AN ILLNESS-DEATH PROCESS WITH TIME-DEPENDENT COVARIATES

A general model for the illness-death stochastic process with covariates has been developed for the analysis of survival data. This model incorporates important baseline and time-dependent covariates to make proper adjustment for the transition probabilities and survival probabilities. The follow-up period is subdivided into small intervals and a constant hazard is assumed for each interval. An approximation formula is derived to estimate the transition parameters when the exact transition time is unknown.^ The method developed is illustrated by using data from a study on the prevention of the recurrence of a myocardial infarction and subsequent mortality, the Beta-Blocker Heart Attack Trial (BHAT). This method provides an analytical approach which simultaneously includes provision for both fatal and nonfatal events in the model. According to this analysis, the effectiveness of the treatment can be compared between the Placebo and Propranolol treatment groups with respect to fatal and nonfatal events. ^

Interim analysis of clinical trials: Simulation studies of fractional Brownian motion

Interim clinical trial monitoring procedures were motivated by ethical and economic considerations. Classical Brownian motion (Bm) techniques for statistical monitoring of clinical trials were widely used. Conditional power argument and α-spending function based boundary crossing probabilities are popular statistical hypothesis testing procedures under the assumption of Brownian motion. However, it is not rare that the assumptions of Brownian motion are only partially met for trial data. Therefore, I used a more generalized form of stochastic process, called fractional Brownian motion (fBm), to model the test statistics. Fractional Brownian motion does not hold Markov property and future observations depend not only on the present observations but also on the past ones. In this dissertation, we simulated a wide range of fBm data, e.g., H = 0.5 (that is, classical Bm) vs. 0.5< H <1, with treatment effects vs. without treatment effects. Then the performance of conditional power and boundary-crossing based interim analyses were compared by assuming that the data follow Bm or fBm. Our simulation study suggested that the conditional power or boundaries under fBm assumptions are generally higher than those under Bm assumptions when H > 0.5 and also matches better with the empirical results. ^

Developing the follow-up schedules for women with breast cancer

Background: The follow-up care for women with breast cancer requires an understanding of disease recurrence patterns and the follow-up visit schedule should be determined according to the times when the recurrence are most likely to occur, so that preventive measure can be taken to avoid or minimize the recurrence. Objective: To model breast cancer recurrence through stochastic process with an aim to generate a hazard function for determining a follow-up schedule. Methods: We modeled the process of disease progression as the time transformed Weiner process and the first-hitting-time was used as an approximation of the true failure time. The women's "recurrence-free survival time" or a "not having the recurrence event" is modeled by the time it takes Weiner process to cross a threshold value which represents a woman experiences breast cancer recurrence event. We explored threshold regression model which takes account of covariates that contributed to the prognosis of breast cancer following development of the first-hitting time model. Using real data from SEER-Medicare, we proposed models of follow-up visits schedule on the basis of constant probability of disease recurrence between consecutive visits. Results: We demonstrated that the threshold regression based on first-hitting-time modeling approach can provide useful predictive information about breast cancer recurrence. Our results suggest the surveillance and follow-up schedule can be determined for women based on their prognostic factors such as tumor stage and others. Women with early stage of disease may be seen less frequently for follow-up visits than those women with locally advanced stages. Our results from SEER-Medicare data support the idea of risk-controlled follow-up strategies for groups of women. Conclusion: The methodology we proposed in this study allows one to determine individual follow-up scheduling based on a parametric hazard function that incorporates known prognostic factors.^

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.

Intra-hippocampal administration of the VEGF receptor blocker PTK787/ZK222584 impairs long-term memory.

A number of studies have established a role for vascular endothelial growth factor (VEGF) in angiogenesis. Recent reports have shown that VEGF overexpression in the hippocampus improves learning and memory and is associated with enhanced neurogenesis. PTK787/ZK222584 (PTK/ZK) is a reported inhibitor of VEGFR signaling that is currently being tested for its effects on lung and colon cancer. However, the influence of this drug on cognition has not been examined. In the present study, we questioned if post-training administration of PTK/ZK influences hippocampus-dependent memory. When administered to rats immediately following massed training in the Morris water maze, PTK/ZK impaired spatial memory retention tested 48 h later. This impairment was evidenced by increased latency to the hidden platform and fewer platform crossings. However, this impairment was not associated with a change in neurogenesis during this time frame. PTK/ZK infusion did not reduce VEGFR or AKT phosphorylation, but increased the phosphorylation of ERK. These studies suggest that VEGFR inhibitors such as PTK/ZK may negatively influence cognition.

