Anand Asthagiri | Northeastern University (original) (raw)

Papers by Anand Asthagiri

Research paper thumbnail of Cell Chemotaxis on Paper for Diagnostics

Analytical Chemistry, 2015

Microfluidic chemotaxis platforms have historically been utilized to probe phenomena such as neut... more Microfluidic chemotaxis platforms have historically been utilized to probe phenomena such as neutrophil migration and are beginning to be developed for diagnostic applications; however, current microfluidic chemotaxis systems require specialized engineering equipment such as syringe pumps and long time frames (hours) to develop a chemokine gradient, and cell chemotaxis typically requires multiple additional hours. The paperfluidic device described in this work is a low-cost, sharp (2 mm wide), quasi-stable (at least 20 min) and rapidly generated (<1 s) chemokine gradient system capable of examining cell migration response over short time frames (20 min) that can be easily assembled. A proof-of-concept experiment on human pan-T cells showed significant (p ≪ 0.01) directed migration to the chemokine gradient over the control condition. This new technique for cell migration studies provides a foundational step in designing microfluidic chemotactic platforms for point-of-care diagnostics.

Research paper thumbnail of Dynamics of integrin-immediated signaling via FAK and ERK2

Integrin-mediated signaling via focal adhesion kinase (FAK) and extracellular-signal regulated ki... more Integrin-mediated signaling via focal adhesion kinase (FAK) and extracellular-signal regulated kinase 2 (ERK2) was quantified in response to modulating α5β1 integrin interaction with its fibronectin ligand. First, the dynamics of the ERK2 and FAK response were analyzed (a) to determine the dependence of each signals' kinetics on integrin-ligand bond number, (b) to gather insight into the activation and deactivation mechanisms regulating the ERK2 signal, and (c) to ascertain the disparate mechanisms that yield divergent ERK2 and FAK time-courses despite their shared integrin-ligand stimulus. Second, metrics were proposed for representing these dynamic signals with distinct time-courses. These metrics quantitatively correlated to integrin-ligand bond number and also were related to their downstream effect on cell proliferation

Research paper thumbnail of The role of transient ERK2 signals in fibronectin- and insulin-mediated DNA synthesis

Journal of cell science, 2000

Both the extracellular matrix and growth factors jointly regulate cell cycle progression via a co... more Both the extracellular matrix and growth factors jointly regulate cell cycle progression via a complex network of signaling pathways. Applying quantitative assays and analysis, we demonstrate here that concurrent stimulation of Chinese hamster ovary (CHO) cells with fibronectin (Fn) and insulin elicits a DNA synthesis response that reveals a synergy far more complex than a simple additive enhancement of response magnitude. CHO cell adhesion to higher Fn density shifts the sensitivity of the DNA synthesis response to insulin concentration from smoothly graded to sharply 'switch-like' and dramatically decreases the insulin concentration required for half-maximal response by about 1000-fold. Conversely, treatment with insulin has a milder and less complex effect on the response to varying Fn concentrations. Governing this DNA synthesis response is a common requirement for a transient, cell area-independent extracellular signal-regulated kinase 2 (ERK2) signal. Moreover, we show...

Research paper thumbnail of Intercellular coupling amplifies fate segregation during Caenorhabditis elegans vulval development

Proceedings of the National Academy of Sciences, 2006

Improved Gradient Perception. Two observations indicate that LIN-3 performs as a prototypical mor... more Improved Gradient Perception. Two observations indicate that LIN-3 performs as a prototypical morphogen whose spatial gradient determines cell fate patterning. First, cell fate is sensitive to LIN-3 dose (1). Second, a gradient in LIN-3 concentration has been

Research paper thumbnail of Tunable interplay between epidermal growth factor and cell-cell contact governs the spatial dynamics of epithelial growth

Proceedings of the National Academy of Sciences, 2009

Contact-inhibition of proliferation constrains epithelial tissue growth, and the loss of contact-... more Contact-inhibition of proliferation constrains epithelial tissue growth, and the loss of contact-inhibition is a hallmark of cancer cells. In most physiological scenarios, cell-cell contact inhibits proliferation in the presence of other growth-promoting cues, such as soluble growth factors (GFs). How cells quantitatively reconcile the opposing effects of cell-cell contact and GFs, such as epidermal growth factor (EGF), remains unclear. Here, using quantitative analysis of single cells within multicellular clusters, we show that contact is not a ''master switch'' that overrides EGF. Only when EGF recedes below a threshold level, contact inhibits proliferation, causing spatial patterns in cell cycle activity within epithelial cell clusters. Furthermore, we demonstrate that the onset of contactinhibition and the timing of spatial patterns in proliferation may be reengineered.

Research paper thumbnail of Predicting Phenotypic Diversity and the Underlying Quantitative Molecular Transitions

PLoS Computational Biology, 2009

During development, signaling networks control the formation of multicellular patterns. To what e... more During development, signaling networks control the formation of multicellular patterns. To what extent quantitative fluctuations in these complex networks may affect multicellular phenotype remains unclear. Here, we describe a computational approach to predict and analyze the phenotypic diversity that is accessible to a developmental signaling network. Applying this framework to vulval development in C. elegans, we demonstrate that quantitative changes in the regulatory network can render ,500 multicellular phenotypes. This phenotypic capacity is an order-of-magnitude below the theoretical upper limit for this system but yet is large enough to demonstrate that the system is not restricted to a select few outcomes. Using metrics to gauge the robustness of these phenotypes to parameter perturbations, we identify a select subset of novel phenotypes that are the most promising for experimental validation. In addition, our model calculations provide a layout of these phenotypes in network parameter space. Analyzing this landscape of multicellular phenotypes yielded two significant insights. First, we show that experimentally well-established mutant phenotypes may be rendered using non-canonical network perturbations. Second, we show that the predicted multicellular patterns include not only those observed in C. elegans, but also those occurring exclusively in other species of the Caenorhabditis genus. This result demonstrates that quantitative diversification of a common regulatory network is indeed demonstrably sufficient to generate the phenotypic differences observed across three major species within the Caenorhabditis genus. Using our computational framework, we systematically identify the quantitative changes that may have occurred in the regulatory network during the evolution of these species. Our model predictions show that significant phenotypic diversity may be sampled through quantitative variations in the regulatory network without overhauling the core network architecture. Furthermore, by comparing the predicted landscape of phenotypes to multicellular patterns that have been experimentally observed across multiple species, we systematically trace the quantitative regulatory changes that may have occurred during the evolution of the Caenorhabditis genus.

