Extended kalman filter for estimation of parameters in nonlinear state-space models of biochemical networks.

It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks.

Cellular dynamic simulator: an event driven molecular simulation environment for cellular physiology.

In this paper, we present the Cellular Dynamic Simulator (CDS) for simulating diffusion and chemical reactions within crowded molecular environments. CDS is based on a novel event driven algorithm specifically designed for precise calculation of the timing of collisions, reactions and other events for each individual molecule in the environment. Generic mesh based compartments allow the creation / importation of very simple or detailed cellular structures that exist in a 3D environment. Multiple levels of compartments and static obstacles can be used to create a dense environment to mimic cellular boundaries and the intracellular space. The CDS algorithm takes into account volume exclusion and molecular crowding that may impact signaling cascades in small sub-cellular compartments such as dendritic spines. With the CDS, we can simulate simple enzyme reactions; aggregation, channel transport, as well as highly complicated chemical reaction networks of both freely diffusing and membrane bound multi-protein complexes. Components of the CDS are generally defined such that the simulator can be applied to a wide range of environments in terms of scale and level of detail. Through an initialization GUI, a simple simulation environment can be created and populated within minutes yet is powerful enough to design complex 3D cellular architecture. The initialization tool allows visual confirmation of the environment construction prior to execution by the simulator. This paper describes the CDS algorithm, design implementation, and provides an overview of the types of features available and the utility of those features are highlighted in demonstrations.

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.

Simulation of Drosophila circadian oscillations, mutations, and light responses by a model with VRI, PDP-1, and CLK.

A model of Drosophila circadian rhythm generation was developed to represent feedback loops based on transcriptional regulation of per, Clk (dclock), Pdp-1, and vri (vrille). The model postulates that histone acetylation kinetics make transcriptional activation a nonlinear function of [CLK]. Such a nonlinearity is essential to simulate robust circadian oscillations of transcription in our model and in previous models. Simulations suggest that two positive feedback loops involving Clk are not essential for oscillations, because oscillations of [PER] were preserved when Clk, vri, or Pdp-1 expression was fixed. However, eliminating positive feedback by fixing vri expression altered the oscillation period. Eliminating the negative feedback loop in which PER represses per expression abolished oscillations. Simulations of per or Clk null mutations, of per overexpression, and of vri, Clk, or Pdp-1 heterozygous null mutations altered model behavior in ways similar to experimental data. The model simulated a photic phase-response curve resembling experimental curves, and oscillations entrained to simulated light-dark cycles. Temperature compensation of oscillation period could be simulated if temperature elevation slowed PER nuclear entry or PER phosphorylation. The model makes experimental predictions, some of which could be tested in transgenic Drosophila.

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.

Structural plasticity can produce metaplasticity.

BACKGROUND: Synaptic plasticity underlies many aspect of learning memory and development. The properties of synaptic plasticity can change as a function of previous plasticity and previous activation of synapses, a phenomenon called metaplasticity. Synaptic plasticity not only changes the functional connectivity between neurons but in some cases produces a structural change in synaptic spines; a change thought to form a basis for this observed plasticity. Here we examine to what extent structural plasticity of spines can be a cause for metaplasticity. This study is motivated by the observation that structural changes in spines are likely to affect the calcium dynamics in spines. Since calcium dynamics determine the sign and magnitude of synaptic plasticity, it is likely that structural plasticity will alter the properties of synaptic plasticity. METHODOLOGY/PRINCIPAL FINDINGS: In this study we address the question how spine geometry and alterations of N-methyl-D-aspartic acid (NMDA) receptors conductance may affect plasticity. Based on a simplified model of the spine in combination with a calcium-dependent plasticity rule, we demonstrated that after the induction phase of plasticity a shift of the long term potentiation (LTP) or long term depression (LTD) threshold takes place. This induces a refractory period for further LTP induction and promotes depotentiation as observed experimentally. That resembles the BCM metaplasticity rule but specific for the individual synapse. In the second phase, alteration of the NMDA response may bring the synapse to a state such that further synaptic weight alterations are feasible. We show that if the enhancement of the NMDA response is proportional to the area of the post synaptic density (PSD) the plasticity curves most likely return to the initial state. CONCLUSIONS/SIGNIFICANCE: Using simulations of calcium dynamics in synaptic spines, coupled with a biophysically motivated calcium-dependent plasticity rule, we find under what conditions structural plasticity can form the basis of synapse specific metaplasticity.

Repeat length and RNA expression level are not primary determinants in CUG expansion toxicity in Drosophila models.

Evidence for an RNA gain-of-function toxicity has now been provided for an increasing number of human pathologies. Myotonic dystrophies (DM) belong to a class of RNA-dominant diseases that result from RNA repeat expansion toxicity. Specifically, DM of type 1 (DM1), is caused by an expansion of CUG repeats in the 3'UTR of the DMPK protein kinase mRNA, while DM of type 2 (DM2) is linked to an expansion of CCUG repeats in an intron of the ZNF9 transcript (ZNF9 encodes a zinc finger protein). In both pathologies the mutant RNA forms nuclear foci. The mechanisms that underlie the RNA pathogenicity seem to be rather complex and not yet completely understood. Here, we describe Drosophila models that might help unravelling the molecular mechanisms of DM1-associated CUG expansion toxicity. We generated transgenic flies that express inducible repeats of different type (CUG or CAG) and length (16, 240, 480 repeats) and then analyzed transgene localization, RNA expression and toxicity as assessed by induced lethality and eye neurodegeneration. The only line that expressed a toxic RNA has a (CTG)(240) insertion. Moreover our analysis shows that its level of expression cannot account for its toxicity. In this line, (CTG)(240.4), the expansion inserted in the first intron of CG9650, a zinc finger protein encoding gene. Interestingly, CG9650 and (CUG)(240.4) expansion RNAs were found in the same nuclear foci. In conclusion, we suggest that the insertion context is the primary determinant for expansion toxicity in Drosophila models. This finding should contribute to the still open debate on the role of the expansions per se in Drosophila and in human pathogenesis of RNA-dominant diseases.

