Formalizing Chemical Physics using the Lean Theorem Prover

Chemical theory can be made more rigorous using the Lean theorem prover, an interactive theorem prover for complex mathematics. We formalize the Langmuir and BET theories of adsorption, making each scientific premise clear and every step of the derivations explicit. Lean's math library, mathlib, provides formally verified theorems for infinite geometries series, which are central to BET theory. While writing these proofs, Lean prompts us to include mathematical constraints that were not originally reported. We also illustrate how Lean flexibly enables the reuse of proofs that build on more complex theories through the use of functions, definitions, and structures. Finally, we construct scientific frameworks for interoperable proofs, by creating structures for classical thermodynamics and kinematics, using them to formalize gas law relationships like Boyle's Law and equations of motion underlying Newtonian mechanics, respectively. This approach can be extended to other fields, enabling the formalization of rich and complex theories in science and engineering

Disruption of Lateral Efferent Pathways: Functional Changes in Auditory Evoked Responses

The functional consequences of selectively lesioning the lateral olivocochlear efferent system in guinea pigs were studied. The lateral superior olive (LSO) contains the cell bodies of lateral olivocochlear neurons. Melittin, a cytotoxic chemical, was injected into the brain stem using stereotaxic coordinates and near-field evoked potentials to target the LSO. Brain stem histology revealed discrete damage to the LSO following the injections. Functional consequences of this damage were reflected in depressed amplitude of the compound action potential of the eighth nerve (CAP) following the lesion. Threshold sensitivity and N1 latencies were relatively unchanged. Onset adaptation of the cubic distortion product otoacoustic emission (DPOAE) was evident, suggesting a reasonably intact medial efferent system. The present results provide the first report of functional changes induced by isolated manipulation of the lateral efferent pathway. They also confirm the suggestion that changes in single-unit auditory nerve activity after cutting the olivocochlear bundle are probably a consequence of disrupting the more lateral of the two olivocochlear efferent pathways.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41379/1/10162_2002_Article_3018.pd

AMPA-preferring glutamate receptors in cochlear physiology of adult guinea-pig

The present study was designed to determine which glutamate (Glu) receptors are involved in excitatory neurotransmission at the first auditory synapse between the inner hair cells and the spiral ganglion neurons.The Glu receptors present at the membrane level were investigated on isolated spiral ganglion neuron somata from guinea-pigs by whole-cell voltage-clamp measurements. Glu and AMPA induced a fast onset inward current that was rapidly desensitized, while kainate induced only a non-desensitizing, steady-state current. NMDA induced no detectable current.To further discriminate between the AMPA and kainate receptors present, we used the receptor-specific desensitization blockers, cyclothiazide and concanavalin A. While no effect was observed with concanavalin A, cyclothiazide greatly enhanced the Glu-, AMPA- and kainate-induced steady-state currents and potentiated Glu-induced membrane depolarization.To extrapolate the results obtained from the somata to the events occurring in situ at the dendrites, the effects of these drugs were evaluated in vivo. Cyclothiazide reversibly increased spontaneous activity of single auditory nerve fibres, while concanavalin A had no effect, suggesting that the functional Glu receptors on the somata may be the same as those at the dendrites.The combination of a moderate-level sound together with cyclothiazide increased and subsequently abolished the spontaneous and the sound-evoked activity of the auditory nerve fibres. Histological examination revealed destruction of the dendrites, suggesting that cyclothiazide potentiates sound-induced Glu excitotoxicity via AMPA receptors.Our results reveal that fast synaptic transmission in the cochlea is mainly mediated by desensitizing AMPA receptors