Bilayer embedded proteins are affected by stress. This general affirmation is, in this thesis, embodied by two types of proteins: membrane spandex and voltage-gated sodium channels. In this work, we essentially explore, using methods from physics, the theoretical consequences of ideas drawn from experimental biology. Membrane spandex was postulated to exist and we study the theoretical implications and possible benefits for a cell to have such proteins embedded in its bilayer. There are no specific membrane spandex proteins, rather any protein with a transition involving a large enough area change between two non-conducting states could act as spandex. Bacterial cells have osmovalve channels which open at near-lytic tensions to protect themselves against rupture. Spandex expanding at tensions just below the osmovalves’ opening tension could relieve tension enough as to avoid costly accidental osmovalve opening due to transient bilayer tension excursions. Another possible role for spandex is a tension-damper: spandex could be used to maintain bilayer tension at a fixed level. This would be useful as many bilayer embedded channels are known to be modulated by tension. The Stress/shear experienced in traumatic brain injury cause an immediate (< 2 min) and irreversible TTX-sensitive rise in axonal calcium. In situ, this underlies an untreatable condition, diffuse axonal injury. TTX sensitivity indicates that leaky voltage-gated sodium (Nav) channels mediate the calcium increase. Wang et al. showed that the mammalian adult CNS Nav isoform, Nav1.6, expressed in Xenopus oocytes becomes “leaky” when subjected to bleb-inducing pipette aspiration. This “leaky” condition is caused by a hyperpolarized-shift (left-shift or towards lower potentials, typically 20 mV) of the kinetically coupled processes of activation and inactivation thus effectively degrading a well-confined window conductance into a TTX-sensitive Na leak. We propose experimental protocols to determine whether this left-shift is the result of an all-or-none or graded process and whether persistent Na currents are also left-shifted by trauma. We also use modeling to assess whether left-shifted Nav channel kinetics could lead to Na+ (and hence Ca2+ ) loading of axons and to study saltatory propagation after traumatizing a single node of Ranvier.

Bilayer embedded proteins are affected by stress. This general affirmation is, in this thesis, embodied by two types of proteins: membrane spandex and voltage-gated sodium channels. In this work, we essentially explore, using methods from physics, the theoretical consequences of ideas drawn from experimental biology. Membrane spandex was postulated to exist and we study the theoretical implications and possible benefits for a cell to have such proteins embedded in its bilayer. There are no specific membrane spandex proteins, rather any protein with a transition involving a large enough area change between two non-conducting states could act as spandex. Bacterial cells have osmovalve channels which open at near-lytic tensions to protect themselves against rupture. Spandex expanding at tensions just below the osmovalves’ opening tension could relieve tension enough as to avoid costly accidental osmovalve opening due to transient bilayer tension excursions. Another possible role for spandex is a tension-damper: spandex could be used to maintain bilayer tension at a fixed level. This would be useful as many bilayer embedded channels are known to be modulated by tension. The Stress/shear experienced in traumatic brain injury cause an immediate (< 2 min) and irreversible TTX-sensitive rise in axonal calcium. In situ, this underlies an untreatable condition, diffuse axonal injury. TTX sensitivity indicates that leaky voltage-gated sodium (Nav) channels mediate the calcium increase. Wang et al. showed that the mammalian adult CNS Nav isoform, Nav1.6, expressed in Xenopus oocytes becomes “leaky” when subjected to bleb-inducing pipette aspiration. This “leaky” condition is caused by a hyperpolarized-shift (left-shift or towards lower potentials, typically 20 mV) of the kinetically coupled processes of activation and inactivation thus effectively degrading a well-confined window conductance into a TTX-sensitive Na leak. We propose experimental protocols to determine whether this left-shift is the result of an all-or-none or graded process and whether persistent Na currents are also left-shifted by trauma. We also use modeling to assess whether left-shifted Nav channel kinetics could lead to Na+ (and hence Ca2+ ) loading of axons and to study saltatory propagation after traumatizing a single node of Ranvier.

