A computational model for early events in B cell antigen receptor signaling: analysis of the roles of Lyn and Fyn

Catalyst: Fast and flexible modeling of reaction networks

We introduce Catalyst.jl, a flexible and feature-filled Julia library for modeling and high-performance simulation of chemical reaction networks (CRNs). Catalyst supports simulating stochastic chemical kinetics (jump process), chemical Langevin equation (stochastic differential equation), and reaction rate equation (ordinary differential equation) representations for CRNs. Through comprehensive benchmarks, we demonstrate that Catalyst simulation runtimes are often one to two orders of magnitude faster than other popular tools. More broadly, Catalyst acts as both a domain-specific language and an intermediate representation for symbolically encoding CRN models as Julia-native objects. This enables a pipeline of symbolically specifying, analyzing, and modifying CRNs; converting Catalyst models to symbolic representations of concrete mathematical models; and generating compiled code for numerical solvers. Leveraging ModelingToolkit.jl and Symbolics.jl, Catalyst models can be analyzed, simplified, and compiled into optimized representations for use in numerical solvers. Finally, we demonstrate Catalyst's broad extensibility and composability by highlighting how it can compose with a variety of Julia libraries, and how existing open-source biological modeling projects have extended its intermediate representation.

Spatial Stochastic Model of the Pre-B Cell Receptor

Survival and proliferation of immature B lymphocytes requires expression and tonic signaling of the pre-B cell receptor (pre-BCR). This low level, ligand-independent signaling is likely achieved through frequent, but short-lived, homo interactions. Tonic signaling is also central in the pathology of precursor B acute lymphoblastic leukemia (B-ALL). In order to understand how repeated, transient events can lead to sustained signaling and to assess the impact of receptor accumulation induced by the membrane landscape, we developed a spatial stochastic model of receptor aggregation and downstream signaling events. Our rule- and agent-based model builds on previous mature BCR signaling models and incorporates novel parameters derived from single particle tracking of pre-BCR on surfaces of two different B-ALL cell lines, 697 and Nalm6. Live cell tracking of receptors on the two cell lines revealed characteristic differences in their dimer dissociation rates and diffusion coefficients. We report here that these differences affect pre-BCR aggregation and consequent signal initiation events. Receptors on Nalm6 cells, which have a lower off-rate and lower diffusion coefficient, more frequently form higher order oligomers than pre-BCR on 697 cells, resulting in higher levels of downstream phosphorylation in the Nalm6 cell line.

Block Search Stochastic Simulation Algorithm (BlSSSA): A Fast Stochastic Simulation Algorithm for Modeling Large Biochemical Networks

Stochastic simulation algorithms are extensively used for exploring stochastic behavior of biochemical pathways/networks. Computational cost of these algorithms is high in simulating real biochemical systems due to their large size, complex structure and stiffness. In order to reduce the computational cost, several algorithms have been developed. It is observed that these algorithms are basically fast in simulating weakly coupled networks. In case of strongly coupled networks, they become slow as their computational cost become high in maintaining complex data structures. Here, we develop Block Search Stochastic Simulation Algorithm (BlSSSA). BlSSSA is not only fast in simulating weakly coupled networks but also fast in simulating strongly coupled and stiff networks. We compare its performance with other existing algorithms using two hypothetical networks, viz., linear chain and colloidal aggregation network, and three real biochemical networks, viz., B cell receptor signaling network, FceRI signaling network and a stiff 1,3-Butadiene Oxidation network. It has been shown that BlSSSA is faster than other algorithms considered in this study.

Reduced IRF4 expression promotes lytic phenotype in Type 2 EBV-infected B cells

Humans are infected with two types of EBV (Type 1 (T1) and Type 2 (T2)) that differ substantially in their EBNA2 and EBNA 3A/B/C latency proteins and have different phenotypes in B cells. T1 EBV transforms B cells more efficiently than T2 EBV in vitro, and T2 EBV-infected B cells are more lytic. We previously showed that both increased NFATc1/c2 activity, and an NFAT-binding motif within the BZLF1 immediate-early promoter variant (Zp-V3) contained in all T2 strains, contribute to lytic infection in T2 EBV-infected B cells. Here we compare cellular and viral gene expression in early-passage lymphoblastoid cell lines (LCLs) infected with either T1 or T2 EBV strains. Using bulk RNA-seq, we show that T2 LCLs are readily distinguishable from T1 LCLs, with approximately 600 differentially expressed cellular genes. Gene Set Enrichment Analysis (GSEA) suggests that T2 LCLs have increased B-cell receptor (BCR) signaling, NFAT activation, and enhanced expression of epithelial-mesenchymal-transition-associated genes. T2 LCLs also have decreased RNA and protein expression of a cellular gene required for survival of T1 LCLs, IRF4. In addition to its essential role in plasma cell differentiation, IRF4 decreases BCR signaling. Knock-down of IRF4 in a T1 LCL (infected with the Zp-V3-containing Akata strain) induced lytic reactivation whereas over-expression of IRF4 in Burkitt lymphoma cells inhibited both NFATc1 and NFATc2 expression and lytic EBV reactivation. Single-cell RNA-seq confirmed that T2 LCLs have many more lytic cells compared to T1 LCLs and showed that lytically infected cells have both increased NFATc1, and decreased IRF4, compared to latently infected cells. These studies reveal numerous differences in cellular gene expression in B cells infected with T1 versus T2 EBV and suggest that decreased IRF4 contributes to both the latent and lytic phenotypes in cells with T2 EBV.

