Melola Discovery

← Melola Discovery

Open access Journal SINTA 1

Mechanistic Modeling of Porphyridium sp. Growth under Photoperiod Variation Using a Droop–Steele Dynamical System

Journal of Mathematical and Fundamental Sciences · Vol. 58 No. 1 (2026) · pp. 44–69

DOI
10.5614/j.math.fund.sci.2026.58.1.4
ISSN
2338-5510, 2337-5760
Published
2026-11-09
Publisher
Directorate for Research and Innovation (DRI) ITB
Language
eng
License
creativecommons.org/licenses/by-nc-nd/4.0

Abstract

Longer illumination can increase Porphyridium sp. biomass but requires more energy. We studied growth under 6 h, 12 h, and 24 h photoperiods using a Droop–Steele dynamical model for external nutrient N, internal quota Q, and cell density X. Photoperiod modifies nutrient uptake through a daily-effective Steele factor. We established forward invariance of the biologically feasible region and ultimate boundedness, derived washout and positive-biomass equilibria, and characterized local stability. Parameters were estimated jointly from 81 container-day observations across nine independent cultures using Bayesian inference. Four Markov chain Monte Carlo chains met the reported convergence criteria (maximum ). Posterior draws were mapped onto analytical persistence and stability conditions and propagated to biomass predictions. All tested photoperiods yielded a feasible, locally stable positive equilibrium within the fitted model. Predicted biomass increased with illumination but showed diminishing gains per additional lighting hour. The fitted effective-light Steele response was nearly linear over the tested range; the modeled flattening was consistent with nutrient depletion and quota limitation without requiring photoinhibition. Droop–Steele had the lowest AICc among the models compared, although Logistic had marginally lower raw log-RMSE. Energy-use and cost data are needed before identifying a cost-optimal photoperiod.

Keywords

Collaboration network of the authors

27 authors · 99 co-authorship links · 33 across different organisations

Hover or tap a name to highlight its co-authors. Double-click to open the author's page.

  • Sumatera Institute of Technology
  • Sunan Gunung Djati State Islamic University Bandung
  • Bandung Institute of Technology
  • Lampung University
  • State University of Semarang
  • Affiliation unknown
  • Different organisations
  • Same organisation
  • Affiliation unknown
  • Thicker line = more joint articles · bigger circle = more articles
Show as table
Co-authorOrganisationJoint articles
Anisa RahmadaniSumatera Institute of Technology2
Nurul Indah SafitriSumatera Institute of Technology2
Suli Windi AstutiSumatera Institute of Technology2
M. Diwa Sandika AditamaSumatera Institute of Technology2
Zunanik MufidahSumatera Institute of Technology2
Sri HaryaniState University of Semarang2
Utriweni MukhaiyarBandung Institute of Technology2
Riani UtamiBandung Institute of Technology2
Rifky FauziSumatera Institute of Technology2
Gres MarettaSumatera Institute of Technology2
Edy SoewonoBandung Institute of Technology2
Saefudin SaefudinAffiliation unknown2
Amalia StyaningrumAffiliation unknown2
Eristia ArfiSumatera Institute of Technology1
Dwi Mutiara PutriSumatera Institute of Technology1
Yeni Gede WibaraniSumatera Institute of Technology1
Ayu ApriantiSumatera Institute of Technology1
Mia Siti KhumaerohSunan Gunung Djati State Islamic University Bandung1
Elvi Syukrina EriantoSunan Gunung Djati State Islamic University Bandung1
Najmudin NuwariSunan Gunung Djati State Islamic University Bandung1

Affiliations come from OpenAlex; journal OAI-PMH metadata carries none. Authors without an OpenAlex ID are matched by name, which can merge or split people.

Metadata source: OAI-PMH (metadata jurnal) https://journals.itb.ac.id/index.php/jmfs/oai, first harvested 9 Nov 2026, last seen 9 Nov 2026.
Original metadata (oai_dc) 
<oai_dc:dc xmlns="http://www.openarchives.org/OAI/2.0/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/  http://www.openarchives.org/OAI/2.0/oai_dc.xsd">
	<dc:title xml:lang="en-US">Mechanistic Modeling of Porphyridium sp. Growth under Photoperiod Variation Using a Droop–Steele Dynamical System</dc:title>
	<dc:creator>Fauzi, Rifky</dc:creator>
	<dc:creator>Andriyanto, Yoga</dc:creator>
	<dc:creator>Rizka, Nela</dc:creator>
	<dc:creator>Edriani, Tiara Shofi</dc:creator>
	<dc:creator>Pribadi, Aswan Anggun</dc:creator>
	<dc:creator>Jati, Ciptaning Weargo</dc:creator>
	<dc:creator>Noor, Dear Michiko Mutiara</dc:creator>
	<dc:subject xml:lang="en-US">Bayesian parameter estimation</dc:subject>
	<dc:subject xml:lang="en-US">Droop–Steele model</dc:subject>
	<dc:subject xml:lang="en-US">photoperiod</dc:subject>
	<dc:subject xml:lang="en-US">Porphyridium sp.</dc:subject>
	<dc:subject xml:lang="en-US">stability</dc:subject>
	<dc:subject xml:lang="en-US">Mathematical Modeling</dc:subject>
	<dc:description xml:lang="en-US">Longer illumination can increase Porphyridium sp. biomass but requires more energy. We studied growth under 6 h, 12 h, and 24 h photoperiods using a Droop–Steele dynamical model for external nutrient N, internal quota Q, and cell density X. Photoperiod modifies nutrient uptake through a daily-effective Steele factor. We established forward invariance of the biologically feasible region and ultimate boundedness, derived washout and positive-biomass equilibria, and characterized local stability. Parameters were estimated jointly from 81 container-day observations across nine independent cultures using Bayesian inference. Four Markov chain Monte Carlo chains met the reported convergence criteria (maximum ). Posterior draws were mapped onto analytical persistence and stability conditions and propagated to biomass predictions. All tested photoperiods yielded a feasible, locally stable positive equilibrium within the fitted model. Predicted biomass increased with illumination but showed diminishing gains per additional lighting hour. The fitted effective-light Steele response was nearly linear over the tested range; the modeled flattening was consistent with nutrient depletion and quota limitation without requiring photoinhibition. Droop–Steele had the lowest AICc among the models compared, although Logistic had marginally lower raw log-RMSE. Energy-use and cost data are needed before identifying a cost-optimal photoperiod.</dc:description>
	<dc:publisher xml:lang="en-US">Directorate for Research and Innovation (DRI) ITB</dc:publisher>
	<dc:date>2026-11-09</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
	<dc:type>info:eu-repo/semantics/publishedVersion</dc:type>
	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://journals.itb.ac.id/index.php/jmfs/article/view/27851</dc:identifier>
	<dc:identifier>10.5614/j.math.fund.sci.2026.58.1.4</dc:identifier>
	<dc:source xml:lang="en-US">Journal of Mathematical and Fundamental Sciences; Vol. 58 No. 1 (2026): (In Progress); 44-69</dc:source>
	<dc:source>2338-5510</dc:source>
	<dc:source>2337-5760</dc:source>
	<dc:language>eng</dc:language>
	<dc:relation>https://journals.itb.ac.id/index.php/jmfs/article/view/27851/7528</dc:relation>
	<dc:rights xml:lang="en-US">Copyright (c) 2026 Journal of Mathematical and Fundamental Sciences</dc:rights>
	<dc:rights xml:lang="en-US">https://creativecommons.org/licenses/by-nc-nd/4.0</dc:rights>
</oai_dc:dc>