David W. Tank

Neural computation of decisions in optimization problems

Highly-interconnected networks of nonlinear analog neurons are shown to be extremely effective in computing. The networks can rapidly provide a collectively-computed solution (a digital output) to a problem on the basis of analog input information. The problems to be solved must be formulated in terms of desired optima, often subject to constraints. The general principles involved in constructing networks to solve specific problems are discussed. Results of computer simulations of a network designed to solve a difficult but well-defined optimization problem-the Traveling-Salesman Problem-are presented and used to illustrate the computational power of the networks. Good solutions to this problem are collectively computed within an elapsed time of only a few neural time constants. The effectiveness of the computation involves both the nonlinear analog response of the neurons and the large connectivity among them. Dedicated networks of biological or microelectronic neurons could provide the computational capabilities described for a wide class of problems having combinatorial complexity. The power and speed naturally displayed by such collective networks may contribute to the effectiveness of biological information processing.

Functional brain mapping by blood oxygenation level-dependent contrast magnetic resonance imaging. A comparison of signal characteristics with a biophysical model.

It recently has been demonstrated that magnetic resonance imaging can be used to map changes in brain hemodynamics produced by human mental operations. One method under development relies on blood oxygenation level-dependent (BOLD) contrast: a change in the signal strength of brain water protons produced by the paramagnetic effects of venous blood deoxyhemoglobin. Here we discuss the basic quantitative features of the observed BOLD-based signal changes, including the signal amplitude and its magnetic field dependence and dynamic effects such as a pronounced oscillatory pattern that is induced in the signal from primary visual cortex during photic stimulation experiments. The observed features are compared with the results of Monte Carlo simulations of water proton intravoxel phase dispersion produced by local field gradients generated by paramagnetic deoxyhemoglobin in nearby venous blood vessels. The simulations suggest that the effect of water molecule diffusion is strong for the case of blood capillaries, but, for larger venous blood vessels, water diffusion is not an important determinant of deoxyhemoglobin-induced signal dephasing. We provide an expression for the apparent in-plane relaxation rate constant (R2*) in terms of the main magnetic field strength, the degree of the oxygenation of the venous blood, the venous blood volume fraction in the tissue, and the size of the blood vessel.

Imaging Large-Scale Neural Activity with Cellular Resolution in Awake, Mobile Mice

We report a technique for two-photon fluorescence imaging with cellular resolution in awake, behaving mice with minimal motion artifact. The apparatus combines an upright, table-mounted two-photon microscope with a spherical treadmill consisting of a large, air-supported Styrofoam ball. Mice, with implanted cranial windows, are head restrained under the objective while their limbs rest on the balls upper surface. Following adaptation to head restraint, mice maneuver on the spherical treadmill as their heads remain motionless. Image sequences demonstrate that running-associated brain motion is limited to approximately 2-5 microm. In addition, motion is predominantly in the focal plane, with little out-of-plane motion, making the application of a custom-designed Hidden-Markov-Model-based motion correction algorithm useful for postprocessing. Behaviorally correlated calcium transients from large neuronal and astrocytic populations were routinely measured, with an estimated motion-induced false positive error rate of <5%.

Intracellular dynamics of hippocampal place cells during virtual navigation

Hippocampal place cells encode spatial information in rate and temporal codes. To examine the mechanisms underlying hippocampal coding, here we measured the intracellular dynamics of place cells by combining in vivo whole-cell recordings with a virtual-reality system. Head-restrained mice, running on a spherical treadmill, interacted with a computer-generated visual environment to perform spatial behaviours. Robust place-cell activity was present during movement along a virtual linear track. From whole-cell recordings, we identified three subthreshold signatures of place fields: an asymmetric ramp-like depolarization of the baseline membrane potential, an increase in the amplitude of intracellular theta oscillations, and a phase precession of the intracellular theta oscillation relative to the extracellularly recorded theta rhythm. These intracellular dynamics underlie the primary features of place-cell rate and temporal codes. The virtual-reality system developed here will enable new experimental approaches to study the neural circuits underlying navigation.

A miniature head-mounted two-photon microscope. high-resolution brain imaging in freely moving animals.

