A reduced model clarifies the role of feedback loops and time delays in the Drosophila circadian oscillator.

Although several detailed models of molecular processes essential for circadian oscillations have been developed, their complexity makes intuitive understanding of the oscillation mechanism difficult. The goal of the present study was to reduce a previously developed, detailed model to a minimal representation of the transcriptional regulation essential for circadian rhythmicity in Drosophila. The reduced model contains only two differential equations, each with time delays. A negative feedback loop is included, in which PER protein represses per transcription by binding the dCLOCK transcription factor. A positive feedback loop is also included, in which dCLOCK indirectly enhances its own formation. The model simulated circadian oscillations, light entrainment, and a phase-response curve with qualitative similarities to experiment. Time delays were found to be essential for simulation of circadian oscillations with this model. To examine the robustness of the simplified model to fluctuations in molecule numbers, a stochastic variant was constructed. Robust circadian oscillations and entrainment to light pulses were simulated with fewer than 80 molecules of each gene product present on average. Circadian oscillations persisted when the positive feedback loop was removed. Moreover, elimination of positive feedback did not decrease the robustness of oscillations to stochastic fluctuations or to variations in parameter values. Such reduced models can aid understanding of the oscillation mechanisms in Drosophila and in other organisms in which feedback regulation of transcription may play an important role.

Structural plasticity can produce metaplasticity.

BACKGROUND: Synaptic plasticity underlies many aspect of learning memory and development. The properties of synaptic plasticity can change as a function of previous plasticity and previous activation of synapses, a phenomenon called metaplasticity. Synaptic plasticity not only changes the functional connectivity between neurons but in some cases produces a structural change in synaptic spines; a change thought to form a basis for this observed plasticity. Here we examine to what extent structural plasticity of spines can be a cause for metaplasticity. This study is motivated by the observation that structural changes in spines are likely to affect the calcium dynamics in spines. Since calcium dynamics determine the sign and magnitude of synaptic plasticity, it is likely that structural plasticity will alter the properties of synaptic plasticity. METHODOLOGY/PRINCIPAL FINDINGS: In this study we address the question how spine geometry and alterations of N-methyl-D-aspartic acid (NMDA) receptors conductance may affect plasticity. Based on a simplified model of the spine in combination with a calcium-dependent plasticity rule, we demonstrated that after the induction phase of plasticity a shift of the long term potentiation (LTP) or long term depression (LTD) threshold takes place. This induces a refractory period for further LTP induction and promotes depotentiation as observed experimentally. That resembles the BCM metaplasticity rule but specific for the individual synapse. In the second phase, alteration of the NMDA response may bring the synapse to a state such that further synaptic weight alterations are feasible. We show that if the enhancement of the NMDA response is proportional to the area of the post synaptic density (PSD) the plasticity curves most likely return to the initial state. CONCLUSIONS/SIGNIFICANCE: Using simulations of calcium dynamics in synaptic spines, coupled with a biophysically motivated calcium-dependent plasticity rule, we find under what conditions structural plasticity can form the basis of synapse specific metaplasticity.

Intact flagellar motor of Borrelia burgdorferi revealed by cryo-electron tomography: evidence for stator ring curvature and rotor/C-ring assembly flexion.

The bacterial flagellar motor is a remarkable nanomachine that provides motility through flagellar rotation. Prior structural studies have revealed the stunning complexity of the purified rotor and C-ring assemblies from flagellar motors. In this study, we used high-throughput cryo-electron tomography and image analysis of intact Borrelia burgdorferi to produce a three-dimensional (3-D) model of the in situ flagellar motor without imposing rotational symmetry. Structural details of B. burgdorferi, including a layer of outer surface proteins, were clearly visible in the resulting 3-D reconstructions. By averaging the 3-D images of approximately 1,280 flagellar motors, a approximately 3.5-nm-resolution model of the stator and rotor structures was obtained. flgI transposon mutants lacked a torus-shaped structure attached to the flagellar rod, establishing the structural location of the spirochetal P ring. Treatment of intact organisms with the nonionic detergent NP-40 resulted in dissolution of the outermost portion of the motor structure and the C ring, providing insight into the in situ arrangement of the stator and rotor structures. Structural elements associated with the stator followed the curvature of the cytoplasmic membrane. The rotor and the C ring also exhibited angular flexion, resulting in a slight narrowing of both structures in the direction perpendicular to the cell axis. These results indicate an inherent flexibility in the rotor-stator interaction. The FliG switching and energizing component likely provides much of the flexibility needed to maintain the interaction between the curved stator and the relatively symmetrical rotor/C-ring assembly during flagellar rotation.

