Mathematical models of basal ganglia dynamics

Physical and biological phenomena that involve oscillations on multiple time scales attract attention of mathematicians because resulting equations include a small parameter that allows for decomposing a three- or higher-dimensional dynamical system into fast/slow subsystems of lower dimensionality and analyzing them independently using geometric singular perturbation theory and other techniques. However, in most life sciences applications observed dynamics is extremely complex, no small parameter exists and this approach fails. Nevertheless, it is still desirable to gain insight into behavior of these mathematical models using the only viable alternative – ad hoc computational analysis. Current dissertation is devoted to this latter approach. Neural networks in the region of the brain called basal ganglia (BG) are capable of producing rich activity patterns. For example, burst firing, i.e. a train of action potentials followed by a period of quiescence in neurons of the subthalamic nucleus (STN) in BG was shown to be related to involuntary shaking of limbs in Parkinson\u27s disease called tremor. The origin of tremor remains unknown; however, a few hypotheses of tremor-generation were proposed recently. The first project of this dissertation examines the BG-thalamo-cortical loop hypothesis for tremor generation by building physiologically-relevant mathematical model of tremor-related circuits with negative delayed feedback. The dynamics of the model is explored under variation of connection strength and delay parameters in the feedback loop using computational methods and data analysis techniques. The model is shown to qualitatively reproduce the transition from irregular physiological activity to pathological synchronous dynamics with varying parameters that are affected in Parkinson\u27s disease. Thus, the proposed model provides an explanation for the basal ganglia-thalamo-cortical loop mechanism of tremor generation. Besides tremor-related bursting activity BG structures in Parkinson\u27s disease also show increased synchronized activity in the beta-band (10-30Hz) that ultimately causes other parkinsonian symptoms like slowness of movement, rigidity etc. Suppression of excessively synchronous beta-band oscillatory activity is believed to suppress hypokinetic motor symptoms in Parkinson\u27s disease. Recently, a lot of interest has been devoted to desynchronizing delayed feedback deep brain stimulation (DBS). This type of synchrony control was shown to destabilize synchronized state in networks of simple model oscillators as well as in networks of coupled model neurons. However, the dynamics of the neural activity in Parkinson\u27s disease exhibits complex intermittent synchronous patterns, far from the idealized synchronized dynamics used to study the delayed feedback stimulation. The second project of this dissertation explores the action of delayed feedback stimulation on partially synchronous oscillatory dynamics, similar to what one observes experimentally in parkinsonian patients. We employ a computational model of the basal ganglia networks which reproduces the fine temporal structure of the synchronous dynamics observed experimentally. Modeling results suggest that delayed feedback DBS in Parkinson\u27s disease may boost rather than suppresses synchronization and is therefore unlikely to be clinically successful. Single neuron dynamics may also have important physiological meaning. For instance, bistability – coexistence of two stable solutions observed experimentally in many neurons is thought to be involved in some short-term memory tasks. Bistability that occurs at the depolarization block, i.e. a silent depolarized state a neuron enters with excessive excitatory input was proposed to play a role in improving robustness of oscillations in pacemaker-type neurons. The third project of this dissertation studies what parameters control bistability at the depolarization block in the three-dimensional conductance-based neuronal model by comparing the reduced dopaminergic neuron model to the Hodgkin-Huxley model of the squid giant axon. Bifurcation analysis and parameter variations revealed that bistability is mainly characterized by the inactivation of the Na+ current, while the activation characteristics of the Na+ and the delayed rectifier K+ currents do not account for the difference in bistability in the two models

Synthetic Gene Network with Positive Feedback Loop Amplifies Cellulase Gene Expression in <i>Neurospora crassa</i>