Modeling the Cluster Size Distribution of Vascular Endothelial Growth Factor (VEGF) Receptors

We previously developed a method of defining receptor clusters in the membrane based on mutual distance and applied it to a set of transmission microscopy images of vascular endothelial growth factor receptors. An optimal length parameter was identified, resulting in cluster identification and a procedure that assigned a geometric shape to each cluster. We showed that the observed particle distribution results were consistent with the random placement of receptors within the clusters and, to a lesser extent, the random placement of the clusters on the cell membrane. Here, we develop and validate a stochastic model of clustering, based on a hypothesis of preexisting domains that have a high affinity for receptors. The proximate objective is to clarify the mechanism behind cluster formation and to estimate the effect on signaling. Receptor-enriched domains may significantly impact signaling pathways that rely on ligand-induced dimerization of receptors. We define a simple statistical model, based on the preexisting domain hypothesis, to predict the probability distribution of cluster sizes. The process yielded sets of parameter values that can readily be used in dynamical calculations as the estimates of the quantitative characteristics of the clustering domains.

Fyn Kinase Activity and Its Role in Neurodegenerative Disease Pathology: a Potential Universal Target?

Fyn is a non-receptor tyrosine kinase belonging to the Src family of kinases (SFKs) which has been implicated in several integral functions throughout the central nervous system (CNS), including myelination and synaptic transmission. More recently, Fyn dysfunction has been associated with pathological processes observed in neurodegenerative diseases, such as multiple sclerosis (MS), Alzheimer's disease (AD) and Parkinson's disease (PD). Neurodegenerative diseases are amongst the leading cause of death and disability worldwide and, due to the ageing population, prevalence is predicted to rise in the coming years. Symptoms across neurodegenerative diseases are both debilitating and degenerative in nature and, concerningly, there are currently no disease-modifying therapies to prevent their progression. As such, it is important to identify potential new therapeutic targets. This review will outline the role of Fyn in normal/homeostatic processes, as well as degenerative/pathological mechanisms associated with neurodegenerative diseases, such as demyelination, pathological protein aggregation, neuroinflammation and cognitive dysfunction.

Antibody:CD47 ratio regulates macrophage phagocytosis through competitive receptor phosphorylation

Cancer immunotherapies often modulate macrophage effector function by introducing either targeting antibodies that activate Fcγ receptors (FcγRs) or blocking antibodies that disrupt inhibitory SIRPα-CD47 engagement. However, how these competing signals are integrated is poorly understood, raising questions about how to effectively titrate immune responses. Here, we find that macrophage phagocytic decisions are regulated by the ratio of activating ligand to inhibitory ligand over a broad range of absolute molecular densities. Using both endogenous and chimeric receptors, we show that activating:inhibitory ligand ratios of at least 10:1 are required to promote phagocytosis of model antibody-opsonized CD47-inhibited targets and that lowering that ratio reduces FcγR phosphorylation because of inhibitory phosphatases recruited to CD47-bound SIRPα. We demonstrate that ratiometric signaling is critical for phagocytosis of tumor cells and can be modified by blocking SIRPα, indicating that balancing targeting and blocking antibodies may be important for controlling macrophage phagocytosis in cancer immunotherapy.

The multi-kinase inhibitor TG02 induces apoptosis and blocks B-cell receptor signaling in chronic lymphocytic leukemia through dual mechanisms of action

The constitutive activation of B-cell receptor (BCR) signaling, together with the overexpression of the Bcl-2 family anti-apoptotic proteins, represents two hallmarks of chronic lymphocytic leukemia (CLL) that drive leukemia cell proliferation and sustain their survival. TG02 is a small molecule multi-kinase inhibitor that simultaneously targets both of these facets of CLL pathogenesis. First, its inhibition of cyclin-dependent kinase 9 blocked the activation of RNA polymerase II and transcription. This led to the depletion of Mcl-1 and rapid induction of apoptosis in the primary CLL cells. This mechanism of apoptosis was independent of CLL prognostic factors or prior treatment history, but dependent on the expression of BAX and BAK. Second, TG02, which inhibits the members of the BCR signaling pathway such as Lck and Fyn, blocked BCR-crosslinking-induced activation of NF-κB and Akt, indicating abrogation of BCR signaling. Finally, the combination of TG02 and ibrutinib demonstrated moderate synergy, suggesting a future combination of TG02 with ibrutinib, or use in patients that are refractory to the BCR antagonists. Thus, the dual inhibitory activity on both the CLL survival pathway and BCR signaling identifies TG02 as a unique compound for clinical development in CLL and possibly other B cell malignancies.

Src Family Protein Kinase Controls the Fate of B Cells in Autoimmune Diseases

There are more than 80 kinds of autoimmune diseases known at present, including rheumatoid arthritis (RA), systemic lupus erythematosus (SLE), systemic sclerosis (SSc), inflammatory bowel disease (IBD), as well as other disorders. Autoimmune diseases have a characteristic of immune responses directly attacking own tissues, leading to systematic inflammation and subsequent tissue damage. B cells play a vital role in the development of autoimmune diseases and differentiate into plasma cells or memory B cells to secrete high-affinity antibody or provide long-lasting function. Drugs targeting B cells show good therapeutic effects for the treatment of autoimmune diseases, such as rituximab (anti-CD20 antibody). Src family protein kinases (SFKs) are believed to play important roles in a variety of cellular functions such as growth, proliferation, and differentiation of B cell via B cell antigen receptor (BCR). Lck/Yes-related novel protein tyrosine kinase (LYN), BLK (B lymphocyte kinase), and Fyn are three different kinds of SFKs mainly expressed in B cells. LYN has a dual role in the BCR signal. On the one hand, positive signals are beneficial to the development and maturation of B cells. On the other hand, LYN can also inhibit excessively activated B cells. BLK is involved in the proliferation, differentiation, and immune tolerance of B lymphocytes, and further affects the function of B cells, which may lead to autoreactive or regulatory cellular responses, increasing the risk of autoimmune diseases. Fyn may affect the development of autoimmune disorders via the differentiation of B cells in the early stage of B cell development. This article reviews the recent advances of SFKs in B lymphocytes in autoimmune diseases.