Research paper thumbnail of Quantitative effect of scaffold abundance on signal propagation

Molecular Systems Biology, 2009

Protein scaffolds bring together multiple components of a signalling pathway, thereby promoting s... more Protein scaffolds bring together multiple components of a signalling pathway, thereby promoting signal propagation along a common physical 'backbone'. Scaffolds play a prominent role in natural signalling pathways and provide a promising platform for synthetic circuits. To better understand how scaffolding quantitatively affects signal transmission, we conducted an in vivo sensitivity analysis of the yeast mating pathway to a broad range of perturbations in the abundance of the scaffold Ste5. Our measurements show that signal throughput exhibits a biphasic dependence on scaffold concentration and that altering the amount of scaffold binding partners reshapes this biphasic dependence. Unexpectedly, the wild-type level of Ste5 is B10-fold below the optimum needed to maximize signal throughput. This sub-optimal configuration may be a tradeoff as increasing Ste5 expression promotes baseline activation of the mating pathway. Furthermore, operating at a sub-optimal level of Ste5 may provide regulatory flexibility as tuning Ste5 expression up or down directly modulates the downstream phenotypic response. Our quantitative analysis reveals performance tradeoffs in scaffold-based modules and defines engineering challenges for implementing molecular scaffolds in synthetic pathways.

Research paper thumbnail of Intercellular mechanotransduction during multicellular morphodynamics

Journal of The Royal Society Interface, 2010

Multicellular structures are held together by cell adhesions. Forces that act upon these adhesion... more Multicellular structures are held together by cell adhesions. Forces that act upon these adhesions play an integral role in dynamically re-shaping multicellular structures during development and disease. Here, we describe different modes by which mechanical forces are transduced in a multicellular context: (i) indirect mechanosensing through compliant substratum, (ii) cytoskeletal 'tug-of-war' between cell -matrix and cell -cell adhesions, (iii) cortical contractility contributing to line tension, (iv) stresses associated with cell proliferation, and (v) forces mediating collective migration. These modes of mechanotransduction are recurring motifs as they play a key role in shaping multicellular structures in a wide range of biological contexts. Tissue morphodynamics may ultimately be understood as different spatio-temporal combinations of a select few multicellular transformations, which in turn are driven by these mechanotransduction motifs that operate at the bicellular to multicellular length scale.

Research paper thumbnail of Quantitatively distinct requirements for signaling-competent cell spreading on engineered versus natural adhesion ligands

Journal of Controlled Release, 2005

To design synthetic microenvironments that elicit desired cell behaviors, we must better understa... more To design synthetic microenvironments that elicit desired cell behaviors, we must better understand the molecular mechanisms by which cells interact with candidate biomaterials. Using cell lines with distinct alpha5beta1 integrin expression profiles, we demonstrate that this integrin mediates cell spreading on substrata coated with genetically engineered artificial extracellular matrix (aECM) proteins containing the RGD sequence (RGD-containing aECM protein [aRGD]) but lacking the PHSRN synergy site. Furthermore, aRGD-mediated adhesion stimulates an intracellular focal adhesion kinase (FAK) signal that is indicative of integrin tethering. Although both aRGD and the natural ECM protein fibronectin (FN) support alpha5beta1 integrin-mediated cell spreading, quantitative single-cell analysis revealed that aRGD-mediated spreading requires ten-fold greater threshold amount of integrin expression than FN-mediated spreading. Our analysis demonstrates that aRGD-based substrata mediate both biophysical (cell spreading) and biochemical (FAK signaling) events via the alpha5beta1 integrin, albeit with efficacy quantitatively distinct from that of natural ECM proteins that possess the full spectrum of adhesion and synergy domains.

Research paper thumbnail of Matrix stiffening sensitizes epithelial cells to EGF and enables the loss of contact inhibition of proliferation

Journal of Cell Science, 2011

Anchorage to a compliant extracellular matrix (ECM) and contact with neighboring cells impose imp... more Anchorage to a compliant extracellular matrix (ECM) and contact with neighboring cells impose important constraints on the proliferation of epithelial cells. How anchorage and contact dependence are inter-related and how cells weigh these adhesive cues alongside soluble growth factors to make a net cell cycle decision remain unclear. Here, we show that a moderate 4.5-fold stiffening of the matrix reduces the threshold amount of epidermal growth factor (EGF) needed to over-ride contact inhibition by over 100-fold. At EGF doses in the range of the dissociation constant (K(d)) for ligand binding, epithelial cells on soft matrices are contact inhibited with DNA synthesis restricted to the periphery of cell clusters. By contrast, on stiff substrates, even EGF doses at sub-K(d) levels over-ride contact inhibition, leading to proliferation throughout the cluster. Thus, matrix stiffening significantly sensitizes cells to EGF, enabling contact-independent spatially uniform proliferation. Contact inhibition on soft substrates requires E-cadherin, and the loss of contact inhibition upon matrix stiffening is accompanied by the disruption of cell-cell contacts, changes in the localization of the EGF receptor and ZO-1, and selective attenuation of ERK, but not Akt, signaling. We propose a quantitative framework for the epigenetic priming (via ECM stiffening) of a classical oncogenic pathway (EGF) with implications for the regulation of tissue growth during morphogenesis and cancer progression.

Research paper thumbnail of A Microtiter Assay for Quantifying Protein-Protein Interactions Associated with Cell-Cell Adhesion

Journal of Biomolecular Screening, 2007

Cell-cell adhesions are a hallmark of epithelial tissues, and the disruption of these contacts pl... more Cell-cell adhesions are a hallmark of epithelial tissues, and the disruption of these contacts plays a critical role in both the early and late stages of oncogenesis. The interaction between the transmembrane protein E-cadherin and the intracellular protein β-catenin plays a crucial role in the formation and maintenance of epithelial cell-cell contacts and is known to be downregulated in many cancers. The authors have developed a protein complex enzyme-linked immunosorbent assay (ELISA) that can quantify the amount of β-catenin bound to E-cadherin in unpurified whole-cell lysates with a Z′ factor of 0.74. The quantitative nature of the E-cadherin:β-catenin ELISA represents a dramatic improvement over the low-throughput assays currently used to characterize endogenous E-cadherin:β-catenin complexes. In addition, the protein complex ELISA format is compatible with standard sandwich ELISAs for parallel measurements of total levels of endogenous E-cadherin and β-catenin. In 2 case studies closely related to cancer cell biology, the authors use the protein complex ELISA and traditional sandwich ELISAs to provide a detailed, quantitative picture of the molecular changes occurring within adherens junctions in vivo. Because the E-cadherin: β-catenin protein complex plays a crucial role in oncogenesis, this protein complex ELISA may prove to be a valuable quantitative prognostic marker of tumor progression. (Journal of Biomolecular Screening 2007:683-693)