Short-Term Plasticity in a Computational Model of the Tail-Withdrawal Circuit in Aplysia.

The tail-withdrawal circuit of Aplysia provides a useful model system for investigating synaptic dynamics. Sensory neurons within the circuit manifest several forms of synaptic plasticity. Here, we developed a model of the circuit and investigated the ways in which depression (DEP) and potentiation (POT) contributed to information processing. DEP limited the amount of motor neuron activity that could be elicited by the monosynaptic pathway alone. POT within the monosynaptic pathway did not compensate for DEP. There was, however, a synergistic interaction between POT and the polysynaptic pathway. This synergism extended the dynamic range of the network, and the interplay between DEP and POT made the circuit responded preferentially to long-duration, low-frequency inputs.

Short-Term Plasticity in a Computational Model of the Tail-Withdrawal Circuit in Aplysia.

The tail-withdrawal circuit of Aplysia provides a useful model system for investigating synaptic dynamics. Sensory neurons within the circuit manifest several forms of synaptic plasticity. Here, we developed a model of the circuit and investigated the ways in which depression (DEP) and potentiation (POT) contributed to information processing. DEP limited the amount of motor neuron activity that could be elicited by the monosynaptic pathway alone. POT within the monosynaptic pathway did not compensate for DEP. There was, however, a synergistic interaction between POT and the polysynaptic pathway. This synergism extended the dynamic range of the network, and the interplay between DEP and POT made the circuit responded preferentially to long-duration, low-frequency inputs.

Functional and motor neuronal analysis of defensive siphon responses in {\it Aplysia californica}

One of the central goals of neuroscience research is to determine how networks of neurons control and modify behavior. One of the most influential model systems for this kind of analysis is the siphon and gill withdrawal reflex of the marine mollusc A. californica. In response to tactile stimulation, the siphon displays 3 different responses: (1) a posterior pointing and leveling (flaring) of the siphon in response to tail stimulation (the siphon T response), (2) constriction and anterior pointing to head stimulation (the siphon H response) and (3) constriction and withdrawal between the animal's parapodia (the siphon S response). The siphon S response is pseudoconditioned by a noxious tail stimulus to resemble the siphon T response. Behavioral and combined behavioral/intracellular studies were conducted to determine the motor neuronal control of these behaviors and to search for mechanisms of siphon response transformation following pseudoconditioning. The present studies have found that the flaring component of pseudoconditioned siphon S responses occurs during mantle pumping (MP) triggered by noxious tail stimulation. Siphon stimulation also triggers MP, as recorded in neurons of the Interneuron II pattern generator which commands MP. The 4 LF$\rm\sb{SB}$ siphon motor neurons (SMNs) were found necessary and sufficient for the siphon T response, while SMNs RD$\rm\sb S$ and LD$\rm\sb{S1}$ were found necessary and sufficient for the siphon H response. Following pseudoconditioning, there is an increase in the number of evoked spikes to the test stimulus for the LF$\rm\sb{SB}$ cells and a decreased number for RD$\rm\sb S.$ Siphon flaring occurring during the pseudoconditioned response correlates with increased LF$\rm\sb{SB}$ activity during triggered MP cycles. This suggests that psuedoconditioning is in part due to reconfiguration of the motor outputs of the Interneuron II network. These results suggest that these defensive responses are controlled and patterned by a well-defined, finite set of motor neurons and interneurons (Interneuron II) that are dedicated to specific behavioral functions, but also have parallel distributed properties. ^

