Large scale functional motions of molecules are studied experimentally using numerous molecular and biophysics techniques, the data from which are subsequently interpreted using diverse models of Brownian molecular dynamics. To unify all rotational physics techniques and motional models, the frame order tensor – a universal statistical mechanics theory based on the rotational ordering of rigid body frames – is herein formulated. The frame ordering is the fundamental physics that governs how motions modulate rotational molecular physics and it defines the properties and maximum information content encoded in the observable physics. Using the tensor to link residual dipolar couplings and pseudo-contact shifts, two distinct information-rich and atomic-level biophysical measurements from the field of nuclear magnetic resonance spectroscopy, to a number of basic mechanical joint models, a highly dynamic state of calmodulin (CaM) bound to a target peptide in a tightly closed conformation was observed. Intra- and inter-domain motions reveal the CaM complex to be entropically primed for peptide release.

We start from a mathematical model which describes the collective motion of bacteria taking into account the underlying biochemistry. This model was first introduced by Keller-Segel [13]. A new formulation of the system of partial differential equations is obtained by the introduction of a new variable (this new variable is similar to the quasi-Fermi level in the framework of semiconductor modelling). This new system of P.D.E. is approximated via a mixed finite element technique. The solution algorithm is then described and finally we give some preliminary numerical results. Especially our method is well adapted to compute the concentration of bacteria.