Death ligand concentration and the membrane proximal signaling module regulate the type 1/type 2 choice in apoptotic death signaling.

Apoptotic death pathways are frequently activated by death ligand induction and subsequent activation of the membrane proximal signaling module. Death receptors cluster upon binding to death ligands, leading to formation of a membrane proximal death-inducing-signaling-complex (DISC). In this membrane proximal signalosome, initiator caspases (caspase 8) are processed resulting in activation of both type 1 and type 2 pathways of apoptosis signaling. How the type 1/type 2 choice is made is an important question in the systems biology of apoptosis signaling. In this study, we utilize a Monte Carlo based in silico approach to elucidate the role of membrane proximal signaling module in the type 1/type 2 choice of apoptosis signaling. Our results provide crucial mechanistic insights into the formation of DISC signalosome and caspase 8 activation. Increased concentration of death ligands was shown to correlate with increased type 1 activation. We also study the caspase 6 mediated system level feedback activation of apoptosis signaling and its role in the type 1/type 2 choice. Our results clarify the basis of cell-to-cell stochastic variability in apoptosis activation and ramifications of this issue is further discussed in the context of therapies for cancer and neurodegenerative disorders.

Low probability activation of Bax/Bak can induce selective killing of cancer cells by generating heterogeneity in apoptosis.

Biomimetic pro-apoptotic agents (e.g., BH3 mimetics) have been shown to activate the intrinsic death pathway (Type 2 apoptosis) selectively in cancer cells, a mechanism that can be key to developing successful anti-cancer therapy. This work reports mathematical modeling and computer simulations to explore the mechanisms for cancer cell apoptosis. The results indicate that a combination of low probability Bid-Bax type reaction along with overexpressed reactant molecules allows specific killing of cancer cells. Low-probability activation of Bax also emerges as a basis for inherent cell-to-cell variability in apoptotic activation. Variations in Bcl-2 to Bax ratio within a cancer cell population can further affect intrinsic fluctuations generated due to the stochastic Bid-Bax reaction. Such heterogeneity in apoptosis resistance can also provide a mechanism for the origin of cells with higher tumorigenic potential (cancer stem-like cells). The implications of our results for cancer therapy, such as in minimizing stochastic fluctuations in cancer cell death, are discussed.

Monte carlo study elucidates the type 1/type 2 choice in apoptotic death signaling in healthy and cancer cells.

Apoptotic cell death is coordinated through two distinct (type 1 and type 2) intracellular signaling pathways. How the type 1/type 2 choice is made remains a central problem in the biology of apoptosis and has implications for apoptosis related diseases and therapy. We study the problem of type 1/type 2 choice in silico utilizing a kinetic Monte Carlo model of cell death signaling. Our results show that the type 1/type 2 choice is linked to deterministic versus stochastic cell death activation, elucidating a unique regulatory control of the apoptotic pathways. Consistent with previous findings, our results indicate that caspase 8 activation level is a key regulator of the choice between deterministic type 1 and stochastic type 2 pathways, irrespective of cell types. Expression levels of signaling molecules downstream also regulate the type 1/type 2 choice. A simplified model of DISC clustering elucidates the mechanism of increased active caspase 8 generation and type 1 activation in cancer cells having increased sensitivity to death receptor activation. We demonstrate that rapid deterministic activation of the type 1 pathway can selectively target such cancer cells, especially if XIAP is also inhibited; while inherent cell-to-cell variability would allow normal cells stay protected.

Formation of BCR oligomers provides a mechanism for B cell affinity discrimination.

B cells encounter antigen over a wide affinity range, from K(A)=10(5) M(-1) to K(A)=10(10) M(-1). The strength of B cell antigen receptor (BCR) signaling in response to antigen increases with affinity, a process known as "affinity discrimination". In this work, we use a computational simulation of B cell surface dynamics and membrane-proximal signaling to show that affinity discrimination can arise from the formation of BCR oligomers. It is known that BCRs form oligomers upon encountering antigen, and that the size and rate of formation of these oligomers both increase with affinity. In our simulation, we have introduced a requirement that only BCR-antigen complexes that are part of an oligomer can engage cytoplasmic signaling molecules such as Src-family kinases. Our simulation shows that as affinity increases, BCR signaling activity increases in addition to the number of collected antigen. Our results are also consistent with the existence of an experimentally-observed threshold affinity of activation at K(A)=10(5)-10(6) M(-1) (no signaling activity below this affinity value) and affinity discrimination ceiling of K(A)=10(10) M(-1) (no affinity discrimination above this affinity value). Comparison with experiments shows that the time scale of BCR oligomer formation predicted by our model (less than 10 s) is well within the time scale of experimentally observed association of BCR with Src-family kinases (10-20 s).

