Traction force microscopy with optimized regularization and automated Bayesian parameter selection for comparing cells

Adherent cells exert traction forces on to their environment, which allows them to migrate, to maintain tissue integrity, and to form complex multicellular structures. This traction can be measured in a perturbation-free manner with traction force microscopy (TFM). In TFM, traction is usually calculated via the solution of a linear system, which is complicated by undersampled input data, acquisition noise, and large condition numbers for some methods. Therefore, standard TFM algorithms either employ data filtering or regularization. However, these approaches require a manual selection of filter- or regularization parameters and consequently exhibit a substantial degree of subjectiveness. This shortcoming is particularly serious when cells in different conditions are to be compared because optimal noise suppression needs to be adapted for every situation, which invariably results in systematic errors. Here, we systematically test the performance of new methods from computer vision and Bayesian inference for solving the inverse problem in TFM. We compare two classical schemes, L1- and L2-regularization, with three previously untested schemes, namely Elastic Net regularization, Proximal Gradient Lasso, and Proximal Gradient Elastic Net. Overall, we find that Elastic Net regularization, which combines L1 and L2 regularization, outperforms all other methods with regard to accuracy of traction reconstruction. Next, we develop two methods, Bayesian L2 regularization and Advanced Bayesian L2 regularization, for automatic, optimal L2 regularization. Using artificial data and experimental data, we show that these methods enable robust reconstruction of traction without requiring a difficult selection of regularization parameters specifically for each data set. Thus, Bayesian methods can mitigate the considerable uncertainty inherent in comparing cellular traction forces

Development of a versatile laser light scattering instrument

A versatile laser light scattering (LLS) instrument is developed for use in microgravity to measure microscopic particles of 30 A to above 3 microns. Since it is an optical technique, LLS does not affect the sample being studied. A LLS instrument built from modules allows several configurations, each optimized for a particular experiment. The multiangle LLS instrument can be mounted in the rack in the Space Shuttle and on Space Station Freedom. It is possible that a Space Shuttle glove-box and a lap-top computer containing a correlator card can be used to perform a number of experiments and to demonstrate the technology needed for more elaborate investigations. This offers simple means of flying a great number of experiments without the additional requirements of full-scale flight hardware experiments

Empirical Bayesian significance measure of neuronal spike response

Background: Functional connectivity analyses of multiple neurons provide a powerful bottom-up approach to reveal functions of local neuronal circuits by using simultaneous recording of neuronal activity. A statistical methodology, generalized linear modeling (GLM) of the spike response function, is one of the most promising methodologies to reduce false link discoveries arising from pseudo-correlation based on common inputs. Although recent advancement of fluorescent imaging techniques has increased the number of simultaneously recoded neurons up to the hundreds or thousands, the amount of information per pair of neurons has not correspondingly increased, partly because of the instruments' limitations, and partly because the number of neuron pairs increase in a quadratic manner. Consequently, the estimation of GLM suffers from large statistical uncertainty caused by the shortage in effective information. Results: In this study, we propose a new combination of GLM and empirical Bayesian testing for the estimation of spike response functions that enables both conservative false discovery control and powerful functional connectivity detection. We compared our proposed method's performance with those of sparse estimation of GLM and classical Granger causality testing. Our method achieved high detection performance of functional connectivity with conservative estimation of false discovery rate and q values in case of information shortage due to short observation time. We also showed that empirical Bayesian testing on arbitrary statistics in place of likelihood-ratio statistics reduce the computational cost without decreasing the detection performance. When our proposed method was applied to a functional multi-neuron calcium imaging dataset from the rat hippocampal region, we found significant functional connections that are possibly mediated by AMPA and NMDA receptors. Conclusions: The proposed empirical Bayesian testing framework with GLM is promising especially when the amount of information per a neuron pair is small because of growing size of observed network