Interlinked dual-time feedback loops can enhance robustness to stochasticity and persistence of memory.

Multiple interlinked positive feedback loops shape the stimulus responses of various biochemical systems, such as the cell cycle or intracellular Ca2+ release. Recent studies with simplified models have identified two advantages of coupling fast and slow feedback loops. This dual-time structure enables a fast response while enhancing resistances of responses and bistability to stimulus noise. We now find that (1) the dual-time structure similarly confers resistance to internal noise due to molecule number fluctuations, and (2) model variants with altered coupling, which better represent some specific biochemical systems, share all the above advantages. We also develop a similar bistable model with coupling of a fast autoactivation loop to a slow loop. This model's topology was suggested by positive feedback proposed to play a role in long-term synaptic potentiation (LTP). The advantages of fast response and noise resistance are also present in this autoactivation model. Empirically, LTP develops resistance to reversal over approximately 1h . The model suggests this resistance may result from increased amounts of synaptic kinases involved in positive feedback.

A model of late long-term potentiation simulates aspects of memory maintenance.

Late long-term potentiation (L-LTP) denotes long-lasting strengthening of synapses between neurons. L-LTP appears essential for the formation of long-term memory, with memories at least partly encoded by patterns of strengthened synapses. How memories are preserved for months or years, despite molecular turnover, is not well understood. Ongoing recurrent neuronal activity, during memory recall or during sleep, has been hypothesized to preferentially potentiate strong synapses, preserving memories. This hypothesis has not been evaluated in the context of a mathematical model representing ongoing activity and biochemical pathways important for L-LTP. In this study, ongoing activity was incorporated into two such models - a reduced model that represents some of the essential biochemical processes, and a more detailed published model. The reduced model represents synaptic tagging and gene induction simply and intuitively, and the detailed model adds activation of essential kinases by Ca(2+). Ongoing activity was modeled as continual brief elevations of Ca(2+). In each model, two stable states of synaptic strength/weight resulted. Positive feedback between synaptic weight and the amplitude of ongoing Ca(2+) transients underlies this bistability. A tetanic or theta-burst stimulus switches a model synapse from a low basal weight to a high weight that is stabilized by ongoing activity. Bistability was robust to parameter variations in both models. Simulations illustrated that prolonged periods of decreased activity reset synaptic strengths to low values, suggesting a plausible forgetting mechanism. However, episodic activity with shorter inactive intervals maintained strong synapses. Both models support experimental predictions. Tests of these predictions are expected to further understanding of how neuronal activity is coupled to maintenance of synaptic strength. Further investigations that examine the dynamics of activity and synaptic maintenance can be expected to help in understanding how memories are preserved for up to a lifetime in animals including humans.

Post-translational regulation of an Aplysia glutamate transporter during long-term facilitation.

Regulation of glutamate transporters accompanies plasticity of some glutamatergic synapses. The regulation of glutamate uptake at the Aplysia sensorimotor synapse during long-term facilitation (LTF) was investigated. Previously, increases in levels of ApGT1 (Aplysia glutamate transporter 1) in synaptic membranes were found to be related to long-term increases in glutamate uptake. In this study, we found that regulation of ApGT1 during LTF appears to occur post-translationally. Serotonin (5-HT) a transmitter that induces LTF did not increase synthesis of ApGT1. A pool of ApGT1 appears to exist in sensory neuron somata, which is transported to the terminals by axonal transport. Blocking the rough endoplasmic reticulum-Golgi-trans-Golgi network (TGN) pathway with Brefeldin A prevented the 5-HT-induced increase of ApGT1 in terminals. Also, 5-HT produced changes in post-translational modifications of ApGT1 as well as changes in the levels of an ApGT1-co-precipitating protein. These results suggest that regulation of trafficking of ApGT1 from the vesicular trafficking system (rough endoplasmic reticulum-Golgi-TGN) in the sensory neuron somata to the terminals by post-translational modifications and protein interactions appears to be the mechanism underlying the increase in ApGT1, and thus, glutamate uptake during memory formation.