Discrimination of membrane antigen affinity by B cells requires dominance of kinetic proofreading over serial engagement.

B-cell receptor signaling in response to membrane-bound antigen increases with antigen affinity, a process known as affinity discrimination. We use computational modeling to show that B-cell affinity discrimination requires that kinetic proofreading predominate over serial engagement. We find that if B-cell receptors become signaling-capable immediately upon antigen binding, which results in decreasing serial engagement as affinity increases, then increasing affinity can lead to weaker signaling. Rather, antigen must stay bound to B-cell receptors for a threshold time of several seconds before becoming signaling-capable, a process similar to kinetic proofreading. This process overcomes the loss in serial engagement due to increasing antigen affinity, and replicates the monotonic increase in B-cell signaling with increasing affinity that has been observed in B-cell activation experiments. This finding matches well with the experimentally observed time (∼20 s) required for the B-cell receptor signaling domains to undergo antigen and lipid raft-mediated conformational changes that lead to Src-family kinase recruitment. We hypothesize that the physical basis for a threshold time of antigen binding might lie in the formation timescale of B-cell receptor dimers. The time required for dimer formation decreases with increasing antigen affinity, thereby resulting in shorter threshold antigen binding times as affinity increases. Such an affinity-dependent kinetic proofreading requirement results in affinity discrimination very similar to that observed in biological experiments. B-cell affinity discrimination is critical to the process of affinity maturation and the production of high-affinity antibodies, and thus our results have important implications in applications such as vaccine design.

Monte Carlo study of B-cell receptor clustering mediated by antigen crosslinking and directed transport.

It is known from experiments that in the presence of soluble antigen, B-cell receptors (BCRs) assemble into microclusters and then collect into a macrocluster known as a 'cap'. However, the mechanisms of BCR cluster formation during recognition of soluble antigens remain unclear. In previous work, we demonstrated that effective intrinsic attractions among BCRs can lead to the formation of small microclusters of BCR molecules. The effective intrinsic attractions could be caused by multivalent antigen binding, association with lipid rafts, or other biochemical factors. In the present study, we have developed and studied a Monte Carlo model of BCR clustering mediated by explicit binding and crosslinking of soluble bivalent antigens. Antigen crosslinking is shown to microcluster BCRs in an affinity-dependent manner and also in a biologically relevant timescale; however, antigen crosslinking alone does not appear to be sufficient for the formation of a single macrocluster of receptor molecules. We show that directed transport of BCRs is needed to drive the formation of large macroclusters. We constructed a simple model of directed transport, where BCR molecules diffuse towards the largest cluster or towards a random BCR microcluster, which results in a single macrocluster of receptor molecules. The mechanisms for both types of directed transport are compared using network-based metrics. We also develop and use appropriate network measures to analyze the effect of BCR and antigen concentration on BCR clustering, the stability of the formed clusters over time and the size of BCR-antigen crosslinked chains.

Nonlinear regulation of commitment to apoptosis by simultaneous inhibition of Bcl-2 and XIAP in leukemia and lymphoma cells.

Apoptosis is a complex pathway regulated by the concerted action of multiple pro- and anti-apoptotic molecules. The intrinsic (mitochondrial) pathway of apoptosis is governed up-stream of mitochondria, by the family of Bcl-2 proteins, and down-stream of mitochondria, by low-probability events, such as apoptosome formation, and by feedback circuits involving caspases and inhibitor of apoptosis proteins (IAPs), such as XIAP. All these regulatory mechanisms ensure that cells only commit to death once a threshold of damage has been reached and the anti-apoptotic reserve of the cell is overcome. As cancer cells are invariably exposed to strong intracellular and extracellular stress stimuli, they are particularly reliant on the expression of anti-apoptotic proteins. Hence, many cancer cells undergo apoptosis when exposed to agents that inhibit anti-apoptotic Bcl-2 molecules, such as BH3 mimetics, while normal cells remain relatively insensitive to single agent treatments with the same class of molecules. Targeting different proteins within the apoptotic network with combinatorial treatment approaches often achieves even greater specificity. This led us to investigate the sensitivity of leukemia and lymphoma cells to a pro-apoptotic action of a BH3 mimetic combined with a small molecule inhibitor of XIAP. Using the computational probabilistic model of the apoptotic pathway, verified by experimental results from human leukemia and lymphoma cell lines, we show that inhibition of XIAP has a non-linear effect on sensitization towards apoptosis induced by the BH3 mimetic HA14-1. This study justifies further ex vivo and animal studies on the potential of the treatment of leukemia and lymphoma with a combination of BH3 mimetics and XIAP inhibitors.

