Bifurcation and singularity analysis of a molecular network for the induction of long-term memory.

Withdrawal reflexes of the mollusk Aplysia exhibit sensitization, a simple form of long-term memory (LTM). Sensitization is due, in part, to long-term facilitation (LTF) of sensorimotor neuron synapses. LTF is induced by the modulatory actions of serotonin (5-HT). Pettigrew et al. developed a computational model of the nonlinear intracellular signaling and gene network that underlies the induction of 5-HT-induced LTF. The model simulated empirical observations that repeated applications of 5-HT induce persistent activation of protein kinase A (PKA) and that this persistent activation requires a suprathreshold exposure of 5-HT. This study extends the analysis of the Pettigrew model by applying bifurcation analysis, singularity theory, and numerical simulation. Using singularity theory, classification diagrams of parameter space were constructed, identifying regions with qualitatively different steady-state behaviors. The graphical representation of these regions illustrates the robustness of these regions to changes in model parameters. Because persistent protein kinase A (PKA) activity correlates with Aplysia LTM, the analysis focuses on a positive feedback loop in the model that tends to maintain PKA activity. In this loop, PKA phosphorylates a transcription factor (TF-1), thereby increasing the expression of an ubiquitin hydrolase (Ap-Uch). Ap-Uch then acts to increase PKA activity, closing the loop. This positive feedback loop manifests multiple, coexisting steady states, or multiplicity, which provides a mechanism for a bistable switch in PKA activity. After the removal of 5-HT, the PKA activity either returns to its basal level (reversible switch) or remains at a high level (irreversible switch). Such an irreversible switch might be a mechanism that contributes to the persistence of LTM. The classification diagrams also identify parameters and processes that might be manipulated, perhaps pharmacologically, to enhance the induction of memory. Rational drug design, to affect complex processes such as memory formation, can benefit from this type of analysis.

Predictive oncology: a review of multidisciplinary, multiscale in silico modeling linking phenotype, morphology and growth.

Empirical evidence and theoretical studies suggest that the phenotype, i.e., cellular- and molecular-scale dynamics, including proliferation rate and adhesiveness due to microenvironmental factors and gene expression that govern tumor growth and invasiveness, also determine gross tumor-scale morphology. It has been difficult to quantify the relative effect of these links on disease progression and prognosis using conventional clinical and experimental methods and observables. As a result, successful individualized treatment of highly malignant and invasive cancers, such as glioblastoma, via surgical resection and chemotherapy cannot be offered and outcomes are generally poor. What is needed is a deterministic, quantifiable method to enable understanding of the connections between phenotype and tumor morphology. Here, we critically assess advantages and disadvantages of recent computational modeling efforts (e.g., continuum, discrete, and cellular automata models) that have pursued this understanding. Based on this assessment, we review a multiscale, i.e., from the molecular to the gross tumor scale, mathematical and computational "first-principle" approach based on mass conservation and other physical laws, such as employed in reaction-diffusion systems. Model variables describe known characteristics of tumor behavior, and parameters and functional relationships across scales are informed from in vitro, in vivo and ex vivo biology. We review the feasibility of this methodology that, once coupled to tumor imaging and tumor biopsy or cell culture data, should enable prediction of tumor growth and therapy outcome through quantification of the relation between the underlying dynamics and morphological characteristics. In particular, morphologic stability analysis of this mathematical model reveals that tumor cell patterning at the tumor-host interface is regulated by cell proliferation, adhesion and other phenotypic characteristics: histopathology information of tumor boundary can be inputted to the mathematical model and used as a phenotype-diagnostic tool to predict collective and individual tumor cell invasion of surrounding tissue. This approach further provides a means to deterministically test effects of novel and hypothetical therapy strategies on tumor behavior.

Hebbian analysis of the transformation of medial entorhinal grid-cell inputs to hippocampal place fields.

The discovery of grid cells in the medial entorhinal cortex (MEC) permits the characterization of hippocampal computation in much greater detail than previously possible. The present study addresses how an integrate-and-fire unit driven by grid-cell spike trains may transform the multipeaked, spatial firing pattern of grid cells into the single-peaked activity that is typical of hippocampal place cells. Previous studies have shown that in the absence of network interactions, this transformation can succeed only if the place cell receives inputs from grids with overlapping vertices at the location of the place cell's firing field. In our simulations, the selection of these inputs was accomplished by fast Hebbian plasticity alone. The resulting nonlinear process was acutely sensitive to small input variations. Simulations differing only in the exact spike timing of grid cells produced different field locations for the same place cells. Place fields became concentrated in areas that correlated with the initial trajectory of the animal; the introduction of feedback inhibitory cells reduced this bias. These results suggest distinct roles for plasticity of the perforant path synapses and for competition via feedback inhibition in the formation of place fields in a novel environment. Furthermore, they imply that variability in MEC spiking patterns or in the rat's trajectory is sufficient for generating a distinct population code in a novel environment and suggest that recalling this code in a familiar environment involves additional inputs and/or a different mode of operation of the network.

Lobe specific Ca2+-calmodulin nano-domain in neuronal spines: a single molecule level analysis.

