Paul Smolen

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. Empirica...

Mutations in the gene encoding CREB-binding protein (CBP) cause deficits in long-term plasticity, learning, and memory. Here, long-term synaptic facilitation (LTF) at Aplysia sensorimotor synapses in cell culture was used as a model system to investigate methods for overcoming deficits in LTF produced by a CBP knockdown. Injecting CBP-siRNA into individual sensory neurons reduced CBP levels and impaired LTF produced by a standard protocol of five 5-min pulses of serotonin (5-HT) delivered at 20 min interstimulus intervals. A computational model, which simulated molecular processes underlying LTF induction, predicted a rescue protocol of five pulses of 5-HT at non-uniform interstimulus intervals that overcame the consequences of reduced CBP and restored LTF. These results suggest that complementary empirical and computational studies can identify methods for ameliorating impairments of learning attributable to molecular lesions.

Memory impairment is often associated with disrupted regulation of gene induction. For example, deficits in cAMP response element-binding protein (CREB) binding protein (CBP; an essential cofactor for activation of transcription by CREB) impair long-term synaptic plasticity and memory. Previously, we showed that small interfering RNA (siRNA)-induced knockdown of CBP in individual sensory neurons significantly reduced levels of CBP and impaired 5-HT-induced long-term facilitation (LTF) in sensorimotor cocultures from Aplysia. Moreover, computational simulations of the biochemical cascades underlying LTF successfully predicted training protocols that restored LTF following CBP knockdown. We examined whether simulations could also predict a training protocol that restores LTF impaired by siRNA-induced knockdown of the transcription factor CREB1. Simulations based on a previously described model predicted rescue protocols that were specific to CREB1 knockdown. Empirical studies demonstr...

Protein synthesis-dependent, late long-term potentiation (LTP) and depression (LTD) at glutamatergic hippocampal synapses are well characterized examples of long-term synaptic plasticity. Persistent increased activity of protein kinase M ζ (PKMζ) is thought essential for maintaining LTP. Additional spatial and temporal features that govern LTP and LTD induction are embodied in the synaptic tagging and capture (STC) and cross capture hypotheses. Only synapses that have been "tagged" by a stimulus sufficient for LTP and learning can "capture" PKMζ. A model was developed to simulate the dynamics of key molecules required for LTP and LTD. The model concisely represents relationships between tagging, capture, LTD, and LTP maintenance. The model successfully simulated LTP maintained by persistent synaptic PKMζ, STC, LTD, and cross capture, and makes testable predictions concerning the dynamics of PKMζ. The maintenance of LTP, and consequently of at least some forms of long-term memory, is predicted to require continual positive feedback in which PKMζ enhances its own synthesis only at potentiated synapses. This feedback underlies bistability in the activity of PKMζ. Second, cross capture requires the induction of LTD to induce dendritic PKMζ synthesis, although this may require tagging of a nearby synapse for LTP. The model also simulates the effects of PKMζ inhibition, and makes additional predictions for the dynamics of CaM kinases. Experiments testing the above predictions would significantly advance the understanding of memory maintenance.

We have developed a reduced model representing feedback loops of transcriptional regulation underlying circadian rhythms in Neurospora crassa. The model contains two delay differential equations that describe the dynamics of two core gene products, FRQ and WCC. In a negative feedback loop, FRQ protein represses frq transcription by binding the white-collar complex (WCC), which consists of the WC-1 and WC-2 proteins. In a positive feedback loop, WCC indirectly enhances its own formation. The model simulates circadian oscillations, light entrainment, and a phase-response curve (PRC) similar to experimental PRCs. The Neurospora model is virtually identical to a model describing Drosophila circadian rhythm generation, illustrating that rhythm generation in these divergent organisms shares important mechanistic elements. Significant dynamic differences were found when the parameter spaces of both models were explored to analyze changes in oscillations and bifurcations to steady states. Stochastic fluctuations in molecule numbers were simulated with the Gillespie algorithm. Circadian oscillations and entrainment to light were simulated with <80 molecules of FRQ and WCC present on average. Simulations suggest that in both Neurospora and Drosophila, only the negative feedback loop is essential for circadian oscillations. Similar models may aid understanding of circadian mechanisms in mammals and other organisms.

The sensorimotor synapse of Aplysia exhibits long-term facilitation (LTF) and long-term depression (LTD) elicited by the neuromodulator serotonin (5-HT) and the peptide Phe-Met-Arg-Phe-NH(2), respectively. 5-HT-induced LTF engages extracellular-regulated kinase (Erk) and CREB1, whereas FMRFa-induced LTD engages p38 MAPK (mitogen-activated protein kinase) and CREB2. The interaction of the 5-HT and FMRFa pathways was recently investigated in Aplysia at the level of gene expression. However, little is known about crosstalk of these pathways at the level of the second messenger cascades. We investigated the potential interaction of the 5-HT and FMRFa pathways at the level of the Erk cascade. We found that FMRFa inhibited basal Erk activity through p38 MAPK. FMRFa also inhibited 5-HT-induced phosphorylation of Erk and nuclear accumulation of phospho-ERK, suggesting that FMRFa may place inhibitory constraints on memory formation through regulation of the Erk MAPK cascade.

Relaxation oscillators that depend on one slow variable, such as the Fitzhugh-Nagumo oscillator, reset in a phase-dependent manner. A complete oscillation can be divided into two parts, the "plateau" and "trough", and a prematurely induced plateau or trough is significantly shorter than normal. The class of square-wave bursting oscillators can be viewed as relaxation oscillators with rapid spikes during the plateau, and reset similarly when modeled with one slow variable. However, it has been reported that a physiological bursting oscillator, the membrane potential of the pancreatic beta-cell, resets in a phase-independent manner, such that a prematurely induced plateau/trough has normal length. A possible model for such an oscillator requires two slow variables, one to control the length of the plateau and the other the length of the trough. Here, we explore the geometric solution structure of two such models, which exhibit the desired resetting. One is a generalization of the Fitzhugh-Nagumo equations, and the other is a bursting oscillator using known beta-cell electrical currents with an additional hypothetical slow outward current.

Many neurological disorders are based on mutations in 1 or more genes. To understand and optimally treat these disorders, it is necessary to understand the functions and regulation of the genes involved. It has become apparent that intuitive descriptions of gene regulation are often insufficient. A mathematical description adds precision and detail. Therefore, a mathematical description is important for networks of genes that underlie development, synaptic plasticity, and other complex biological processes. A mathematical description is also important to represent the combined effects of multiple genes that contribute to the phenotype of complex neurological disorders. In such gene networks, it is common for some of the gene products to regulate the expression of other network members. Also, the expression of all or some network members is commonly coregulated. Gene product proteins that regulate transcription are termed transcription factors (TFs), and many genes are activated by multiple TFs.