C.1. Modeling the Effects of Nitric Oxide on Apoptosis

C.1.1. Investigators/Areas of Scientific Expertise: T. R. Billiar (PI) & Y. Vodovotz (Surgery, Pitt); C. C. Chow (co-PI) & B. Ermentrout (Math, Pitt); I. Bahar (Comp Biology & Bioinformatics, Pitt); J. R. Stiles (PSC); C. Ho (Biology, CMU); S. Watkins (Cell Biology & Physiology, Pitt)

C.1.2. Specific Aims

Nitric oxide (NO) has been implicated both as a mediator and an inhibitor of apoptosis, usually in different cell types. This apparent paradox mirrors similar dichotomous effects of NO in diverse settings of cancer, cellular proliferation, sepsis, ischemia reperfusion injury, neuronal function, and organ transplantation. Our goal in this module of the planning grant is to lay the groundwork for a complete mathematical model of the effects of NO on apoptosis. To this end, we propose:

(i) Specific Aim 1: to establish first generation mathematical models of receptor-mediated and/or -independent apoptosis, and test in vitro the validity of key points of these models,

(ii) Specific Aim 2: to establish a first-generation model and simulation of the enzymatic production of NO in a cell and test in vitro the validity of key points of these models,

(iii) Specific Aim 3: to model the effects of NO on both receptor-mediated and mitochondria-dependent apoptosis, and to test in vitro the validity of key points of these models.

C.1.3. Background and Significance

C.1.3.1. Apoptosis occurs via receptor-dependent and –independent pathways. Programmed cell death, also known as apoptosis, is biologically initiated in some cases by ligation of specific death receptors of the tumor necrosis factor receptor (TNF-R) family via formation of the death-inducing signaling complex (DISC), in which the FADD (Fas-associated death domain) protein plays a crucial role. FADD associates with the TRADD (TNF-R-associated death domain) of clustered TNF-Rs. The resulting DISC complex then recruits and activates protease zymogens called procaspases (144). Apoptosis can also be triggered in a receptor-independent fashion, involving depolarization of the mitochondrial membrane and release of cytochrome c (cyt c), also leading to activation of procaspases (145). Thus, caspases, a family of cysteine proteases, play an essential role in both receptor-dependent and –independent signaling cascades (146). They propagate death signals by cleaving a number of protein substrates, also including procaspases that are cleaved into active proteases, leading ultimately to apoptosis. Caspases-8, -9 and -10 are initiator caspases. They transduce signals by directly activating the downstream executioner caspases-3, -6, and –7 (147).

C.1.3.2. The chemistry and production rate of NO dictate its diverse biological effects. NO is a short-lived, ubiquitous modulator of cellular function. It is rapidly synthesized from L-arginine by a family of NO synthase (NOS) isoenzymes. The inducible NOS (iNOS) isoform is expressed in many cells including cytokine-stimulated macrophages and hepatocytes where they can produce large amounts of NO (148). NO is a lipophilic and highly diffusible molecule whose actions are dependent on both its concentration and chemical form within the cell. These characteristics have been amenable to mathematical modeling (149). The biological chemistry of NO hinges around its unpaired electron, which makes NO a free, but stable radical (150). One central signaling pathway for NO is through direct activation of soluble guanylate cyclase and subsequent generation of cyclic guanosine monophosphate (cGMP) (151). NO alone does not interact readily with proteins or nucleic acids. It combines with local electron-accepting species like oxygen, transition metal ions, or superoxide radicals to generate potent S-nitrosylating species (e.g. N₂O₃, NO⁺, and ONOO^-) (150). S-nitrosylation of proteins, in turn, is an important post-translational modification that can modulate function. This, along with the high turnover and range of reactivity of NO with diverse biomolecules, has been demonstrated to either induce or suppress apoptosis (152;153). This dichotomy has stymied investigators, and new paradigms are needed in order to understand this fundamental issue. It is our contention that mathematical modeling of apoptotic pathways, coupled with modeling of NO pathways, will at the very least generate hypotheses to address this paradox.

