A biophysical model of synaptic plasticity and metaplasticity can account for the dynamics of the backward shift of hippocampal place fields.

Hippocampal place cells in the rat undergo experience-dependent changes when the rat runs stereotyped routes. One such change, the backward shift of the place field center of mass, has been linked by previous modeling efforts to spike-timing-dependent plasticity (STDP). However, these models did not account for the termination of the place field shift and they were based on an abstract implementation of STDP that ignores many of the features found in cortical plasticity. Here, instead of the abstract STDP model, we use a calcium-dependent plasticity (CaDP) learning rule that can account for many of the observed properties of cortical plasticity. We use the CaDP learning rule in combination with a model of metaplasticity to simulate place field dynamics. Without any major changes to the parameters of the original model, the present simulations account both for the initial rapid place field shift and for the subsequent slowing down of this shift. These results suggest that the CaDP model captures the essence of a general cortical mechanism of synaptic plasticity, which may underlie numerous forms of synaptic plasticity observed both in vivo and in vitro.

Temporal and spatial regulation of cell division by the nucleoid in Escherichia coli

Selection of division sites and coordination of cytokinesis with other cell cycle events are critical for every organism to proliferate. In E. coli, the nucleoid is proposed to exclude division from the site of the chromosome (nucleoid occlusion model). We studied the effect of the nucleoid on timing and placement of cell division. An early cell division protein, FtsZ, was used to follow development of the division septum. FtsZ forms a ring structure (Z ring) at potential division sites. The dynamics of Z ring was visualized in live cells by fusing FtsZ with a green fluorescent protein (GFP). Emanating FtsZ-GFP polymers from the constricted septum or aggregates in daughter cells were also observed, probably representing the FtsZ depolymerization and immature FtsZ nucleation processes. We next examined the nucleoid occlusion model. Mutants carrying abnormally positioned chromosomes were employed. In chromosomal partition mutants, replicated chromosomes cannot segregate. The Z ring was excluded from midcell to the edge of the nucleoid. This negative effect of nucleoids was further confirmed in replication deficient dnaA mutants, in which only a single chromosome is present in the cell center. These results suggest that the nucleoid, replicating or not, inhibits division in the area where the chromosome occupies. In addition, increasing the level of FtsZ does not overcome nucleoid inhibition. Interestingly in anucleate cells produced by both mutants, the Z ring was localized in the central part of the cell, which indicates that the nucleoid is not required for FtsZ assembly. Relaxation of chromosomes by reducing the gyrase activity or disruption of protein translation/translocation did not abolish the division inhibition capacity of the nucleoid. However, preventing transcription did compromise the nucleoid occlusion effect, leading to formation of multiple FtsZ rings above the nucleoid. In summary, we demonstrate that nucleoids negatively regulate the timing and position of division by inhibiting FtsZ assembly at unselected sites. Relief of this inhibition at midcell is coincident with the completion of DNA replication. On the other hand, FtsZ assembly does not require the nucleoid. ^

The dynamics of calmodulin signaling revealed using optical methods

The Ca2+-binding protein calmodulin (CaM) is a key transducer of Ca2+ oscillations by virtue of its ability to bind Ca 2+ selectively and then interact specifically with a large number of downstream enzymes and proteins. It remains unclear whether Ca2+ -dependent signaling alone can activate the full range of Ca 2+/CaM regulated processes or whether other regulatory schemes in the cell exist that allow specific targeting of CaM to subsets of Ca 2+/CaM binding sites or regions of the cell. Here we investigate the possibility that alterations of the availability of CaM may serve as a potential cellular mechanism for regulating the activation of CaM-dependent targets. By utilizing sensitive optical techniques with high spatial and temporal resolution, we examine the intracellular dynamics of CaM signaling at a resolution previously unattainable. After optimizing and characterizing both the optical methods and fluorescently labeled probes for intracellular measurements, the diffusion of CaM in the cytoplasm of HEK293 cells was analyzed. It was discovered that the diffusion characteristics of CaM are similar to that of a comparably sized inert molecule. Independent manipulation of experimental parameters, including increases in total concentrations of CaM and intracellular Ca2+ levels, did not change the diffusion of CaM in the cytoplasm. However, changes in diffusion were seen when the concentration of Ca2+/CaM-binding targets was increased in conjunction with elevated Ca2+. This indicates that CaM is not normally limiting for the activation of Ca 2+/CaM-dependent enzymes in HEK293 cells but reveals that the ratio of CaM to CaM-dependent targets is a potential mechanism for changing CaM availability. Next we considered whether cellular compartmentalization may act to regulate concentrations of available Ca2+/CaM in hippocampal neurons. We discovered changes in diffusion parameters of CaM under elevated Ca2+ conditions in the soma, neurite and nucleus which suggest that either the composition of cytoplasm is different in these compartments and/or they are composed of unique families of CaM-binding proteins. Finally, we return to the HEK293 cell and for the first time directly show the intracellular binding of CaM and CaMKII, an important target for CaM critical for neuronal function and plasticity. Furthermore, we analyzed the complex binding stoichiometry of this molecular interaction in the basal, activated and autophosphorylated states of CaMKII and determined the impact of this binding on CaM availability in the cell. Overall these results demonstrate that regulation of CaM availability is a viable cellular mechanism for regulating the output of CaM-dependent processes and that this process is tuned to the specific functional needs of a particular cell type and subcellular compartment. ^

NONLINEAR TIME SERIES/SYSTEM ANALYSIS (STATE-SPACE, DYNAMICS, INTERVENTION, RESILIENCE, KALMAN)

A discussion of nonlinear dynamics, demonstrated by the familiar automobile, is followed by the development of a systematic method of analysis of a possibly nonlinear time series using difference equations in the general state-space format. This format allows recursive state-dependent parameter estimation after each observation thereby revealing the dynamics inherent in the system in combination with random external perturbations.^ The one-step ahead prediction errors at each time period, transformed to have constant variance, and the estimated parametric sequences provide the information to (1) formally test whether time series observations y(,t) are some linear function of random errors (ELEM)(,s), for some t and s, or whether the series would more appropriately be described by a nonlinear model such as bilinear, exponential, threshold, etc., (2) formally test whether a statistically significant change has occurred in structure/level either historically or as it occurs, (3) forecast nonlinear system with a new and innovative (but very old numerical) technique utilizing rational functions to extrapolate individual parameters as smooth functions of time which are then combined to obtain the forecast of y and (4) suggest a measure of resilience, i.e. how much perturbation a structure/level can tolerate, whether internal or external to the system, and remain statistically unchanged. Although similar to one-step control, this provides a less rigid way to think about changes affecting social systems.^ Applications consisting of the analysis of some familiar and some simulated series demonstrate the procedure. Empirical results suggest that this state-space or modified augmented Kalman filter may provide interesting ways to identify particular kinds of nonlinearities as they occur in structural change via the state trajectory.^ A computational flow-chart detailing computations and software input and output is provided in the body of the text. IBM Advanced BASIC program listings to accomplish most of the analysis are provided in the appendix. ^