Beta 1-integrins are required for hippocampal AMPA receptor-dependent synaptic transmission, synaptic plasticity, and working memory.

Integrins comprise a large family of cell adhesion receptors that mediate diverse biological events through cell-cell and cell-extracellular matrix interactions. Recent studies have shown that several integrins are localized to synapses with suggested roles in synaptic plasticity and memory formation. We generated a postnatal forebrain and excitatory neuron-specific knock-out of beta1-integrin in the mouse. Electrophysiological studies demonstrated that these mutants have impaired synaptic transmission through AMPA receptors and diminished NMDA receptor-dependent long-term potentiation. Despite the impairment in hippocampal synaptic transmission, the mutants displayed normal hippocampal-dependent spatial and contextual memory but were impaired in a hippocampal-dependent, nonmatching-to-place working memory task. These phenotypes parallel those observed in animals carrying knock-outs of the GluR1 (glutamate receptor subunit 1) subunit of the AMPA receptor. These observations suggest a new function of beta1-integrins as regulators of synaptic glutamate receptor function and working memory.

Dynamics of a minimal model of interlocked positive and negative feedback loops of transcriptional regulation by cAMP-response element binding proteins.

cAMP-response element binding (CREB) proteins are involved in transcriptional regulation in a number of cellular processes (e.g., neural plasticity and circadian rhythms). The CREB family contains activators and repressors that may interact through positive and negative feedback loops. These loops can be generated by auto- and cross-regulation of expression of CREB proteins, via CRE elements in or near their genes. Experiments suggest that such feedback loops may operate in several systems (e.g., Aplysia and rat). To understand the functional implications of such feedback loops, which are interlocked via cross-regulation of transcription, a minimal model with a positive and negative loop was developed and investigated using bifurcation analysis. Bifurcation analysis revealed diverse nonlinear dynamics (e.g., bistability and oscillations). The stability of steady states or oscillations could be changed by time delays in the synthesis of the activator (CREB1) or the repressor (CREB2). Investigation of stochastic fluctuations due to small numbers of molecules of CREB1 and CREB2 revealed a bimodal distribution of CREB molecules in the bistability region. The robustness of the stable HIGH and LOW states of CREB expression to stochastic noise differs, and a critical number of molecules was required to sustain the HIGH state for days or longer. Increasing positive feedback or decreasing negative feedback also increased the lifetime of the HIGH state, and persistence of this state may correlate with long-term memory formation. A critical number of molecules was also required to sustain robust oscillations of CREB expression. If a steady state was near a deterministic Hopf bifurcation point, stochastic resonance could induce oscillations. This comparative analysis of deterministic and stochastic dynamics not only provides insights into the possible dynamics of CREB regulatory motifs, but also demonstrates a framework for understanding other regulatory processes with similar network architecture.

Long-lasting synaptic potentiation induced by depolarization under conditions that eliminate detectable Ca2+ signals.