C.1.3.3. Significance and unique scientific opportunities. To our knowledge, this would be the first mathematical simulation of the effects of NO in a complex biological network. We will take advantage of, and further advance, the mathematical model recently developed by Fussenegger et al. (154) for caspase function in apoptosis. The mathematical and computational researchers from Pitt (Chow, Ermentrout, Bahar), and PSC (Stiles) will be exposed for the first time to a wealth of experimental data and extensive knowledge provided by a group of leading scientists in Pitt Surgery Dept (Billiar & Vodovotz) in the field of NO and apoptosis. Billiar’s laboratory has already started a collaboration with the Biology Department at CMU (C. Ho)(155), and two team members from different schools at Pitt (Chow & Vodovotz) collaborate in modeling sepsis. The opposing, anti- and pro-apoptotic effects of NO could be an example of bistability – a hallmark of many nonlinear systems, in which transient and small effects can lead to irreversible or ultrasensitive end results (117). Models and methods of system dynamics (§ A.3.3), in conjunction with MC simulations of microphysiological processes (§A.3.2) should provide us a framework for testing hypotheses and capturing features that are not intuitively apparent. More broadly, these models could be used in the future to address such issues as how NO can either induce or suppress cancer, protect or destroy neurons, and help or hinder organ transplantation.

C.1.4. Preliminary Studies

As evidenced by our publication record, members of our group have extensive experience in the biology of NO (148) and in the analysis of the modulation of apoptosis by NO in various cell types (153;156). We are capable of measuring NO production and delivery from NO donors (157). Enzymatic production of NO within the cell follows the upregulation of iNOS or through gene transfer. Unique to Pitt is the availability of numerous vectors, including an adenoviral vector (AdiNOS) which expresses human iNOS gene driven by the cytomegalovirus (CMV) promoter, that we have used both in vitro and in vivo (158-161). In particular, we have used this vector to either suppress or induce apoptosis in vitro (161-163).

In this feasibility proposal, we will seek to provide proof-of-concept preliminary data on the effects of NO on apoptosis. Herein, we highlight several salient points about the anti-apoptotic role of NO in hepatocytes vis-à-vis the mechanism of apoptosis. We have shown that NO suppresses apoptosis induced by TNF-a and actinomycin D (TNF-a/ActD) by mechanisms dependent on or independent of cGMP generation (164). All caspases contain a single cysteine at the catalytic site, which is susceptible to redox modification. Recently, we and others have shown that generation of NO can lead to the nitrosylation of this cysteine (165-168), which leads to reduced caspase activation and activity. For example, NO inhibits caspase-3 via S-nitrosylation, in addition to a cGMP-dependent mechanism that can be restored with a reducing agent, dithiothreitol (164). NO also interrupts the cleavage of BID, a downstream substrate of caspase-3 which would trigger the stress-induced release of mitochondrial cyt c if cleaved by caspase-3 (169). We also showed that NO stimulates heat shock protein 70 (HSP70) expression, and that this confers resistance to TNF-a induced apoptosis (170). Finally, we have recently shown that NO modulates the expression of genes associated with apoptosis, decreasing in particular the pro-apoptotic bNIP3 (171).

Collaborative work was initiated between the groups of Drs. Billiar, Bahar, Ermentrout and Chow on preliminary modeling of caspase cascades, based on the work of Fussenegger et al (154). We focused on yet another novel aspect of the work in the Billiar laboratory, in which we used an adenovirus (AdFADD) expressing the mouse FADD gene driven by the CMV promoter. Mathematical modeling predicts that elevation in the initial expression level of FADD will cause higher caspase-8 activity which also induces with a time lag an increase in caspase-9 activity (Figure C.1.1a) in accord with the results from our experiments (Figure C.1.1b). We intend to expand these experiments to include the role of NO (see below). Our laboratory also has an adenovirus (Ad-ASFADD) that expresses the mouse antisense FADD, which protects hepatocytes from apoptosis induced by TNF-a/ActD (data not shown).

Taken together, these data demonstrate that we have taken an integrated, multifaceted approach to the analysis of the anti-apoptotic roles of NO, and that we are well-versed in the analysis of apoptosis as well as in the analysis of and manipulation of NO using various means, as required to validate the mathematical models generated under this proposal.

C.1.5. Research Design and Methods

C.1.5.1. Specific Aim 1: to establish first generation mathematical models of receptor-mediated and/or -independent apoptosis and test in vitro the validity of the key points from these models. Table C.1 summarizes the components that will be explicitly included in the network to be analyzed. This does not necessarily represent a complete set, and we will consider the possibility of including other elements. The recent work of Fussenegger, Bailey and Varner on the activation of caspases is an excellent starting model for our analysis (154). A wealth of experimental observations on the complex role and interactions of these enzymes has been compiled and organized therein in a network of pathways (see Fig 1 in (154)), and mapped into a series of ODEs using reaction kinetics laws coupled with mass balance equations. These ODEs are readily solvable with MATLAB 5.3 package Simulink 2.0 using the code and parameters that the authors kindly made accessible on the internet. See for example the results from our preliminary calculations in Fig C.1.1a-b obtained with this software after private communication with M. Fussenegger.

