Modularity and predictability in cell signaling and decision making

Reframing macrophage diversity with network motifs

A binary classification of macrophage activation as inflammatory or resolving does not capture the diversity of macrophage states observed in tissues. However, framing macrophage activation as a continuous spectrum of states overlooks the intracellular and extracellular networks that regulate and coordinate macrophage responses. Here, we suggest that the systems biology concept of network motifs, which incorporate rules of local molecular interactions, is useful for reframing macrophage activation. Because network motifs can be used to regulate distinct biological functions, they offer a simplified unit that can be compared across organismal, tissue, and disease contexts. Moreover, defining macrophage states as combinations of functional modules regulated by network motifs offers a framework to ultimately predict and target macrophage responses arising in complex environments.

Dynamics and Sensitivity of Signaling Pathways

Purpose of Review

Signaling pathways serve to communicate information about extracellular conditions into the cell, to both the nucleus and cytoplasmic processes to control cell responses. Genetic mutations in signaling network components are frequently associated with cancer and can result in cells acquiring an ability to divide and grow uncontrollably. Because signaling pathways play such a significant role in cancer initiation and advancement, their constituent proteins are attractive therapeutic targets. In this review, we discuss how signaling pathway modeling can assist with identifying effective drugs for treating diseases, such as cancer. An achievement that would facilitate the use of such models is their ability to identify controlling biochemical parameters in signaling pathways, such as molecular abundances and chemical reaction rates, because this would help determine effective points of attack by therapeutics.

Recent Findings

We summarize the current state of understanding the sensitivity of phosphorylation cycles with and without sequestration. We also describe some basic properties of regulatory motifs including feedback and feedforward regulation.

Summary

Although much recent work has focused on understanding the dynamics and particularly the sensitivity of signaling networks in eukaryotic systems, there is still an urgent need to build more scalable models of signaling networks that can appropriately represent their complexity across different cell types and tumors.

A modular approach for modeling the cell cycle based on functional response curves

Modeling biochemical reactions by means of differential equations often results in systems with a large number of variables and parameters. As this might complicate the interpretation and generalization of the obtained results, it is often desirable to reduce the complexity of the model. One way to accomplish this is by replacing the detailed reaction mechanisms of certain modules in the model by a mathematical expression that qualitatively describes the dynamical behavior of these modules. Such an approach has been widely adopted for ultrasensitive responses, for which underlying reaction mechanisms are often replaced by a single Hill function. Also time delays are usually accounted for by using an explicit delay in delay differential equations. In contrast, however, S-shaped response curves, which by definition have multiple output values for certain input values and are often encountered in bistable systems, are not easily modeled in such an explicit way. Here, we extend the classical Hill function into a mathematical expression that can be used to describe both ultrasensitive and S-shaped responses. We show how three ubiquitous modules (ultrasensitive responses, S-shaped responses and time delays) can be combined in different configurations and explore the dynamics of these systems. As an example, we apply our strategy to set up a model of the cell cycle consisting of multiple bistable switches, which can incorporate events such as DNA damage and coupling to the circadian clock in a phenomenological way.

Bistability plays an important role in many biochemical processes and typically emerges from complex interaction patterns such as positive and double negative feedback loops. Here, we propose to theoretically study the effect of bistability in a larger interaction network. We explicitly incorporate a functional expression describing an S-shaped input-output curve in the model equations, without the need for considering the underlying biochemical events. This expression can be converted into a functional module for an ultrasensitive response, and a time delay is easily included as well. Exploiting the fact that several of these modules can easily be combined in larger networks, we construct a cell cycle model consisting of multiple bistable switches and show how this approach can account for a number of known properties of the cell cycle.

Regulation and dynamics of force transmission at individual cell-matrix adhesion bonds

Integrin-based adhesion complexes link the cytoskeleton to the extracellular matrix (ECM) and are central to the construction of multicellular animal tissues. How biological function emerges from the tens to thousands of proteins present within a single adhesion complex remains unclear. We used fluorescent molecular tension sensors to visualize force transmission by individual integrins in living cells. These measurements revealed an underlying functional modularity in which integrin class controlled adhesion size and ECM ligand specificity, while the number and type of connections between integrins and F-actin determined the force per individual integrin. In addition, we found that most integrins existed in a state of near-mechanical equilibrium, a result not predicted by existing models of cytoskeletal force transduction. A revised model that includes reversible cross-links within the F-actin network can account for this result and suggests one means by which cellular mechanical homeostasis can arise at the molecular level.

