Thesis (MSc (Biochemistry))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: The Hodgkin-Huxley model, created in 1952, was one of the first models in computational neuroscience and remains the best studied neuronal model to date. Although many other models have a more detailed system description than the Hodgkin-Huxley model, it nonetheless gives an accurate account of various high-level neuronal behaviours. The fields of computational neuroscience and Systems Biology have developed as separate disciplines for a long time and only fairly recently has the neurosciences started to incorporate methods from Systems Biology. Metabolic Control Analysis (MCA), a Systems Biology tool, has not been used in the neurosciences. This study aims to further bring these two fields together, by testing the feasibility of an MCA approach to analyse the Hodgkin-Huxley model. In MCA it is not the parameters of the system that are perturbed, as in the more traditional sensitivity analysis, but the system processes, allowing the formulation of summation and connectivity theorems. In order to determine if MCA can be performed on the Hodgkin-Huxley model, we identified all the discernable model processes of the neuronal system. We performed MCA and quantified the control of the model processes on various high-level time invariant system observables, e.g. the action potential (AP) peak, firing threshold, propagation speed and firing frequency. From this analysis we identified patterns in process control, e.g. the processes that would cause an increase in sodium current, would also cause the AP threshold to lower (decrease its negative value) and the AP peak, propagation speed and firing frequency to increase. Using experimental inhibitor titrations from literature we calculated the control of the sodium channel on AP characteristics and compared it with control coefficients derived from our model simulation. Additionally, we performed MCA on the model’s time-dependent state variables during an AP. This revealed an intricate linking of the system variables via the membrane potential. We developed a method to quantify the contribution of the individual feedback loops in the system. We could thus calculate the percentage contribution of the sodium, potassium and leak currents leading to the observed global change after a system perturbation. Lastly, we compared ion channel mutations to our model simulations and showed how MCA can be useful in identifying targets to counter the effect of these mutations. In this thesis we extended the framework of MCA to neuronal systems and have successfully applied the analysis framework to quantify the contribution of the system processes to the model behaviour. / AFRIKAANSE OPSOMMINMG: Die Hodgkin-Huxley-model, wat in 1952 ontwikkel is, was een van die eerste modelle in rekenaarmagtige neurowetenskap en is vandag steeds een van die bes-bestudeerde neuronmodelle. Hoewel daar vele modelle bestaan met ’n meer uitvoerige sisteembeskrywing as die Hodgkin-Huxley-model gee dié model nietemin ’n akkurate beskrywing van verskeie hoëvlak-sisteemverskynsels. Die twee velde van sisteembiologie en neurowetenskap het lank as onafhanklike dissiplines ontwikkel en slegs betreklik onlangs het die veld van neurowetenskap begin om metodes van sisteembiologie te benut. ’n Sisteembiologiemetode genaamd metaboliese kontrole-analise (MKA) is tot dusver nog nie in die neurowetenskap gebruik nie. Hierdie studie het gepoog om die twee velde nader aan mekaar te bring deurdat die toepasbaarheid van die MKA-raamwerk op die Hodgkin-Huxley-model getoets word. In MKA is dit nie die parameters van die sisteem wat geperturbeer word soos in die meer tradisionele sensitiwiteitsanalise nie, maar die sisteemprosesse. Dit laat die formulering van sommasie- en konnektiwiteitsteoremas toe. Om die toepasbaarheid van die MKA-raamwerk op die Hodgkin-Huxleymodel te toets, is al die onderskeibare modelprosesse van die neurale sisteem geïdentifiseer. Ons het MKA toegepas en die kontrole van die model-prosesse op verskeie hoëvlak, tydsonafhanklike waarneembare sisteemvlak-eienskappe, soos die aksiepotensiaal-kruin, aksiepotensiaal-drempel, voortplantingspoed en aksiepotensiaal-frekwensie, gekwantifiseer. Vanuit hierdie analise kon daar patrone in die proseskontrole geïdentifiseer word, naamlik dat die prosesse wat ’n toename in die natriumstroom veroorsaak, ook sal lei tot ’n afname in die aksiepotensiaal-drempel (die negatiewe waarde verminder) en tot ’n toename in die aksiepotensiaal-kruin, voortplantingspoed en aksiepotensiaalfrekwensie. Deur gebruik te maak van eksperimentele stremmer-titrasies vanuit die literatuur kon die kontrole van die natriumkanaal op die aksiepotensiaaleienskappe bereken en vergelyk word met die kontrole-koëffisiënte vanuit die modelsimulasie. Ons het ook MKA op die model se tydsafhanklike veranderlikes deur die verloop van die aksiepotensiaal uitgevoer. Die analise het getoon dat die sisteemveranderlikes ingewikkeld verbind is via die membraanpotensiaal. Ons het ’n metode ontwikkel om die bydrae van die individuele terugvoerlusse in die sisteem te kwantifiseer. Die persentasie-bydrae van die natrium-, kalium- en lekstrome wat tot die waarneembare globale verandering ná ’n sisteemperturbasie lei, kon dus bepaal word. Laastens het ons ioonkanaalmutasies met ons modelsimulasies vergelyk en getoon hoe MKA nuttig kan wees in die identifisering van teikens om die effek van hierdie mutasies teen te werk. In hierdie tesis het ons die raamwerk van MKA uitgebrei na neurale sisteme en die analise-raamwerk suksesvol toegepas om die bydrae van die sisteemprosesse tot die modelgedrag te kwantifiseer.

