Intracellular transport in eukarya is attributed to motor proteins that transduce chemical energy into directed mechanical energy. This suggests that, in nonequilibrium systems, fluctuations may be oriented or organized to do work. Here we seek to understand how this is manifested by quantitative mathematical portrayals of these systems.
⋆ ⋆ ⋆ Page xvii ⋆ ⋆ ⋆ First bullet item " The core: " Add the following as a footnote: Caveat: The complete proof of Theorem 8.20 relies on material outside the core. In particular, the proof of part (a) requires the Hermitian inner product, which is covered in section 3.6. The proof of the general version of part (c), when the matrix A has multiple… (More)
Intracellular transport in eukarya is attributed to motor proteins that transduce chemical energy into directed mechanical motion. Nanoscale motors like kinesins tow organelles and other cargo on microtubules or filaments, have a role separating the mitotic spindle during the cell cycle, and perform many other functions. The simplest description gives rise… (More)
In this note we discuss transport properties of weakly coupled parabolic systems of evolution equations. These arise in the study of molecular motors, like conventional kinesin, which are responsible for eukaryotic intracellular transport. It falls under the rubric of what we call diffusion mediated transport. Diffusion mediated transport generally concerns… (More)
We describe a dissipation principle/variational principle which may be useful in modeling motion in small viscous systems and provide brief illustrations to brownian motor or molecular rachet situations which are found in intracellular transport. Monge-Kantorovich mass transport and Wasserstein metric play an interesting role in these developments. Some… (More)
In 1992 G. B. Ermentrout and J. B. McLeod published a landmark study of travelling wave fronts for a differential-integral equation modeling a neural network. Since then a number of authors have extended the model by adding an additional equation for a " recovery variable " , thus allowing the possibility of travelling pulse type solutions. In a recent… (More)
It is well known that to determine a triangle up to congruence requires three measurements: three sides, two sides and the included angle, or one side and two angles. We consider various generalizations of this fact to two and three dimensions. In particular we consider the following question: given a convex polyhedron P , how many measurements are required… (More)