Research paper thumbnail of Quantitative Relationship among Integrin-Ligand Binding, Adhesion, and Signaling via Focal Adhesion Kinase and Extracellular Signal-regulated Kinase 2

Journal of Biological Chemistry, 1999

Because integrin-mediated signals are transferred through a physical architecture and synergistic... more Because integrin-mediated signals are transferred through a physical architecture and synergistic biochemical network whose properties are not well defined, quantitative relationships between extracellular integrin-ligand binding events and key intracellular responses are poorly understood. We begin to address this by quantifying integrin-mediated FAK and ERK2 responses in CHO cells for varied alpha(5)beta(1) expression level and substratum fibronectin density. Plating cells on fibronectin-coated surfaces initiated a transient, biphasic ERK2 response, the magnitude and kinetics of which depended on integrin-ligand binding properties. Whereas ERK2 activity initially increased with a rate proportional to integrin-ligand bond number for low fibronectin density, the desensitization rate was independent of integrin and fibronectin amount but proportional to the ERK2 activity level with an exponential decay constant of 0.3 (+/- 0.08) min(-1). Unlike the ERK2 activation time course, FAK phosphorylation followed a superficially disparate time course. However, analysis of the early kinetics of the two signals revealed them to be correlated. The initial rates of FAK and ERK2 signal generation exhibited similar dependence on fibronectin surface density, with both rates monotonically increasing with fibronectin amount until saturating at high fibronectin density. Because of this similar initial rate dependence on integrin-ligand bond formation, the disparity in their time courses is attributed to differences in feedback regulation of these signals. Whereas FAK phosphorylation increased to a steady-state level as new integrin-ligand bond formation continued during cell spreading, ERK2 activity was decoupled from the integrin-ligand stimulus and decayed back to a basal level. Accordingly, we propose different functional metrics for representing these two disparate dynamic signals: the steady-state tyrosine phosphorylation level for FAK and the integral of the pulse response for ERK2. These measures of FAK and ERK2 activity were found to correlate with short term cell-substratum adhesivity, indicating that signaling via FAK and ERK2 is proportional to the number of integrin-fibronectin bonds.

Research paper thumbnail of Selective Desensitization of Growth Factor Signaling by Cell Adhesion to Fibronectin

Journal of Biological Chemistry, 2007

Cell adhesion to the extracellular matrix is required to execute growth factor (GF)-mediated cell... more Cell adhesion to the extracellular matrix is required to execute growth factor (GF)-mediated cell behaviors, such as proliferation. A major underlying mechanism is that cell adhesion enhances GF-mediated intracellular signals, such as extracellular signal-regulated kinase (Erk). However, because GFs use distinct mechanisms to activate Ras-Erk signaling, it is unclear whether adhesion-mediated enhancement of Erk signaling is universal to all GFs. We examined this issue by quantifying the dynamics of Erk signaling induced by epidermal growth factor, basic fibroblast growth factor (bFGF), and platelet-derived growth factor (PDGF) in NIH-3T3 fibroblasts. Adhesion to fibronectin-coated surfaces enhances Erk signaling elicited by epidermal growth factor but not by bFGF or PDGF. Unexpectedly, adhesion is not always a positive influence on GF-mediated signaling. At critical subsaturating doses of PDGF or bFGF, cell adhesion ablates Erk signaling; that is, adhesion desensitizes the cell to GF stimulation, rendering the signaling pathway unresponsive to GF. Interestingly, the timing of growth factor stimulation proved critical to the desensitization process. Erk activation significantly improved only when pre-exposure to adhesion was completely eliminated; thus, concurrent stimulation by GF and adhesion was able to partially rescue adhesionmediated desensitization of PDGF-and bFGF-mediated Erk and Akt signaling. These findings suggest that adhesion-mediated desensitization occurs with rapid kinetics and targets a regulatory point upstream of Ras and proximal to GF receptor activation. Thus, adhesion-dependent Erk signaling is not universal to all GFs but, rather, is GF-specific with quantitative features that depend strongly on the dose and timing of GF exposure.

Research paper thumbnail of FGF signaling regulates Wnt ligand expression to control vulval cell lineage polarity in C. elegans

Development, 2013

The interpretation of extracellular cues leading to the polarization of intracellular components ... more The interpretation of extracellular cues leading to the polarization of intracellular components and asymmetric cell divisions is a fundamental part of metazoan organogenesis. The Caenorhabditis elegans vulva, with its invariant cell lineage and interaction of multiple cell signaling pathways, provides an excellent model for the study of cell polarity within an organized epithelial tissue. Here, we show that the fibroblast growth factor (FGF) pathway acts in concert with the Frizzled homolog LIN-17 to influence the localization of SYS-1, a component of the Wnt/β-catenin asymmetry pathway, indirectly through the regulation of cwn-1. The source of the FGF ligand is the primary vulval precursor cell (VPC) P6.p, which controls the orientation of the neighboring secondary VPC P7.p by signaling through the sex myoblasts (SMs), activating the FGF pathway. The Wnt CWN-1 is expressed in the posterior body wall muscle of the worm as well as in the SMs, making it the only Wnt expressed on the posterior and anterior sides of P7.p at the time of the polarity decision. Both sources of cwn-1 act instructively to influence P7.p polarity in the direction of the highest Wnt signal. Using single molecule fluorescence in situ hybridization, we show that the FGF pathway regulates the expression of cwn-1 in the SMs. These results demonstrate an interaction between FGF and Wnt in C. elegans development and vulval cell lineage polarity, and highlight the promiscuous nature of Wnts and the importance of Wnt gradient directionality within C. elegans.