Activity-dependent alterations of synaptic transmission important for learning and memory are often induced by Ca(2+) signals generated by depolarization. While it is widely assumed that Ca(2+) is the essential transducer of depolarization into cellular plasticity, little effort has been made to test whether Ca(2+)-independent responses to depolarization might also induce memory-like alterations. It was recently discovered that peripheral axons of nociceptive sensory neurons in Aplysia display long-lasting hyperexcitability triggered by conditioning depolarization in the absence of Ca(2+) entry (using nominally Ca(2+)-free solutions containing EGTA, "0Ca/EGTA") or the absence of detectable Ca(2+) transients (adding BAPTA-AM, "0Ca/EGTA/BAPTA-AM"). The current study reports that depolarization of central ganglia to approximately 0 mV for 2 min in these same solutions induced hyperexcitability lasting >1 h in sensory neuron processes near their synapses onto motor neurons. Furthermore, conditioning depolarization in these solutions produced a 2.5-fold increase in excitatory postsynaptic potential (EPSP) amplitude 1-3 h afterward despite a drop in motor neuron input resistance. Depolarization in 0 Ca/EGTA produced long-term potentiation (LTP) of the EPSP lasting > or = 1 days without changing postsynaptic input resistance. When re-exposed to extracellular Ca(2+) during synaptic tests, prior exposure to 0Ca/EGTA or to 0Ca/EGTA/BAPTA-AM decreased sensory neuron survival. However, differential effects on neuronal health are unlikely to explain the observed potentiation because conditioning depolarization in these solutions did not alter survival rates. These findings suggest that unrecognized Ca(2+)-independent signals can transduce depolarization into long-lasting synaptic potentiation, perhaps contributing to persistent synaptic alterations following large, sustained depolarizations that occur during learning, neural injury, or seizures.

Molluscan memory of injury: evolutionary insights into chronic pain and neurological disorders.

Molluscan preparations have yielded seminal discoveries in neuroscience, but the experimental advantages of this group have not, until now, been complemented by adequate molecular or genomic information for comparisons to genetically defined model organisms in other phyla. The recent sequencing of the transcriptome and genome of Aplysia californica, however, will enable extensive comparative studies at the molecular level. Among other benefits, this will bring the power of individually identifiable and manipulable neurons to bear upon questions of cellular function for evolutionarily conserved genes associated with clinically important neural dysfunction. Because of the slower rate of gene evolution in this molluscan lineage, more homologs of genes associated with human disease are present in Aplysia than in leading model organisms from Arthropoda (Drosophila) or Nematoda (Caenorhabditis elegans). Research has hardly begun in molluscs on the cellular functions of gene products that in humans are associated with neurological diseases. On the other hand, much is known about molecular and cellular mechanisms of long-term neuronal plasticity. Persistent nociceptive sensitization of nociceptors in Aplysia displays many functional similarities to alterations in mammalian nociceptors associated with the clinical problem of chronic pain. Moreover, in Aplysia and mammals the same cell signaling pathways trigger persistent enhancement of excitability and synaptic transmission following noxious stimulation, and these highly conserved pathways are also used to induce memory traces in neural circuits of diverse species. This functional and molecular overlap in distantly related lineages and neuronal types supports the proposal that fundamental plasticity mechanisms important for memory, chronic pain, and other lasting alterations evolved from adaptive responses to peripheral injury in the earliest neurons. Molluscan preparations should become increasingly useful for comparative studies across phyla that can provide insight into cellular functions of clinically important genes.

Long-lasting hyperexcitability induced by depolarization in the absence of detectable Ca2+ signals.

Learning and memory depend on neuronal alterations induced by electrical activity. Most examples of activity-dependent plasticity, as well as adaptive responses to neuronal injury, have been linked explicitly or implicitly to induction by Ca(2+) signals produced by depolarization. Indeed, transient Ca(2+) signals are commonly assumed to be the only effective transducers of depolarization into adaptive neuronal responses. Nevertheless, Ca(2+)-independent depolarization-induced signals might also trigger plastic changes. Establishing the existence of such signals is a challenge because procedures that eliminate Ca(2+) transients also impair neuronal viability and tolerance to cellular stress. We have taken advantage of nociceptive sensory neurons in the marine snail Aplysia, which exhibit unusual tolerance to extreme reduction of extracellular and intracellular free Ca(2+) levels. The axons of these neurons exhibit a depolarization-induced memory-like hyperexcitability that lasts a day or longer and depends on local protein synthesis for induction. Here we show that transient localized depolarization of these axons in an excised nerve-ganglion preparation or in dissociated cell culture can induce short- and intermediate-term axonal hyperexcitability as well as long-term protein synthesis-dependent hyperexcitability under conditions in which Ca(2+) entry is prevented (by bathing in nominally Ca(2+) -free solutions containing EGTA) and detectable Ca(2+) transients are eliminated (by adding BAPTA-AM). Disruption of Ca(2+) release from intracellular stores by pretreatment with thapsigargin also failed to affect induction of axonal hyperexcitability. These findings suggest that unrecognized Ca(2+)-independent signals exist that can transduce intense depolarization into adaptive cellular responses during neuronal injury, prolonged high-frequency activity, or other sustained depolarizing events.

