Probing molecular free energy landscapes by periodic loading

Single molecule pulling experiments provide information about interactions in biomolecules that cannot be obtained by any other method. However, the reconstruction of the molecule's free energy profile from the experimental data is still a challenge, in particular for the unstable barrier regions. We propose a new method for obtaining the full profile by introducing a periodic ramp and using Jarzynski's identity for obtaining equilibrium quantities from non-equilibrium data. Our simulated experiments show that this method delivers significant more accurate data than previous methods, under the constraint of equal experimental effort.Comment: 4 pages, 3 figure

Optical sorting and detection of sub-micron objects in a motional standing wave

An extended interference pattern close to surface may result in both a transmissive or evanescent surface fields for large area manipulation of trapped particles. The affinity of differing particle sizes to a moving standing wave light pattern allows us to hold and deliver them in a bi-directional manner and importantly demonstrate experimentally particle sorting in the sub-micron region. This is performed without the need of fluid flow (static sorting). Theoretical calculations experimentally confirm that certain sizes of colloidal particles thermally hop more easily between neighboring traps. A new generic method is also presented for particle position detection in an extended periodic light pattern and applied to characterization of optical traps and particle behaviorComment: 5 pages, 6 figures, Optical Trapping pape

Stability of adhesion clusters under constant force

We solve the stochastic equations for a cluster of parallel bonds with shared constant loading, rebinding and the completely dissociated state as an absorbing boundary. In the small force regime, cluster lifetime grows only logarithmically with bond number for weak rebinding, but exponentially for strong rebinding. Therefore rebinding is essential to ensure physiological lifetimes. The number of bonds decays exponentially with time for most cases, but in the intermediate force regime, a small increase in loading can lead to much faster decay. This effect might be used by cell-matrix adhesions to induce signaling events through cytoskeletal loading.Comment: Revtex, 4 pages, 4 Postscript files include

On Iterated Twisted Tensor Products of Algebras

We introduce and study the definition, main properties and applications of iterated twisted tensor products of algebras, motivated by the problem of defining a suitable representative for the product of spaces in noncommutative geometry. We find conditions for constructing an iterated product of three factors, and prove that they are enough for building an iterated product of any number of factors. As an example of the geometrical aspects of our construction, we show how to construct differential forms and involutions on iterated products starting from the corresponding structures on the factors, and give some examples of algebras that can be described within our theory. We prove a certain result (called ``invariance under twisting'') for a twisted tensor product of two algebras, stating that the twisted tensor product does not change when we apply certain kind of deformation. Under certain conditions, this invariance can be iterated, containing as particular cases a number of independent and previously unrelated results from Hopf algebra theory.Comment: 44 pages, 21 figures. More minor typos corrections, one more example and some references adde

Escape from a metastable well under a time-ramped force

Thermally activated escape of an over-damped particle from a metastable well under the action of a time-ramped force is studied. We express the mean first passage time (MFPT) as the solution to a partial differential equation, which we solve numerically for a model case. We discuss two approximations of the MFPT, one of which works remarkably well over a wide range of loading rates, while the second is easy to calculate and can provide a valuable first estimate.Comment: 9 pages, including 2 figure

Small Universal Accepting Networks of Evolutionary Processors with Filtered Connections

In this paper, we present some results regarding the size complexity of Accepting Networks of Evolutionary Processors with Filtered Connections (ANEPFCs). We show that there are universal ANEPFCs of size 10, by devising a method for simulating 2-Tag Systems. This result significantly improves the known upper bound for the size of universal ANEPFCs which is 18. We also propose a new, computationally and descriptionally efficient simulation of nondeterministic Turing machines by ANEPFCs. More precisely, we describe (informally, due to space limitations) how ANEPFCs with 16 nodes can simulate in O(f(n)) time any nondeterministic Turing machine of time complexity f(n). Thus the known upper bound for the number of nodes in a network simulating an arbitrary Turing machine is decreased from 26 to 16

Rupture of multiple parallel molecular bonds under dynamic loading

Biological adhesion often involves several pairs of specific receptor-ligand molecules. Using rate equations, we study theoretically the rupture of such multiple parallel bonds under dynamic loading assisted by thermal activation. For a simple generic type of cooperativity, both the rupture time and force exhibit several different scaling regimes. The dependence of the rupture force on the number of bonds is predicted to be either linear, like a square root or logarithmic.Comment: 8 pages, 2 figure

Elastic properties of grafted microtubules

We use single-particle tracking to study the elastic properties of single microtubules grafted to a substrate. Thermal fluctuations of the free microtubule's end are recorded, in order to measure position distribution functions from which we calculate the persistence length of microtubules with contour lengths between 2.6 and 48 micrometers. We find the persistence length to vary by more than a factor of 20 over the total range of contour lengths. Our results support the hypothesis that shearing between protofilaments contributes significantly to the mechanics of microtubules.Comment: 9 pages, 3 figure

The Kepler Problem with Anisotropic Perturbations

We study a 2-body problem given by the sum of the Newtonian potential and an anisotropic perturbation that is a homogeneous function of degree $-\beta$, $\beta\ge 2$. For $\beta>2$, the sets of initial conditions leading to collisions/ejections and the one leading to escapes/captures have positive measure. For $\beta>2$ and $\beta\ne 3$, the flow on the zero-energy manifold is chaotic. For $\beta=2$, a case we prove integrable, the infinity manifold of the zero-energy level is a disconnected set, which has heteroclinic connections with the collision manifold