Timing is everything: stochastic origins of cell-to-cell variability in cancer cell death.

The diversity of cell populations is regulated by extracellular and intracellular variability. The latter includes genetic, epigenetic and stochastic variability, all contributing to the experimentally observed heterogeneity in response to external death-inducing stimuli. Studies of sources and regulation of variability in commitment to apoptotic cancer cell death are likely to identify the fundamental features of apoptotic protein networks that are responsible for determining the ultimate cell fate. Systems biology approaches, involving computer simulations of the biochemical reactions accompanied, if possible, by experimental verification of selected components of the model, are proving useful in determining the origins of cell-to-cell variability in response to external stress stimuli. Here we summarize our current understanding of the origins of stochastic variability in cells' commitment to apoptosis, and its implications in the field on cancer therapy.

Monte Carlo investigation of diffusion of receptors and ligands that bind across opposing surfaces.

Studies of receptor diffusion on a cell surface show a variety of behaviors, such as diffusive, sub-diffusive, or super-diffusive motion. However, most studies to date focus on receptor molecules diffusing on a single cell surface. We have previously studied receptor diffusion to probe the molecular mechanism of receptor clustering at the cell-cell junction between two opposing cell surfaces. Here, we characterize the diffusion of receptors and ligands that bind to each other across two opposing cell surfaces, as in cell-cell and cell-bilayer interactions. We use a Monte Carlo method, where receptors and ligands are simulated as independent agents that bind and diffuse probabilistically. We vary receptor-ligand binding affinity and plot the molecule-averaged mean square displacement (MSD) of ligand molecules as a function of time. Our results show that MSD plots are qualitatively different for flat and curved interfaces, as well as between the cases of presence and absence of directed transport of receptor-ligand complexes toward a specific location on the interface. Receptor-ligand binding across two opposing surfaces leads to transient sub-diffusive motion at early times provided the interface is flat. This effect is entirely absent if the interface is curved, however, in this instance we observe sub-diffusive motion. In addition, a decrease in the equilibrium value of the MSD occurs as affinity increases, something which is absent for a flat interface. In the presence of directed transport of receptor-ligand complexes, we observe super-diffusive motion at early times for a flat interface. Super-diffusive motion is absent for a curved interface, however, in this case we observe a transient decrease in MSD with time prior to equilibration for high-affinity values.

A role for human neuroglobin in apoptosis.

Over the past decade, following the discovery of the human heme protein neuroglobin, many studies have searched for evidence for this protein's mechanism of action. Much data has accrued showing that high levels of neuroglobin will protect cells from apoptotic cell death, following a wide range of challenges. Various explanations of its actions, based on measured reactivity with oxygen, nitric oxide, or free radicals, have been proposed, but none have, as yet, been substantiated in vivo. Following preliminary experiments, it was previously hypothesised that "the central role of neuroglobin in highly metabolically active cells and retinal and brain neurons is to reset the trigger level of mitochondrial cytochrome c release necessary to commit the cells to apoptosis" (I.U.M.B.M. Life (2008) 60, 398). In this article, we review the evidence, which has accumulated to support this hypothesised mechanism of action of neuroglobin and integrate this data, with other reported intracellular functions of neuroglobin, to suggest a plausible central role for neuroglobin in the control of apoptosis.

Modeling of B cell Synapse Formation by Monte Carlo Simulation Shows That Directed Transport of Receptor Molecules Is a Potential Formation Mechanism.