Calmodulin (CaM) is a ubiquitous Ca(2+) buffer and second messenger that affects cellular function as diverse as cardiac excitability, synaptic plasticity, and gene transcription. In CA1 pyramidal neurons, CaM regulates two opposing Ca(2+)-dependent processes that underlie memory formation: long-term potentiation (LTP) and long-term depression (LTD). Induction of LTP and LTD require activation of Ca(2+)-CaM-dependent enzymes: Ca(2+)/CaM-dependent kinase II (CaMKII) and calcineurin, respectively. Yet, it remains unclear as to how Ca(2+) and CaM produce these two opposing effects, LTP and LTD. CaM binds 4 Ca(2+) ions: two in its N-terminal lobe and two in its C-terminal lobe. Experimental studies have shown that the N- and C-terminal lobes of CaM have different binding kinetics toward Ca(2+) and its downstream targets. This may suggest that each lobe of CaM differentially responds to Ca(2+) signal patterns. Here, we use a novel event-driven particle-based Monte Carlo simulation and statistical point pattern analysis to explore the spatial and temporal dynamics of lobe-specific Ca(2+)-CaM interaction at the single molecule level. We show that the N-lobe of CaM, but not the C-lobe, exhibits a nano-scale domain of activation that is highly sensitive to the location of Ca(2+) channels, and to the microscopic injection rate of Ca(2+) ions. We also demonstrate that Ca(2+) saturation takes place via two different pathways depending on the Ca(2+) injection rate, one dominated by the N-terminal lobe, and the other one by the C-terminal lobe. Taken together, these results suggest that the two lobes of CaM function as distinct Ca(2+) sensors that can differentially transduce Ca(2+) influx to downstream targets. We discuss a possible role of the N-terminal lobe-specific Ca(2+)-CaM nano-domain in CaMKII activation required for the induction of synaptic plasticity.

Behavioral and cellular analysis of classical conditioning of feeding behavior in Aplysia

In classical conditioning, an associative form of learning, animals learn to associate two stimuli. Cellular and molecular mechanisms for the induction and consolidation of associative learning and memory at the level of single cells and synaptic connections have been studied in both vertebrate and invertebrate animals. The majority of studies, however, relied on aversive stimuli to induce learning. This bias may limit the extent to which identified mechanisms generalize to other forms of associative learning and memory, such as appetitive forms. The goal of the present study was to develop a classical conditioning procedure for the marine mollusk Aplysia californica using appetitive reinforcement, and to analyze associative learning using behavioral and electrophysiological techniques. ^ Using tactile stimulation of the lips as the conditional stimulus (CS) and food as the unconditional stimulus (US) a training protocol was developed that reliably induced classical conditioning of feeding behavior. Memory persisted for at least 24 hours. The gross organization of reinforcement-mediating pathways was analyzed in additional behavioral experiments. Moreover, neurophysiological correlates of classical conditioning were identified and characterized in an in vitro preparation containing the circuitry for feeding behavior. In vitro stimulation of a nerve (AT4) that may mediate the CS during training, resulted in a greater number of buccal motor patterns (BMPs) in brains from conditioned animals, as compared to control animals. The majority of these BMPs were ingestion-like, consistent with the increased number of bites in response to the CS after classical conditioning. Moreover, classical conditioning correlated with increased excitatory synaptic input to BMP-initiating neuron B31/32, in response to stimulation of AT 4, as compared to controls. The expression of the correlates of classical conditioning identified in this study was specific to stimulation of AT 4, which is consistent the stimulus specificity that is characteristic for classical conditioning. ^ The identification of cellular correlates of classical conditioning documented here provides the basis for future, more detailed analyses of an appetitive form of associative learning and memory, that may extend the working knowledge of the cellular and molecular mechanisms for associative plasticity in general. ^

Learning -dependent plasticity of movement representations in the primate primary motor cortex

Primary motor cortex (M1) is involved in the production of voluntary movement and contains a complete functional representation, or map, of the skeletal musculature. This functional map can be altered by pathological experiences, such as peripheral nerve injury or stroke, by pharmacological manipulation, and by behavioral experience. The process by which experience-dependent alterations of cortical function occur is termed plasticity. In this thesis, plasticity of M1 functional organization as a consequence of behavioral experience was examined in adult primates (squirrel monkeys). Maps of movement representations were derived under anesthesia using intracortical microstimulation, whereby a microelectrode was inserted into the cortex to electrically stimulate corticospinal neurons at low current levels and evoke movements of the forelimb, principally of the hand. Movement representations were examined before and at several times after training on behavioral tasks that emphasized use of the fingers. Two behavioral tasks were utilized that dissociated the repetition of motor activity from the acquisition of motor skills. One task was easy to perform, and as such promoted repetitive motor activity without learning. The other task was more difficult, requiring the acquisition of motor skills for successful performance. Kinematic analysis indicated that monkeys used a consistent set of forelimb movements during pellet extractions. Functional mapping revealed that repetitive motor activity during the easier task did not produce plastic changes in movement representations. Instead, map plasticity, in the form of selective expansions of task-related movement representations, was only produced following skill acquisition on the difficult task. Additional studies revealed that, in general, map plasticity persisted without further training for up to three months, in parallel with the retention of task-related motor skills. Also, extensive additional training on the small well task produced further improvements in performance, and further changes in movement maps. In sum, these experiments support the following three conclusions regarding the role of M1 in motor learning. First, behaviorally-driven plasticity is learning-dependent, not activity-dependent. Second, plastic changes in M1 functional representations represent a neural correlate of acquired motor skills. Third, the persistence of map plasticity suggests that M1 is part of the neural substrate for the memory of motor skills. ^