Parallel Tempering with Lasso for model reduction in systems biology

Systems Biology models reveal relationships between signaling inputs and observable molecular or cellular behaviors. The complexity of these models, however, often obscures key elements that regulate emergent properties. We use a Bayesian model reduction approach that combines Parallel Tempering with Lasso regularization to identify minimal subsets of reactions in a signaling network that are sufficient to reproduce experimentally observed data. The Bayesian approach finds distinct reduced models that fit data equivalently. A variant of this approach that uses Lasso to perform selection at the level of reaction modules is applied to the NF-κB signaling network to test the necessity of feedback loops for responses to pulsatile and continuous pathway stimulation. Taken together, our results demonstrate that Bayesian parameter estimation combined with regularization can isolate and reveal core motifs sufficient to explain data from complex signaling systems.

Cells respond to diverse environmental cues using complex networks of interacting proteins and other biomolecules. Mathematical and computational models have become invaluable tools to understand these networks and make informed predictions to rationally perturb cell behavior. However, the complexity of detailed models that try to capture all known biochemical elements of signaling networks often makes it difficult to determine the key regulatory elements that are responsible for specific cell behaviors. Here, we present a Bayesian computational approach, PTLasso, to automatically extract minimal subsets of detailed models that are sufficient to explain experimental data. The method simultaneously calibrates and reduces models, and the Bayesian approach samples globally, allowing us to find alternate mechanistic explanations for the data if present. We demonstrate the method on both synthetic and real biological data and show that PTLasso is an effective method to isolate distinct parts of a larger signaling model that are sufficient for specific data.

Empowering statistical methods for cellular and molecular biologists

We provide guidelines for using statistical methods to analyze the types of experiments reported in cellular and molecular biology journals such as Molecular Biology of the Cell. Our aim is to help experimentalists use these methods skillfully, avoid mistakes, and extract the maximum amount of information from their laboratory work. We focus on comparing the average values of control and experimental samples. A Supplemental Tutorial provides examples of how to analyze experimental data using R software.

Network inference reveals novel connections in pathways regulating growth and defense in the yeast salt response

Cells respond to stressful conditions by coordinating a complex, multi-faceted response that spans many levels of physiology. Much of the response is coordinated by changes in protein phosphorylation. Although the regulators of transcriptome changes during stress are well characterized in Saccharomyces cerevisiae, the upstream regulatory network controlling protein phosphorylation is less well dissected. Here, we developed a computational approach to infer the signaling network that regulates phosphorylation changes in response to salt stress. We developed an approach to link predicted regulators to groups of likely co-regulated phospho-peptides responding to stress, thereby creating new edges in a background protein interaction network. We then use integer linear programming (ILP) to integrate wild type and mutant phospho-proteomic data and predict the network controlling stress-activated phospho-proteomic changes. The network we inferred predicted new regulatory connections between stress-activated and growth-regulating pathways and suggested mechanisms coordinating metabolism, cell-cycle progression, and growth during stress. We confirmed several network predictions with co-immunoprecipitations coupled with mass-spectrometry protein identification and mutant phospho-proteomic analysis. Results show that the cAMP-phosphodiesterase Pde2 physically interacts with many stress-regulated transcription factors targeted by PKA, and that reduced phosphorylation of those factors during stress requires the Rck2 kinase that we show physically interacts with Pde2. Together, our work shows how a high-quality computational network model can facilitate discovery of new pathway interactions during osmotic stress.

Cells sense and respond to stressful environments by utilizing complex signaling networks that integrate diverse signals to coordinate a multi-faceted physiological response. Much of this response is controlled by post-translational protein phosphorylation. Although many regulators that mediate changes in protein phosphorylation are known, how these regulators inter-connect in a single regulatory network that can transmit cellular signals is not known. It is also unclear how regulators that promote growth and regulators that activate the stress response interconnect to reorganize resource allocation during stress. Here, we developed an integrated experimental and computational workflow to infer the signaling network that regulates phosphorylation changes during osmotic stress in the budding yeast Saccharomyces cerevisiae. The workflow integrates data measuring protein phosphorylation changes in response to osmotic stress with known physical interactions between yeast proteins from large-scale datasets, along with other information about how regulators recognize their targets. The resulting network suggested new signaling connections between regulators and pathways, including those involved in regulating growth and defense, and predicted new regulators involved in stress defense. Our work highlights the power of using network inference to deliver new insight on how cells coordinate a diverse adaptive strategy to stress.

