Chapter 6. Modeling and Analysis of Intracellular Signaling Pathways Copyright © 2014 Elsevier Inc. All rights reserved

Figure 6.1 Symmetry can allow advantageous division into volume elements to model diffusion. (A) Longitudinal diffusion in a cylinder (blue arrow). The cylinder is divided into thin slabs of width δl. (B) Radially symmetric diffusion in a region that approximates a synaptic cleft. The disk is divided into concentric annuli of width δr. Copyright © 2014 Elsevier Inc. All rights reserved

Figure 6.3 Autophosphorylation of CaMKII may lead to bistability in enzyme activity. (A) Schematic illustrating multiple phosphorylation states. Assuming 10 subunits per holoenzyme, there are a large number of possible states, but if CaMKII activity depends only on the number of phosphorylated subunits and not their location within the holoenzyme, there are only 11 states of differing enzyme activity. Five of these states are shown, corresponding to 0, 1, 2, 3, and 10 phosphorylated subunits. Phosphate groups are orange. A calmodulin molecule with bound Ca 2+ (not shown) must be bound to a subunit for phosphorylation to be possible. (B) Schematic illustrating bistability. The x-axis represents intracellular Ca 2+ concentration. For a range of Ca 2+ concentrations, there is both a low and a high stable steady state for CaMKII activity (blue region of graph). The stable states are separated by an unstable steady state (dashed). Copyright © 2014 Elsevier Inc. All rights reserved

Figure 6.4 A mechanism for generating ultrasensitivity in the stimulus-response curve of a MAP kinase signaling cascade. (A) The kinetic scheme illustrating double phosphorylations of both MAPKK and MAPK. Phosphorylations are reversible. (B) Stimulus-response curves for the activities of MAPK (top, red curve) and MAPKK (dark green curve) based on the kinetic scheme of (A). For both enzymes, the activity is assumed proportional to the fraction that is doubly phosphorylated. For further details see Huang and Ferrell (1996). For comparison, two stimulus-response curves are also shown for which the response strength is given as a sigmoidal Hill function of the stimulus strength, with a Hill coefficient of 5 (n H =5, brown curve), and with a less steep Hill function with a coefficient of 2 (blue curve). To construct these two curves, the x-axis represents [L] in Eq. 6.10a and the y-axis represents the value of the Hill function. Copyright © 2014 Elsevier Inc. All rights reserved

Figure 6.5 A model that relates glutamate exposure at hippocampal synapses to long-term synaptic strengthening. (A) Signaling pathways. Glutamate can act through metabotropic glutamate receptors (mGluR) to activate G proteins (G). Glutamate also acts through NMDA and AMPA receptors to increase levels of free Ca 2+ and Ca 2+ bound to calmodulin. These events lead to activation of phospholipase C β (PLCβ), CaMKII, calcineurin (CaN), adenylyl cyclase (AC) and PKA. Two forms of crosstalk are illustrated. PKA activation leads to the inhibition of PP1. This inhibition relieves dephosphorylation of CaMKII by PP1, helping sustain CaMKII autophosphorylation. Also, MAPK activates phospholipase A 2 (PLA 2 ) and the resulting increase in arachidonic acid (AA) activates PKC. PKC in turn activates MAPKK, which further activates MAPK. MAPK, PKA, and CaMKII regulate gene expression, and cytosolic components such as the cytoskeleton, that are essential for synaptic strengthening. (B) Part of a compartmental model of a hippocampal neuron. A spine and part of the dendritic shaft are shown. The spine head, the spine neck, and the dendritic shaft are each modeled as a series of cylindrical compartments. The compartments are necessary to model Ca 2+ diffusion. Stimuli are modeled as pulses of Ca 2+ influx into the spine. The components of the biochemical model of (A) are placed in the terminal spine compartment. Copyright © 2014 Elsevier Inc. All rights reserved

Figure 6.6 Dynamics of a model of the late phase of LTP. (A) Model schematic. Synaptic stimulation elevates Ca 2+ and cAMP and activates Raf, the initial kinase in the MAPK cascade. Ca 2+ activates CaMKII and CaM kinase kinase (CaMKK). CaMKK activates CaM kinase IV (CaMKIV). cAMP activates PKA. Activated synaptic MAPK, PKA, and CaMKII all contribute to the setting of a synaptic tag (variable TAG) required for L-LTP. Activated nuclear MAPK and CaMKIV induce a gene necessary for L-LTP, with a protein product denoted GPROD. L-LTP is modeled as an increase in a synaptic weight W. (B). Time courses of the levels of active CaMKII, active synaptic MAPK, active nuclear MAPK, and the synaptic tag during and after three simulated tetanic stimuli. (C) Time courses of GPROD, the synaptic tag, and the synaptic weight W. Copyright © 2014 Elsevier Inc. All rights reserved