Research paper thumbnail of Automated quantitative analysis of epithelial cell scatter

Cell Adhesion & Migration, 2008

Epithelial cell scatter is a well-known in vitro model for the study of epithelial-mesenchymal tr... more Epithelial cell scatter is a well-known in vitro model for the study of epithelial-mesenchymal transition (EMT). Scatter recapitulates many of the events that occur during EMT, including the dissociation of multicellular structures and increased cell motility. Because it has been implicated in tumor invasion and metastasis, much effort has been made to identify the molecular signals that regulate EMT. To better understand the quantitative contributions of these signals, we have developed metrics that quantitatively describe multiple aspects of cell scatter. One metric (cluster size) quantifies the disruption of intercellular adhesions while a second metric (nearest-neighbor distance) quantifies cell dispersion. We demonstrate that these metrics delineate the effects of individual cues and detect synergies between them. Specifically, we find epidermal growth factor (EGF), cholera toxin (CT) and insulin to synergistically reduce cluster sizes and increase nearest-neighbor distances. To facilitate the rapid measurement of our metrics from live-cell images, we have also developed automated techniques to identify cell nuclei and cell clusters in fluorescence images. Taken together, these studies provide broadly applicable quantitative image analysis techniques and insight into the control of epithelial cell scatter, both of which will contribute to the understanding of EMT and metastasis.

Research paper thumbnail of Signal Processing during Developmental Multicellular Patterning

Biotechnology Progress, 2008

Developing design strategies for tissue engineering and regenerative medicine is limited by our n... more Developing design strategies for tissue engineering and regenerative medicine is limited by our nascent understanding of how cell populations "self-organize" into multicellular structures on synthetic scaffolds. Mechanistic insights can be gleaned from the quantitative analysis of biomolecular signals that drive multicellular patterning during the natural processes of embryonic and adult development. This review describes three critical layers of signal processing that govern multicellular patterning: spatiotemporal presentation of extracellular cues, intracellular signaling networks that mediate crosstalk among extracellular cues, and finally, intranuclear signal integration at the level of transcriptional regulation. At every level in this hierarchy, the quantitative attributes of signals have a profound impact on patterning. We discuss how experiments and mathematical models are being used to uncover these quantitative features and their impact on multicellular phenotype.

Research paper thumbnail of A Computational Study of Feedback Effects on Signal Dynamics in a Mitogen-Activated Protein Kinase (MAPK) Pathway Model

Biotechnology Progress, 2001

Exploiting signaling pathways for the purpose of controlling cell function entails identifying an... more Exploiting signaling pathways for the purpose of controlling cell function entails identifying and manipulating the information content of intracellular signals. As in the case of the ubiquitously expressed, eukaryotic mitogen-activated protein kinase (MAPK) signaling pathway, this information content partly resides in the signals' dynamical properties. Here, we utilize a mathematical model to examine mechanisms that govern MAPK pathway dynamics, particularly the role of putative negative feedback mechanisms in generating complete signal adaptation, a term referring to the reset of a signal to prestimulation levels. In addition to yielding adaptation of its direct target, feedback mechanisms implemented in our model also indirectly assist in the adaptation of signaling components downstream of the target under certain conditions. In fact, model predictions identify conditions yielding ultra-desensitization of signals in which complete adaptation of target and downstream signals culminates even while stimulus recognition (i.e., receptor-ligand binding) continues to increase. Moreover, the rate at which signal decays can follow first-order kinetics with respect to signal intensity, so that signal adaptation is achieved in the same amount of time regardless of signal intensity or ligand dose. All of these features are consistent with experimental findings recently obtained for the Chinese hamster ovary (CHO) cell lines (Asthagiri et al., J. Biol. Chem. 1999, 274, 27119-27127). Our model further predicts that although downstream effects are independent of whether an enzyme or adaptor protein is targeted by negative feedback, adaptor-targeted feedback can "backpropagate" effects upstream of the target, specifically resulting in increased steadystate upstream signal. Consequently, where these upstream components serve as nodes within a signaling network, feedback can transfer signaling through these nodes into alternate pathways, thereby promoting the sort of signaling cross-talk that is becoming more widely appreciated.

Research paper thumbnail of Resistance to signal activation governs design features of the MAP kinase signaling module

Biotechnology and Bioengineering, 2004

Given its broad influence over numerous cell functions, redesigning the mitogen-activated protein... more Given its broad influence over numerous cell functions, redesigning the mitogen-activated protein (MAP) kinase signaling module would offer a powerful means to engineer cell behavior. Early challenges include identifying quantitative module features most relevant to biological function and developing simple design rules to predictably modify these features. This computational study delineates how features such as signal amplification, input potency, and dynamic range of output may be tuned by manipulating chief module components. Importantly, the model construction identifies a metric of resistance to signal activation that quantitatively predicts module features and design trade-offs for broad perturbations in kinase and phosphatase expression. Its predictive utility extends to dynamic properties such as signal lifetime, which often dictates MAP kinase effect on cell function. Taken together, we propose that predictably altering MAP kinase signaling by tuning resistance is not only a feasible engineering strategy, but also one exploited by natural systems to allow each MAP kinase to exert pleiotropic effects in a context-dependent manner. External stimuli not only activate kinases, but also alter phosphatase expression and activity, thereby reconfiguring a single module for quantitatively distinct modes of signaling such as transient vs. sustained dynamics, each with unique effects on cell function. B

Research paper thumbnail of Application of 3D Traction Force Microscopy to Mechanotransduction of Cell Clusters

Applied Mechanics and Materials, 2011

Research paper thumbnail of Bioengineering models of cell signaling

Annual Review of Biomedical Engineering, 2000

Key Words biochemical circuits, biomolecular networks, biophysical interactions, mechanotransduct... more Key Words biochemical circuits, biomolecular networks, biophysical interactions, mechanotransduction s Abstract Strategies for rationally manipulating cell behavior in cell-based technologies and molecular therapeutics and understanding effects of environmental agents on physiological systems may be derived from a mechanistic understanding of underlying signaling mechanisms that regulate cell functions. Three crucial attributes of signal transduction necessitate modeling approaches for analyzing these systems: an ever-expanding plethora of signaling molecules and interactions, a highly interconnected biochemical scheme, and concurrent biophysical regulation. Because signal flow is tightly regulated with positive and negative feedbacks and is bidirectional with commands traveling both from outside-in and inside-out, dynamic models that couple biophysical and biochemical elements are required to consider information processing both during transient and steady-state conditions. Unique mathematical frameworks will be needed to obtain an integrated perspective on these complex systems, which operate over wide length and time scales. These may involve a two-level hierarchical approach wherein the overall signaling network is modeled in terms of effective "circuit" or "algorithm" modules, and then each module is correspondingly modeled with more detailed incorporation of its actual underlying biochemical/biophysical molecular interactions.

