields a and the gauge fields Acμ are fundamental objects of the theory. The traditional gauge field is similar to the connection coefficient in the riemannian geometry covariant derivative, and the field-strength tensor is similar to the curvature tensor. In contrast, the connection in riemannian geometry is derived from the metric or an embedding space. Guided by the physical principal of increasing symmetry among the four forces, we propose a different construction. Instead of defining the transformation properties of a fundamental gauge field, we derive the gauge theory from an embedding of a gauge fiber F = n or F = n into a trivial, embedding vector bundle = N or = N where n

Noncompact simulations of SU(2)3

>N>n. Our new action is symmetric between the gauge theory and the riemannian geometry. By expressing gauge-covariant fields in terms of the orthonormal gauge basis vectors, we recover a traditional, SO(n) or U(n) gauge theory. In contrast, the new theory has all matter fields on a particular fiber couple with the same coupling constant. Even the matter fields on a 1 fiber, which have a U(1) symmetry group, couple with the same charge of ±q. The physical origin of this unique coupling constant is a generalization of the general relativity equivalence principle. Because our action is independent of the choice of basis, its natural invariance group is GL(n,) or GL(n,). Last, the new action also requires a small correction to the general-relativity action proportional to the square of the curvature tensor.

Comparison of the simplicial method with Wilson's lattice gauge theory for U(1)3

Abstract The action density and Wilson loops for SU(2) in three dimensions have been measured using both a noncompact version of lattice gauge theory and Wilsons version. As a standard of comparison, the Creutz ratio χ of a quartet of Wilson loops has been calculated in the exact theory to order 1/β 2 . The noncompact method gave χs that are between 2 and 23% below the one-loop calculation for the smaller loops at β = 30 and 60 on a 24 3 lattice. Wilsons method gave χs that are above the one-loop calculation by comparable amounts. For β ⩽10, the noncompact χs are closer than the Wilson χs to the one-loop calculation. Also some noncompact simulations were done in the temporal gauge; the results agree subtantially with those done without gauge fixing, providing evidence for the gauge independence of the noncompact method. By comparing the χs of the 12 3 lattice at β = 30 with those of the 24 3 lattice at β = 30 and 60, evidence was found that the accuracy of the noncompact method improves both as the volume of the lattice grows and as the lattice spacing shrinks.

Cell-penetrating peptides, electroporation and drug delivery

Abstract In the simplicial version of lattice gauge theory, euclidean path integrals are approximated by tiling spacetime with simplexes and by linearly interpolating the fields throughout each simplex from their values at the vertices. This method is compared with Wilsons lattice gauge theory for U(1) in three dimensions. As a standard of comparison, the exact values of Creutz ratios of Wilson loops in the continuum theory are computed. Monte Carlo computations using the simplicial method give Creutz ratios within a few percent of the exact values for reasonably sized loops at β = 1,2,and10. Similar computations using Wilsons method give ratios that typically differ from the exact values by factors of two or more for 1 ⩽ β ⩽ 3.5 and that have the wrong β dependence. The better accuracy of the simplicial method is due to its use of the action and domain of integration of the exact theory, unaltered apart from the granularity of the simplicial lattice. Data on the action density and the mass gap are also presented.

Helices in biomolecules

Certain short polycations, such as trans-activating transcriptional activator and oligoarginine, rapidly pass through the plasma membranes of mammalian cells by a mechanism called transduction, as well as by endocytosis and macropinocytosis. These cell-penetrating peptides can carry with them cargos of 30 amino acids, more than the nominal limit of 500 Da and enough to be therapeutic. An analysis of the electrostatics of a charge outside the cell membrane and some recent experiments suggest that transduction may proceed by molecular electroporation. Ways to target diseased cells, rather than all cells, are discussed.

Testing two versions of lattice gauge theory: Creutz ratios inU(1)3

Identical objects, regularly assembled, form a helix, which is the principal motif of nucleic acids, proteins, and viral capsids.

Simplicial interpolations for path integrals

In our simplicial version of lattice gauge theory, we approximate Euclidean path integrals by tiling space-time with simplexes and by linearly interpolating the fields throughout each simplex from their values at the vertices. We compare this method with Wilsons lattice gauge theory forU(1) in three dimensions. As a standard of comparison, we compute the exact values of Creutz ratios of Wilson loops in the continuum theory. Monte Carlo computations using the simplicial method give Creutz ratios within a few percent of the exact values for reasonably sized loop atβ=1, 2, and 10. Similar computations using Wilsons method give ratios that typically differ from the exact values by factors of 2 or more for 1⩽β⩽3.5 and that have the wrongβ dependence. The better accuracy of the simplicial method is due to its use of the action and domain of integration of the exact theory, unaltered apart from the granularity of the simplicial lattice. We also present data on the action density and the mass gap.

Simulations of protein folding

Abstract We suggest approximating path integrals by tilting spacetime with simplexes and by interpolating the fields throughout each simplex from their values on the vertices. This simplicial interpolative method uses unaltered the action of the contrinuum theory. We present several tests of the method. Both in one dimension, for the harmonic oscillator, and in two dimensions, for the free massive scalar field, it was about twice as accurate as ordinary lattice theory. We also computed Wilson loops in two dimensions for free quantum electrodynamics. By using huge lattices, we achieved an accuracy of better than 0.5% and observed a remarkable restoration of translational and rotational invariance.