A Precise Cdk Activity Threshold Determines Passage through the Restriction Point

At the restriction point (R), mammalian cells irreversibly commit to divide. R has been viewed as a point in G1 that is passed when growth factor signaling initiates a positive feedback loop of Cdk activity. However, recent studies have cast doubt on this model by claiming R occurs prior to positive feedback activation in G1 or even before completion of the previous cell cycle. Here we reconcile these results and show that whereas many commonly used cell lines do not exhibit a G1 R, primary fibroblasts have a G1 R that is defined by a precise Cdk activity threshold and the activation of cell-cycle-dependent transcription. A simple threshold model, based solely on Cdk activity, predicted with more than 95% accuracy whether individual cells had passed R. That a single measurement accurately predicted cell fate shows that the state of complex regulatory networks can be assessed using a few critical protein activities.

Non-Lytic Egression of Infectious Bursal Disease Virus (IBDV) Particles from Infected Cells

Infectious bursal disease virus (IBDV), a member of the Birnaviridae family, is responsible for a devastating immunosuppressive disease affecting juvenile domestic chickens. IBDV particles are naked icosahedrons enclosing a bipartite double-stranded RNA genome harboring three open reading frames (ORF). One of these ORFs codes for VP5, a non-structural polypeptide dispensable for virus replication in tissue culture but essential for IBDV pathogenesis. Using two previously described recombinant viruses, whose genomes differ in a single nucleotide, expressing or not the VP5 polypeptide, we have analyzed the role of this polypeptide during the IBDV replication process. Here, we show that VP5 is not involved in house-keeping steps of the virus replication cycle; i.e. genome transcription/replication, protein translation and virus assembly. Although infection with the VP5 expressing and non-expressing viruses rendered similar intracellular infective progeny yields, striking differences were detected on the ability of their progenies to exiting infected cells. Experimental data shows that the bulk of the VP5-expressing virus progeny efficiently egresses infected cells during the early phase of the infection, when viral metabolism is peaking and virus-induced cell death rates are as yet minimal, as determined by qPCR, radioactive protein labeling and quantitative real-time cell death analyses. In contrast, the release of the VP5-deficient virus progeny is significantly abridged and associated to cell death. Taken together, data presented in this report show that IBDV uses a previously undescribed VP5-dependent non-lytic egress mechanism significantly enhancing the virus dissemination speed. Ultrastructural analyses revealed that newly assembled IBDV virions associate to a vesicular network apparently facilitating their trafficking from virus assembly factories to the extracellular milieu, and that this association requires the expression of the VP5 polypeptide.

Positive Feedback Keeps Duration of Mitosis Temporally Insulated from Upstream Cell-Cycle Events

Cell division is characterized by a sequence of events by which a cell gives rise to two daughter cells. Quantitative measurements of cell-cycle dynamics in single cells showed that despite variability in G1-, S-, and G2 phases, duration of mitosis is short and remarkably constant. Surprisingly, there is no correlation between cell-cycle length and mitotic duration, suggesting that mitosis is temporally insulated from variability in earlier cell-cycle phases. By combining live cell imaging and computational modeling, we showed that positive feedback is the molecular mechanism underlying the temporal insulation of mitosis. Perturbing positive feedback gave rise to a sluggish, variable entry and progression through mitosis and uncoupled duration of mitosis from variability in cell cycle length. We show that positive feedback is important to keep mitosis short, constant, and temporally insulated and anticipate it might be a commonly used regulatory strategy to create modularity in other biological systems.

