Multitaper estimates of phase-amplitude coupling

Phase-amplitude coupling (PAC) is the association of the amplitude of a high-frequency oscillation with the phase of a low-frequency oscillation. In neuroscience, this relationship provides a mechanism by which neural activity might be coordinated between distant regions. The dangers and pitfalls of assessing PAC with commonly used statistical measures have been well-documented. The limitations of these measures include: (1) response to non-oscillatory, high-frequency, broad-band activity, (2) response to high-frequency components of the low-frequency oscillation, (3) adhoc selection of analysis frequency-intervals, and (4) reliance upon data shuffling to assess statistical significance.Objective.To address issues (1)-(4) by introducing a nonparametric multitaper estimator of PAC.Approach.In this work, a multitaper PAC estimator is proposed that addresses these issues. Specifically, issue (1) is addressed by replacing the analytic signal envelope estimator computed using the Hilbert transform with a multitaper estimator that down-weights non-sinusoidal activity using a classical, multitaper super-resolution technique. Issue (2) is addressed by replacing coherence between the low-frequency and high-frequency components in a standard PAC estimator with multitaper partial coherence, while issue (3) is addressed with a physical argument regarding meaningful neural oscillation. Finally, asymptotic statistical assessment of the multitaper estimator is introduced to address issue (4).Main results.Multitaper estimates of PAC are introduced. Their efficacy is demonstrated in simulation and on human intracranial recordings obtained from epileptic patients.Significance.This work facilitates a more informative statistical assessment of PAC, a phenomena exhibited by many neural systems, and provides a basis upon which further nonparametric multitaper-related methods can be developed.

Excited State Intervalence Transfer in a Rigid Polymeric Film

The ligand-bridged complex cis,cis-[(bpy)2ClRu(pz)RuCl(bpy)2]2+ as the PF6- salt, (1)(PF6)2, is stabilized toward photochemical ligand loss in poly(methyl methacrylate) (PMMA). Stabilization allows measurement of metal-to-ligand charge transfer (MLCT) photophysical properties--emission and transient absorption. This includes appearance of an intervalence transfer absorption band in the near IR spectrum of the photochemically prepared, mixed valence form, [(bpy)2ClRuIII(pz(-*))RuIICl(bpy)2](PF6)2* (1*(PF6)2). Comparison of its IT band properties with those of ground state cis,cis-(bpy)2ClRuIII(pz)RuIICl(bpy)2]3+ in CD3CN allows a comparison to be made between pz and pz(-*) as bridging ligands. A model based on differences between rigid and fluid media provides an explanation for decreased IT band energies and widths in PMMA and provides important insight into electron transfer in rigid media.

Rigid Medium Stabilization of Metal-to-Ligand Charge Transfer Excited States

The salts [Ru(bpy)3](PF6)2, cis-[Ru(bpy)2(py)2](PF6)2, trans-[Ru(bpy)2(4-Etpy)2](PF6)2, [Ru(tpy)2](PF6)2, and [Re(bpy)(CO)3(4-Etpy)](PF6) (bpy=2,2'-bipyridine, py=pyridine, 4-Etpy=4-ethylpyridine, and tpy=2,2':6',2-terpyridine) have been incorporated into poly(methyl methacrylate) (PMMA) films and their photophysical properties examined by both steady-state and time-resolved absorption and emission measurements. Excited-state lifetimes for the metal salts incorporated in PMMA are longer and emission energies enhanced due to a rigid medium effect when compared to fluid CH3CN solution. In PMMA part of the fluid medium reorganization energy, lambdaoo, contributes to the energy gap with lambdaoo approximately 700 cm-1 for [Ru(bpy)3](PF6)2 from emission measurements. Enhanced lifetimes can be explained by the energy gap law and the influence of the excited-to-ground state energy gap, Eo, on nonradiative decay. From the results of emission spectral fitting on [Ru(bpy)3](PF6)2* in PMMA, Eo is temperature dependent above 200 K with partial differentialEo/ partial differentialT=2.8 cm-1/deg. cis-[Ru(bpy)2(py)2](PF6)2 and trans-[Ru(bpy)2(4-Etpy)2](PF6)2 are nonemissive in CH3CN and undergo photochemical ligand loss. Both emit in PMMA and are stable toward ligand loss even for extended photolysis periods. The lifetime of cis-[Ru(bpy)2(py)2](PF6)2* in PMMA is temperature dependent, consistent with a contribution to excited-state decay from thermal population and decay through a low-lying dd state or states. At temperatures above 190 K, coinciding with the onset of the temperature dependence of Eo for [Ru(bpy)3](PF6)2*, lifetimes become significantly nonexponential. The nonexponential behavior is attributed to dynamic coupling between MLCT and dd states, with the lifetime of the latter greatly enhanced in PMMA with tau approximately 3 ns. On the basis of these data and data in 4:1 (v/v) EtOH/MeOH, the energy gap between the MLCT and dd states is decreased by approximately 700 cm-1 in PMMA with the dd state at higher energy by DeltaH0 approximately 1000 cm-1. The "rigid medium stabilization effect" for cis-[Ru(bpy)2(py)2](PF6)2* in PMMA is attributed to inhibition of metal-ligand bond breaking and a photochemical cage effect.

