Phasor representation of oscillatory biochemical pathways

Kilian, Joshua (2021-12)

Thesis (MSc)--Stellenbosch University, 2021.

Thesis

ENGLISH ABSTRACT: Oscillations or rhythms arise in many biological systems such as biochemical pathways. Numerous mathematical models and experimental data sets of such systems display sustained oscillations in both the metabolite and reaction rate concentrations. The oscillating chemical species and reaction rates throughout a biochemical pathway oscillate with an identical frequency in the limit-cycle. In this thesis biological oscillators were analysed using phasor representations (or phasor diagrams) which are commonly used in electrical circuit analysis, but not for biological oscillators. These phasor diagrams provide a visual representation of the peak amplitude and phase angle of multiple periodic signals. Phasor diagrams have previously been used (du Preez, 2009) and this previous work (which is a proof of concept that a periodic oscillating biochemical network can be represented using phasors) is used as a foundation for this thesis. A Wolfram Mathematica software package was developed to render the phasor diagrams and compute quantitative information that defines component interactions. The underlying mathematics of the analysis is based on well- established principles used extensively in the field of electrical engineering. The phasor analysis was objectively compared to two classic visual dynamical analyses (polar phase plane plots and phase plane diagrams) to identify its strengths and weaknesses. The phasor analysis has the advantage of incorporating the reaction rate oscillations which results in a visual representation of the pathway’s network structure. Quantitative descriptions of the interactions between rate and metabolite phasors are determined using the underlying mathematics of the analysis, the pathway stoichiometry, and the kinetic rate equations. The transduction and absorption of oscillations throughout the pathway are determined using the relative phases and amplitudes of the connected species and reaction rate phasors. The analysis was applied to numerous core and detailed kinetic models and experimental data sets of the oscillatory yeast glycolytic pathway. The network structure (relative phases and amplitudes) of the components were compared between the data sets. The difference in transduction and absorption of oscillations throughout the pathway was analysed by identifying large amplitude phasors and large phase changes between consecutive reaction phasors. The relative phases and amplitudes of the upper glycolytic intermediates were comparable in the majority of the data sets. The data sets display a phase change between the reactions separating upper and lower glycolysis. The quantitative analysis revealed the importance of phosphofructokinase (PFK) in all of the data sets. PFK was found to be important in the maintenance of oscillations in the upper glycolytic intermediates (fructose 6-phosphate and fructose 1,6-bisphosphate (F6P and F16P)) and the adenosine triphosphate (ATP) metabolite. These results indicate a greater contribution of the allosteric regulation of PFK compared with the autocatalytic stoichiometry of glycolysis. Furthermore, application of the analysis to the kinetic rate equations revealed the importance of the adenylates in the oscillation of PFK and multiple other reactions. An important finding was that the phasor analysis indicates quantitative similarities (magnitude of component interactions) between seemingly different data sets such as data sets of cell extracts and data sets of intact cells or models of different dimensionality.

AFRIKAANSE OPSOMMING: Ossillasies of ritmes ontstaan in baie biologiese sisteme soos biochemiese padweë. Talle wiskundige modelle en eksperimentele datastelle van sulke stelsels vertoon volgehoue ossillasies in beide die metaboliet- en reaksietempo-konsentrasies. Die ossillerende chemiese spesies en reaksies regdeur 'n biochemiese pad ossilleer met 'n identiese frekwensie in die limietsiklus. In hierdie tesis is biologiese ossillators ontleed met behulp van fasorvoorstellings (of fasordiagramme) wat algemeen in elektriese stroombaananalise gebruik word, maar nie vir biologiese ossillators nie. Hierdie fasordiagramme verskaf 'n visuele voorstelling van die piekamplitude en fasehoek van veelvuldige periodieke seine. Fasordiagramme is voorheen gebruik (du Preez, 2009) en hierdie vorige werk (wat 'n konsepbewys is dat 'n periodieke ossillerende biochemiese netwerk met behulp van fasors voorgestel kan word) word as grondslag vir hierdie tesis gebruik. 'n Wolfram Mathematica-sagtewarepakket is ontwikkel om die fasordiagramme te genereer en kwantitatiewe inligting te bereken wat komponentinteraksies definieer. Die onderliggende wiskunde van die analise is gebaseer op goed-gevestigde beginsels wat op groot skaal in die veld van elektriese ingenieurswese gebruik word. Die fasoranalise is objektief vergelyk met twee klassieke visuele dinamiese ontledings (polêre fasevlak-grafieke en fasevlakdiagramme) om die sterk- en swakpunte daarvan te identifiseer. Die fasoranalise het die voordeel om die reaksietempo-ossillasies in te sluit wat lei tot 'n visuele voorstelling van die pad se netwerkstruktuur. Kwantitatiewe beskrywings van die interaksies tussen tempo en metaboliet fasors word bepaal deur gebruik te maak van die onderliggende wiskunde van die analise, die pad stoïgiometrie en die kinetiese snelheidsvergelykings. Die transduksie en absorpsie van ossillasies deur die pad word bepaal deur die relatiewe fases en amplitudes van die gekoppelde spesies en reaksietempo fasors te gebruik. Die analise is toegepas op talle kern- en gedetailleerde kinetiese modelle en eksperimentele datastelle van die ossillatoriese glikolitiese pad in gis. Die netwerkstruktuur (relatiewe fases en amplitudes) van die komponente is tussen die datastelle vergelyk. Die verskil in transduksie en absorpsie van ossillasies regdeur die pad is ontleed deur groot amplitude fasors en groot fase veranderinge tussen opeenvolgende reaksie-fasors te identifiseer. Die relatiewe fases en amplitudes van die boonste glikolitiese tussenprodukte was vergelykbaar in die meerderheid van die datastelle. Die datastelle vertoon 'n faseverandering tussen die reaksies wat die boonste en onderste dele van glikolise skei. Die kwantitatiewe analise het die belangrikheid van fosfofruktokinase (PFK) in al die datastelle aan die lig gebring. Daar is gevind dat PFK belangrik is in die handhawing van ossillasies in die boonste glikolitiese tussenprodukte (fruktose 6-fosfaat en fruktose 1,6-bisfosfaat (F6P en F16P)) en die adenosientrifosfaat (ATP) metaboliet. Hierdie resultate dui op 'n groter bydrae van die allosteriese regulering van PFK in vergelyking met die outokatalistiese stoïgiometrie van glikolise. Verder het toepassing van die analise op die kinetiese snelheidsvergelykings die belangrikheid van die adenilate in die ossillasie van PFK en veelvuldige ander reaksies geopenbaar. 'n Belangrike bevinding was dat die fasoranalise kwantitatiewe ooreenkomste (grootte van komponentinteraksies) tussen skynbaar verskillende datastelle soos datastelle van selekstrakte en datastelle van heelselle, of modelle van verskillende dimensionaliteit aandui.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/124228
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