Estimation of parameters from time traces originating from an Ornstein-Uhlenbeck process

Statistical analysis of the autocorrelation function in fluorescence correlation spectroscopy

Fluorescence correlation spectroscopy (FCS) is a powerful method to measure concentration, mobility, and stoichiometry in solution and in living cells, but quantitative analysis of FCS data remains challenging due to the correlated noise in the autocorrelation function (ACF) of FCS. We demonstrate here that least-squares fitting of the conventional ACF is incompatible with the χ2 goodness-of-fit test and systematically underestimates the true fit parameter uncertainty. To overcome this challenge, a simple method to fit the ACF is introduced that allows proper calculation of goodness-of-fit statistics and that provides more tightly constrained parameter estimates than the conventional least-squares fitting method, achieving the theoretical minimum uncertainty. Because this method requires significantly more data than the standard method, we further introduce an approximate method that requires fewer data. We demonstrate both these new methods using experiments and simulations of diffusion. Finally, we apply our method to FCS data of the peripheral membrane protein HRas, which has a slow-diffusing membrane-bound population and a fast-diffusing cytoplasmic population. Despite the order-of-magnitude difference of the diffusion times, conventional FCS fails to reliably resolve the two species, whereas the new method identifies the correct model and provides robust estimates of the fit parameters for both species.

Autocorrelation function of finite-length data in fluorescence correlation spectroscopy

The experimental autocorrelation function of fluorescence correlation spectroscopy calculated from finite-length data is a biased estimator of the theoretical correlation function. This study presents a new theoretical framework that explicitly accounts for the data length to allow for unbiased analysis of experimental autocorrelation functions. To validate our theory, we applied it to experiments and simulations of diffusion and characterized the accuracy and precision of the resulting parameter estimates. Because measurements in living cells are often affected by instabilities of the fluorescence signal, autocorrelation functions are typically calculated on segmented data to improve their robustness. Our reformulated theory extends the range of usable segment times down to timescales approaching the diffusion time. This flexibility confers unique advantages for live-cell data that contain intensity variations and instabilities. We describe several applications of short segmentation to analyze data contaminated with unwanted fluctuations, drifts, or spikes in the intensity that are not suited for conventional fluorescence correlation analysis. These results demonstrate the potential of our theoretical framework to significantly expand the experimental systems accessible to fluorescence correlation spectroscopy.

A flexible Bayesian framework for unbiased estimation of timescales

Timescales characterize the pace of change for many dynamic processes in nature. Timescales are usually estimated by fitting the exponential decay of data autocorrelation in the time or frequency domain. Here we show that this standard procedure often fails to recover the correct timescales due to a statistical bias arising from the finite sample size. We develop an alternative approach which estimates timescales by fitting the sample autocorrelation or power spectrum with a generative model based on a mixture of Ornstein-Uhlenbeck (OU) processes using adaptive approximate Bayesian computations (aABC). Our method accounts for finite sample size and noise in data and returns a posterior distribution of timescales that quantifies the estimation uncertainty and can be used for model selection. We demonstrate the accuracy of our method on synthetic data and illustrate its application to recordings from primate cortex. We provide a customizable Python package implementing our framework with different generative models suitable for diverse applications.

Empirical Bayes method using surrounding pixel information for number and brightness analysis

Number and brightness (N&B) analysis is useful for monitoring the spatial distribution of the concentration and oligomeric state of fluorescently labeled proteins in cells. N&B analysis is based on the statistical analysis of fluorescence images by using the method of moments (MoM). Furthermore, N&B analysis can determine the particle number and particle brightness, which indicate the concentration and oligomeric state, respectively. However, the statistical accuracy and precision are limited in actual experiments with fluorescent proteins, owing to low excitation and the limited number of images. In this study, we applied maximum likelihood (ML) estimation and maximum a posteriori (MAP) estimation coupled with the empirical Bayes (EB) method (referred to as EB-MAP). In EB-MAP, we constructed a simple prior distribution for a pixel to utilize the information of the surrounding pixels. To evaluate the accuracy and precision of our method, we conducted simulations and experiments and compared the results of MoM, ML, and EB-MAP. The results showed that MoM estimated the particle number with many outliers. The outliers hampered the visibility of the spatial distribution and cellular structure. In contrast, EB-MAP suppressed the number of outliers and improved the visibility notably. The precision of EB-MAP was better by an order of magnitude in terms of particle number and 1.5 times better in terms of particle brightness compared with those of MoM. The proposed method (EB-MAP-N&B) is applicable to studies on fluorescence imaging and would aid in accurately recognizing changes in the concentration and oligomeric state in cells. Our results hold significant importance because quantifying the concentration and oligomeric state would contribute to the understanding of dynamic processes in molecular mechanism in cells.

Deep learning of the role of interleukin IL-17 and its action in promoting cancer

In breast cancer patients, metastasis remains a major cause of death. The metastasis formation process is given by an interaction between the cancer cells and the microenvironment that surrounds them. In this article, we develop a mathematical model that analyzes the role of interleukin IL-17 and its action in promoting cancer and in facilitating tissue metastasis in breast cancer, using a dynamic analysis based on a stochastic process that accounts for the local and global action of this molecule. The model uses the Ornstein–Uhlembeck and Markov process in continuous time. It focuses on the oncological expansion and the interaction between the interleukin IL-17 and cell populations This analysis tends to clarify the processes underlying the metastasis expansion mechanism both for a better understanding of the pathological event and for a possible better control of therapeutic strategies.

IL-17 is a proinflammatory interleukin that acts when there is tissue damage or when there is a pathological situation caused by an external pathogen or by a pathological condition such as cancer.

This research is focused on the role of interleukin IL-17 which, especially in the case of breast cancer, turns out to be a dominant “communication pin” since it interconnects with the activity of different cell populations affected by the oncological phenomenon. Stochastic modeling strategies, specially the Ornstein-Uhlenbeck process, with the aid of numerical algorithms are elaborated in this review.

The role of IL-17 is discussed in this manuscript at all the stages of cancer. It is discussed that IL-17 also acts as “metastasis promoter” as a result of its proinflammatory nature. The stochastic nature of IL-17 is discussed based on the evidence provided by recent literature.

The resulting dynamical analysis can help to select the most appropriate therapeutic strategy.

Cancer cells, in the case of breast cancer, have high level of IL-17 receptors (IL-17R); therefore the interleukin itself has direct effects on these cells. Immunotherapy research, focused on this cytokine and interlinked with the stochastic modeling, seems to be a promising avenue.

Making Sense of Computational Psychiatry

In psychiatry we often speak of constructing "models." Here we try to make sense of what such a claim might mean, starting with the most fundamental question: "What is (and isn't) a model?" We then discuss, in a concrete measurable sense, what it means for a model to be useful. In so doing, we first identify the added value that a computational model can provide in the context of accuracy and power. We then present limitations of standard statistical methods and provide suggestions for how we can expand the explanatory power of our analyses by reconceptualizing statistical models as dynamical systems. Finally, we address the problem of model building-suggesting ways in which computational psychiatry can escape the potential for cognitive biases imposed by classical hypothesis-driven research, exploiting deep systems-level information contained within neuroimaging data to advance our understanding of psychiatric neuroscience.