Research paper thumbnail of Cell Chemotaxis on Paper for Diagnostics

Analytical Chemistry, 2015

Microfluidic chemotaxis platforms have historically been utilized to probe phenomena such as neut... more Microfluidic chemotaxis platforms have historically been utilized to probe phenomena such as neutrophil migration and are beginning to be developed for diagnostic applications; however, current microfluidic chemotaxis systems require specialized engineering equipment such as syringe pumps and long time frames (hours) to develop a chemokine gradient, and cell chemotaxis typically requires multiple additional hours. The paperfluidic device described in this work is a low-cost, sharp (2 mm wide), quasi-stable (at least 20 min) and rapidly generated (<1 s) chemokine gradient system capable of examining cell migration response over short time frames (20 min) that can be easily assembled. A proof-of-concept experiment on human pan-T cells showed significant (p ≪ 0.01) directed migration to the chemokine gradient over the control condition. This new technique for cell migration studies provides a foundational step in designing microfluidic chemotactic platforms for point-of-care diagnostics.

Research paper thumbnail of Dynamics of integrin-immediated signaling via FAK and ERK2

Integrin-mediated signaling via focal adhesion kinase (FAK) and extracellular-signal regulated ki... more Integrin-mediated signaling via focal adhesion kinase (FAK) and extracellular-signal regulated kinase 2 (ERK2) was quantified in response to modulating α5β1 integrin interaction with its fibronectin ligand. First, the dynamics of the ERK2 and FAK response were analyzed (a) to determine the dependence of each signals' kinetics on integrin-ligand bond number, (b) to gather insight into the activation and deactivation mechanisms regulating the ERK2 signal, and (c) to ascertain the disparate mechanisms that yield divergent ERK2 and FAK time-courses despite their shared integrin-ligand stimulus. Second, metrics were proposed for representing these dynamic signals with distinct time-courses. These metrics quantitatively correlated to integrin-ligand bond number and also were related to their downstream effect on cell proliferation

Research paper thumbnail of The role of transient ERK2 signals in fibronectin- and insulin-mediated DNA synthesis

Journal of cell science, 2000

Both the extracellular matrix and growth factors jointly regulate cell cycle progression via a co... more Both the extracellular matrix and growth factors jointly regulate cell cycle progression via a complex network of signaling pathways. Applying quantitative assays and analysis, we demonstrate here that concurrent stimulation of Chinese hamster ovary (CHO) cells with fibronectin (Fn) and insulin elicits a DNA synthesis response that reveals a synergy far more complex than a simple additive enhancement of response magnitude. CHO cell adhesion to higher Fn density shifts the sensitivity of the DNA synthesis response to insulin concentration from smoothly graded to sharply 'switch-like' and dramatically decreases the insulin concentration required for half-maximal response by about 1000-fold. Conversely, treatment with insulin has a milder and less complex effect on the response to varying Fn concentrations. Governing this DNA synthesis response is a common requirement for a transient, cell area-independent extracellular signal-regulated kinase 2 (ERK2) signal. Moreover, we show...

Research paper thumbnail of Intercellular coupling amplifies fate segregation during Caenorhabditis elegans vulval development

Proceedings of the National Academy of Sciences, 2006

Improved Gradient Perception. Two observations indicate that LIN-3 performs as a prototypical mor... more Improved Gradient Perception. Two observations indicate that LIN-3 performs as a prototypical morphogen whose spatial gradient determines cell fate patterning. First, cell fate is sensitive to LIN-3 dose (1). Second, a gradient in LIN-3 concentration has been

Research paper thumbnail of Tunable interplay between epidermal growth factor and cell-cell contact governs the spatial dynamics of epithelial growth

Proceedings of the National Academy of Sciences, 2009

Contact-inhibition of proliferation constrains epithelial tissue growth, and the loss of contact-... more Contact-inhibition of proliferation constrains epithelial tissue growth, and the loss of contact-inhibition is a hallmark of cancer cells. In most physiological scenarios, cell-cell contact inhibits proliferation in the presence of other growth-promoting cues, such as soluble growth factors (GFs). How cells quantitatively reconcile the opposing effects of cell-cell contact and GFs, such as epidermal growth factor (EGF), remains unclear. Here, using quantitative analysis of single cells within multicellular clusters, we show that contact is not a ''master switch'' that overrides EGF. Only when EGF recedes below a threshold level, contact inhibits proliferation, causing spatial patterns in cell cycle activity within epithelial cell clusters. Furthermore, we demonstrate that the onset of contactinhibition and the timing of spatial patterns in proliferation may be reengineered.

Research paper thumbnail of Predicting Phenotypic Diversity and the Underlying Quantitative Molecular Transitions

PLoS Computational Biology, 2009

During development, signaling networks control the formation of multicellular patterns. To what e... more During development, signaling networks control the formation of multicellular patterns. To what extent quantitative fluctuations in these complex networks may affect multicellular phenotype remains unclear. Here, we describe a computational approach to predict and analyze the phenotypic diversity that is accessible to a developmental signaling network. Applying this framework to vulval development in C. elegans, we demonstrate that quantitative changes in the regulatory network can render ,500 multicellular phenotypes. This phenotypic capacity is an order-of-magnitude below the theoretical upper limit for this system but yet is large enough to demonstrate that the system is not restricted to a select few outcomes. Using metrics to gauge the robustness of these phenotypes to parameter perturbations, we identify a select subset of novel phenotypes that are the most promising for experimental validation. In addition, our model calculations provide a layout of these phenotypes in network parameter space. Analyzing this landscape of multicellular phenotypes yielded two significant insights. First, we show that experimentally well-established mutant phenotypes may be rendered using non-canonical network perturbations. Second, we show that the predicted multicellular patterns include not only those observed in C. elegans, but also those occurring exclusively in other species of the Caenorhabditis genus. This result demonstrates that quantitative diversification of a common regulatory network is indeed demonstrably sufficient to generate the phenotypic differences observed across three major species within the Caenorhabditis genus. Using our computational framework, we systematically identify the quantitative changes that may have occurred in the regulatory network during the evolution of these species. Our model predictions show that significant phenotypic diversity may be sampled through quantitative variations in the regulatory network without overhauling the core network architecture. Furthermore, by comparing the predicted landscape of phenotypes to multicellular patterns that have been experimentally observed across multiple species, we systematically trace the quantitative regulatory changes that may have occurred during the evolution of the Caenorhabditis genus.