PAG1 directs SRC-family kinase intracellular localization to mediate receptor tyrosine kinase-induced differentiation

All receptor tyrosine kinases (RTKs) activate similar downstream signaling pathways through a common set of effectors, yet it is not fully understood how different receptors elicit distinct cellular responses to cause cell proliferation, differentiation, or other cell fates. We tested the hypothesis that regulation of SRC family kinase (SFK) signaling by the scaffold protein, PAG1, influences cell fate decisions following RTK activation. We generated a neuroblastoma cell line expressing a PAG1 fragment that lacks the membrane-spanning domain (PAG1TM-) and localized to the cytoplasm. PAG1TM- cells exhibited higher amounts of active SFKs and increased growth rate. PAG1TM- cells were unresponsive to TRKA and RET signaling, two RTKs that induce neuronal differentiation, but retained responses to EGFR and KIT. Under differentiation conditions, PAG1TM- cells continued to proliferate and did not extend neurites or increase β-III tubulin expression. FYN and LYN were sequestered in multivesicular bodies (MVBs), and dramatically more FYN and LYN were in the lumen of MVBs in PAG1TM- cells. In particular, activated FYN was sequestered in PAG1TM- cells, suggesting that disruption of FYN localization led to the observed defects in differentiation. The results demonstrate that PAG1 directs SFK intracellular localization to control activity and to mediate signaling by RTKs that induce neuronal differentiation.

Constitutive Activation of the B Cell Receptor Underlies Dysfunctional Signaling in Chronic Lymphocytic Leukemia

In cancer biology, the functional interpretation of genomic alterations is critical to achieve the promise of genomic profiling in the clinic. For chronic lymphocytic leukemia (CLL), a heterogeneous disease of B-lymphocytes maturing under constitutive B cell receptor (BCR) stimulation, the functional role of diverse clonal mutations remains largely unknown. Here, we demonstrate that alterations in BCR signaling dynamics underlie the progression of B cells toward malignancy. We reveal emergent dynamic features—bimodality, hypersensitivity, and hysteresis—in the BCR signaling pathway of primary CLL B cells. These signaling abnormalities in CLL quantitatively derive from BCR clustering and constitutive signaling with positive feedback reinforcement, as demonstrated through single-cell analysis of phospho-responses, computational modeling, and super-resolution imaging. Such dysregulated signaling segregates CLL patients by disease severity and clinical presentation. These findings provide a quantitative framework and methodology to assess complex and heterogeneous leukemia pathology and to inform therapeutic strategies in parallel with genomic profiling.

Using phospho-flow cytometry and computational modeling, Ziegler et al. find that B cell receptor clustering and positive feedback through SYK and LYN drive signaling hypersensitivity, bistability, and hysteresis in chronic lymphocytic leukemic B cells. Super-resolution microscopy confirms membrane auto-aggregation in leukemic B cells, and variability in signaling dysfunction predicts disease severity.

Sphingomyelin synthase 1 enhances BCR signaling to promote lupus-like autoimmune response

BACKGROUND

Sphingomyelin synthase 1 (SMS1) has been reported to participate in hepatitis and atherosclerosis. However, its role in autoimmune response is not clear. This study investigates the possible involvement of SMS1 in B-cell activation and lupus-like autoimmunity.

METHODS

SMS1 knockout lupus-like animal model and SLE patient samples were utilized. B-cell activation and associated signal transduction were detected by flow cytometry, confocal analysis and western blotting. The SMS1 expression in B cells was measured by real-time qPCR.

FINDINGS

SMS1 deficiency suppressed B-cell activation in culture, which was restored by exogenous SM supplementation. The BCR-mediated early signal transduction including the colocalization of BCR with F-actin or pY/pBtk, and the phosphorylation of intracellular Fyn and Syk were impaired in SMS1 knockout B cells. Furthermore, SMS1 knockout mice showed reduced production and deposition of autoantibodies, accompanied by less severe kidney pathological changes after pristane induction. SMS1 deficiency also displayed lower autoantibody titers and 24 h urine protein excretion in bm12-induced lupus, which were associated with reduced B-cell activation. Adoptively transferred wide-type B cells partially recovered B-cell activation and autoantibody production in SMS1 deficient bm12-induced lupus mice. Moreover, the SMS1 mRNA level in B cells of SLE patients was increased and positively correlated with the serum anti-dsDNA level, IgG and globulin titers.

INTERPRETATION

These data suggest that SMS1 is involved in lupus-like autoimmunity via regulating BCR signal transduction and B cell activation. (Word count for the abstract: 230).

Epstein-Barr virus microRNAs regulate B cell receptor signal transduction and lytic reactivation

MicroRNAs (miRNAs) are post-transcriptional regulatory RNAs that can modulate cell signaling and play key roles in cell state transitions. Epstein-Barr virus (EBV) expresses >40 viral miRNAs that manipulate both viral and cellular gene expression patterns and contribute to reprogramming of the host environment during infection. Here, we identified a subset of EBV miRNAs that desensitize cells to B cell receptor (BCR) stimuli, and attenuate the downstream activation of NF-kappaB or AP1-dependent transcription. Bioinformatics and pathway analysis of Ago PAR-CLIP datasets identified multiple EBV miRNA targets related to BCR signal transduction, including GRB2, SOS1, MALT1, RAC1, and INPP5D, which we validated in reporter assays. BCR signaling is critical for B cell activation, proliferation, and differentiation, and for EBV, is linked to reactivation. In functional assays, we demonstrate that EBV miR-BHRF1-2-5p contributes to the growth of latently infected B cells through GRB2 regulation. We further determined that activities of EBV miR-BHRF1-2-5p, EBV miR-BART2-5p, and a cellular miRNA, miR-17-5p, directly regulate virus reactivation triggered by BCR engagement. Our findings provide mechanistic insight into some of the key miRNA interactions impacting the proliferation of latently infected B cells and importantly, governing the latent to lytic switch.