Within the scope of this specific aim we will further elaborate on this mathematical model using experimental and theoretical methods. The individual components will be represented in multiple forms (complexed/uncomplexed, isolated/ aggregated, cytoplasmic/mitochondrial), as needed. A number of reactions were defined to be rate-controlling in previous work (154), and pseudo-steady state assumptions were made for others: fast (pre-equilibrated) reactions include ligand binding to FAS, inhibition of Apaf-1 by Bcl-2 family members, binding of procaspase-8 to DISC, procaspase-9 binding to Apaf-/ cyt c complex, while other events such as the aggregation of TNF-Rs, binding of the first FADD, complexation of cyt c and Apaf-1, and proteolytic cleavage of procaspases, were assumed to be slow, rate controlling steps. We will consider the consequences of hindering or enhancing individual steps in a systematic way using the XPPAUT software suite developed by Ermentrout. We will introduce minor modifications in the formulations, essentially replacing the concentrations expressed in terms of the equilibrium constants of rate controlling steps by their instantaneous values (see for example eqs 6 and 9 in (154) expressed in terms of K_A and K_H , the respective equilibrium constants the first-FADD binding and complexation of cyt c and Apaf-1). We will also introduce additional interactions, including for example, the BID protein mentioned above. We will focus on p53 as a possible switch for the pro- and anti-apoptotic effects of NO, since NO-mediated apoptosis in some cell types is a p53-dependent process (153;172). It will be of interest to explore the outcome from two or more competing effects; for example to induce an anti-apoptotic effect (e.g. inhibit caspase-3 by increasing the IAP or NO concentration) and an apoptotic effect (e.g. increase the binding rate of FADD), and observe if there is a an inversion in cellular fate at a certain combination (or ratio) of parameters.

Table C.1. Components of a minimal model of apoptosis

Receptor-dependent components	Receptor-independent Components	Downstream elements and other effectors
TNF-a receptor (FAS), FAS ligand; FADD; procaspase-8, caspase-8, ICE proteins	cyt c; Bid; Bcl-XL; Bcl-2; Bax; p53, Apaf-1, procaspase-9, caspase-9	procaspase-3; caspase-3, PARP , NO, iNOS IAP (inhibitor of apoptosis protein)

We will then proceed to preliminary testing of this model, using TNF-a/ActD to induce apoptosis in hepatocytes. We will analyze caspase cleavage by Western blot and assay caspase activity using tagged peptide substrates whose cleavage is specific for each targeted caspases, as described in our previous work (165;168). Due to experimental limitations, we can assess the concentrations of some analytes (e.g. NO, p53, cyt c, pro-caspases), while measuring the activity of others (e.g. caspases). Thus, though we will consider all relevant components in our mathematical model, we will generate data for measurable quantities, only. Additionally, we will examine the effects of selective elimination of members of the apoptotic cascade, and compare the predictions to experiments using specific inhibitors. We expect to modify and improve the ingredients of our mathematical model (the system of components and their connectivity, the assumptions on rate controlling steps, and the range of input parameters) as new factors influencing apoptosis are identified and new data become available.

C.1.5.2. Specific Aim 2: to establish a first-generation model and simulation of the enzymatic production of NO in a cell and test in vitro the validity of key points of these models.

A diagram of the model to be considered to this aim is proposed in Figure C.1.2. We expect to enlarge and modify this mechanistic model so as to make it more comprehensive and as new NO-modulated factors influencing apoptosis are identified.

Experimentally, we will test the predictions of this model by stimulating mouse hepatocytes with cytomix and analyzing (i) NO, measured as NO₂^- + NO₃^- using commercially available kits (Alexis, San Diego) (ii) iNOS protein expression, as measured by Western blot; (iii) targets of NO, as measured by total S-nitrosothiol content of hepatocyte lysates; and (iv) intra- and extra-cellular cGMP levels as described in our earlier work (173). We will also treat hepatocytes with the chemical NO donor S-nitroso-N-acetyl-D,L-penicillamine (SNAP) and analyze NO (NO₂^-) and total S-nitrosothiol content as described elsewhere (168). After enough time, we will include detailed time courses and dose curves of cytomix; using AdiNOS at various multiplicities of infection to induce NO, and induction of iNOS with other stimulation regimens (single cytokines such as IL-1) at multiple time points. Furthermore, we plan to examine the effect of cytokines, such as TGF-b1 (174), that suppress the expression of iNOS. Ultimately, it will be of interest in a more detailed proposal to examine the effects of factors thought to modulate the chemical fate of NO (e.g. thiol content, antioxidant enzymes) to understand how these parameters influence the fate of NO, cell viability, and apoptotic signaling events.