<p>Cardiac arrhythmias triggered by both reentrant and focal sources are closely correlated with regions of tissue characterized by significant structural heterogeneity. Experimental and modeling studies of electrical activity in the heart have shown that local microscopic heterogeneities which average out at the macroscale in healthy tissue play a much more important role in diseased and aging cardiac tissue which have low levels of coupling and abnormal or reduced membrane excitability. However, it is still largely unknown how various combinations of microheterogeneity in the intracellular and interstitial spaces affect wavefront propagation in these critical regimes. </p> <p>This thesis uses biophysically realistic 1-D and 2-D computer models to investigate how heterogeneity in the interstitial and intracellular spaces influence both the initiation of ectopic beats and the escape of multiple ectopic beats from a poorly coupled region of tissue into surrounding well-coupled tissue. An approximate discrete monodomain model that incorporates local heterogeneity in both the interstitial and intracellular spaces was developed to represent the tissue domain. </p> <p>The results showed that increasing the effective interstitial resistivity in poorly coupled fibers alters the distribution of electrical load at the microscale and causes propagation to become more like that observed in continuous fibers. In poorly coupled domains, this nearly continuous state is modulated by cell length and is characterized by decreased gap junction delay, sustained conduction velocity, increased sodium current, reduced maximum upstroke velocity, and increased safety factor. In inhomogeneous fibers with adjacent well-coupled and poorly coupled regions, locally increasing the effective interstitial resistivity in the poorly coupled region reduces the size of the focal source needed to generate an ectopic beat, reduces dispersion of repolarization, and delays the onset of conduction block that is caused by source-load mismatch at the boundary between well-coupled and poorly-coupled regions. In 2-D tissue models, local increases in effective interstitial resistivity as well as microstructural variations in cell arrangement at the boundary between poorly coupled and well-coupled regions of tissue modulate the distribution of maximum sodium current which facilitates the unidirectional escape of focal beats. Variations in the distribution of sodium current as a function of cell length and width lead to directional differences in the response to increased effective interstitial resistivity. Propagation in critical regimes such as the ectopic substrate is very sensitive to source-load interactions and local increases in maximum sodium current caused by microheterogeneity in both intracellular and interstitial structure.</p> / Dissertation

The purpose of this thesis work is to model the gate control theory, which explains the modulation of pain signals, with a motivation of finding new possible targets for pain treatment and to find novel control algorithms that can be used in engineering practice. The difference of the current study from the previous modeling trials is that morphologies of neurons that constitute gate control system are also included in the model by which structure-function relationship can be observed. Model of an excitable neuron is constructed and the response of the model for different perturbations are investigated. The simulation results of the excitable cell model is obtained and when compared with the experimental findings obtained by using crayfish, it is found that they are in good agreement. Model encodes stimulation intensity information as firing frequency and also it can add sub-threshold inputs and fire action potentials as real neurons. Moreover, model is able to predict depolarization block. Absolute refractory period of the single cell model is found as 3.7 ms. The developed model, produces no action potentials when the sodium channels are blocked by tetrodotoxin. Also, frequency and amplitudes of generated action potentials increase when the reversal potential of Na is increased. In addition, propagation of signals along myelinated and unmyelinated fibers is simulated and input current intensity-frequency relationships for both type of fibers are constructed. Myelinated fiber starts to conduct when current input is about 400 pA whereas this minimum threshold value for unmyelinated fiber is around 1100 pA. Propagation velocity in the 1 cm long unmyelinated fiber is found as 0.43 m/s whereas velocity along myelinated fiber with the same length is found to be 64.35 m/s. Developed synapse model exhibits the summation and tetanization properties of real synapses while simulating the time dependency of neurotransmitter concentration in the synaptic cleft. Morphometric analysis of neurons that constitute gate control system are done in order to find electrophysiological properties according to dimensions of the neurons. All of the individual parts of the gate control system are connected and the whole system is simulated. For different connection configurations, results of the simulations predict the observed phenomena for the suppression of pain. If the myelinated fiber is dissected, the projection neuron generates action potentials that would convey to brain and elicit pain. However, if the unmyelinated fiber is dissected, projection neuron remains silent. In this study all of the simulations are preformed using Simulink.