Dynamics of a minimal model of interlocked positive and negative feedback loops of transcriptional regulation by cAMP-response element binding proteins.

cAMP-response element binding (CREB) proteins are involved in transcriptional regulation in a number of cellular processes (e.g., neural plasticity and circadian rhythms). The CREB family contains activators and repressors that may interact through positive and negative feedback loops. These loops can be generated by auto- and cross-regulation of expression of CREB proteins, via CRE elements in or near their genes. Experiments suggest that such feedback loops may operate in several systems (e.g., Aplysia and rat). To understand the functional implications of such feedback loops, which are interlocked via cross-regulation of transcription, a minimal model with a positive and negative loop was developed and investigated using bifurcation analysis. Bifurcation analysis revealed diverse nonlinear dynamics (e.g., bistability and oscillations). The stability of steady states or oscillations could be changed by time delays in the synthesis of the activator (CREB1) or the repressor (CREB2). Investigation of stochastic fluctuations due to small numbers of molecules of CREB1 and CREB2 revealed a bimodal distribution of CREB molecules in the bistability region. The robustness of the stable HIGH and LOW states of CREB expression to stochastic noise differs, and a critical number of molecules was required to sustain the HIGH state for days or longer. Increasing positive feedback or decreasing negative feedback also increased the lifetime of the HIGH state, and persistence of this state may correlate with long-term memory formation. A critical number of molecules was also required to sustain robust oscillations of CREB expression. If a steady state was near a deterministic Hopf bifurcation point, stochastic resonance could induce oscillations. This comparative analysis of deterministic and stochastic dynamics not only provides insights into the possible dynamics of CREB regulatory motifs, but also demonstrates a framework for understanding other regulatory processes with similar network architecture.

ROLE OF SYNAPSIN IN LONG-TERM SYNAPTIC FACILITATION IN APLYSIA

Enhanced expression of the presynaptic protein synapsin has been correlated with certain forms of long-term plasticity and learning and memory. However, the regulation and requirement for enhanced synapsin expression in long-term memory remains unknown. In the present study the technical advantages of the marine mollusc Aplysia were exploited in order to address this issue. In Aplysia, learning-induced enhancement in synaptic strength is modulated by serotonin (5-HT) and treatment with 5-HT in vitro of the sensorimotor synapse induces long-term facilitation (LTF) of synaptic transmission, which lasts for days, as well as the formation of new connections between the sensory and motor neuron. Results from immunofluorescence analysis indicated that 5-HT treatment upregulates synapsin protein levels within sensory neuron varicosities, the presumed site of neurotransmitter release. To investigate the mechanisms underlying increased synapsin expression, the promoter region of the Aplysia synapsin gene was cloned and a cAMP response element (CRE) was identified, raising the possibility that the transcriptional activator cAMP response element-binding protein-1 (CREB1) mediates the 5-HT-induced regulation of synapsin. Results from Chromatin Immunoprecipitation (ChIP) assays indicated that 5-HT treatment enhanced association of CREB1 surrounding the CRE site in the synapsin promoter and led to increased acetylation of histones H3 and H4 and decreased association of histone deacetylase 5 surrounding the CRE site in the synapsin promoter, a sign of transcriptional activation. In addition, sensory neurons injected with an enhanced green fluorescent protein (EGFP) reporter vector driven by the synapsin promoter exhibited a significant increase in EGFP expression following treatment with 5-HT. These results suggest that synapsin expression is regulated by 5-HT in part through transcriptional activation of the synapsin gene and through CREB1 association with the synapsin promoter. Furthermore, RNA interference that blocks 5-HT-induced elevation of synapsin expression also blocked long-term synaptic facilitation. These results indicate that 5-HT-induced regulation of synapsin is necessary for LTF and that synapsin is part of the cascade of synaptic events involved in the consolidation of memory.