Multicellular Models Bridging Intracellular Signaling and Gene Transcription to Population Dynamics

Cell signaling and gene transcription occur at faster time scales compared to cellular death, division, and evolution. Bridging these multiscale events in a model is computationally challenging. We introduce a framework for the systematic development of multiscale cell population models. Using message passing interface (MPI) parallelism, the framework creates a population model from a single-cell biochemical network model. It launches parallel simulations on a single-cell model and treats each stand-alone parallel process as a cell object. MPI mediates cell-to-cell and cell-to-environment communications in a server-client fashion. In the framework, model-specific higher level rules link the intracellular molecular events to cellular functions, such as death, division, or phenotype change. Cell death is implemented by terminating a parallel process, while cell division is carried out by creating a new process (daughter cell) from an existing one (mother cell). We first demonstrate these capabilities by creating two simple example models. In one model, we consider a relatively simple scenario where cells can evolve independently. In the other model, we consider interdependency among the cells, where cellular communication determines their collective behavior and evolution under a temporally evolving growth condition. We then demonstrate the framework’s capability by simulating a full-scale model of bacterial quorum sensing, where the dynamics of a population of bacterial cells is dictated by the intercellular communications in a time-evolving growth environment.

An Overview of Network-Based and -Free Approaches for Stochastic Simulation of Biochemical Systems

Stochastic simulation has been widely used to model the dynamics of biochemical reaction networks. Several algorithms have been proposed that are exact solutions of the chemical master equation, following the work of Gillespie. These stochastic simulation approaches can be broadly classified into two categories: network-based and -free simulation. The network-based approach requires that the full network of reactions be established at the start, while the network-free approach is based on reaction rules that encode classes of reactions, and by applying rule transformations, it generates reaction events as they are needed without ever having to derive the entire network. In this study, we compare the efficiency and limitations of several available implementations of these two approaches. The results allow for an informed selection of the implementation and methodology for specific biochemical modeling applications.

A multiscale modeling study of particle size effects on the tissue penetration efficacy of drug-delivery nanoparticles

BACKGROUND

Particle size is a key parameter for drug-delivery nanoparticle design. It is believed that the size of a nanoparticle may have important effects on its ability to overcome the transport barriers in biological tissues. Nonetheless, such effects remain poorly understood. Using a multiscale model, this work investigates particle size effects on the tissue distribution and penetration efficacy of drug-delivery nanoparticles.

RESULTS

We have developed a multiscale spatiotemporal model of nanoparticle transport in biological tissues. The model implements a time-adaptive Brownian Dynamics algorithm that links microscale particle-cell interactions and adhesion dynamics to tissue-scale particle dispersion and penetration. The model accounts for the advection, diffusion, and cellular uptakes of particles. Using the model, we have analyzed how particle size affects the intra-tissue dispersion and penetration of drug delivery nanoparticles. We focused on two published experimental works that investigated particle size effects in in vitro and in vivo tissue conditions. By analyzing experimental data reported in these two studies, we show that particle size effects may appear pronounced in an in vitro cell-free tissue system, such as collagen matrix. In an in vivo tissue system, the effects of particle size could be relatively modest. We provide a detailed analysis on how particle-cell interactions may determine distribution and penetration of nanoparticles in a biological tissue.

CONCLUSION

Our work suggests that the size of a nanoparticle may play a less significant role in its ability to overcome the intra-tissue transport barriers. We show that experiments involving cell-free tissue systems may yield misleading observations of particle size effects due to the absence of advective transport and particle-cell interactions.

Automated visualization of rule-based models

Frameworks such as BioNetGen, Kappa and Simmune use "reaction rules" to specify biochemical interactions compactly, where each rule specifies a mechanism such as binding or phosphorylation and its structural requirements. Current rule-based models of signaling pathways have tens to hundreds of rules, and these numbers are expected to increase as more molecule types and pathways are added. Visual representations are critical for conveying rule-based models, but current approaches to show rules and interactions between rules scale poorly with model size. Also, inferring design motifs that emerge from biochemical interactions is an open problem, so current approaches to visualize model architecture rely on manual interpretation of the model. Here, we present three new visualization tools that constitute an automated visualization framework for rule-based models: (i) a compact rule visualization that efficiently displays each rule, (ii) the atom-rule graph that conveys regulatory interactions in the model as a bipartite network, and (iii) a tunable compression pipeline that incorporates expert knowledge and produces compact diagrams of model architecture when applied to the atom-rule graph. The compressed graphs convey network motifs and architectural features useful for understanding both small and large rule-based models, as we show by application to specific examples. Our tools also produce more readable diagrams than current approaches, as we show by comparing visualizations of 27 published models using standard graph metrics. We provide an implementation in the open source and freely available BioNetGen framework, but the underlying methods are general and can be applied to rule-based models from the Kappa and Simmune frameworks also. We expect that these tools will promote communication and analysis of rule-based models and their eventual integration into comprehensive whole-cell models.

Slow update stochastic simulation algorithms for modeling complex biochemical networks

The stochastic simulation algorithm (SSA) based modeling is a well recognized approach to predict the stochastic behavior of biological networks. The stochastic simulation of large complex biochemical networks is a challenge as it takes a large amount of time for simulation due to high update cost. In order to reduce the propensity update cost, we proposed two algorithms: slow update exact stochastic simulation algorithm (SUESSA) and slow update exact sorting stochastic simulation algorithm (SUESSSA). We applied cache-based linear search (CBLS) in these two algorithms for improving the search operation for finding reactions to be executed. Data structure used for incorporating CBLS is very simple and the cost of maintaining this during propensity update operation is very low. Hence, time taken during propensity updates, for simulating strongly coupled networks, is very fast; which leads to reduction of total simulation time. SUESSA and SUESSSA are not only restricted to elementary reactions, they support higher order reactions too. We used linear chain model and colloidal aggregation model to perform a comparative analysis of the performances of our methods with the existing algorithms. We also compared the performances of our methods with the existing ones, for large biochemical networks including B cell receptor and FcϵRI signaling networks.