The formation of the protein segregation structure known as the "immunological synapse" in the contact region between B cells and antigen presenting cells appears to precede antigen (Ag) uptake by B cells. The mature B cell synapse consists of a central cluster of B cell receptor/Antigen (BCR/Ag) complexes surrounded by a ring of LFA-1/ICAM-1 complexes. In this study, we used an in silico model to investigate whether cytoskeletally driven transport of molecules toward the center of the contact zone is a potential mechanism of immunological synapse formation in B cells. We modeled directed transport by the cytoskeleton in an effective manner, by biasing the diffusion of molecules toward the center of the contact zone. Our results clearly show that biased diffusion of BCR/Ag complexes on the B cell surface is sufficient to produce patterns similar to experimentally observed immunological synapses. This is true even in the presence of significant membrane deformation as a result of receptor-ligand binding, which in previous work we showed had a detrimental effect on synapse formation at high antigen affinity values. Comparison of our model's results to those of experiments shows that our model produces synapses for realistic length, time, and affinity scales. Our results also show that strong biased diffusion of free molecules has a negative effect on synapse formation by excluding BCR/Ag complexes from the center of the contact zone. However, synapses may still form provided the bias in diffusion of free molecules is an order-of-magnitude weaker than that of BCR/Ag complexes. We also show how diffusion trajectories obtained from single-molecule tracking experiments can generate insight into the mechanism of synapse formation.

A minimal model of signaling network elucidates cell-to-cell stochastic variability in apoptosis.

BACKGROUND: Signaling networks are designed to sense an environmental stimulus and adapt to it. We propose and study a minimal model of signaling network that can sense and respond to external stimuli of varying strength in an adaptive manner. The structure of this minimal network is derived based on some simple assumptions on its differential response to external stimuli. METHODOLOGY: We employ stochastic differential equations and probability distributions obtained from stochastic simulations to characterize differential signaling response in our minimal network model. Gillespie's stochastic simulation algorithm (SSA) is used in this study. CONCLUSIONS/SIGNIFICANCE: We show that the proposed minimal signaling network displays two distinct types of response as the strength of the stimulus is decreased. The signaling network has a deterministic part that undergoes rapid activation by a strong stimulus in which case cell-to-cell fluctuations can be ignored. As the strength of the stimulus decreases, the stochastic part of the network begins dominating the signaling response where slow activation is observed with characteristic large cell-to-cell stochastic variability. Interestingly, this proposed stochastic signaling network can capture some of the essential signaling behaviors of a complex apoptotic cell death signaling network that has been studied through experiments and large-scale computer simulations. Thus we claim that the proposed signaling network is an appropriate minimal model of apoptosis signaling. Elucidating the fundamental design principles of complex cellular signaling pathways such as apoptosis signaling remains a challenging task. We demonstrate how our proposed minimal model can help elucidate the effect of a specific apoptotic inhibitor Bcl-2 on apoptotic signaling in a cell-type independent manner. We also discuss the implications of our study in elucidating the adaptive strategy of cell death signaling pathways.

Bcl-2 inhibits apoptosis by increasing the time-to-death and intrinsic cell-to-cell variations in the mitochondrial pathway of cell death.

BH3 mimetics have been proposed as new anticancer therapeutics. They target anti-apoptotic Bcl-2 proteins, up-regulation of which has been implicated in the resistance of many cancer cells, particularly leukemia and lymphoma cells, to apoptosis. Using probabilistic computational modeling of the mitochondrial pathway of apoptosis, verified by single-cell experimental observations, we develop a model of Bcl-2 inhibition of apoptosis. Our results clarify how Bcl-2 imparts its anti-apoptotic role by increasing the time-to-death and cell-to-cell variability. We also show that although the commitment to death is highly impacted by differences in protein levels at the time of stimulation, inherent stochastic fluctuations in apoptotic signaling are sufficient to induce cell-to-cell variability and to allow single cells to escape death. This study suggests that intrinsic cell-to-cell stochastic variability in apoptotic signaling is sufficient to cause fractional killing of cancer cells after exposure to BH3 mimetics. This is an unanticipated facet of cancer chemoresistance.

Neuroglobin protects nerve cells from apoptosis by inhibiting the intrinsic pathway of cell death.

