A Markovian Entropy Measure for the Analysis of Calcium Activity Time Series
Abstract
Methods to analyze the dynamics of calcium activity often rely on visually distinguishable features in time series data such as spikes, waves, or oscillations. However, systems such as the developing nervous system display a complex, irregular type of calcium activity which makes the use of such methods less appropriate. Instead, for such systems there exists a class of methods (including information theoretic, power spectral, and fractal analysis approaches) which use more fundamental properties of the time series to analyze the observed calcium dynamics. We present a new analysis method in this class, the Markovian Entropy measure, which is an easily implementable calcium time series analysis method which represents the observed calcium activity as a realization of a Markov Process and describes its dynamics in terms of the level of predictability underlying the transitions between the states of the process. We applied our and other commonly used calcium analysis methods on a dataset from Xenopus laevis neural progenitors which displays irregular calcium activity and a dataset from murine synaptic neurons which displays activity time series that are well-described by visually-distinguishable features. We find that the Markovian Entropy measure is able to distinguish between biologically distinct populations in both datasets, and that it can separate biologically distinct populations to a greater extent than other methods in the dataset exhibiting irregular calcium activity. These results support the benefit of using the Markovian Entropy measure to analyze calcium dynamics, particularly for studies using time series data which do not exhibit easily distinguishable features.
Additional Information
© 2016 Marken et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Received: July 19, 2016; Accepted: November 29, 2016; Published: December 15, 2016. Data Availability: All relevant data are within the paper and its Supporting Information files or deposited at https://github.com/jpmarken/markovian-entropy-calcium. This study was supported by National Institutes of Health grants R15NS067566 and 1R15HD077624-01 to MS, National Science Foundation grant 1257895 to MS, Howard Hughes Medical Institute grant 52006919 to the College of William and Mary, Arnold and Mabel Beckman Foundation Beckman Scholar Award to AH. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Author Contributions: Conceptualization: MSS JPM ADH PK. Data curation: JPM ADH MCL CAG. Formal analysis: JPM ADH AR PK MCL CAG. Funding acquisition: MSS. Investigation: LO. Methodology: MSS PK JPM ADH AR. Project administration: MSS PK. Resources: MSS. Software: JPM ADH AR PK. Supervision: MSS PK. Validation: MSS JPM ADH. Visualization: CAG. Writing – original draft: JPM ADH. Writing – review & editing: JPM ADH PK MSS. The authors have declared that no competing interests exist.Attached Files
Published - journal.pone.0168342.pdf
Supplemental Material - S1Fig.tif
Supplemental Material - journal.pone.0168342.s002.tif
Supplemental Material - journal.pone.0168342.s003.tif
Supplemental Material - journal.pone.0168342.s004.tif
Supplemental Material - journal.pone.0168342.s005.tif
Supplemental Material - journal.pone.0168342.s006.xlsx
Supplemental Material - journal.pone.0168342.s007.xlsx
Supplemental Material - journal.pone.0168342.s008.pdf
Supplemental Material - journal.pone.0168342.s009.pdf
Supplemental Material - journal.pone.0168342.s010.pdf
Supplemental Material - journal.pone.0168342.s011.pdf
Supplemental Material - journal.pone.0168342.s012.pdf
Supplemental Material - journal.pone.0168342.s013.pdf
Supplemental Material - journal.pone.0168342.s014.pdf
Supplemental Material - journal.pone.0168342.s015.pdf
Files
Name | Size | Download all |
---|---|---|
md5:a1c2f2c7c67b2371ed7afec96748d423
|
52.7 MB | Preview Download |
md5:86ffa3d86c2ac38066fecfd54d922e70
|
64.3 MB | Preview Download |
md5:443843b5587ede5e245ee12fab9dd623
|
124.2 kB | Preview Download |
md5:1f6971d4c3c0e862a524759b9d10b55d
|
158.5 kB | Preview Download |
md5:ca24d05edb5cf2d045afbebe781614bc
|
18.2 MB | Preview Download |
md5:edd5a335823214c1687e0d0041cd5eb8
|
74.0 kB | Preview Download |
md5:3f8215eaac70a85ab90028e71f4c94f7
|
8.5 MB | Preview Download |
md5:0eb08e8b472466e335fdd9177114c9bb
|
18.3 MB | Preview Download |
md5:245b1c10f67f5e439e0c905720b5323e
|
36.4 kB | Download |
md5:f7aa2d0dfcc8c84f1bbcadd47cc4ada1
|
5.2 MB | Preview Download |
md5:665c7eba58e40b8443a81a29a3f3453e
|
50.9 kB | Download |
md5:bd9ac4bab60b99ef2458a177d2ea98e6
|
64.3 MB | Preview Download |
md5:53c8958382221acb7d993c0363cf07c6
|
52.6 MB | Preview Download |
md5:732484b9db38613059a6038e79b909a6
|
604.1 kB | Preview Download |
md5:b9d82ecbde509502b7d79d0ed2813d35
|
1.7 MB | Preview Download |
md5:4e9acfc2ec7796582424e7d7ca6c3484
|
690.6 kB | Preview Download |
Additional details
- PMCID
- PMC5158058
- Eprint ID
- 73764
- Resolver ID
- CaltechAUTHORS:20170126-160544721
- R15NS067566
- NIH
- 1R15HD077624-01
- NIH
- IOS-1257895
- NSF
- 52006919
- Howard Hughes Medical Institute (HHMI)
- Arnold and Mabel Beckman Foundation
- Created
-
2017-01-27Created from EPrint's datestamp field
- Updated
-
2021-11-11Created from EPrint's last_modified field