Efficient Constant-Time Complexity Algorithm for Stochastic Simulation of Large Reaction Networks

Exact stochastic simulation is an indispensable tool for a quantitative study of biochemical reaction networks. The simulation realizes the time evolution of the model by randomly choosing a reaction to fire and update the system state according to a probability that is proportional to the reaction propensity. Two computationally expensive tasks in simulating large biochemical networks are the selection of next reaction firings and the update of reaction propensities due to state changes. We present in this work a new exact algorithm to optimize both of these simulation bottlenecks. Our algorithm employs the composition-rejection on the propensity bounds of reactions to select the next reaction firing. The selection of next reaction firings is independent of the number reactions while the update of propensities is skipped and performed only when necessary. It therefore provides a favorable scaling for the computational complexity in simulating large reaction networks. We benchmark our new algorithm with the state of the art algorithms available in literature to demonstrate its applicability and efficiency.

Effective Combination Therapies for B-cell Lymphoma Predicted by a Virtual Disease Model

The complexity of cancer signaling networks limits the efficacy of most single-agent treatments and brings about challenges in identifying effective combinatorial therapies. In this study, we used chronic active B-cell receptor (BCR) signaling in diffuse large B-cell lymphoma as a model system to establish a computational framework to optimize combinatorial therapy in silico We constructed a detailed kinetic model of the BCR signaling network, which captured the known complex cross-talk between the NFκB, ERK, and AKT pathways and multiple feedback loops. Combining this signaling model with a data-derived tumor growth model, we predicted viability responses of many single drug and drug combinations in agreement with experimental data. Under this framework, we exhaustively predicted and ranked the efficacy and synergism of all possible combinatorial inhibitions of eleven currently targetable kinases in the BCR signaling network. Ultimately, our work establishes a detailed kinetic model of the core BCR signaling network and provides the means to explore the large space of possible drug combinations. Cancer Res; 77(8); 1818-30. ©2017 AACR.

Mathematical Models for Immunology: Current State of the Art and Future Research Directions

The advances in genetics and biochemistry that have taken place over the last 10 years led to significant advances in experimental and clinical immunology. In turn, this has led to the development of new mathematical models to investigate qualitatively and quantitatively various open questions in immunology. In this study we present a review of some research areas in mathematical immunology that evolved over the last 10 years. To this end, we take a step-by-step approach in discussing a range of models derived to study the dynamics of both the innate and immune responses at the molecular, cellular and tissue scales. To emphasise the use of mathematics in modelling in this area, we also review some of the mathematical tools used to investigate these models. Finally, we discuss some future trends in both experimental immunology and mathematical immunology for the upcoming years.

On the rejection-based algorithm for simulation and analysis of large-scale reaction networks

Stochastic simulation for in silico studies of large biochemical networks requires a great amount of computational time. We recently proposed a new exact simulation algorithm, called the rejection-based stochastic simulation algorithm (RSSA) [Thanh et al., J. Chem. Phys. 141(13), 134116 (2014)], to improve simulation performance by postponing and collapsing as much as possible the propensity updates. In this paper, we analyze the performance of this algorithm in detail, and improve it for simulating large-scale biochemical reaction networks. We also present a new algorithm, called simultaneous RSSA (SRSSA), which generates many independent trajectories simultaneously for the analysis of the biochemical behavior. SRSSA improves simulation performance by utilizing a single data structure across simulations to select reaction firings and forming trajectories. The memory requirement for building and storing the data structure is thus independent of the number of trajectories. The updating of the data structure when needed is performed collectively in a single operation across the simulations. The trajectories generated by SRSSA are exact and independent of each other by exploiting the rejection-based mechanism. We test our new improvement on real biological systems with a wide range of reaction networks to demonstrate its applicability and efficiency.

Characteristics of B cell‑associated gene expression in patients with coronary artery disease

The current study aimed to identify differentially expressed B cell‑associated genes in peripheral blood mononuclear cells and observe the changes in B cell activation at different stages of coronary artery disease. Groups of patients with acute myocardial infarction (AMI) and stable angina (SA), as well as healthy volunteers, were recruited into the study (n=20 per group). Whole human genome microarray analysis was performed to examine the expression of B cell‑associated genes among these three groups. The mRNA expression levels of 60 genes associated with B cell activity and regulation were measured using reverse transcription‑quantitative polymerase chain reaction. The mRNA expression of the B cell antigen receptor (BCR)‑associated genes, CD45, NFAM, SYK and LYN, were significantly upregulated in patients with AMI; however, FCRL3, CD79B, CD19, CD81, FYN, BLK, CD22 and CD5 mRNA expression levels were significantly downregulated, compared with patients in the SA and control group. The mRNA levels of the T‑independent B cell‑associated genes, CD16, CD32, LILRA1 and TLR9, were significantly increased in AMI patients compared with SA and control patients. The mRNA expression of genes associated with T‑dependent B cells were also measured: EMR2 and CD97 were statistically upregulated, whereas SLAMF1, LY9, CD28, CD43, CD72, ICOSL, PD1, CD40 and CD20 mRNAs were significantly downregulated in AMI group patients compared with the two other groups. Additionally the gene expression levels of B cell regulatory genes were measured. In patients with AMI, CR1, LILRB2, LILRB3 and VAV1 mRNA expression levels were statistically increased, whereas, CS1 and IL4I1 mRNAs were significantly reduced compared with the SA and control groups. There was no statistically significant difference in B cell‑associated gene expression levels between patients with SA and the control group. The present study identified the downregulation of genes associated with BCRs, B2 cells and B cell regulators in patients with AMI, indicating a weakened T cell‑B cell interaction and reduced B2 cell activation during AMI. Thus, improving B2 cell‑mediated humoral immunity may be a potential target for medical intervention in patients with AMI.

