From point defects to plate tectonic faults

Understanding and explaining emergent constitutive laws in the multi-scale evolution from point defects, dislocations and two-dimensional defects to plate tectonic scales is an arduous challenge in condensed matter physics. The Earth appears to be the only planet known to have developed stable plate tectonics as a means to get rid of its heat. The emergence of plate tectonics out of mantle convection appears to rely intrinsically on the capacity to form extremely weak faults in the top 100 km of the planet. These faults have a memory of at least several hundred millions of years, yet they appear to rely on the effects of water on line defects. This important phenomenon was first discovered in laboratory and dubbed ``hydrolytic weakening''. At the large scale it explains cycles of co-located resurgence of plate generation and consumption (the Wilson cycle), but the exact physics underlying the process itself and the enormous spanning of scales still remains unclear. We present an attempt to use the multi-scale non-equilibrium thermodynamic energy evolution inside the deforming lithosphere to move phenomenological laws to laws derived from basic scaling quantities, develop self-consistent weakening laws at lithospheric scale and give a fully coupled deformation-weakening constitutive framework. At meso- to plate scale we encounter in a stepwise manner three basic domains governed by the diffusion/reaction time scales of grain growth, thermal diffusion and finally water mobility through point defects in the crystalline lattice. The latter process governs the planetary scale and controls the stability of its heat transfer mode.

Restriction of intramuscular neurite branching and extension is lost in agrin and rapsyn-deficient mice

The phrenic nerve enters the diaphragm at approximately embryonic day 12.5 (E12.5) in the mouse. The secondary nerve trunk advances along the centre of the diaphragm muscle and extends tertiary branches primarily towards the lateral side during normal embryonic development. In the present study we quantified the intramuscular neurite branching in the most ventral region of the diaphragm at E15.5 and E18.5 in wild-type mice, agrin knock-out mice (KOAG) and rapsyn knock-out mice (KORAP). KOAG and KORAP have decreased muscle contraction due to their inability to maintain/form acetylcholine receptor (AChR) clusters during embryonic development. Heterozygote mothers were anaesthetised via an overdose of Nembutal (30 mg; Boeringer Ingelheim, Ridgefield, CT, USA) and killed via cervical dislocation. There were increases in the number of branches exiting the medial side of the phrenic nerve trunk in KOAG and KORAP compared to wild-type mice, but not on the lateral side at E15.5 and E18.5. However, the number of bifurcations in the periphery significantly increased on both the medial and lateral sides of the diaphragm at E15.5 and E18.5 in KOAG and KORAP compared to control mice. Furthermore, neurites extended further on both the medial and lateral sides of the diaphragm at E15.5 and E18.5 in KOAG and KORAP compared to wild-type mice. Together these results show that the restriction of neurite extension and bifurcations from the secondary nerve trunk is lost in both KOAG and KORAP allowing us the opportunity to investigate the factors that restrict motoneuron behaviour in mammalian muscles.

The motor neurite terminal determines where neuromuscular synapses form in the absence of agrin

Agrin is a proteoglycan secreted by motor neurite terminals that functions to initiate and maintain AChR clusters at the nerve terminal. This led to the theory that neurite terminals decide where neuromuscular synapses form by secreting agrin. However, initiation of AChR clustering occurs in the absence of the innervating motoneuron and in the absence of agrin. In this instance, the muscle, not the nerve, is deciding the location of neuromuscular synapses by drawing neurite terminals towards pre-existing AChR clusters. If this were true, one would expect the initial innervation patterns to be the same in agrin-deficient mice and wild-type mice. To test this we quantified the intramuscular axonal branching and synapse formation in the diaphragm at E14.5 in agrin-deficient mice and wild-type mice. Heterozygote mothers were anaesthetised with Nembutal (30 mg) and killed via cervical dislocation. In the diaphragm, the nerve trunk runs down the centre of the muscle and extends branches primarily toward the lateral side. In agrin-deficient mice however, we found significantly more branches exited the phrenic nerve trunk, branched in the periphery and extended further on the medial side. Moreover, we found that the percentage α-bungarotoxin/synaptophysin colocalisations, markers of pre- and postsynaptic differentiation, respectively, was the same in agrin-deficient mice and wild-type mice. These results show that initial innervation patterns are not the same in agrin-deficient mice and wild-type mice indicating neurite terminals, not muscle, decide the placement of neuromuscular synapses in the absence of agrin.