Theoretical connections between mathematical neuronal models corresponding to different expressions of noise. (7th October 2016)

• Record Type: Journal Article
• Authors: Dumont, Grégory; Henry, Jacques; Tarniceriu, Carmen Oana
• Is Part Of: Journal of theoretical biology. Volume 406(2016)
• Page Start: 31
• Page End: 41
• Publication Date: 2016-10-07
• Subjects: Neural noise -- Noisy Leaky Integrate-and-Fire model -- Escape rate -- Fokker–Planck equation -- Age structured model; Biology -- Periodicals; Biological Science Disciplines -- Periodicals; Biology -- Periodicals; Biologie -- Périodiques; Theoretische biologie; Biology; Periodicals; 571.05
• DOI: 10.1016/j.jtbi.2016.06.022
• Languages: English
• ISSNs: 0022-5193

Abstract

Abstract: Identifying the right tools to express the stochastic aspects of neural activity has proven to be one of the biggest challenges in computational neuroscience. Even if there is no definitive answer to this issue, the most common procedure to express this randomness is the use of stochastic models. In accordance with the origin of variability, the sources of randomness are classified as intrinsic or extrinsic and give rise to distinct mathematical frameworks to track down the dynamics of the cell. While the external variability is generally treated by the use of a Wiener process in models such as the Integrate-and-Fire model, the internal variability is mostly expressed via a random firing process. In this paper, we investigate how those distinct expressions of variability can be related. To do so, we examine the probability density functions to the corresponding stochastic models and investigate in what way they can be mapped one to another via integral transforms. Our theoretical findings offer a new insight view into the particular categories of variability and it confirms that, despite their contrasting nature, the mathematical formalization of internal and external variability is strikingly similar. Abstract : Highlights: Analytical connections between noisy leaky integrate and fire and escape rate models. The two models express different ways of noise implementation in neuronal models. The connections are made via integral transforms. Our results explain the similarity of the statistical activity of the two models.