In the past few years, overwhelming evidence has accrued that a high level of expression of the protein neuroglobin protects neurons in vitro, in animal models, and in humans, against cell death associated with hypoxic and amyloid insult. However, until now, the exact mechanism of neuroglobin's protective action has not been determined. Using cell biology and biochemical approaches we demonstrate that neuroglobin inhibits the intrinsic pathway of apoptosis in vitro and intervenes in activation of pro-caspase 9 by interaction with cytochrome c. Using systems level information of the apoptotic signalling reactions we have developed a quantitative model of neuroglobin inhibition of apoptosis, which simulates neuroglobin blocking of apoptosome formation at a single cell level. Furthermore, this model allows us to explore the effect of neuroglobin in conditions not easily accessible to experimental study. We found that the protection of neurons by neuroglobin is very concentration sensitive. The impact of neuroglobin may arise from both its binding to cytochrome c and its subsequent redox reaction, although the binding alone is sufficient to block pro-caspase 9 activation. These data provides an explanation the action of neuroglobin in the protection of nerve cells from unwanted apoptosis.

How can we kill cancer cells: Insights from the computational models of apoptosis.

Cancer cells are widely known to be protected from apoptosis, a phenomenon that is a major hurdle to successful anticancer therapy. Over-expression of several anti-apoptotic proteins, or mutations in pro-apoptotic factors, has been recognized to confer such resistance. Development of new experimental strategies, such as in silico modeling of biological pathways, can increase our understanding of how abnormal regulation of apoptotic pathway in cancer cells can lead to tumour chemoresistance. Monte Carlo simulations are in particular well suited to study inherent variability, such as spatial heterogeneity and cell-to-cell variations in signaling reactions. Using this approach, often in combination with experimental validation of the computational model, we observed that large cell-to-cell variability could explain the kinetics of apoptosis, which depends on the type of pathway and the strength of stress stimuli. Most importantly, Monte Carlo simulations of apoptotic signaling provides unexpected insights into the mechanisms of fractional cell killing induced by apoptosis-inducing agents, showing that not only variation in protein levels, but also inherent stochastic variability in signaling reactions, can lead to survival of a fraction of treated cancer cells.

The network of receptors characterize B cell receptor micro- and macroclustering in a Monte Carlo model.

During the recognition of soluble antigens, B cell receptors (BCR) are known to form signaling clusters that can crucially modulate intracellular activation pathways and B cell response. Little is known about the precise nature of receptor cluster and its formation mechanism for the case of soluble antigens. Initial experiments have shown that B cell receptors first microcluster upon ligation with soluble antigens, and then coarsen into a macroscopic cap structure at one pole of a B cell. Such a mutual receptor-receptor attraction can arise locally due to cross-linking by soluble antigens among other possibilities. We develop an energy based Monte Carlo model to investigate the mechanism of B-cell receptor clustering upon ligation with soluble antigens. Our results show that mutual attraction between nearest neighbor receptor pairs can lead to microclustering of B cell receptors, but it is not sufficient for receptor macroclustering. A simple model of biased diffusion where BCR molecules experience a biased directed motion toward the largest cluster is then applied, which results in a single macrocluster of receptor molecules. The various types of receptor clusters are analyzed using the developed network-based metrics such as the average distance between any pairs of receptors.

Monte Carlo simulation of cell death signaling predicts large cell-to-cell stochastic fluctuations through the type 2 pathway of apoptosis.

Apoptosis, or genetically programmed cell death, is a crucial cellular process that maintains the balance between life and death in cells. The precise molecular mechanism of apoptosis signaling and the manner in which type 1 and type 2 pathways of the apoptosis signaling network are differentially activated under distinct apoptotic stimuli is poorly understood. Based on Monte Carlo stochastic simulations, we show that the type 1 pathway becomes activated under strong apoptotic stimuli, whereas the type 2 mitochondrial pathway dominates apoptotic signaling in response to a weak death signal. Our results also show signaling in the type 2 pathway is stochastic; the population average over many cells does not capture the cell-to-cell fluctuations in the time course (approximately 1-10 h) of downstream caspase-3 activation. On the contrary, the probability distribution of caspase-3 activation for the mitochondrial pathway shows a distinct bimodal behavior that can be used to characterize the stochastic signaling in type 2 apoptosis and other similar complex signaling processes. Interestingly, such stochastic fluctuations in apoptosis signaling occur even in the presence of large numbers of signaling molecules.