Computational. In principle, the kinetics of the above system of interactions can be modeled with the mathematical models and methods used and developed within the scope of Aim 1. Additionally, we will take advantage of the previous simulations of NO dynamics, which provide insights as to suitable assumptions and parameters to be used (149;175). NO is a short-lived effector; its half-life ranges 0.09 to > 2 s, depending on O₂ concentration (175). Stochastic variability plays a significant role in such systems with low levels of reactants. We will take a two-pronged approach to address this feature.  The first will be to derive the stochastic Master equation for the entire system (104). Using a large volume expansion, a set of equations for the average and variances of all the quantities can be obtained. The equations for the average will correspond to the simple mass-action kinetics assuming a well-mixed system. We will also consider a Langevin formulation of the problem by supplementing the mass-action equations with stochastic forcing terms, and simulate it using XPPAUT (7) (http://www.pitt.edu/~bard/xpp/xpp.html). The second is, guided by these results, a fully spatial MC simulation algorithm to be built on MCell (see § A.3.2). MCell is designed to simulate the stochastics of diffusion-limited reactions of small molecules in spatially realistic but static environment. NO pathways comprised of a combination of small molecules and proteins are ideally suited for the extension of the methodology to include protein mobilities. The system and parameters adopted in the two approaches will be identical, - but the methodologies will be different and space dependence will be explicitly accounted for in MCell. The two formalisms will accordingly be used to ‘cross-calibrate' each other (see § A.4.4) and with the experiments.  In such a way a hierarchy of models with increasing levels of detail will be built to bridge between simple models that are amenable to analysis and more complicated ones which can be compared directly to experiments.

C.1.5.3. Specific Aim 3: to model the effects of NO on apoptosis, and to test in vitro the validity of key points of these models. We will integrate the information generated in Aims 1 and 2. We chose to separate aims 1 and 2 for two reasons: (i) simplicity, since it will be easier to compartmentalize the analysis into apoptosis and NO production initially; and (ii) universal applicability, since separate models of apoptosis and NO production will be invaluable for numerous other biological questions. However, our ultimate goal is to develop an integrative model that combines the NO production and NO effects with apoptotic pathways. A diagram illustrating the NO regulation of apoptosis is presented in our earlier work (176), which will be exploited and further expanded using more detailed block diagrams of cell cycle regulation and apoptosis in mammalian cells (177). Specific aim 3 will not necessarily involve new biological and biochemical experimentation other than those already performed within the scope of aims 1 and 2, except for the more detailed characterization of the subcellular regions of interest with imaging techniques, towards the development of more realistic cell simulation algorithms. Microscopic images provided by Watkins (Center for Biologic Imaging, Pitt) are expected to provide us crucial information for reconstructing in our MC simulations the local environmental characteristics of the simulated events, and building spatially realistic models as described in our previous studies (17;18). It is expected that the mathematical approaches developed with macroscopic rate laws and mass balance equations will indicate which subcellular events, or cascades of interactions need to be focused upon, which components of the network are more susceptible to perturbations, or more likely to trigger synergistic effects; and MCell would then specialize on these particular aspects/ components of the network. For example, the diffusion of cyt c from the mitochondria to the cytoplasm modulated by downstream effectors and inhibitors of caspase pathways can be modeled similarly to the diffusion of neurotransmitters across a synaptic cleft (17). The fundamental question to be answered is again to assess the minimal level of complexity to be incorporated in the model, and the most plausible assumptions to be adopted, in order to capture and explain experimental observations, and accurately address the biological problem of interest.

While the specific aims of DP-1 concern the development mathematical and microphysiological models that complement each other, the results from these studies will also provide us with information on molecular targets for therapeutic control or regulation of apoptosis. These and the targets identified in DP-2 and DP-3 will be explored in the future center using the computational tools developed in Specific Aim 1(i) of the Pre-NPEBC.