title: 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.
authors.affiliation: Department of Mathematics, College of William and Mary, Williamsburg, Virginia, United States of America.
authors.forename: John P
authors.initials: JP
authors.lastname: Marken
authors.affiliation: Department of Mathematics, College of William and Mary, Williamsburg, Virginia, United States of America.|Department of Biology, College of William and Mary, Williamsburg, Virginia, United States of America.
authors.forename: Andrew D
authors.identifier: http://orcid.org/0000-0001-8720-1451
authors.initials: AD
authors.lastname: Halleran
authors.affiliation: Department of Computer Science, College of William and Mary, Williamsburg, Virginia, United States of America.
authors.forename: Atiqur
authors.initials: A
authors.lastname: Rahman
authors.affiliation: Department of Biology, College of William and Mary, Williamsburg, Virginia, United States of America.
authors.forename: Laura
authors.initials: L
authors.lastname: Odorizzi
authors.affiliation: Department of Mathematics, College of William and Mary, Williamsburg, Virginia, United States of America.|Department of Biology, College of William and Mary, Williamsburg, Virginia, United States of America.
authors.forename: Michael C
authors.initials: MC
authors.lastname: LeFew
authors.affiliation: Department of Mathematics, College of William and Mary, Williamsburg, Virginia, United States of America.|Department of Biology, College of William and Mary, Williamsburg, Virginia, United States of America.
authors.forename: Caroline A
authors.initials: CA
authors.lastname: Golino
authors.affiliation: Department of Computer Science, College of William and Mary, Williamsburg, Virginia, United States of America.
authors.forename: Peter
authors.initials: P
authors.lastname: Kemper
authors.affiliation: Department of Biology, College of William and Mary, Williamsburg, Virginia, United States of America.
authors.forename: Margaret S
authors.initials: MS
authors.lastname: Saha
mesh_terms: D000818:Animals; D002118:Calcium / Q000378:metabolism*; D020013:Calcium Signaling / Q000502:physiology; D004625:Embryo, Nonmammalian; D019277:Entropy; D008390:Markov Chains; D008954:Models, Biological; D054258:Neural Plate / Q000196:embryology / Q000378:metabolism; D009474:Neurons / Q000502:physiology; D013997:Time Factors; D014982:Xenopus laevis / Q000196:embryology
chemical_list: D002118:Calcium