Research paper thumbnail of Quantitative effect of scaffold abundance on signal propagation

Molecular Systems Biology, 2009

Protein scaffolds bring together multiple components of a signalling pathway, thereby promoting s... more Protein scaffolds bring together multiple components of a signalling pathway, thereby promoting signal propagation along a common physical 'backbone'. Scaffolds play a prominent role in natural signalling pathways and provide a promising platform for synthetic circuits. To better understand how scaffolding quantitatively affects signal transmission, we conducted an in vivo sensitivity analysis of the yeast mating pathway to a broad range of perturbations in the abundance of the scaffold Ste5. Our measurements show that signal throughput exhibits a biphasic dependence on scaffold concentration and that altering the amount of scaffold binding partners reshapes this biphasic dependence. Unexpectedly, the wild-type level of Ste5 is B10-fold below the optimum needed to maximize signal throughput. This sub-optimal configuration may be a tradeoff as increasing Ste5 expression promotes baseline activation of the mating pathway. Furthermore, operating at a sub-optimal level of Ste5 may provide regulatory flexibility as tuning Ste5 expression up or down directly modulates the downstream phenotypic response. Our quantitative analysis reveals performance tradeoffs in scaffold-based modules and defines engineering challenges for implementing molecular scaffolds in synthetic pathways.

Research paper thumbnail of Intercellular mechanotransduction during multicellular morphodynamics

Journal of The Royal Society Interface, 2010

Multicellular structures are held together by cell adhesions. Forces that act upon these adhesion... more Multicellular structures are held together by cell adhesions. Forces that act upon these adhesions play an integral role in dynamically re-shaping multicellular structures during development and disease. Here, we describe different modes by which mechanical forces are transduced in a multicellular context: (i) indirect mechanosensing through compliant substratum, (ii) cytoskeletal 'tug-of-war' between cell -matrix and cell -cell adhesions, (iii) cortical contractility contributing to line tension, (iv) stresses associated with cell proliferation, and (v) forces mediating collective migration. These modes of mechanotransduction are recurring motifs as they play a key role in shaping multicellular structures in a wide range of biological contexts. Tissue morphodynamics may ultimately be understood as different spatio-temporal combinations of a select few multicellular transformations, which in turn are driven by these mechanotransduction motifs that operate at the bicellular to multicellular length scale.

Research paper thumbnail of Quantitatively distinct requirements for signaling-competent cell spreading on engineered versus natural adhesion ligands

Journal of Controlled Release, 2005

To design synthetic microenvironments that elicit desired cell behaviors, we must better understa... more To design synthetic microenvironments that elicit desired cell behaviors, we must better understand the molecular mechanisms by which cells interact with candidate biomaterials. Using cell lines with distinct alpha5beta1 integrin expression profiles, we demonstrate that this integrin mediates cell spreading on substrata coated with genetically engineered artificial extracellular matrix (aECM) proteins containing the RGD sequence (RGD-containing aECM protein [aRGD]) but lacking the PHSRN synergy site. Furthermore, aRGD-mediated adhesion stimulates an intracellular focal adhesion kinase (FAK) signal that is indicative of integrin tethering. Although both aRGD and the natural ECM protein fibronectin (FN) support alpha5beta1 integrin-mediated cell spreading, quantitative single-cell analysis revealed that aRGD-mediated spreading requires ten-fold greater threshold amount of integrin expression than FN-mediated spreading. Our analysis demonstrates that aRGD-based substrata mediate both biophysical (cell spreading) and biochemical (FAK signaling) events via the alpha5beta1 integrin, albeit with efficacy quantitatively distinct from that of natural ECM proteins that possess the full spectrum of adhesion and synergy domains.

Research paper thumbnail of Matrix stiffening sensitizes epithelial cells to EGF and enables the loss of contact inhibition of proliferation

Journal of Cell Science, 2011

Anchorage to a compliant extracellular matrix (ECM) and contact with neighboring cells impose imp... more Anchorage to a compliant extracellular matrix (ECM) and contact with neighboring cells impose important constraints on the proliferation of epithelial cells. How anchorage and contact dependence are inter-related and how cells weigh these adhesive cues alongside soluble growth factors to make a net cell cycle decision remain unclear. Here, we show that a moderate 4.5-fold stiffening of the matrix reduces the threshold amount of epidermal growth factor (EGF) needed to over-ride contact inhibition by over 100-fold. At EGF doses in the range of the dissociation constant (K(d)) for ligand binding, epithelial cells on soft matrices are contact inhibited with DNA synthesis restricted to the periphery of cell clusters. By contrast, on stiff substrates, even EGF doses at sub-K(d) levels over-ride contact inhibition, leading to proliferation throughout the cluster. Thus, matrix stiffening significantly sensitizes cells to EGF, enabling contact-independent spatially uniform proliferation. Contact inhibition on soft substrates requires E-cadherin, and the loss of contact inhibition upon matrix stiffening is accompanied by the disruption of cell-cell contacts, changes in the localization of the EGF receptor and ZO-1, and selective attenuation of ERK, but not Akt, signaling. We propose a quantitative framework for the epigenetic priming (via ECM stiffening) of a classical oncogenic pathway (EGF) with implications for the regulation of tissue growth during morphogenesis and cancer progression.

Research paper thumbnail of A Microtiter Assay for Quantifying Protein-Protein Interactions Associated with Cell-Cell Adhesion

Journal of Biomolecular Screening, 2007

Cell-cell adhesions are a hallmark of epithelial tissues, and the disruption of these contacts pl... more Cell-cell adhesions are a hallmark of epithelial tissues, and the disruption of these contacts plays a critical role in both the early and late stages of oncogenesis. The interaction between the transmembrane protein E-cadherin and the intracellular protein β-catenin plays a crucial role in the formation and maintenance of epithelial cell-cell contacts and is known to be downregulated in many cancers. The authors have developed a protein complex enzyme-linked immunosorbent assay (ELISA) that can quantify the amount of β-catenin bound to E-cadherin in unpurified whole-cell lysates with a Z′ factor of 0.74. The quantitative nature of the E-cadherin:β-catenin ELISA represents a dramatic improvement over the low-throughput assays currently used to characterize endogenous E-cadherin:β-catenin complexes. In addition, the protein complex ELISA format is compatible with standard sandwich ELISAs for parallel measurements of total levels of endogenous E-cadherin and β-catenin. In 2 case studies closely related to cancer cell biology, the authors use the protein complex ELISA and traditional sandwich ELISAs to provide a detailed, quantitative picture of the molecular changes occurring within adherens junctions in vivo. Because the E-cadherin: β-catenin protein complex plays a crucial role in oncogenesis, this protein complex ELISA may prove to be a valuable quantitative prognostic marker of tumor progression. (Journal of Biomolecular Screening 2007:683-693)