Evidence for Through-Space Electron Transfer in the Distance Dependence of Normal and Inverted Electron Transfer in Oligoproline Arrays

Four new helical oligoproline assemblies containing 16, 17, 18, and 19 proline residues and ordered arrays of a Ru(II)-bipyridyl chromophore and a phenothiazine electron-transfer donor have been synthesized in a modular fashion by solid-phase peptide synthesis. These arrays are illustrated and abbreviated as CH(3)CO-Pro(6)-Pra(PTZ)-Pro(n)()-Pra(Ru(II)b(2)m)(2+)-Pro(6)-NH(2), where PTZ is 3-(10H-phenothiazine-10)propanoyl and (Ru(II)b'(2)m)(2+) is bis(4,4'-diethylamide-2,2'-bipyridine)(4-methyl,4'-carboxylate,2,2'-bipyridine)ruthenium(II) dication with n = 2 (2), 3 (3), 4 (4), and 5 (5). They contain PTZ as an electron-transfer donor and (Ru(II)b'(2)m)(2+) as a metal-to-ligand charge transfer (MLCT) light absorber and are separated by proline-to-proline through-space distances ranging from 0 (n = 2) to 12.9 A (n = 5) relative to the n = 2 case. They exist in the proline-II helix form in water, as shown by circular dichroism measurements. Following laser flash Ru(II) --> b'(2)m MLCT excitation at 460 nm in water, excited-state PTZ --> Ru(2+) quenching (k(2)) occurs by reductive electron transfer, followed by Ru(+) --> PTZ(+) back electron transfer (k(3)), as shown by transient absorption and emission measurements in water at 25 degrees C. Quenching with DeltaG degrees = -0.1 eV is an activated process, while back electron transfer occurs in the inverted region, DeltaG degrees = -1.8 eV, and is activationless, as shown by temperature dependence measurements. Coincidentally, both reactions have comparable distance dependences, with k(2)( )()varying from = 1.9 x 10(9) (n = 2) to 2.2 x 10(6) s(-)(1) (n = 4) and k(3) from approximately 2.0 x 10(9) (n = 2) to 2.2 x 10(6) s(-)(1) (n = 4). For both series there is a rate constant enhancement of approximately 10 for n = 5 compared to n = 4 and a linear decrease in ln k with the through-space separation distance, pointing to a significant and probably dominant through-space component to intrahelical electron transfer.

Nanosecond Redox Equilibrium Method for Determining Oxidation Potentials in Organic Media

A general, nanosecond equilibrium method is described for determining thermodynamically meaningful oxidation potentials in organic media for compounds that form highly reactive cation radicals upon one-electron oxidation. The method provides oxidation potentials with unusually high precision and accuracy. Redox ladders have been constructed of appropriate reference compounds in dichloromethane and in acetonitrile that can be used to set up electron-transfer equilibria with compounds with unknown oxidation potentials. The method has been successfully applied to determining equilibrium oxidation potentials for a series of aryl-alkylcyclopropanes, whose oxidation potentials were imprecisely known previously. Structure-property trends for oxidation potentials of the cyclopropanes are discussed.

Turning the [Ru(bpy)2dppz]2+ light-switch on and off with temperature

We report temperature-dependent excited-state lifetime measurements on [Ru(bpy)(2)dppz](2+) in both protic and aprotic solvents. These experiments yield a unifying picture of the excited-state photophysics that accounts for observations in both types of solvent. Our measurements support the notion of bpy-like and phz-like states associated with the dppz ligand and show that the ligand orbital associated with the bright state is similar in size to the corresponding orbital in the (3)MLCT state of [Ru(bpy)(3)](2+). In contrast to the current thinking, the experiments presented here indicate that the light-switch effect is not driven by a state reversal. Rather, they suggest that the dark state is always lowest in energy, even in aprotic solvents, and that the light-switch behavior is the result of a competition between energetic factors that favor the dark state and entropic factors that favor the bright (bpy) state.

Ultrafast excited-state energy migration dynamics in an efficient light-harvesting antenna polymer based on Ru(II) and Os(II) polypyridyl complexes

A detailed study of the excited state energy migration dynamics that take place within an assembly of Ru(II) and Os(II) polypyridyl complexes linked together through a polymer backbone is presented. The energy migration process is initiated by the photoexcitation of the metal-to-ligand charge transfer (MLCT) transition in one of the Ru(II) complexes and terminated by energy transfer to a lower energy Os(II) trap. Energy transfer sensitization of Os(II) can occur in a single step if the excited state is formed adjacent to a trap, or after a series of hops between isoenergetic rutheniums prior to reaching a trap. The dynamics of the energy transfer process are followed by monitoring the growth of Os(II) luminescence at 780 nm. The kinetics of the growth are complex and can be fit by a sum of two exponentials. This kinetic complexity arises both from the presence of a distribution of donor-acceptor distances and the variety of time scales by which Os(II) can be formed. We have augmented the time-resolved experiments with Monte Carlo simulations, which provide insight into the polymer array's structure and at the same time form the basis of a molecular-level description of the energy migration dynamics. The simulations indicate that the most probable Ru-->Os energy transfer time is approximately 400 ps while the time scale for Ru-->Ru hopping is approximately 1-4 ns. The time scale for Ru-->Ru hopping relative to its natural lifetime (1000 ns) suggests that this polymer system could be extended to considerably longer dimensions without an appreciable loss in its overall efficiency.