Second-generation or lignocellulosic biofuels are a tangible source of renewable energy, which is critical to combat climate change by reducing the carbon footprint. Filamentous fungi secrete cellulose-degrading enzymes called cellulases, which are used for production of lignocellulosic biofuels. However, inefficient production of cellulases is a major obstacle for industrial-scale production of second-generation biofuels. We used computational simulations to design and implement synthetic positive feedback loops to increase gene expression of a key transcription factor, CLR-2, that activates a large number of cellulases in a filamentous fungus, <i>Neurospora crassa</i>. Overexpression of CLR-2 reveals previously unappreciated roles of CLR-2 in lignocellulosic gene network, which enabled simultaneous induction of approximately 50% of 78 lignocellulosic degradation-related genes in our engineered <i>Neurospora</i> strains. This engineering results in dramatically increased cellulase activity due to cooperative orchestration of multiple enzymes involved in the cellulose degradation pathway. Our work provides a proof of principle in utilizing mathematical modeling and synthetic biology to improve the efficiency of cellulase synthesis for second-generation biofuel production

Buprenorfin and its use in drug addicts

V mé diplomové práci jsem shromáždila informace o možnostech využití buprenorfinu v léčbě drogových závislostí a zároveň jsem se zabývala možnostmi jeho zneužívání. Buprenorfin je látka, která se v současné době využívá k léčbě bolestí, ale především jako látka pro detoxifikaci a substituční terapii při závislosti na opioidech. Buprenorfin je léčivo, které bývá velmi často zneužíváno, a proto by se tomuto problému mělo věnovat více pozornosti.In my diploma paper I collected information about possibilities of using buprenorphine in a treatment of drug dependence as well as I dealt with possibilities of its abuse. Buprenorphine is substance, which is currently used in the treatment of pain, but mainly like a substance in a detoxification and maintenance therapy of opioid dependence. Buprenorphine is a medicament, which is abused very often and therefore we should take more care in studying of this problem.Katedra farmakologie a toxikologieDepartment of Pharmacology and ToxicologyFaculty of Pharmacy in Hradec KrálovéFarmaceutická fakulta v Hradci Králov

Synthetic Gene Network with Positive Feedback Loop Amplifies Cellulase Gene Expression in <i>Neurospora crassa</i>

Second-generation or lignocellulosic biofuels are a tangible source of renewable energy, which is critical to combat climate change by reducing the carbon footprint. Filamentous fungi secrete cellulose-degrading enzymes called cellulases, which are used for production of lignocellulosic biofuels. However, inefficient production of cellulases is a major obstacle for industrial-scale production of second-generation biofuels. We used computational simulations to design and implement synthetic positive feedback loops to increase gene expression of a key transcription factor, CLR-2, that activates a large number of cellulases in a filamentous fungus, <i>Neurospora crassa</i>. Overexpression of CLR-2 reveals previously unappreciated roles of CLR-2 in lignocellulosic gene network, which enabled simultaneous induction of approximately 50% of 78 lignocellulosic degradation-related genes in our engineered <i>Neurospora</i> strains. This engineering results in dramatically increased cellulase activity due to cooperative orchestration of multiple enzymes involved in the cellulose degradation pathway. Our work provides a proof of principle in utilizing mathematical modeling and synthetic biology to improve the efficiency of cellulase synthesis for second-generation biofuel production

Synthetic Gene Network with Positive Feedback Loop Amplifies Cellulase Gene Expression in <i>Neurospora crassa</i>

Second-generation or lignocellulosic biofuels are a tangible source of renewable energy, which is critical to combat climate change by reducing the carbon footprint. Filamentous fungi secrete cellulose-degrading enzymes called cellulases, which are used for production of lignocellulosic biofuels. However, inefficient production of cellulases is a major obstacle for industrial-scale production of second-generation biofuels. We used computational simulations to design and implement synthetic positive feedback loops to increase gene expression of a key transcription factor, CLR-2, that activates a large number of cellulases in a filamentous fungus, <i>Neurospora crassa</i>. Overexpression of CLR-2 reveals previously unappreciated roles of CLR-2 in lignocellulosic gene network, which enabled simultaneous induction of approximately 50% of 78 lignocellulosic degradation-related genes in our engineered <i>Neurospora</i> strains. This engineering results in dramatically increased cellulase activity due to cooperative orchestration of multiple enzymes involved in the cellulose degradation pathway. Our work provides a proof of principle in utilizing mathematical modeling and synthetic biology to improve the efficiency of cellulase synthesis for second-generation biofuel production