Directed Evolution of a Highly Specific FN3 Monobody to the SH3 Domain of Human Lyn Tyrosine Kinase

Affinity reagents of high affinity and specificity are very useful for studying the subcellular locations and quantities of individual proteins. To generate high-quality affinity reagents for human Lyn tyrosine kinase, a phage display library of fibronectin type III (FN3) monobodies was affinity selected with a recombinant form of the Lyn SH3 domain. While a highly specific monobody, TA8, was initially isolated, we chose to improve its affinity through directed evolution. A secondary library of 1.2 × 10⁹ variants was constructed and screened by affinity selection, yielding three variants, two of which have affinities of ~ 40 nM, a 130-fold increase over the original TA8 monobody. One of the variants, 2H7, displayed high specificity to the Lyn SH3 domain, as shown by ELISA and probing arrays of 150 SH3 domains. Furthermore, the 2H7 monobody was able to pull down endogenous Lyn from a lysate of Burkitt's lymphoma cells, thereby demonstrating its utility as an affinity reagent for detecting Lyn in a complex biological mixture.

Modeling for (physical) biologists: an introduction to the rule-based approach

Models that capture the chemical kinetics of cellular regulatory networks can be specified in terms of rules for biomolecular interactions. A rule defines a generalized reaction, meaning a reaction that permits multiple reactants, each capable of participating in a characteristic transformation and each possessing certain, specified properties, which may be local, such as the state of a particular site or domain of a protein. In other words, a rule defines a transformation and the properties that reactants must possess to participate in the transformation. A rule also provides a rate law. A rule-based approach to modeling enables consideration of mechanistic details at the level of functional sites of biomolecules and provides a facile and visual means for constructing computational models, which can be analyzed to study how system-level behaviors emerge from component interactions.

Modeling biomolecular site dynamics in immunoreceptor signaling systems

The immune system plays a central role in human health. The activities of immune cells, whether defending an organism from disease or triggering a pathological condition such as autoimmunity, are driven by the molecular machinery of cellular signaling systems. Decades of experimentation have elucidated many of the biomolecules and interactions involved in immune signaling and regulation, and recently developed technologies have led to new types of quantitative, systems-level data. To integrate such information and develop nontrivial insights into the immune system, computational modeling is needed, and it is essential for modeling methods to keep pace with experimental advances. In this chapter, we focus on the dynamic, site-specific, and context-dependent nature of interactions in immunoreceptor signaling (i.e., the biomolecular site dynamics of immunoreceptor signaling), the challenges associated with capturing these details in computational models, and how these challenges have been met through use of rule-based modeling approaches.

A Computational Study of the Effects of Syk Activity on B Cell Receptor Signaling Dynamics

The kinase Syk is intricately involved in early signaling events in B cells and is required for proper response when antigens bind to B cell receptors (BCRs). Experiments using an analog-sensitive version of Syk (Syk-AQL) have better elucidated its role, but have not completely characterized its behavior. We present a computational model for BCR signaling, using dynamical systems, which incorporates both wild-type Syk and Syk-AQL. Following the use of sensitivity analysis to identify significant reaction parameters, we screen for parameter vectors that produced graded responses to BCR stimulation as is observed experimentally. We demonstrate qualitative agreement between the model and dose response data for both mutant and wild-type kinases. Analysis of our model suggests that the level of NF-κB activation, which is reduced in Syk-AQL cells relative to wild-type, is more sensitive to small reductions in kinase activity than Erkp activation, which is essentially unchanged. Since this profile of high Erkp and reduced NF-κB is consistent with anergy, this implies that anergy is particularly sensitive to small changes in catalytic activity. Also, under a range of forward and reverse ligand binding rates, our model of Erkp and NF-κB activation displays a dependence on a power law affinity: the ratio of the forward rate to a non-unit power of the reverse rate. This dependence implies that B cells may respond to certain details of binding and unbinding rates for ligands rather than simple affinity alone.

From proteomes to complexomes in the era of systems biology

Protein complexes carry out almost the entire signaling and functional processes in the cell. The protein complex complement of a cell, and its network of complex-complex interactions, is referred to here as the complexome. Computational methods to predict protein complexes from proteomics data, resulting in network representations of complexomes, have recently being developed. In addition, key advances have been made toward understanding the network and structural organization of complexomes. We review these bioinformatics advances, and their discovery-potential, as well as the merits of integrating proteomics data with emerging methods in systems biology to study protein complex signaling. It is envisioned that improved integration of proteomics and systems biology, incorporating the dynamics of protein complexes in space and time, may lead to more predictive models of cell signaling networks for effective modulation.

Phosphorylation site dynamics of early T-cell receptor signaling

In adaptive immune responses, T-cell receptor (TCR) signaling impacts multiple cellular processes and results in T-cell differentiation, proliferation, and cytokine production. Although individual protein-protein interactions and phosphorylation events have been studied extensively, we lack a systems-level understanding of how these components cooperate to control signaling dynamics, especially during the crucial first seconds of stimulation. Here, we used quantitative proteomics to characterize reshaping of the T-cell phosphoproteome in response to TCR/CD28 co-stimulation, and found that diverse dynamic patterns emerge within seconds. We detected phosphorylation dynamics as early as 5 s and observed widespread regulation of key TCR signaling proteins by 30 s. Development of a computational model pointed to the presence of novel regulatory mechanisms controlling phosphorylation of sites with central roles in TCR signaling. The model was used to generate predictions suggesting unexpected roles for the phosphatase PTPN6 (SHP-1) and shortcut recruitment of the actin regulator WAS. Predictions were validated experimentally. This integration of proteomics and modeling illustrates a novel, generalizable framework for solidifying quantitative understanding of a signaling network and for elucidating missing links.