Monte Carlo study of single molecule diffusion can elucidate the mechanism of B cell synapse formation.

B cell receptors have been shown to cluster at the intercellular junction between a B cell and an antigen-presenting cell in the form of a segregated pattern of B cell receptor/antigen complexes known as an immunological synapse. We use random walk-based theoretical arguments and Monte Carlo simulations to study the effect of diffusion of surface-bound molecules on B cell synapse formation. Our results show that B cell synapse formation is optimal for a limited range of receptor-ligand complex diffusion coefficient values, typically one-to-two orders of magnitude lower than the diffusion coefficient of free receptors. Such lower mobility of receptor-ligand complexes can significantly affect the diffusion of a tagged receptor or ligand in an affinity dependent manner, as the binding/unbinding of such receptor or ligand molecules crucially depends on affinity. Our work shows how single molecule tracking experiments can be used to estimate the order of magnitude of the diffusion coefficient of receptor-ligand complexes, which is difficult to measure directly in experiments due to the finite lifetime of receptor-ligand bonds. We also show how such antigen movement data at the single molecule level can provide insight into the B cell synapse formation mechanism. Thus, our results can guide further single molecule tracking experiments to elucidate the synapse formation mechanism in B cells, and potentially in other immune cells.

Mechanisms of B-cell synapse formation predicted by Monte Carlo simulation.

The clustering of B-cell receptor (BCR) molecules and the formation of the protein segregation structure known as the "immunological synapse" at the contact region between B cells and antigen presenting cells appears to precede antigen (Ag) uptake by B cells. The mature B-cell synapse is characterized by a central cluster of BCR/Ag molecular complexes surrounded by a ring of LFA-1/ICAM-1 complexes. In this study, we investigate the biophysical mechanisms that drive immunological synapse formation in B cells by means of Monte Carlo simulation. Our approach simulates individual reaction and diffusion events on cell surfaces in a probabilistic manner with a clearly defined mapping between our model's probabilistic parameters and their physical equivalents. Our model incorporates the bivalent nature of the BCR as well as changes in membrane shape due to receptor-ligand binding. We find that differences in affinity and bond stiffness between BCR/Ag and LFA-1/ICAM-1 are sufficient to drive synapse formation in the absence of membrane deformation. When significant membrane deformation occurs as a result of receptor-ligand binding, our model predicts the affinity-dependent mechanism needs to be complemented by a BCR signaling-driven shift in LFA-1 affinity from low to high in order for synapses to form.

Leukocyte function-associated antigen 1-mediated adhesion stability is dynamically regulated through affinity and valency during bond formation with intercellular adhesion molecule-1.

Neutrophil rolling and transition to arrest on inflamed endothelium are dynamically regulated by the affinity of the beta(2) integrin CD11a/CD18 (leukocyte function associated antigen 1 (LFA-1)) for binding intercellular adhesion molecule (ICAM)-1. Conformational shifts are thought to regulate molecular affinity and adhesion stability. Also critical to adhesion efficiency is membrane redistribution of active LFA-1 into dense submicron clusters where multimeric interactions occur. We examined the influences of affinity and dimerization of LFA-1 on LFA-1/ICAM-1 binding by engineering a cell-free model in which two recombinant LFA-1 heterodimers are bound to respective Fab domains of an antibody attached to latex microspheres. Binding of monomeric and dimeric ICAM-1 to dimeric LFA-1 was measured in real time by fluorescence flow cytometry. ICAM-1 dissociation kinetics were measured while LFA-1 affinity was dynamically shifted by the addition of allosteric small molecules. High affinity LFA-1 dissociated 10-fold faster when bound to monomeric compared with dimeric ICAM-1, corresponding to bond lifetimes of 25 and 330 s, respectively. Downshifting LFA-1 into an intermediate affinity state with the small molecule I domain allosteric inhibitor IC487475 decreased the difference in dissociation rates between monomeric and dimeric ICAM-1 to 4-fold. When LFA-1 was shifted into the low affinity state by lovastatin, both monomeric and dimeric ICAM-1 dissociated in less than 1 s, and the dissociation rates were within 50% of each other. These data reveal the respective importance of LFA-1 affinity and proximity in tuning bond lifetime with ICAM-1 and demonstrate a nonlinear increase in the bond lifetime of the dimer versus the monomer at higher affinity.