Tumor heterogeneity dictates sensitivity to gefitinib (Iressa(TM)/ZD1839) in solid tumor models

The epidermal growth factor receptor (EGFR) and its ligands are overexpressed in many human tumors, including bladder and pancreas, correlating with a more aggressive tumor phenotype and poor patient prognosis. We initiated the present study to characterize the heterogeneity of gefitinib responsiveness in a panel of human bladder and pancreatic cancer cell lines in order to identify the biological characteristics of EGFR-dependent proliferation that could be used to prospectively identify drug-sensitive tumors. A second objective was to elucidate how to best exploit these results by utilizing gefitinib in combination therapy. To these ends, we examined the effects of the EGFR antagonist gefitinib on proliferation and apoptosis in a panel of 18 human bladder cancer cell lines and 9 human pancreatic cancer cell lines. Our data confirmed the existence of marked heterogeneity in Iressa responsiveness with less than half of the cell lines displaying significant growth inhibition by clinically relevant concentrations of the drug. Gefitinib responsiveness was found to be p27 kip1 dependent as DNA synthesis was restored following exposure to p27siRNA. Unfortunately, Iressa responsiveness was not closely linked to surface EGFR or TGF-α expression in the bladder cancer cells, however, cellular TGF-α expression correlated directly with Iressa sensitivity in the pancreatic cancer cell lines. These findings provide the potential for prospectively identifying patients with drug-sensitive tumors. ^ Further studies aimed at exploiting gefitinib-mediated cell cycle effects led us to investigate if gefitinib-mediated TRAIL sensitization correlated with increased p27kip1 accumulation. We observed that increased TRAIL sensitivity following gefitinib exposure was not dependent on p27 kip1 expression. Additional studies initiated to examine the role(s) of Akt and Erk signaling demonstrated that exposure to PI3K or MEK inhibitors significantly enhanced TRAIL-induced apoptosis at concentrations that block target phosphorylation. Furthermore, combinations of TRAIL and the PI3K or MEK inhibitors increased procaspase-8 processing above levels observed with TRAIL alone, indicating that the effects were exerted at the level of caspase-8 activation, considered the earliest step in the TRAIL pathway. ^

BIOLOGICAL MECHANISMS AND CLINICAL IMPLICATIONS OF BCR-ABL-INDUCED MITOCHONDRIAL OXIDATIVE STRESS AND CELL SURVIVAL IN CHRONIC MYELOID LEUKEMIA

Chronic myeloid leukemia (CML), a myeloproliferative disorder, represents approximately 15-20% of all adult leukemia. The development of CML is clearly linked to the constitutively active protein-tyrosine kinase BCR-ABL, which is encoded by BCR-ABL fusion gene as the result of chromosome 9/22 translocation (Philadelphia chromosome). Previous studies have demonstrated that oxidative stress-associated genetic, metabolic and biological alterations contribute to CML cell survival and drug refractory. Mitochondria and NAD(P)H oxidase (NOX) are the major sources of BCR-ABL-induced cellular reactive oxygen species (ROS) production. However, it is still unknown how CML cells maintain the altered redox status, while escaping from the persistent oxidative stress-induced cell death. Therefore, elucidation of the mechanisms by which CML cells cope with oxidative stress will provide new insights into CML leukemogenesis. The major goal of this study is to identify the survival factors protecting CML cells against oxidative stress and develop novel therapeutic strategies to overcome drug resistance. Several experimental models were used to test CML cell redox status and cellular sensitivity to oxidative stress, including BCR-ABL inducible cell lines, BCR-ABL stably transformed cell lines and BCR-ABL-expressing CML blast crisis cells with differential BCL-XL/BCL-2 expressions. Additionally, an artificial CML cell model with heterogenic BCL-XL/BCL-2 expression was established to assess the correlation between differential survival factor expression patterns and cell sensitivity to Imatinib and oxidative stress. In this study, BCL-XL and GSH have been identified as the major survival factors responsive to BCR-ABL-promoted cellular oxidative stress and play a dominant role in regulating the threshold of oxidative stress-induced apoptosis. Cell survival factors BCL-XL and BCL-2 differentially protect mitochondria under oxidative stress. BCL-XL is an essential survival factor in preventing excessive ROS-induced cell death while BCL-2 seems to play a relatively minor role. Furthermore, the redox modulating reagent β-phenethyl isothiocyanate (PEITC) has been found to efficiently deplete GSH and induce potent cell killing effects in drug-resistant CML cells. Combination of PEITC with BCL-XL/BCL2 inhibitor ABT737 or suppression of BCL-XL by BCR-ABL inhibitor Gleevec dramatically sensitizes CML cells to apoptosis. These results have suggested that elevation of BCL-XL and cellular GSH are important for the development of CML, and that redox-directed therapy is worthy of further clinical investigations in CML.