Shedding light on the dark and weakly fluorescent states of green fluorescent proteins

Recent experiments on various similar green fluorescent protein (GFP) mutants at the single-molecule level and in solution provide evidence of previously unknown short- and long-lived “dark” states and of related excited-state decay channels. Here, we present quantum chemical calculations on cis-trans photoisomerization paths of neutral, anionic, and zwitterionic GFP chromophores in their ground and first singlet excited states that explain the observed behaviors from a common perspective. The results suggest that favorable radiationless decay channels can exist for the different protonation states along these isomerizations, which apparently proceed via conical intersections. These channels are suggested to rationalize the observed dramatic reduction of fluorescence in solution. The observed single-molecule fast blinking is attributed to conversions between the fluorescent anionic and the dark zwitterionic forms whereas slow switching is attributed to conversions between the anionic and the neutral forms. The predicted nonadiabatic crossings are seen to rationalize the origins of a variety of experimental observations on a common basis and may have broad implications for photobiophysical mechanisms in GFP.

Singular value decomposition for genome-wide expression data processing and modeling

We describe the use of singular value decomposition in transforming genome-wide expression data from genes × arrays space to reduced diagonalized “eigengenes” × “eigenarrays” space, where the eigengenes (or eigenarrays) are unique orthonormal superpositions of the genes (or arrays). Normalizing the data by filtering out the eigengenes (and eigenarrays) that are inferred to represent noise or experimental artifacts enables meaningful comparison of the expression of different genes across different arrays in different experiments. Sorting the data according to the eigengenes and eigenarrays gives a global picture of the dynamics of gene expression, in which individual genes and arrays appear to be classified into groups of similar regulation and function, or similar cellular state and biological phenotype, respectively. After normalization and sorting, the significant eigengenes and eigenarrays can be associated with observed genome-wide effects of regulators, or with measured samples, in which these regulators are overactive or underactive, respectively.

Behavior of several two-dimensional fluid equations in singular scenarios

We give conditions that rule out formation of sharp fronts for certain two-dimensional incompressible flows. We show that a necessary condition of having a sharp front is that the flow has to have uncontrolled velocity growth. In the case of the quasi-geostrophic equation and two-dimensional Euler equation, we obtain estimates on the formation of semi-uniform fronts.

Quantum groups with invariant integrals

Quantum groups have been studied intensively for the last two decades from various points of view. The underlying mathematical structure is that of an algebra with a coproduct. Compact quantum groups admit Haar measures. However, if we want to have a Haar measure also in the noncompact case, we are forced to work with algebras without identity, and the notion of a coproduct has to be adapted. These considerations lead to the theory of multiplier Hopf algebras, which provides the mathematical tool for studying noncompact quantum groups with Haar measures. I will concentrate on the *-algebra case and assume positivity of the invariant integral. Doing so, I create an algebraic framework that serves as a model for the operator algebra approach to quantum groups. Indeed, the theory of locally compact quantum groups can be seen as the topological version of the theory of quantum groups as they are developed here in a purely algebraic context.

Modeling back propagating action potential in weakly excitable dendrites of neocortical pyramidal cells.

Simultaneous recordings from the soma and apical dendrite of layer V neocortical pyramidal cells of young rats show that, for any location of current input, an evoked action potential (AP) always starts at the axon and then propagates actively, but decrementally, backward into the dendrites. This back-propagating AP is supported by a low density (-gNa = approximately 4 mS/cm2) of rapidly inactivating voltage-dependent Na+ channels in the soma and the apical dendrite. Investigation of detailed, biophysically constrained, models of reconstructed pyramidal cells shows the following. (i) The initiation of the AP first in the axon cannot be explained solely by morphological considerations; the axon must be more excitable than the soma and dendrites. (ii) The minimal Na+ channel density in the axon that fully accounts for the experimental results is about 20-times that of the soma. If -gNa in the axon hillock and initial segment is the same as in the soma [as recently suggested by Colbert and Johnston [Colbert, C. M. & Johnston, D. (1995) Soc. Neurosci. Abstr. 21, 684.2]], then -gNa in the more distal axonal regions is required to be about 40-times that of the soma. (iii) A backward propagating AP in weakly excitable dendrites can be modulated in a graded manner by background synaptic activity. The functional role of weakly excitable dendrites and a more excitable axon for forward synaptic integration and for backward, global, communication between the axon and the dendrites is discussed.

Turbulent diffusion phase transition is due to singular energy spectrum.

The phase transition for turbulent diffusion, reported by Avellaneda and Majda [Avellaneda, M. & Majda, A. J. (1994) Philos. Trans. R. Soc. London A 346, 205-233, and several earlier papers], is traced to a modeling assumption in which the energy spectrum of the turbulent fluid is singularly dependent on the viscosity in the inertial range. Phenomenological models of turbulence and intermittency, by contrast, require that the energy spectrum be independent of the viscosity in the inertial range. When the energy spectrum is assumed to be consistent with the phenomenological models, there is no phase transition for turbulent diffusion.