Figure 6.7 A model predicts how different patterns of stimuli activate convergent signaling pathways that cooperate to induce long- term synaptic facilitation (LTF). (A) Model schematic. 5-HT activates PKA via cAMP and activates MAPK via Raf-MAPKK. cAMP dissociates PKA into separate regulatory and catalytic subunits (Chapter 4). Free catalytic subunit (PKA C ) is autonomously active. PKA and MAPK interact, in part via phosphorylation of transcription factors, to induce LTF. The variable inducer represents the PKA/MAPK interaction. (B–C) Simulated time courses of activated PKA (PKA C, red traces), activated MAPK (MAPK pp, orange traces), and inducer (green traces) in response to five, 5-min pulses of 5-HT (blue traces). The Standard Protocol (B) represents the pulse timing generally used in studies of LTF in vitro. The Enhanced Protocol (C) produced the largest peak in the concentration of inducer. The patterns of 5-HT pulses are illustrated in each panel. The Standard Protocol had uniform interstimulus intervals (ISIs, onset to onset) of 20 min, whereas the Enhanced Protocol had ISIs of 10, 10, 5 and 30 min. Concentrations are in μM. Copyright © 2014 Elsevier Inc. All rights reserved

Figure 6.8 Signaling pathway involving transcriptional regulation by CREB. Neurotransmitters such as serotonin bind to receptors and act through G proteins to elevate levels of intracellular messengers (e.g., cAMP, Ca 2+ ). Kinases such as PKA are activated, resulting in phosphorylation of CREB and related TFs. Possible feedback interactions among the genes coding for CREB and related TFs are shown. A positive feedback loop (green arrows) may regulate CREB synthesis. In this loop, CREB binds to CREs near creb and activates creb transcription. The repressor ICER is an element of a negative feedback loop (blue arrows). Transcription of icer is increased when the level of CREB increases, and ICER in turn can bind to CREs near creb, repressing creb transcription. Copyright © 2014 Elsevier Inc. All rights reserved

Figure 6.10 Gene regulatory schemes that generate bistability and oscillations. (A) A two-gene regulatory scheme that generates bistability. TF-A activates expression of its own gene and represses the tf- b gene, whereas TF-B activates its own gene and represses the tf-a gene. Both TFs compete as homodimers for binding to response elements. (B) A two-gene regulatory scheme that generates oscillations. A second transcription factor, TF-R, is added to the model of Fig. 6.9A. TF-A activates transcription by binding to TF-RE response elements, which are present near the promoters of both tf-a and tf-r. TF-R represses transcription by competing with the TF-A dimer for binding to both TF-REs. (C) Sustained oscillations of [TF-A] produced by this scheme. Copyright © 2014 Elsevier Inc. All rights reserved

Figure 6.11 Generation of circadian rhythmicity by negative transcriptional feedback. (A) The kinetic scheme. A transcription factor (TF) can undergo multiple phosphorylation steps. Ten sequential phosphorylations are assumed. As indicated by the dashed box, all forms of TF protein are assumed capable of repressing tf transcription. A time delay is included between the appearance of tf mRNA and TF protein. Only fully phosphorylated TF can degrade. Over a day, virtually all TF protein becomes fully phosphorylated and then degrades. This relieves tf repression so that another “burst” of tf transcription can occur. (B) Circadian oscillations in the levels of tf mRNA and protein simulated by the model of (A). Copyright © 2014 Elsevier Inc. All rights reserved

Figure 6.12 Stochastic fluctuations in molecule numbers may destabilize steady states of genetic regulatory systems. (A) Without fluctuations, a set of equations based on Fig. 6.10A exhibits bistability. Initial levels of tf-1 (and tf-2) mRNA and protein are low (<2 nM) and steady. At t=7.5 hr the rate of tf-1 transcription is increased by a constant amount for 10 hrs (horizontal bar), causing a transition to a stable state with high tf-1 mRNA and protein levels. (B) The initial state of (A) is spontaneously destabilized within ~20 hrs when stochastic fluctuations are incorporated. No induced increase in tf-1 transcription is included in this simulation, which is otherwise the same as in (A) except for a scaling factor converting the units of the variables from concentrations to molecule numbers. Copyright © 2014 Elsevier Inc. All rights reserved