A versatile toolkit to produce sensitive FRET biosensors to visualize signaling in time and space

Genetically encoded, ratiometric biosensors based on fluorescence resonance energy transfer (FRET) are powerful tools to study the spatiotemporal dynamics of cell signaling. However, many biosensors lack sensitivity. We present a biosensor library that contains circularly permutated mutants for both the donor and acceptor fluorophores, which alter the orientation of the dipoles and thus better accommodate structural constraints imposed by different signaling molecules while maintaining FRET efficiency. Our strategy improved the brightness and dynamic range of preexisting RhoA and extracellular signal-regulated protein kinase (ERK) biosensors. Using the improved RhoA biosensor, we found micrometer-sized zones of RhoA activity at the tip of F-actin bundles in growth cone filopodia during neurite extension, whereas RhoA was globally activated throughout collapsing growth cones. RhoA was also activated in filopodia and protruding membranes at the leading edge of motile fibroblasts. Using the improved ERK biosensor, we simultaneously measured ERK activation dynamics in multiple cells using low-magnification microscopy and performed in vivo FRET imaging in zebrafish. Thus, we provide a construction toolkit consisting of a vector set, which enables facile generation of sensitive biosensors.

Vector spaces of entire functions of unbounded type

Let E be an infinite dimensional complex Banach space. We prove the existence of an infinitely generated algebra, an infinite dimensional closed subspace and a dense subspace of entire functions on E whose non-zero elements are functions of unbounded type. We also show that the τδ topology on the space of all holomorphic functions cannot be obtained as a countable inductive limit of Fr´echet spaces. RESUMEN. Sea E un espacio de Banach complejo de dimensión infinita y sea H(E) el espacio de funciones holomorfas definidas en E. En el artículo se demuestra la existencia de un álgebra infinitamente generada en H(E), un subespacio vectorial en H(E) cerrado de dimensión infinita y un subespacio denso en H(E) cuyos elementos no nulos son funciones de tipo no acotado. También se demuestra que el espacio de funciones holomorfas con la topología ? no es un límite inductivo numberable de espacios de Fréchet.

A method for revealing phase space structures of general time dependent dynamical systems

In this paper we develop new techniques for revealing geometrical structures in phase space that are valid for aperiodically time dependent dynamical systems, which we refer to as Lagrangian descriptors. These quantities are based on the integration, for a finite time, along trajectories of an intrinsic bounded, positive geometrical and/or physical property of the trajectory itself. We discuss a general methodology for constructing Lagrangian descriptors, and we discuss a “heuristic argument” that explains why this method is successful for revealing geometrical structures in the phase space of a dynamical system. We support this argument by explicit calculations on a benchmark problem having a hyperbolic fixed point with stable and unstable manifolds that are known analytically. Several other benchmark examples are considered that allow us the assess the performance of Lagrangian descriptors in revealing invariant tori and regions of shear. Throughout the paper “side-by-side” comparisons of the performance of Lagrangian descriptors with both finite time Lyapunov exponents (FTLEs) and finite time averages of certain components of the vector field (“time averages”) are carried out and discussed. In all cases Lagrangian descriptors are shown to be both more accurate and computationally efficient than these methods. We also perform computations for an explicitly three dimensional, aperiodically time-dependent vector field and an aperiodically time dependent vector field defined as a data set. Comparisons with FTLEs and time averages for these examples are also carried out, with similar conclusions as for the benchmark examples.

Lagrangian descriptors: a method for revealing phase space structures of general time dependent dynamical systems

Lagrangian descriptors are a recent technique which reveals geometrical structures in phase space and which are valid for aperiodically time dependent dynamical systems. We discuss a general methodology for constructing them and we discuss a "heuristic argument" that explains why this method is successful. We support this argument by explicit calculations on a benchmark problem. Several other benchmark examples are considered that allow us to assess the performance of Lagrangian descriptors with both finite time Lyapunov exponents (FTLEs) and finite time averages of certain components of the vector field ("time averages"). In all cases Lagrangian descriptors are shown to be both more accurate and computationally efficient than these methods.

Stable and efficient gene transfer into the retina using an HIV-based lentiviral vector

The development of methods for efficient gene transfer to terminally differentiated retinal cells is important to study the function of the retina as well as for gene therapy of retinal diseases. We have developed a lentiviral vector system based on the HIV that can transduce terminally differentiated neurons of the brain in vivo. In this study, we have evaluated the ability of HIV vectors to transfer genes into retinal cells. An HIV vector containing a gene encoding the green fluorescent protein (GFP) was injected into the subretinal space of rat eyes. The GFP gene under the control of the cytomegalovirus promoter was efficiently expressed in both photoreceptor cells and retinal pigment epithelium. However, the use of the rhodopsin promoter resulted in expression predominantly in photoreceptor cells. Most successfully transduced eyes showed that photoreceptor cells in >80% of the area of whole retina expressed the GFP. The GFP expression persisted for at least 12 weeks with no apparent decrease. The efficient gene transfer into photoreceptor cells by HIV vectors will be useful for gene therapy of retinal diseases such as retinitis pigmentosa.

