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Mathematical Models in Cellular Biophysics
KTH, School of Engineering Sciences (SCI), Applied Physics.
2007 (English)Licentiate thesis, comprehensive summary (Other scientific)
Abstract [en]

Cellular biophysics deals with, among other things, transport processes within cells. This thesis presents two studies where mathematical models have been used to explain how two of these processes occur.

Cellular membranes separate cells from their exterior environment and also divide a cell into several subcellular regions. Since the 1970s lateral diffusion in these membranes has been studied, one the most important experimental techniques in these studies is fluorescence recovery after photobleach (FRAP). A mathematical model developed in this thesis describes how dopamine 1 receptors (D1R) diffuse in a neuronal dendritic membrane. Analytical and numerical methods have been used to solve the partial differential equations that are expressed in the model. The choice of method depends mostly on the complexity of the geometry in the model.

Calcium ions (Ca2+) are known to be involved in several intracellular signaling mechanisms. One interesting concept within this field is a signaling microdomain where the inositol 1,4,5-triphosphate receptor (IP3R) in the endoplasmic reticulum (ER) membrane physically interacts with plasma membrane proteins. This microdomain has been shown to cause the intracellular Ca2+ level to oscillate. The second model in this thesis describes a signaling network involving both ER membrane bound and plasma membrane Ca2+ channels and pumps, among them store-operated Ca2+ (SOC) channels. A MATLAB® toolbox was developed to implement the signaling networks and simulate its properties. This model was also implemented using Virtual cell.

The results show a high resemblance between the mathematical model and FRAP data in the D1R study. The model shows a distinct difference in recovery characteristics of simulated FRAP experiments on whole dendrites and dendritic spines, due to differences in geometry. The model can also explain trapping of D1R in dendritic spines.

The results of the Ca2+ signaling model show that stimulation of IP3R can cause Ca2+ oscillations in the same frequency range as has been seen in experiments. The removing of SOC channels from the model can alter the characteristics as well as qualitative appearance of Ca2+ oscillations.

Abstract [sv]

Cellulär biofysik behandlar bland annat transportprocesser i celler. I denna avhandling presenteras två studier där matematiska modeller har använts för att förklara hur två av dess processer uppkommer.

Cellmembran separerar celler från deras yttre miljö och delar även upp en cell i flera subcellulära regioner. Sedan 1970-talet har lateral diffusion i dessa membran studerats, en av de viktigaste experimentella metoderna i dessa studier är fluorescence recovery after photobleach (FRAP). En matematisk modell utvecklad i denna avhandling beskriver hur dopamin 1-receptorer (D1R) diffunderar i en neural dendrits membran. Analytiska och numeriska metoder har använts för att lösa de partiella differentialekvationer som uttrycks i modellen. Valet av metod beror främst på komplexiteten hos geometrin i modellen.

Kalciumjoner (Ca2+) är kända för att ingå i flera intracellulära signalmekanismer. Ett intressant koncept inom detta fält är en signalerande mikrodomän där inositol 1,4,5-trifosfatreceptorn (IP3R) i endoplasmatiska nätverksmembranet (ER-membranet) fysiskt interagerar med proteiner i plasmamembranet. Denna mikrodomän har visats vara orsak till oscillationer i den intracellulära Ca2+-nivån. Den andra modellen i denna avhandling beskriver ett signalerande nätverk där både Ca2+-kanaler och pumpar bundna i ER-membranet och i plasmamembranet, däribland store-operated Ca2+(SOC)-kanaler, ingår. Ett MATLAB®-verktyg utvecklades för att implementera signalnätverket och simulera dess egenskaper. Denna modell implementerades även i Virtual cell.

Resultaten visar en stark likhet mellan den matematiska modellen och FRAP-datat i D1R-studien. Modellen visar en distinkt skillnad i återhämtningsegenskaper hos simulerade FRAP-experiment på hela dendriter och dendritiska spines, beroende på skillnader i geometri. Modellen kan även förklara infångning av D1R i dendritiska spines.

Resultaten från Ca2+-signaleringmodellen visar att stimulering av IP3R kan orsaka Ca2+-oscillationer inom samma frekvensområde som tidigare setts i experiment. Att ta bort SOC-kanaler från modellen kan ändra karaktär hos, såväl som den kvalitativa uppkomsten av Ca2+-oscillationer.

