Biological systems manifest continuous weak autoluminescence, which is present even in the absence of external stimuli. Since this autoluminescence arises from internal metabolic and physiological processes, several works suggested that it could carry information in the time series of the detected photon counts. However, there is little experimental work which would show any difference of this signal from random Poisson noise and some works were prone to artifacts due to lacking or improper reference signals. Here we apply rigorous statistical methods and advanced reference signals to test the hypothesis whether time series of autoluminescence from germinating mung beans display any intrinsic correlations. Utilizing the fractional Brownian bridge that employs short samples of time series in the method kernel, we suggest that the detected autoluminescence signal from mung beans is not totally random, but it seems to involve a process with a negative memory. Our results contribute to the development of the rigorous methodology of signal analysis of photonic biosignals.

Czech Technical University Faculty of Nuclear Sciences and Physical Engineering Trojanova 12 Praha Czechia

Department of Circuit Theory of the Faculty of Electrical Engineering at Czech Technical University Prague Technická 2 Praha 6 Czechia

Institute of Photonics and Electronics of the Czech Academy of Sciences Chaberská 57 Praha 8 Czechia

Zobrazit více v PubMed

Kucera O, Cervinkova K, Nerudova M, Cifra M. Spectral perspective on the electromagnetic activity of cells. Current topics in medicinal chemistry. 2015;15(6):513–522. 10.2174/1568026615666150225103105 PubMed DOI

Tilbury R, Quickenden T. Luminescence from the yeast Candida utilis and comparisons across three genera. Luminescence. 1992;7(4):245–253. PubMed

Quickenden TI, Tilbury RN. Luminescence spectra of exponential and stationary phase cultures of respiratory deficient Saccharomyces cerevisiae. Journal of Photochemistry and Photobiology B: Biology. 1991;8(2):169–174. 10.1016/1011-1344(91)80055-M PubMed DOI

Vogel R, Guo X, Süssmuth R. Chemiluminescence patterns from bacterial cultures undergoing bacteriophage induced mass lysis. Bioelectrochemistry and Bioenergetics. 1998;46(1):59–64.

Vogel R, Süssmuth R. Weak light emission patterns from lactic acid bacteria. Luminescence. 1999;14(2):99–105. 10.1002/(SICI)1522-7243(199903/04)14:2<99::AID-BIO519>3.0.CO;2-7 PubMed DOI

Burgos RCR, Červinková K, van der Laan T, Ramautar R, van Wijk EPA, Cifra M, et al. Tracking biochemical changes correlated with ultra-weak photon emission using metabolomics. Journal of Photochemistry and Photobiology B: Biology. 2016;163:237–245. 10.1016/j.jphotobiol.2016.08.030 PubMed DOI

Burgos RCR, Schoeman JC, Winden LJv, Červinková K, Ramautar R, Van Wijk EPA, et al. Ultra-weak photon emission as a dynamic tool for monitoring oxidative stress metabolism. Scientific Reports. 2017;7(1):1229 10.1038/s41598-017-01229-x PubMed DOI PMC

Rác M, Sedlářová M, Pospíšil P. The formation of electronically excited species in the human multiple myeloma cell suspension. Scientific Reports. 2015;5:8882 10.1038/srep08882 PubMed DOI PMC

de Mello Gallep C. Ultraweak, spontaneous photon emission in seedlings: toxicological and chronobiological applications: UPE in seedlings—applications. Luminescence. 2014;29(8):963–968. 10.1002/bio.2658 PubMed DOI

Gallep CM, Moraes TA, Dos Santos SR, Barlow PW. Coincidence of biophoton emission by wheat seedlings during simultaneous, transcontinental germination tests. Protoplasma. 2013;250(3):793–796. 10.1007/s00709-012-0447-x PubMed DOI

Gallep CM, Moraes TA, Červinková K, Cifra M, Katsumata M, Barlow PW. Lunisolar tidal synchronism with biophoton emission during intercontinental wheat-seedling germination tests. Plant Signaling & Behavior. 2014;9(5):e28671 10.4161/psb.28671 PubMed DOI PMC

Guo J, Zhu G, Li L, Liu H, Liang S. Ultraweak photon emission in strawberry fruit during ripening and aging is related to energy level. Open Life Sciences. 2017;12(1). 10.1515/biol-2017-0046 DOI

Rafieiolhosseini N, Poplová M, Sasanpour P, Rafii-Tabar H, Alhossaini MR, Cifra M. Photocount statistics of ultra-weak photon emission from germinating mung bean. Journal of Photochemistry and Photobiology B: Biology. 2016;162:50–55. 10.1016/j.jphotobiol.2016.06.001 PubMed DOI

van Wijk E, Kobayashi M, van Wijk R, van der Greef J. Imaging of Ultra-Weak Photon Emission in a Rheumatoid Arthritis Mouse Model. PLoS ONE. 2013;8(12):e84579 10.1371/journal.pone.0084579 PubMed DOI PMC