Bilayer embedded proteins are affected by stress. This general affirmation is, in this thesis, embodied by two types of proteins: membrane spandex and voltage-gated sodium channels. In this work, we essentially explore, using methods from physics, the theoretical consequences of ideas drawn from experimental biology. Membrane spandex was postulated to exist and we study the theoretical implications and possible benefits for a cell to have such proteins embedded in its bilayer. There are no specific membrane spandex proteins, rather any protein with a transition involving a large enough area change between two non-conducting states could act as spandex. Bacterial cells have osmovalve channels which open at near-lytic tensions to protect themselves against rupture. Spandex expanding at tensions just below the osmovalves’ opening tension could relieve tension enough as to avoid costly accidental osmovalve opening due to transient bilayer tension excursions. Another possible role for spandex is a tension-damper: spandex could be used to maintain bilayer tension at a fixed level. This would be useful as many bilayer embedded channels are known to be modulated by tension. The Stress/shear experienced in traumatic brain injury cause an immediate (< 2 min) and irreversible TTX-sensitive rise in axonal calcium. In situ, this underlies an untreatable condition, diffuse axonal injury. TTX sensitivity indicates that leaky voltage-gated sodium (Nav) channels mediate the calcium increase. Wang et al. showed that the mammalian adult CNS Nav isoform, Nav1.6, expressed in Xenopus oocytes becomes “leaky” when subjected to bleb-inducing pipette aspiration. This “leaky” condition is caused by a hyperpolarized-shift (left-shift or towards lower potentials, typically 20 mV) of the kinetically coupled processes of activation and inactivation thus effectively degrading a well-confined window conductance into a TTX-sensitive Na leak. We propose experimental protocols to determine whether this left-shift is the result of an all-or-none or graded process and whether persistent Na currents are also left-shifted by trauma. We also use modeling to assess whether left-shifted Nav channel kinetics could lead to Na+ (and hence Ca2+ ) loading of axons and to study saltatory propagation after traumatizing a single node of Ranvier.

Bilayer embedded proteins are affected by stress. This general affirmation is, in this thesis, embodied by two types of proteins: membrane spandex and voltage-gated sodium channels. In this work, we essentially explore, using methods from physics, the theoretical consequences of ideas drawn from experimental biology. Membrane spandex was postulated to exist and we study the theoretical implications and possible benefits for a cell to have such proteins embedded in its bilayer. There are no specific membrane spandex proteins, rather any protein with a transition involving a large enough area change between two non-conducting states could act as spandex. Bacterial cells have osmovalve channels which open at near-lytic tensions to protect themselves against rupture. Spandex expanding at tensions just below the osmovalves’ opening tension could relieve tension enough as to avoid costly accidental osmovalve opening due to transient bilayer tension excursions. Another possible role for spandex is a tension-damper: spandex could be used to maintain bilayer tension at a fixed level. This would be useful as many bilayer embedded channels are known to be modulated by tension. The Stress/shear experienced in traumatic brain injury cause an immediate (< 2 min) and irreversible TTX-sensitive rise in axonal calcium. In situ, this underlies an untreatable condition, diffuse axonal injury. TTX sensitivity indicates that leaky voltage-gated sodium (Nav) channels mediate the calcium increase. Wang et al. showed that the mammalian adult CNS Nav isoform, Nav1.6, expressed in Xenopus oocytes becomes “leaky” when subjected to bleb-inducing pipette aspiration. This “leaky” condition is caused by a hyperpolarized-shift (left-shift or towards lower potentials, typically 20 mV) of the kinetically coupled processes of activation and inactivation thus effectively degrading a well-confined window conductance into a TTX-sensitive Na leak. We propose experimental protocols to determine whether this left-shift is the result of an all-or-none or graded process and whether persistent Na currents are also left-shifted by trauma. We also use modeling to assess whether left-shifted Nav channel kinetics could lead to Na+ (and hence Ca2+ ) loading of axons and to study saltatory propagation after traumatizing a single node of Ranvier.