The significance of the 1-kinase/1-phosphatase activities of the PPIP5K family

The inositol pyrophosphates (diphosphoinositol polyphosphates), which include 1-InsP₇, 5-InsP₇, and InsP₈, are highly 'energetic' signaling molecules that play important roles in many cellular processes, particularly with regards to phosphate and bioenergetic homeostasis. Two classes of kinases synthesize the PP-InsPs: IP6Ks and PPIP5Ks. The significance of the IP6Ks - and their 5-InsP₇ product - has been widely reported. However, relatively little is known about the biological significance of the PPIP5Ks. The purpose of this review is to provide an update on developments in our understanding of key features of the PPIP5Ks, which we believe strengthens the hypothesis that their catalytic activities serve important cellular functions. Central to this discussion is the recent discovery that the PPIP5K is a rare example of a single protein that catalyzes a kinase/phosphatase futile cycle.

Switch-like Transitions Insulate Network Motifs to Modularize Biological Networks

Cellular decisions are made by complex networks that are difficult to analyze. Although it is common to analyze smaller sub-networks known as network motifs, it is unclear whether this is valid, because these motifs are embedded in complex larger networks. Here, we address the general question of modularity by examining the S. cerevisiae pheromone response. We demonstrate that the feedforward motif controlling the cell-cycle inhibitor Far1 is insulated from cell-cycle dynamics by the positive feedback switch that drives reentry to the cell cycle. Before cells switch on positive feedback, the feedforward motif model predicts the behavior of the larger network. Conversely, after the switch, the feedforward motif is dismantled and has no discernable effect on the cell cycle. When insulation is broken, the feedforward motif no longer predicts network behavior. This work illustrates how, despite the interconnectivity of networks, the activity of motifs can be insulated by switches that generate well-defined cellular states.

Half dozen of one, six billion of the other: What can small- and large-scale molecular systems biology learn from one another?

Small-scale molecular systems biology, by which we mean the understanding of a how a few parts work together to control a particular biological process, is predicated on the assumption that cellular regulation is arranged in a circuit-like structure. Results from the omics revolution have upset this vision to varying degrees by revealing a high degree of interconnectivity, making it difficult to develop a simple, circuit-like understanding of regulatory processes. We here outline the limitations of the small-scale systems biology approach with examples from research into genetic algorithms, genetics, transcriptional network analysis, and genomics. We also discuss the difficulties associated with deriving true understanding from the analysis of large data sets and propose that the development of new, intelligent, computational tools may point to a way forward. Throughout, we intentionally oversimplify and talk about things in which we have little expertise, and it is likely that many of our arguments are wrong on one level or another. We do believe, however, that developing a true understanding via molecular systems biology will require a fundamental rethinking of our approach, and our goal is to provoke thought along these lines.

Phylogenetic Profiling for Probing the Modular Architecture of the Human Genome

Information about functional connections between genes can be derived from patterns of coupled loss of their homologs across multiple species. This comparative approach, termed phylogenetic profiling, has been successfully used to infer genetic interactions in bacteria and eukaryotes. Rapid progress in sequencing eukaryotic species has enabled the recent phylogenetic profiling of the human genome, resulting in systematic functional predictions for uncharacterized human genes. Importantly, groups of co-evolving genes reveal widespread modularity in the underlying genetic network, facilitating experimental analyses in human cells as well as comparative studies of conserved functional modules across species. This strategy is particularly successful in identifying novel metabolic proteins and components of multi-protein complexes. The targeted sequencing of additional key eukaryotes and the incorporation of improved methods to generate and compare phylogenetic profiles will further boost the predictive power and utility of this evolutionary approach to the functional analysis of gene interaction networks.

From Structural Variation of Gene Molecules to Chromatin Dynamics and Transcriptional Bursting

Transcriptional activation of eukaryotic genes is accompanied, in general, by a change in the sensitivity of promoter chromatin to endonucleases. The structural basis of this alteration has remained elusive for decades; but the change has been viewed as a transformation of one structure into another, from "closed" to "open" chromatin. In contradistinction to this static and deterministic view of the problem, a dynamical and probabilistic theory of promoter chromatin has emerged as its solution. This theory, which we review here, explains observed variation in promoter chromatin structure at the level of single gene molecules and provides a molecular basis for random bursting in transcription-the conjecture that promoters stochastically transition between transcriptionally conducive and inconducive states. The mechanism of transcriptional regulation may be understood only in probabilistic terms.