Research paper thumbnail of Quantitative Relationship among Integrin-Ligand Binding, Adhesion, and Signaling via Focal Adhesion Kinase and Extracellular Signal-regulated Kinase 2

Journal of Biological Chemistry, 1999

Because integrin-mediated signals are transferred through a physical architecture and synergistic... more Because integrin-mediated signals are transferred through a physical architecture and synergistic biochemical network whose properties are not well defined, quantitative relationships between extracellular integrin-ligand binding events and key intracellular responses are poorly understood. We begin to address this by quantifying integrin-mediated FAK and ERK2 responses in CHO cells for varied alpha(5)beta(1) expression level and substratum fibronectin density. Plating cells on fibronectin-coated surfaces initiated a transient, biphasic ERK2 response, the magnitude and kinetics of which depended on integrin-ligand binding properties. Whereas ERK2 activity initially increased with a rate proportional to integrin-ligand bond number for low fibronectin density, the desensitization rate was independent of integrin and fibronectin amount but proportional to the ERK2 activity level with an exponential decay constant of 0.3 (+/- 0.08) min(-1). Unlike the ERK2 activation time course, FAK phosphorylation followed a superficially disparate time course. However, analysis of the early kinetics of the two signals revealed them to be correlated. The initial rates of FAK and ERK2 signal generation exhibited similar dependence on fibronectin surface density, with both rates monotonically increasing with fibronectin amount until saturating at high fibronectin density. Because of this similar initial rate dependence on integrin-ligand bond formation, the disparity in their time courses is attributed to differences in feedback regulation of these signals. Whereas FAK phosphorylation increased to a steady-state level as new integrin-ligand bond formation continued during cell spreading, ERK2 activity was decoupled from the integrin-ligand stimulus and decayed back to a basal level. Accordingly, we propose different functional metrics for representing these two disparate dynamic signals: the steady-state tyrosine phosphorylation level for FAK and the integral of the pulse response for ERK2. These measures of FAK and ERK2 activity were found to correlate with short term cell-substratum adhesivity, indicating that signaling via FAK and ERK2 is proportional to the number of integrin-fibronectin bonds.

Research paper thumbnail of Selective Desensitization of Growth Factor Signaling by Cell Adhesion to Fibronectin

Journal of Biological Chemistry, 2007

Cell adhesion to the extracellular matrix is required to execute growth factor (GF)-mediated cell... more Cell adhesion to the extracellular matrix is required to execute growth factor (GF)-mediated cell behaviors, such as proliferation. A major underlying mechanism is that cell adhesion enhances GF-mediated intracellular signals, such as extracellular signal-regulated kinase (Erk). However, because GFs use distinct mechanisms to activate Ras-Erk signaling, it is unclear whether adhesion-mediated enhancement of Erk signaling is universal to all GFs. We examined this issue by quantifying the dynamics of Erk signaling induced by epidermal growth factor, basic fibroblast growth factor (bFGF), and platelet-derived growth factor (PDGF) in NIH-3T3 fibroblasts. Adhesion to fibronectin-coated surfaces enhances Erk signaling elicited by epidermal growth factor but not by bFGF or PDGF. Unexpectedly, adhesion is not always a positive influence on GF-mediated signaling. At critical subsaturating doses of PDGF or bFGF, cell adhesion ablates Erk signaling; that is, adhesion desensitizes the cell to GF stimulation, rendering the signaling pathway unresponsive to GF. Interestingly, the timing of growth factor stimulation proved critical to the desensitization process. Erk activation significantly improved only when pre-exposure to adhesion was completely eliminated; thus, concurrent stimulation by GF and adhesion was able to partially rescue adhesionmediated desensitization of PDGF-and bFGF-mediated Erk and Akt signaling. These findings suggest that adhesion-mediated desensitization occurs with rapid kinetics and targets a regulatory point upstream of Ras and proximal to GF receptor activation. Thus, adhesion-dependent Erk signaling is not universal to all GFs but, rather, is GF-specific with quantitative features that depend strongly on the dose and timing of GF exposure.

Research paper thumbnail of FGF signaling regulates Wnt ligand expression to control vulval cell lineage polarity in C. elegans

Development, 2013

The interpretation of extracellular cues leading to the polarization of intracellular components ... more The interpretation of extracellular cues leading to the polarization of intracellular components and asymmetric cell divisions is a fundamental part of metazoan organogenesis. The Caenorhabditis elegans vulva, with its invariant cell lineage and interaction of multiple cell signaling pathways, provides an excellent model for the study of cell polarity within an organized epithelial tissue. Here, we show that the fibroblast growth factor (FGF) pathway acts in concert with the Frizzled homolog LIN-17 to influence the localization of SYS-1, a component of the Wnt/β-catenin asymmetry pathway, indirectly through the regulation of cwn-1. The source of the FGF ligand is the primary vulval precursor cell (VPC) P6.p, which controls the orientation of the neighboring secondary VPC P7.p by signaling through the sex myoblasts (SMs), activating the FGF pathway. The Wnt CWN-1 is expressed in the posterior body wall muscle of the worm as well as in the SMs, making it the only Wnt expressed on the posterior and anterior sides of P7.p at the time of the polarity decision. Both sources of cwn-1 act instructively to influence P7.p polarity in the direction of the highest Wnt signal. Using single molecule fluorescence in situ hybridization, we show that the FGF pathway regulates the expression of cwn-1 in the SMs. These results demonstrate an interaction between FGF and Wnt in C. elegans development and vulval cell lineage polarity, and highlight the promiscuous nature of Wnts and the importance of Wnt gradient directionality within C. elegans.