Two-photon microscopy has enabled anatomical and functional fluorescence imaging in the intact brain of rats. Here, we extend two-photon imaging from anesthetized, head-stabilized to awake, freely moving animals by using a miniaturized head-mounted microscope. Excitation light is conducted to the microscope in a single-mode optical fiber, and images are scanned using vibrations of the fiber tip. Microscope performance was first characterized in the neocortex of anesthetized rats. We readily obtained images of vasculature filled with fluorescently labeled blood and of layer 2/3 pyramidal neurons filled with a calcium indicator. Capillary blood flow and dendritic calcium transients were measured with high time resolution using line scans. In awake, freely moving rats, stable imaging was possible except during sudden head movements.

Probing the limits to positional information.

The reproducibility and precision of biological patterning is limited by the accuracy with which concentration profiles of morphogen molecules can be established and read out by their targets. We consider four measures of precision for the Bicoid morphogen in the Drosophila embryo: the concentration differences that distinguish neighboring cells, the limits set by the random arrival of Bicoid molecules at their targets (which depends on absolute concentration), the noise in readout of Bicoid by the activation of Hunchback, and the reproducibility of Bicoid concentration at corresponding positions in multiple embryos. We show, through a combination of different experiments, that all of these quantities are approximately 10%. This agreement among different measures of accuracy indicates that the embryo is not faced with noisy input signals and readout mechanisms; rather, the system exerts precise control over absolute concentrations and responds reliably to small concentration differences, approaching the limits set by basic physical principles.

Direct Measurement of Coupling Between Dendritic Spines and Shafts

Characterization of the diffusional and electrotonic coupling of spines to the dendritic shaft is crucial to understanding neuronal integration and synaptic plasticity. Two-photon photobleaching and photorelease of fluorescein dextran were used to generate concentration gradients between spines and shafts in rat CA1 pyramidal neurons. Diffusional reequilibration was monitored with two-photon fluorescence imaging. The time course of reequilibration was exponential, with time constants in the range of 20 to 100 milliseconds, demonstrating chemical compartmentalization on such time scales. These values imply that electrical spine neck resistances are unlikely to exceed 150 megohms and more likely range from 4 to 50 megohms.

Dendritic Integration in Mammalian Neurons, a Century after Cajal

We thank A. Borst, B. W. Connors, T. Freund, S. J. Redman, W. N. Ross, T. J. Sejnowski, and R. D. Traub for sharing their results before publication, A. Borst, S. Cash, B. W. Connors, W. Denk, S. R. Golob, R. Llinas, W. Regehr, P. A. Rhodes, I. Segev, and K. Svoboda for helpful comments, and A. Gelperin, J. Lichtman, Z. Mainem, V. Murthy, G. M. Shepherd, L. Trussell, and R. O. L. Wong for their help. R. Y. was supported by the Office of Naval Research.

Functional imaging of hippocampal place cells at cellular resolution during virtual navigation

Spatial navigation is often used as a behavioral task in studies of the neuronal circuits that underlie cognition, learning and memory in rodents. The combination of in vivo microscopy with genetically encoded indicators has provided an important new tool for studying neuronal circuits, but has been technically difficult to apply during navigation. Here we describe methods for imaging the activity of neurons in the CA1 region of the hippocampus with subcellular resolution in behaving mice. Neurons that expressed the genetically encoded calcium indicator GCaMP3 were imaged through a chronic hippocampal window. Head-restrained mice performed spatial behaviors in a setup combining a virtual reality system and a custom-built two-photon microscope. We optically identified populations of place cells and determined the correlation between the location of their place fields in the virtual environment and their anatomical location in the local circuit. The combination of virtual reality and high-resolution functional imaging should allow a new generation of studies to investigate neuronal circuit dynamics during behavior.

Stability and Nuclear Dynamics of the Bicoid Morphogen Gradient

Patterning in multicellular organisms results from spatial gradients in morphogen concentration, but the dynamics of these gradients remain largely unexplored. We characterize, through in vivo optical imaging, the development and stability of the Bicoid morphogen gradient in Drosophila embryos that express a Bicoid-eGFP fusion protein. The gradient is established rapidly (approximately 1 hr after fertilization), with nuclear Bicoid concentration rising and falling during mitosis. Interphase levels result from a rapid equilibrium between Bicoid uptake and removal. Initial interphase concentration in nuclei in successive cycles is constant (+/-10%), demonstrating a form of gradient stability, but it subsequently decays by approximately 30%. Both direct photobleaching measurements and indirect estimates of Bicoid-eGFP diffusion constants (D < or = 1 microm(2)/s) provide a consistent picture of Bicoid transport on short ( approximately min) time scales but challenge traditional models of long-range gradient formation. A new model is presented emphasizing the possible role of nuclear dynamics in shaping and scaling the gradient.