Electrical microstimulation suggests two different forms of representation of head-centered space in the intraparietal sulcus of rhesus monkeys.

We examined the effects of eye position on saccades evoked by electrical stimulation of the intraparietal sulcus (IPS) of rhesus monkeys. Microstimulation evoked saccades from sites on the posterior bank, floor, and the medial bank of the IPS. The size and direction of the eye movements varied as a function of initial eye position before microstimulation. At many stimulation sites, eye position affected primarily the amplitude and not the direction of the evoked saccades. These "modified vector saccades" were characteristic of most stimulation-sensitive zones in the IPS, with the exception of a narrow strip located mainly on the floor of the sulcus. Stimulation in this "intercalated zone" evoked saccades that moved the eyes into a particular region in head-centered space, independent of the starting position of the eyes. This latter response is compatible with the stimulation site representing a goal zone in head-centered coordinates. On the other hand, the modified vector saccades observed outside the intercalated zone are indicative of a more distributed representation of head-centered space. A convergent projection from many modified vector sites onto each intercalated site may be a basis for a transition from a distributed to a more explicit representation of space in head-centered coordinates.

Methods of Visualization and Analysis of Cardiac Depolarization in the Three Dimensional Space

Research analysis of electrocardiograms (ECG) today is carried out mostly using time depending signals of different leads shown in the graphs. Definition of ECG parameters is performed by qualified personnel, and requiring particular skills. To support decoding the cardiac depolarization phase of ECG there are methods to analyze space-time convolution charts in three dimensions where the heartbeat is described by the trajectory of its electrical vector. Based on this, it can be assumed that all available options of the classical ECG analysis of this time segment can be obtained using this technique. Investigated ECG visualization techniques in three dimensions combined with quantitative methods giving additional features of cardiac depolarization and allow a better exploitation of the information content of the given ECG signals.

Measurements of solar vector magnetic fields : proceedings of the MSFC workshop /

Includes bibliographies.

Solid rocket thrust vector control.

Cover title.

A first course in Hilbert space.

"These notes summarize a course in Hilbert space, offered at the State University of Iowa in the Fall semester of 1957."

Tracking the states of a nonlinear and nonstationary system in the weight-space of artificial neural networks

We propose a novel interpretation and usage of Neural Network (NN) in modeling physiological signals, which are allowed to be nonlinear and/or nonstationary. The method consists of training a NN for the k-step prediction of a physiological signal, and then examining the connection-weight-space (CWS) of the NN to extract information about the signal generator mechanism. We de. ne a novel feature, Normalized Vector Separation (gamma(ij)), to measure the separation of two arbitrary states i and j in the CWS and use it to track the state changes of the generating system. The performance of the method is examined via synthetic signals and clinical EEG. Synthetic data indicates that gamma(ij) can track the system down to a SNR of 3.5 dB. Clinical data obtained from three patients undergoing carotid endarterectomy of the brain showed that EEG could be modeled (within a root-means-squared-error of 0.01) by the proposed method, and the blood perfusion state of the brain could be monitored via gamma(ij), with small NNs having no more than 21 connection weight altogether.

Improving support vector solutions by selecting a sequence of training subsets

In this paper we demonstrate that it is possible to gradually improve the performance of support vector machine (SVM) classifiers by using a genetic algorithm to select a sequence of training subsets from the available data. Performance improvement is possible because the SVM solution generally lies some distance away from the Bayes optimal in the space of learning parameters. We illustrate performance improvements on a number of benchmark data sets.

Statistical mechanics of support vector networks

Using methods of Statistical Physics, we investigate the generalization performance of support vector machines (SVMs), which have been recently introduced as a general alternative to neural networks. For nonlinear classification rules, the generalization error saturates on a plateau, when the number of examples is too small to properly estimate the coefficients of the nonlinear part. When trained on simple rules, we find that SVMs overfit only weakly. The performance of SVMs is strongly enhanced, when the distribution of the inputs has a gap in feature space.

Decomposition of Banach Space into a Direct Sum of Separable and Reflexive Subspaces and Borel Maps

* This paper was supported in part by the Bulgarian Ministry of Education, Science and Technologies under contract MM-506/95.

PC Points and their Application to Vector Optimization

AMS subject classification: 90C29, 90C48