Research paper thumbnail of Automated quantitative analysis of epithelial cell scatter

Cell Adhesion & Migration, 2008

Epithelial cell scatter is a well-known in vitro model for the study of epithelial-mesenchymal tr... more Epithelial cell scatter is a well-known in vitro model for the study of epithelial-mesenchymal transition (EMT). Scatter recapitulates many of the events that occur during EMT, including the dissociation of multicellular structures and increased cell motility. Because it has been implicated in tumor invasion and metastasis, much effort has been made to identify the molecular signals that regulate EMT. To better understand the quantitative contributions of these signals, we have developed metrics that quantitatively describe multiple aspects of cell scatter. One metric (cluster size) quantifies the disruption of intercellular adhesions while a second metric (nearest-neighbor distance) quantifies cell dispersion. We demonstrate that these metrics delineate the effects of individual cues and detect synergies between them. Specifically, we find epidermal growth factor (EGF), cholera toxin (CT) and insulin to synergistically reduce cluster sizes and increase nearest-neighbor distances. To facilitate the rapid measurement of our metrics from live-cell images, we have also developed automated techniques to identify cell nuclei and cell clusters in fluorescence images. Taken together, these studies provide broadly applicable quantitative image analysis techniques and insight into the control of epithelial cell scatter, both of which will contribute to the understanding of EMT and metastasis.

Research paper thumbnail of Signal Processing during Developmental Multicellular Patterning

Biotechnology Progress, 2008

Developing design strategies for tissue engineering and regenerative medicine is limited by our n... more Developing design strategies for tissue engineering and regenerative medicine is limited by our nascent understanding of how cell populations "self-organize" into multicellular structures on synthetic scaffolds. Mechanistic insights can be gleaned from the quantitative analysis of biomolecular signals that drive multicellular patterning during the natural processes of embryonic and adult development. This review describes three critical layers of signal processing that govern multicellular patterning: spatiotemporal presentation of extracellular cues, intracellular signaling networks that mediate crosstalk among extracellular cues, and finally, intranuclear signal integration at the level of transcriptional regulation. At every level in this hierarchy, the quantitative attributes of signals have a profound impact on patterning. We discuss how experiments and mathematical models are being used to uncover these quantitative features and their impact on multicellular phenotype.

Research paper thumbnail of A Computational Study of Feedback Effects on Signal Dynamics in a Mitogen-Activated Protein Kinase (MAPK) Pathway Model

Biotechnology Progress, 2001

Exploiting signaling pathways for the purpose of controlling cell function entails identifying an... more Exploiting signaling pathways for the purpose of controlling cell function entails identifying and manipulating the information content of intracellular signals. As in the case of the ubiquitously expressed, eukaryotic mitogen-activated protein kinase (MAPK) signaling pathway, this information content partly resides in the signals' dynamical properties. Here, we utilize a mathematical model to examine mechanisms that govern MAPK pathway dynamics, particularly the role of putative negative feedback mechanisms in generating complete signal adaptation, a term referring to the reset of a signal to prestimulation levels. In addition to yielding adaptation of its direct target, feedback mechanisms implemented in our model also indirectly assist in the adaptation of signaling components downstream of the target under certain conditions. In fact, model predictions identify conditions yielding ultra-desensitization of signals in which complete adaptation of target and downstream signals culminates even while stimulus recognition (i.e., receptor-ligand binding) continues to increase. Moreover, the rate at which signal decays can follow first-order kinetics with respect to signal intensity, so that signal adaptation is achieved in the same amount of time regardless of signal intensity or ligand dose. All of these features are consistent with experimental findings recently obtained for the Chinese hamster ovary (CHO) cell lines (Asthagiri et al., J. Biol. Chem. 1999, 274, 27119-27127). Our model further predicts that although downstream effects are independent of whether an enzyme or adaptor protein is targeted by negative feedback, adaptor-targeted feedback can "backpropagate" effects upstream of the target, specifically resulting in increased steadystate upstream signal. Consequently, where these upstream components serve as nodes within a signaling network, feedback can transfer signaling through these nodes into alternate pathways, thereby promoting the sort of signaling cross-talk that is becoming more widely appreciated.

Research paper thumbnail of Resistance to signal activation governs design features of the MAP kinase signaling module

Biotechnology and Bioengineering, 2004

Given its broad influence over numerous cell functions, redesigning the mitogen-activated protein... more Given its broad influence over numerous cell functions, redesigning the mitogen-activated protein (MAP) kinase signaling module would offer a powerful means to engineer cell behavior. Early challenges include identifying quantitative module features most relevant to biological function and developing simple design rules to predictably modify these features. This computational study delineates how features such as signal amplification, input potency, and dynamic range of output may be tuned by manipulating chief module components. Importantly, the model construction identifies a metric of resistance to signal activation that quantitatively predicts module features and design trade-offs for broad perturbations in kinase and phosphatase expression. Its predictive utility extends to dynamic properties such as signal lifetime, which often dictates MAP kinase effect on cell function. Taken together, we propose that predictably altering MAP kinase signaling by tuning resistance is not only a feasible engineering strategy, but also one exploited by natural systems to allow each MAP kinase to exert pleiotropic effects in a context-dependent manner. External stimuli not only activate kinases, but also alter phosphatase expression and activity, thereby reconfiguring a single module for quantitatively distinct modes of signaling such as transient vs. sustained dynamics, each with unique effects on cell function. B

Research paper thumbnail of Application of 3D Traction Force Microscopy to Mechanotransduction of Cell Clusters

Applied Mechanics and Materials, 2011

Research paper thumbnail of Bioengineering models of cell signaling

Annual Review of Biomedical Engineering, 2000

Key Words biochemical circuits, biomolecular networks, biophysical interactions, mechanotransduct... more Key Words biochemical circuits, biomolecular networks, biophysical interactions, mechanotransduction s Abstract Strategies for rationally manipulating cell behavior in cell-based technologies and molecular therapeutics and understanding effects of environmental agents on physiological systems may be derived from a mechanistic understanding of underlying signaling mechanisms that regulate cell functions. Three crucial attributes of signal transduction necessitate modeling approaches for analyzing these systems: an ever-expanding plethora of signaling molecules and interactions, a highly interconnected biochemical scheme, and concurrent biophysical regulation. Because signal flow is tightly regulated with positive and negative feedbacks and is bidirectional with commands traveling both from outside-in and inside-out, dynamic models that couple biophysical and biochemical elements are required to consider information processing both during transient and steady-state conditions. Unique mathematical frameworks will be needed to obtain an integrated perspective on these complex systems, which operate over wide length and time scales. These may involve a two-level hierarchical approach wherein the overall signaling network is modeled in terms of effective "circuit" or "algorithm" modules, and then each module is correspondingly modeled with more detailed incorporation of its actual underlying biochemical/biophysical molecular interactions.