Der Charakter der Schwellwertdynamik vieler physikalischer, chemischer und biologischer Systeme hat sich in neueren Experimenten als im wesentlichen nicht Markowsch herausgestellt. In diesem Fall sind die "Ubergangsraten von der Zeit und den Anfangsbedingungen abh"angig und es stellen sich komplexe Wahrscheinlichkeitsverteilungen f"ur die erste Durchgangszeit ein. In dieser Arbeit werden verschiedene Aspekte nicht Markowscher Schwellwertprobleme und deren Anwendung bei der Beschreibung der Dynamik von Neuronen untersucht. In dieser Arbeit entwickeln wir einen analytischen Zugang zu nicht Markowschen Problemen, dem die Theorie der Schwellwert"uberschreitung zu Grunde liegt. Im Ergebnis erhalten wir mehrere analytische N"aherungen f"ur die Wahrscheinlichkeitsverteilung der ersten Durchgangszeit f"ur Zufallsprozesse mit differenzierbaren Trajektorien. Die Qualit"at und der G"ultigkeitsbereich der N"aherungen werden von uns sorgf"altig untersucht. Die abgeleiteten N"aherungen decken dabei den gesamten Bereich zwischen fast Markowschen und stark nicht Markowschen Problemen ab. Diese analytischen N"aherungen werden in Kombination mit numerischen Methoden genutzt, um Spikemuster in resonanten und nicht-resonanten Neuronen zu untersuchen. Im Besonderen haben wir uns dabei f"ur die Entstehung spontaner, durch zellinternes Rauschen hervorgerufener, Spikemuster in stellaten (resonanten) und pyramidalen (nicht-resonanten) Zellen des entorhinalen Kortex in Ratten interessiert. Diese zwei Neuronentypen zeigten deutliche Unterschiede in den Spikemustern, die den jeweiligen Unterschieden in den unterschwelligen Dynamiken zuzuordnen sind. Des weiteren wurden negative Korrelationen in den Spikesequenzen f"ur beide Neuronentypen gefunden. Um diese negativen Korrelationen angemessen zu beschreiben, haben wir einen nicht erneuerbaren Schwellenmechanismus in das Resonate-and-Fire Modell integriert. / Recent experiments revealed the non-Markovian character of the escape dynamics in many physical, chemical and biological systems on time scales prior to relaxation. The escape rates in the non-Markovian case are time-dependent and the escape times are dictated by the initial conditions. Complex, multipeak distributions of the first passage time are characteristic for the non-Markovian case. In this thesis we investigate various aspects of the non-Markovian first passage time problem and in particular its application to the dynamics of neurons. We elaborate an analytical approach to the non-Markovian first passage time problem, which is based on the theory of level-crossings, and obtain several analytical approximations for the first passage time density of a random process with differentiable trajectories. We compare the quality of these approximations and ascertain their regions of validity. Our approximations are applicable and provide accurate results for different types of dynamics, ranging from almost Markovian to strongly non-Markovian cases. These analytical approximations in combination with numerical methods are applied to investigate the spike patterns observed in resonant and nonresonant neurons. In particular, we focus on spontaneous (driven by intrinsic noise) spike patterns obtained in stellate (resonant) and pyramidal (nonresonant) cells in the entorhinal cortex in rat. These two types of neurons exhibit striking different spike patterns attributed to the differences in their subthreshold dynamics. We show that the resonate-and-fire model with experimentally estimated parameter values can quantitatively reproduce the interspike interval distributions measured in resonant as well as in nonresonant cells. We also found negative interspike interval correlations in both types of neurons. To capture these negative correlations, we introduce a novel nonrenewal threshold mechanism in the resonate-and-fire model.

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