Place, publisher, year, edition, pages
Stockholm: KTH , 2007. , v, 50 p.
Trita-FYS, ISSN 0280-316X ; 2007:33
Keyword [en]
Calcium oscillations, Diffusion, Dopamine receptors, Mathematical models, Computer simulations, FRAP
National Category
Physical Sciences
URN: urn:nbn:se:kth:diva-4361ISBN: 978-91-7178-660-9OAI: diva2:11961
2007-05-22, FA32, AlbaNova Universitetscentrum, Roslagstullsbacken 21, Stockholm, 10:00
QC 20101111Available from: 2007-05-08 Created: 2007-05-08 Last updated: 2010-11-11Bibliographically approved
List of papers
1. Allosteric changes of the NMDA receptor trap diffusible dopamine 1 receptors in spines
Open this publication in new window or tab >>Allosteric changes of the NMDA receptor trap diffusible dopamine 1 receptors in spines
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2006 (English)In: Proceedings of the National Academy of Sciences of the United States of America, ISSN 0027-8424, E-ISSN 1091-6490, Vol. 103, no 3, 762-767 p.Article in journal (Refereed) Published
Abstract [en]

The dopaminergic and glutamatergic systems interact to initiate and organize normal behavior, a communication that may be perturbed in many neuropsychiatric diseases, including schizophrenia. We show here that NMDA, by allosterically modifying NMDA receptors, can act as a scaffold to recruit laterally diffusing dopamine D1 receptors (D1R) to neuronal spines. Using organotypic culture from rat striatum transfected with D1R fused to a fluorescent protein, we show that the majority of dendritic D1R are in lateral diffusion and that their mobility is confined by interaction with NMDA receptors. Exposure to NMDA reduces the diffusion coefficient for D1R and causes an increase in the number of D1R-positive spines. Unexpectedly, the action of NMDA in potentiating D1R recruitment was independent of calcium flow via the NMDA receptor channel. Thus, a highly energy-efficient, diffusion-trap mechanism can account for intraneuronal interaction between the glutamatergic and dopaminergic systems and for regulation of the number of D1R-positive spines. This diffusion trap system represents a molecular mechanism for brain plasticity and offers a promising target for development of antipsychotic therapy

Fluorescence recovery after photo-bleaching; Lateral diffusion; Organotypic cultures; Receptor movement
National Category
Condensed Matter Physics
urn:nbn:se:kth:diva-7063 (URN)10.1073/pnas.0505557103 (DOI)000234727800047 ()2-s2.0-31444439409 (ScopusID)
QC 20100726Available from: 2007-05-08 Created: 2007-05-08 Last updated: 2010-11-11Bibliographically approved
2. Modeling the impact of store-operated Ca2+ entry on intracellular Ca2+ oscillations
Open this publication in new window or tab >>Modeling the impact of store-operated Ca2+ entry on intracellular Ca2+ oscillations
2006 (English)In: Mathematical biosciences, ISSN 0025-5564, Vol. 204, no 2, 232-249 p.Article in journal (Refereed) Published
Abstract [en]

Calcium (Ca2+) oscillations play fundamental roles in various cell signaling processes and have been the subject of numerous modeling studies. Here we have implemented a general mathematical model to simulate the impact of store-operated Ca2+ entry on intracellular Ca2+ oscillations. In addition, we have compared two different models of the inositol 1,4,5-trisphosphate (IP3) receptor (IP3R) and their influences on intracellular Ca2+ oscillations. Store-operated Ca2+ entry following Ca2+ depletion of endoplasmic reticulum (ER) is an important component of Ca2+ signaling. We have developed a phenomenological model of store-operated Ca2+ entry via store-operated Ca2+ (SOC) channels, which are activated upon ER Ca2+ depletion. The depletion evokes a bi-phasic Ca2+ signal, which is also produced in our mathematical model. The IP3R is an important regulator of intracellular Ca2+ signals. This IP3 sensitive Ca2+ channel is also regulated by Ca2+. We apply two IP3R models, the Mak-McBride-Foskett model and the De Young and Keizer model, with significantly different channel characteristics. Our results show that the two separate IP3R models evoke intracellular Ca2+ oscillations with different frequencies and amplitudes. Store-operated Ca2+ entry affects the oscillatory behavior of these intracellular Ca2+ oscillations. The IP3 threshold is altered when store-operated Ca2+ entry is excluded from the model. Frequencies and amplitudes of intracellular Ca2+ oscillations are also altered without store-operated Ca2+ entry. Under certain conditions, when intracellular Ca2+ oscillations are absent, excluding store-operated Ca2+ entry induces an oscillatory response. These findings increase knowledge concerning store-operated Ca2+ entry and its impact on intracellular Ca2+ oscillations.

calcium; oscillation; SOC
National Category
Condensed Matter Physics
urn:nbn:se:kth:diva-7064 (URN)10.1016/j.mbs.2006.03.001 (DOI)000242902200005 ()2-s2.0-33750721337 (ScopusID)
QC 20100726Available from: 2007-05-08 Created: 2007-05-08 Last updated: 2010-12-06Bibliographically approved

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