Ou-Yang H. The application of ultra-weak photon emission in dermatology. Journal of Photochemistry and Photobiology B: Biology. 2014;139:63–70. 10.1016/j.jphotobiol.2013.10.003 PubMed DOI

Zhao X, Wijk Ev, Yan Y, Wijk Rv, Yang H, Zhang Y, et al. Ultra-weak photon emission of hands in aging prediction. Journal of Photochemistry and Photobiology B: Biology. 2016;162:529–534. 10.1016/j.jphotobiol.2016.07.030 PubMed DOI

Zhao X, Pang J, Fu J, Wang Y, Yang M, Liu Y, et al. Spontaneous photon emission: A promising non-invasive diagnostic tool for breast cancer. Journal of Photochemistry and Photobiology B: Biology. 2017;166:232–238. 10.1016/j.jphotobiol.2016.12.009 PubMed DOI

Cifra M, Pospíšil P. Ultra-weak photon emission from biological samples: Definition, mechanisms, properties, detection and applications. Journal of Photochemistry and Photobiology B: Biology. 2014;139:2–10. 10.1016/j.jphotobiol.2014.02.009 PubMed DOI

Wang J, Yu Y. Relationship between ultra-weak bioluminescence and vigour or irradiation dose of irradiated wheat. Luminescence. 2009;24(4):209–212. 10.1002/bio.1096 PubMed DOI

Saeidfirozeh H, Shafiekhani A, Cifra M, Masoudi AA. Endogenous Chemiluminescence from Germinating Arabidopsis Thaliana Seeds. Scientific Reports. 2018;8(1):16231 10.1038/s41598-018-34485-6 PubMed DOI PMC

Popp FA, Nagl W, Li K, Scholz W, Weingärtner O, Wolf R. Biophoton emission: New evidence for coherence and DNA as source. Cell Biochemistry and Biophysics. 1984;6(1):33–52. 10.1007/BF02788579 PubMed DOI

Bajpai RP. Biophoton emission in a squeezed state from a sample of Parmelia tinctorum. Physics Letters A. 2004;322(1-2):131–136. 10.1016/j.physleta.2003.12.050 DOI

Cifra M, Brouder C, Nerudová M, Kučera O. Biophotons, coherence and photocount statistics: A critical review. Journal of Luminescence. 2015;164:38–51. 10.1016/j.jlumin.2015.03.020 DOI

Pospíšil P, Prasad A, Rác M. Role of reactive oxygen species in ultra-weak photon emission in biological systems. Journal of Photochemistry and Photobiology B: Biology. 2014;139:11–23. 10.1016/j.jphotobiol.2014.02.008 PubMed DOI

Prasad A, Pospísil P. Ultraweak photon emission induced by visible light and ultraviolet A radiation via photoactivated skin chromophores: in vivo charge coupled device imaging. Journal of biomedical optics. 2012;17(8):085004 10.1117/1.JBO.17.8.085004 PubMed DOI

Yang M, Pang J, Liu J, Liu Y, Fan H, Han J. Spectral discrimination between healthy people and cold patients using spontaneous photon emission. Biomedical Optics Express. 2015;6(4):1331 10.1364/BOE.6.001331 PubMed DOI PMC

Kobayashi M, Iwasa T, Tada M. Polychromatic spectral pattern analysis of ultra-weak photon emissions from a human body. Journal of Photochemistry and Photobiology B: Biology. 2016;159:186–190. 10.1016/j.jphotobiol.2016.03.037 PubMed DOI

Nerudová M, Červinková K, Hašek J, Cifra M. Optical spectral analysis of ultra-weak photon emission from tissue culture and yeast cells. In: Tománek P, Senderáková D, Páta P, editors. SPIE Proceedings; 2015. p. 94500O. Available from: http://proceedings.spiedigitallibrary.org/proceeding.aspx?doi=10.1117/12.2069897.

Zhao X, Yang M, Wang Y, Pang J, Wijk EV, Liu Y, et al. Spectrum of spontaneous photon emission as a promising biophysical indicator for breast cancer research. Scientific Reports. 2017;7(1). PubMed PMC

Eke A, Herman P, Kocsis L, Kozak LR. Fractal characterization of complexity in temporal physiological signals. Physiological Measurement. 2002;23(1):R1–R38. 10.1088/0967-3334/23/1/201 PubMed DOI

Mandelbrot B, Ness JV. Fractional Brownian Motions, Fractional Noises and Applications. SIAM Review. 1968;10(4):422–437. 10.1137/1010093 DOI

Hurst HE. Methods of Using Long-Term Storage in Reservoirs. Proceedings of the Institution of Civil Engineers. 1956;5(5):519–543. 10.1680/iicep.1956.11503 DOI

Julian M, Alcaraz R, Rieta JJ. Application of Hurst exponents to assess atrial reverse remodeling in paroxysmal atrial fibrillation. Physiol Meas. 2015;36(11):2231–2246. 10.1088/0967-3334/36/11/2231 PubMed DOI

Erramilli A, Willinger W, Pruthi P. Fractal traffic flows in high-speed communications networks. Fractals. 1994;2(03):409–412. 10.1142/S0218348X94000545 DOI

Li D, Fan Q. Multi-fractal Modeling of Network Video Traffic and Performance Analysis. Journal of Internet Technology. 2018;19(7):2089–2095.

