László Hatvani

A New Quantitative Film Autoradiographic Method of Quantifying mRNA Transcripts for In Situ Hybridization

We developed and tested a novel quantitative method for the quantification of film autoradiographs, involving a mathematical model and a dot-blot-based membrane standard scale. The exponential model introduced here, ROD = p 1(1 - exp[p 2 x]), appropriately (r 2<0.999), describes the relation between relative optical density (ROD) and radioactivity (x) in the range between 0 and 240 gray scale values (using a 256-gray scale level digitizer). By means of this model, standard curves with distinct quenching properties can be exactly interconverted, permitting the tissue-equivalent calibration of different standard scales. The membrane standard scale employed here has several advantages, including the flexible radioactivity range, the facile and rapid preparation technique, and the compact size. The feasibility of the quantification procedure is exemplified by the comparative quantification of multiple calmodulin mRNAs in the rat brain by in situ hybridization with [35S]-cRNA probes. The procedure for quantification provides a significant improvement in that the direct and exact comparison of radiolabeled species, even from different experiments, can be reliably performed. Further, the procedure can be adapted to the quantification of autoradiographs produced by other methods.

Methods for quantification of in situ hybridization signals obtained by film autoradiography and phosphorimaging applied for estimation of regional levels of calmodulin mRNA classes in the rat brain

Comparative analysis of the regional abundances of the various mRNAs in neural tissues requires the quantitation of target nucleic acid sequences while their tissue distribution is preserved. A quantitative in situ hybridization protocol is presented for the assessment of regional levels of calmodulin (CaM) I, II and III mRNAs in the rat brain. Coronal brain cryostat sections were hybridized with multiple CaM [35S]cRNA probes and co-exposed to an autoradiographic film or storage phosphor screen, together with a membrane-based radioactive standard scale. The membrane scale was calibrated against a brain paste standard scale. Regression analyses of the sensitometric graphs of standard scales corresponding to the autoradiographic film and to the storage phosphor screen were performed by means of exponential (ROD=p(1)(1-exp[-p(2)x])) and linear (LI=ax) functions, respectively (ROD is relative optical density, LI is labeling intensity, and x is radioactivity). The ROD/LI values for the hybridized brain regions were converted into cRNA probe copy numbers (estimations of mRNA copy numbers) through use of the above standard scales. This method was applied to compare the regional abundances of multiple CaM mRNAs in the brains of control, dehydrated, chronic ethanol-treated and ethanol withdrawal-treated animals.

On the asymptotic stability for nonautonomous functional differential equations by Lyapunov functionals

Sufficient conditions are given for the asymptotic stability and uniform asymptotic stability of the zero solution of the nonautonomous FDEs whose right-hand sides can be unbounded functions of the time. The theorems are based upon Lyapunov-Krasovskii functionals whose derivatives with respect to the equations are negative semidefinite and can vanish at long intervals. The functionals and their derivatives are estimated by either x(t), the norm of the instantaneous value of the solutions or ∥x t ∥ 2 , the L 2 -norm of the phase segment of the solutions. Examples are given to show that the conditions are sharp, and the main theorems with the two different types of estimates are independent and improve earlier results. The theorems are applied to linear and nonlinear retarded FDEs with one delay and with distributed delays.

On partial asymptotic stability by the method of limiting equation

SummaryThe extensions of the Barbashin-Krasovskij theorem to the partial asymptotic stability of the zero solution of a differential system require the boundedness of the uncontrolled coordinates along the solutions. In this paper the Barbashin-Krasovskij method is generalized without supposing «a priori» knowledges on the solutions. At the same time, the results extend one of C. Risitos theorem to nonautonomous differential equations. As an application, stability properties of the equilibrium state of nonholonomic dissipative mechanical systems are studied.

Stability problems for the mathematical pendulum

AbstractThe first part of this review paper is devoted to the simple (undamped, unforced) pendulum with a varying coefficient. If the coefficient is a step function, then small oscillations are described by the equation

Lyapunov functions of the mechanical energy type

\ddot x + a^2 (t)x = 0,a(t): = a_k ift_{k - 1} \leqslant t < t_k ,k = 1,2,....

Stability theorems for nonautonomous functional-differential equations by Liapunov functionals

Using a probability approach, we assume that (ak)k=1∞ is given, and {tk}k=1∞ is chosen at random so that tk − tk−1 are independent random variables. The first problem is to guarantee that all solutions tend to zero, as t → ∞, provided that ak ↗ ∞ (k → ∞). In the problem of swinging the coefficient a2 takes only two different values alternating each others, and tk − tk−1 are identically distributed. One has to find the distributions and their critical expected values such that the amplitudes of the oscillations tend to ∞ in some (probabilistic) sense. In the second part we deal with the damped forced pendulum equation