An Interaction Library for the FcεRI Signaling Network

Antigen receptors play a central role in adaptive immune responses. Although the molecular networks associated with these receptors have been extensively studied, we currently lack a systems-level understanding of how combinations of non-covalent interactions and post-translational modifications are regulated during signaling to impact cellular decision-making. To fill this knowledge gap, it will be necessary to formalize and piece together information about individual molecular mechanisms to form large-scale computational models of signaling networks. To this end, we have developed an interaction library for signaling by the high-affinity IgE receptor, FcεRI. The library consists of executable rules for protein–protein and protein–lipid interactions. This library extends earlier models for FcεRI signaling and introduces new interactions that have not previously been considered in a model. Thus, this interaction library is a toolkit with which existing models can be expanded and from which new models can be built. As an example, we present models of branching pathways from the adaptor protein Lat, which influence production of the phospholipid PIP₃ at the plasma membrane and the soluble second messenger IP₃. We find that inclusion of a positive feedback loop gives rise to a bistable switch, which may ensure robust responses to stimulation above a threshold level. In addition, the library is visualized to facilitate understanding of network circuitry and identification of network motifs.

Roles of raft-anchored adaptor Cbp/PAG1 in spatial regulation of c-Src kinase

The tyrosine kinase c-Src is upregulated in numerous human cancers, implying a role for c-Src in cancer progression. Previously, we have shown that sequestration of activated c-Src into lipid rafts via a transmembrane adaptor, Cbp/PAG1, efficiently suppresses c-Src-induced cell transformation in Csk-deficient cells, suggesting that the transforming activity of c-Src is spatially regulated via Cbp in lipid rafts. To dissect the molecular mechanisms of the Cbp-mediated regulation of c-Src, a combined analysis was performed that included mathematical modeling and in vitro experiments in a c-Src- or Cbp-inducible system. c-Src activity was first determined as a function of c-Src or Cbp levels, using focal adhesion kinase (FAK) as a crucial c-Src substrate. Based on these experimental data, two mathematical models were constructed, the sequestration model and the ternary model. The computational analysis showed that both models supported our proposal that raft localization of Cbp is crucial for the suppression of c-Src function, but the ternary model, which includes a ternary complex consisting of Cbp, c-Src, and FAK, also predicted that c-Src function is dependent on the lipid-raft volume. Experimental analysis revealed that c-Src activity is elevated when lipid rafts are disrupted and the ternary complex forms in non-raft membranes, indicating that the ternary model accurately represents the system. Moreover, the ternary model predicted that, if Cbp enhances the interaction between c-Src and FAK, Cbp could promote c-Src function when lipid rafts are disrupted. These findings underscore the crucial role of lipid rafts in the Cbp-mediated negative regulation of c-Src-transforming activity, and explain the positive role of Cbp in c-Src regulation under particular conditions where lipid rafts are perturbed.

Rule-based modeling: a computational approach for studying biomolecular site dynamics in cell signaling systems

Rule-based modeling was developed to address the limitations of traditional approaches for modeling chemical kinetics in cell signaling systems. These systems consist of multiple interacting biomolecules (e.g., proteins), which themselves consist of multiple parts (e.g., domains, linear motifs, and sites of phosphorylation). Consequently, biomolecules that mediate information processing generally have the potential to interact in multiple ways, with the number of possible complexes and posttranslational modification states tending to grow exponentially with the number of binary interactions considered. As a result, only large reaction networks capture all possible consequences of the molecular interactions that occur in a cell signaling system, which is problematic because traditional modeling approaches for chemical kinetics (e.g., ordinary differential equations) require explicit network specification. This problem is circumvented through representation of interactions in terms of local rules. With this approach, network specification is implicit and model specification is concise. Concise representation results in a coarse graining of chemical kinetics, which is introduced because all reactions implied by a rule inherit the rate law associated with that rule. Coarse graining can be appropriate if interactions are modular, and the coarseness of a model can be adjusted as needed. Rules can be specified using specialized model-specification languages, and recently developed tools designed for specification of rule-based models allow one to leverage powerful software engineering capabilities. A rule-based model comprises a set of rules, which can be processed by general-purpose simulation and analysis tools to achieve different objectives (e.g., to perform either a deterministic or stochastic simulation).

Spontaneous NF-κB activation by autocrine TNFα signaling: a computational analysis

NF-κB is a key transcription factor that regulates innate immune response. Its activity is tightly controlled by numerous feedback loops, including two negative loops mediated by NF-κB inducible inhibitors, IκBα and A20, which assure oscillatory responses, and by positive feedback loops arising due to the paracrine and autocrine regulation via TNFα, IL-1 and other cytokines. We study the NF-κB system of interlinked negative and positive feedback loops, combining bifurcation analysis of the deterministic approximation with stochastic numerical modeling. Positive feedback assures the existence of limit cycle oscillations in unstimulated wild-type cells and introduces bistability in A20-deficient cells. We demonstrated that cells of significant autocrine potential, i.e., cells characterized by high secretion of TNFα and its receptor TNFR1, may exhibit sustained cytoplasmic-nuclear NF-κB oscillations which start spontaneously due to stochastic fluctuations. In A20-deficient cells even a small TNFα expression rate qualitatively influences system kinetics, leading to long-lasting NF-κB activation in response to a short-pulsed TNFα stimulation. As a consequence, cells with impaired A20 expression or increased TNFα secretion rate are expected to have elevated NF-κB activity even in the absence of stimulation. This may lead to chronic inflammation and promote cancer due to the persistent activation of antiapoptotic genes induced by NF-κB. There is growing evidence that A20 mutations correlate with several types of lymphomas and elevated TNFα secretion is characteristic of many cancers. Interestingly, A20 loss or dysfunction also leaves the organism vulnerable to septic shock and massive apoptosis triggered by the uncontrolled TNFα secretion, which at high levels overcomes the antiapoptotic action of NF-κB. It is thus tempting to speculate that some cancers of deregulated NF-κB signaling may be prone to the pathogen-induced apoptosis.