Dubovikov MM, Starchenko NV, Dubovikov MS. Dimension of the minimal cover and fractal analysis of time series. Physica A: Statistical Mechanics and its Applications. 2004;339(3-4):591–608. 10.1016/j.physa.2004.03.025 DOI

Bohdalová M, Greguš M. Fractal Analysis of Forward Exchange Rates. Acta Polytechnica Hungarica. 2010;7(4):14.

Dlask M, Kukal J, Sovka P. Fractional Brownian Bridge Model for Alzheimer Disease Detection from EEG Signal. In: 2018 International Conference on Signal Processing and Information Security (ICSPIS); 2018. p. 1–4.

Captur G, Karperien AL, Hughes AD, Francis DP, Moon JC. The fractal heart—embracing mathematics in the cardiology clinic. Nature Reviews Cardiology. 2017;14(1):56–64. 10.1038/nrcardio.2016.161 PubMed DOI PMC

Dlask M, Kukal J. Hurst exponent estimation from short time series. Signal, Image and Video Processing. 2018;.

Kobayashi M, Inaba H. Photon statistics and correlation analysis of ultraweak light originating from living organisms for extraction of biological information. Applied Optics. 2000;39(1):183–192. 10.1364/ao.39.000183 PubMed DOI

Van Wijk R, Van Wijk EPA, Bajpai RP. Photocount distribution of photons emitted from three sites of a human body. Journal of Photochemistry and Photobiology B: Biology. 2006;84(1):46–55. 10.1016/j.jphotobiol.2006.01.010 PubMed DOI

Van Wijk EPA, Wijk RV, Bajpai RP, van der Greef J. Statistical analysis of the spontaneously emitted photon signals from palm and dorsal sides of both hands in human subjects. Journal of Photochemistry and Photobiology B: Biology. 2010;99(3):133–143. 10.1016/j.jphotobiol.2010.03.008 PubMed DOI

Collinson MM, Wightman RM. Observation of individual chemical reactions in solution. Science. 1995;268(5219):1883 10.1126/science.268.5219.1883 PubMed DOI

Budagovsky AV. On the ability of cells to distinguish the coherence of optical radiation. Quantum Electronics. 2005;35(4):369–374. 10.1070/QE2005v035n04ABEH002837 DOI

Kučera O, Cifra M. Cell-to-cell signaling through light: just a ghost of chance? Cell Communication and Signaling. 2013;11(1):1. PubMed PMC

Prasad A, Rossi C, Lamponi S, Pospíšil P, Foletti A. New perspective in cell communication: Potential role of ultra-weak photon emission. Journal of Photochemistry and Photobiology B: Biology. 2014;139:47–53. 10.1016/j.jphotobiol.2014.03.004 PubMed DOI

Scholkmann F, Fels D, Cifra M. Non-chemical and non-contact cell-to-cell communication: a short review. American journal of translational research. 2013;5(6):586 PubMed PMC

Laager F. Light based cellular interactions: hypotheses and perspectives. Frontiers in Physics. 2015;3 10.3389/fphy.2015.00055 DOI

Walls DF, Milburn GJ. Quantum optics. Springer; 2008.

Bajpai RP. Squeezed state description of spectral decompositions of a biophoton signal. Physics Letters A. 2005;337(4-6):265–273. 10.1016/j.physleta.2005.01.079 DOI

Iranifam M, Segundo MA, Santos JLM, Lima JLFC, Sorouraddin MH. Oscillating chemiluminescence systems: state of the art. Luminescence. 2010;25(6):409–418. 10.1002/bio.1203 PubMed DOI

Poplová M, Sovka P, Cifra M. Poisson pre-processing of nonstationary photonic signals: Signals with equality between mean and variance. PLOS ONE. 2017;12(12):e0188622 10.1371/journal.pone.0188622 PubMed DOI PMC

Scholkmann F, Cifra M, Moraes TA, de Mello Gallep C. Using multifractal analysis of ultra-weak photon emission from germinating wheat seedlings to differentiate between two grades of intoxication with potassium dichromate. Journal of Physics: Conference Series. 2011;329:012020.