Respiratory rhythm generation: A modeling study of the respiratory central pattern generator and the phrenic motor neuron

The respiratory central pattern generator is a collection of medullary neurons that generates the rhythm of respiration. The respiratory central pattern generator feeds phrenic motor neurons, which, in turn, drive the main muscle of respiration, the diaphragm. The purpose of this thesis is to understand the neural control of respiration through mathematical models of the respiratory central pattern generator and phrenic motor neurons. ^ We first designed and validated a Hodgkin-Huxley type model that mimics the behavior of phrenic motor neurons under a wide range of electrical and pharmacological perturbations. This model was constrained physiological data from the literature. Next, we designed and validated a model of the respiratory central pattern generator by connecting four Hodgkin-Huxley type models of medullary respiratory neurons in a mutually inhibitory network. This network was in turn driven by a simple model of an endogenously bursting neuron, which acted as the pacemaker for the respiratory central pattern generator. Finally, the respiratory central pattern generator and phrenic motor neuron models were connected and their interactions studied. ^ Our study of the models has provided a number of insights into the behavior of the respiratory central pattern generator and phrenic motor neurons. These include the suggestion of a role for the T-type and N-type calcium channels during single spikes and repetitive firing in phrenic motor neurons, as well as a better understanding of network properties underlying respiratory rhythm generation. We also utilized an existing model of lung mechanics to study the interactions between the respiratory central pattern generator and ventilation. ^

STUDYING AGGREGATE FORMATION BY AMYOTROPHIC LATERAL SCLEROSIS-ASSOCIATED MUTANT SOD1 PROTEIN IN DROSOPHILA MODEL

A common pathological hallmark of most neurodegenerative disorders is the presence of protein aggregates in the brain. Understanding the regulation of aggregate formation is thus important for elucidating disease pathogenic mechanisms and finding effective preventive avenues and cures. Amyotrophic Lateral Sclerosis (ALS), also known as Lou Gehrig’s disease, is a selective neurodegenerative disorder predominantly affecting motor neurons. The majority of ALS cases are sporadic, however, mutations in superoxide dismutase 1 (SOD1) are responsible for about 20% of familial ALS (fALS). Mutated SOD1 proteins are prone to misfold and form protein aggregates, thus representing a good candidate for studying aggregate formation. The long-term goal of this project is to identify regulators of aggregate formation by mutant SOD1 and other ALS-associated disease proteins. The specific aim of this thesis project is to assess the possibility of using the well-established Drosophila model system to study aggregation by human SOD1 (hSOD1) mutants. To this end, using wild type and the three mutant hSOD1 (A4V, G85R and G93A) most commonly found among fALS, I have generated 16 different SOD1 constructs containing either eGFP or mCherry in-frame fluorescent reporters, established and tested both cell- and animal-based Drosophila hSOD1 models. The experimental strategy allows for clear visualization of ectopic hSOD1 expression as well as versatile co-expression schemes to fully investigate protein aggregation specifically by mutant hSOD1. I have performed pilot cell-transfection experiments and verified induced expression of hSOD1 proteins. Using several tissue- or cell type-specific Gal4 lines, I have confirmed the proper expression of hSOD1 from established transgenic fly lines. Interestingly, in both Drosophila S2 cells and different fly tissues including the eye and motor neurons, robust aggregate formation by either wild type or mutant hSOD1 proteins was not observed. These preliminary observations suggest that Drosophila might not be a good experimental organism to study aggregation and toxicity of mutant hSOD1 protein. Nevertheless this preliminary conclusion implies the potential existence of a potent protective mechanism against mutant hSOD1 aggregation and toxicity in Drosophila. Thus, results from my SOD1-ALS project in Drosophila will help future studies on how to best employ this classic model organism to study ALS and other human brain degenerative diseases.