Human kinome analysis reveals novel kinases contributing to virus infection and retinoic-acid inducible gene I-induced type I and type III IFN gene expression

Activation of host innate antiviral responses are mediated by retinoic-acid inducible gene I (RIG-I)-like receptors, RIG-I and melanoma differentiation-associated gene 5, and TLRs 3, 7, 8 and 9, recognising different types of viral nucleic acids. The major components of the RIG-I- and TLR pathways have putatively been identified, but previously unrecognised kinases may contribute to virus infection-induced activation of the IFN response. Here, we screened a human kinase cDNA library, termed the kinome, using an IFN-λ1 promoter-driven luciferase reporter assay in HEK293 cells during Sendai virus infection. Of the 568 kinases analysed, nearly 50 enhanced IFN-λ1 gene expression at least twofold in response to Sendai virus infection. The best activators were FYN (FYN oncogene related to SRC, FGR, YES), serine/threonine kinase 24, activin A receptor type 1 and SRPK1 (SFRS protein kinase 1). These kinases enhanced RIG-I-dependent IFN-λ1 promoter activation via IFN-stimulated response and NF-κB elements, as confirmed using mutant IFN-λ1 promoter constructs. FYN and SRPK1 enhanced IFN-λ1 and CXCL10 protein production via the RIG-I pathway, and stimulated RIG-I and MyD88-dependent phosphorylation of IRF3 and IRF7 transcription factors, respectively. We conclude that several previously unrecognised kinases, particularly FYN and SRPK1, positively regulate IFN-λ1 and similarly regulated cytokine and chemokine genes during viral infection.

Efficient stochastic simulation of chemical kinetics networks using a weighted ensemble of trajectories

We apply the "weighted ensemble" (WE) simulation strategy, previously employed in the context of molecular dynamics simulations, to a series of systems-biology models that range in complexity from a one-dimensional system to a system with 354 species and 3680 reactions. WE is relatively easy to implement, does not require extensive hand-tuning of parameters, does not depend on the details of the simulation algorithm, and can facilitate the simulation of extremely rare events. For the coupled stochastic reaction systems we study, WE is able to produce accurate and efficient approximations of the joint probability distribution for all chemical species for all time t. WE is also able to efficiently extract mean first passage times for the systems, via the construction of a steady-state condition with feedback. In all cases studied here, WE results agree with independent "brute-force" calculations, but significantly enhance the precision with which rare or slow processes can be characterized. Speedups over "brute-force" in sampling rare events via the Gillespie direct Stochastic Simulation Algorithm range from ~10(12) to ~10(18) for characterizing rare states in a distribution, and ~10(2) to ~10(4) for finding mean first passage times.

Single-cell measurements of IgE-mediated FcεRI signaling using an integrated microfluidic platform

Heterogeneity in responses of cells to a stimulus, such as a pathogen or allergen, can potentially play an important role in deciding the fate of the responding cell population and the overall systemic response. Measuring heterogeneous responses requires tools capable of interrogating individual cells. Cell signaling studies commonly do not have single-cell resolution because of the limitations of techniques used such as Westerns, ELISAs, mass spectrometry, and DNA microarrays. Microfluidics devices are increasingly being used to overcome these limitations. Here, we report on a microfluidic platform for cell signaling analysis that combines two orthogonal single-cell measurement technologies: on-chip flow cytometry and optical imaging. The device seamlessly integrates cell culture, stimulation, and preparation with downstream measurements permitting hands-free, automated analysis to minimize experimental variability. The platform was used to interrogate IgE receptor (FcεRI) signaling, which is responsible for triggering allergic reactions, in RBL-2H3 cells. Following on-chip crosslinking of IgE-FcεRI complexes by multivalent antigen, we monitored signaling events including protein phosphorylation, calcium mobilization and the release of inflammatory mediators. The results demonstrate the ability of our platform to produce quantitative measurements on a cell-by-cell basis from just a few hundred cells. Model-based analysis of the Syk phosphorylation data suggests that heterogeneity in Syk phosphorylation can be attributed to protein copy number variations, with the level of Syk phosphorylation being particularly sensitive to the copy number of Lyn.

Specification, annotation, visualization and simulation of a large rule-based model for ERBB receptor signaling

BACKGROUND

Mathematical/computational models are needed to understand cell signaling networks, which are complex. Signaling proteins contain multiple functional components and multiple sites of post-translational modification. The multiplicity of components and sites of modification ensures that interactions among signaling proteins have the potential to generate myriad protein complexes and post-translational modification states. As a result, the number of chemical species that can be populated in a cell signaling network, and hence the number of equations in an ordinary differential equation model required to capture the dynamics of these species, is prohibitively large. To overcome this problem, the rule-based modeling approach has been developed for representing interactions within signaling networks efficiently and compactly through coarse-graining of the chemical kinetics of molecular interactions.

RESULTS

Here, we provide a demonstration that the rule-based modeling approach can be used to specify and simulate a large model for ERBB receptor signaling that accounts for site-specific details of protein-protein interactions. The model is considered large because it corresponds to a reaction network containing more reactions than can be practically enumerated. The model encompasses activation of ERK and Akt, and it can be simulated using a network-free simulator, such as NFsim, to generate time courses of phosphorylation for 55 individual serine, threonine, and tyrosine residues. The model is annotated and visualized in the form of an extended contact map.

CONCLUSIONS

With the development of software that implements novel computational methods for calculating the dynamics of large-scale rule-based representations of cellular signaling networks, it is now possible to build and analyze models that include a significant fraction of the protein interactions that comprise a signaling network, with incorporation of the site-specific details of the interactions. Modeling at this level of detail is important for understanding cellular signaling.