Dlask M, Kukal J, Tran QV. Revisited Zero-Crossing Method for Hurst Exponent Estimation in Time Series. In: Martincik D, editor. Mathematical Methods in Economics Proceedings 2015. vol. 1. University of West Bohemia, Cheb, Czech Republic: University of West Bohemia, Plzen; 2015. p. 115–120.

Ondrušová B. Measurement Optimization and Analysis of Selected Physical and Chemical Effects on the Ultra-Weak Proton Emission from a Human Hand. CZECH TECHNICAL UNIVERSITY IN PRAGUE, Faculty of Electrical Engineering, Department of Circuit Theory; 2016. Available from: https://dspace.cvut.cz/handle/10467/64862?show=full.

Seber G, Wild C. Nonlinear regression. Hoboken, N.J.: Wiley; 2003.

Casella G, Berger RL. Statistical Inference. Cengage Learning; 2001. Available from: https://www.amazon.com/Statistical-Inference-George-Casella/dp/0534243126?SubscriptionId=0JYN1NVW651KCA56C102&tag=techkie-20&linkCode=xm2&camp=2025&creative=165953&creativeASIN=0534243126.

Anscombe FJ. The Transformation of Poisson, Binomial and Negative-Binomial Data. Biometrika. 1948;35(3/4):246 10.1093/biomet/35.3-4.246 DOI

Kristoufek L. Spectrum-based estimators of the bivariate Hurst exponent. PHYSICAL REVIEW E. 2014;90(6). PubMed

Li C. Rescaled-range and power spectrum analyses on well-logging data. GEOPHYSICAL JOURNAL INTERNATIONAL. 2003;153(1):201–212. 10.1046/j.1365-246X.2003.01893.x DOI

Dietrich CR, Newsam GN. Fast and Exact Simulation of Stationary Gaussian Processes through Circulant Embedding of the Covariance Matrix. SIAM J Sci Comput. 1997;18(4):1088–1107. 10.1137/S1064827592240555 DOI

Delignières D. Correlation Properties of (Discrete) Fractional Gaussian Noise and Fractional Brownian Motion. Mathematical Problems in Engineering. 2015;2015:1–7.

Weiss M, Elsner M, Kartberg F, Nilsson T. Anomalous Subdiffusion Is a Measure for Cytoplasmic Crowding in Living Cells. Biophysical Journal. 2004;87(5):3518–3524. 10.1529/biophysj.104.044263 PubMed DOI PMC

Aon MA, Cortassa S. On the fractal nature of cytoplasm. FEBS letters. 1994;344(1):1–4. 10.1016/0014-5793(94)00321-1 PubMed DOI

Ratto TV, Longo ML. Anomalous Subdiffusion in Heterogeneous Lipid Bilayers†. Langmuir. 2003;19(5):1788–1793. 10.1021/la0261803 DOI

Prasad J, Kopelman R. Fractal-like molecular reaction kinetics: solute photochemistry in porous membranes. Journal of Physical Chemistry. 1987;91(2):265–266. 10.1021/j100286a007 DOI

Kopelman R. Fractal reaction kinetics. Science. 1988;241(4873):1620–1626. 10.1126/science.241.4873.1620 PubMed DOI

Bénichou O, Chevalier C, Klafter J, Meyer B, Voituriez R. Geometry-controlled kinetics. Nature Chemistry. 2010;2(6):472–477. 10.1038/nchem.622 PubMed DOI

Aon M. CHAOTIC DYNAMICS AND FRACTAL SPACE IN BIOCHEMISTRY: SIMPLICITY UNDERLIES COMPLEXITY. Cell Biology International. 2000;24(8):581–587. 10.1006/cbir.2000.0572 PubMed DOI

Saxton MJ. Wanted: A Positive Control for Anomalous Subdiffusion. Biophysical Journal. 2012;103(12):2411–2422. 10.1016/j.bpj.2012.10.038 PubMed DOI PMC

Martin DS, Forstner MB, Käs JA. Apparent Subdiffusion Inherent to Single Particle Tracking. Biophysical Journal. 2002;83(4):2109–2117. 10.1016/S0006-3495(02)73971-4 PubMed DOI PMC

Oliver CJ, Pike ER. Measurement of low light flux by photon counting. Journal of Physics D: Applied Physics. 1968;1(11):1459–1468. 10.1088/0022-3727/1/11/310 DOI

Foord R, Jones R, Oliver CJ, Pike ER. The Use of Photomultiplier Tubes for Photon Counting. Applied Optics. 1969;8(10):1975 10.1364/AO.8.001975 PubMed DOI

Johnson FA, Jones R, McLean TP, Pike ER. Dead-Time Corrections to Photon Counting Distributions. Physical Review Letters. 1966;16(13):589–592. 10.1103/PhysRevLett.16.589 DOI