Scaffold proteins tether and orient components of a signaling cascade to facilitate signaling. Although much is known about how scaffolds colocalize signaling proteins, it is unclear whether scaffolds promote signal amplification. Here, we used arrestin-3, a scaffold of the ASK1-MKK4/7-JNK3 cascade, as a model to understand signal amplification by a scaffold protein. We found that arrestin-3 exhibited >15-fold higher affinity for inactive JNK3 than for active JNK3, and this change involved a shift in the binding site following JNK3 activation. We used systems biochemistry modeling and Bayesian inference to evaluate how the activation of upstream kinases contributed to JNK3 phosphorylation. Our combined experimental and computational approach suggested that the catalytic phosphorylation rate of JNK3 at Thr-221 by MKK7 is two orders of magnitude faster than the corresponding phosphorylation of Tyr-223 by MKK4 with or without arrestin-3. Finally, we showed that the release of activated JNK3 was critical for signal amplification. Collectively, our data suggest a “conveyor belt” mechanism for signal amplification by scaffold proteins. This mechanism informs on a long-standing mystery for how few upstream kinase molecules activate numerous downstream kinases to amplify signaling.

Mathematical models of biomolecular networks are commonly used to study mechanisms of cellular processes, but their usefulness is often questioned due to parameter uncertainty. Here, we employ Bayesian parameter inference and dynamic network analysis to study dominant reaction fluxes in models of extrinsic apoptosis. Although a simplified model yields thousands of parameter vectors with equally good fits to data, execution modes based on reaction fluxes clusters to three dominant execution modes. A larger model with increased parameter uncertainty shows that signal flow is constrained to eleven execution modes that use 53 out of 2067 possible signal subnetworks. Each execution mode exhibits different behaviors to in silico perturbations, due to different signal execution mechanisms. Machine learning identifies informative parameters to guide experimental validation. Our work introduces a probability-based paradigm of signaling mechanisms, highlights systems-level interactions that modulate signal flow, and provides a methodology to understand mechanistic model predictions with uncertain parameters.

The function M ean whose domain is the set of all finite sequences on X and is defined by M ean(π) = { x | x is a mean of π} is called the mean function on X. In this note, the mean function on finite trees is characterized axiomatically.

SummaryVisualization plays a central role in the analysis of biochemical network models to identify patterns that arise from reaction dynamics and perform model exploratory analysis. To facilitate these analyses, we developed PyViPR, a visualization tool that generates static and dynamic representations of biochemical network processes within a Python-based environment. PyViPR embeds network visualizations within Jupyter notebooks, thus enabling integration with modeling, simulation, and analysis workflows. To present the capabilities of PyViPR, we explore execution mechanisms of extrinsic apoptosis in HeLa cells. We show that community-detection algorithms identify groups of molecular species that capture key biological functions and ease exploration of the apoptosis network. We then show how different kinetic parameter sets that fit the experimental data equally well exhibit significantly different signal-execution dynamics as the system progresses toward mitochondrial outer-membrane permeabilization. Therefore, PyViPR aids the conceptual understanding of dynamic network processes and accelerates hypothesis generation for further testing and validation.

A p-value of a sequence π = (x 1 , x 2 , . . . , x k ) of elements of a finite metric space (X , d ) is an element x for whichThe function p with domain the set of all finite sequences defined by p (π) = {x : x is a p-value of π } is called the p -function on X . The p -functions with p = 1 and p = 2 are the well-studied median and mean functions respectively. In this article, the p -function on finite trees is characterized axiomatically.

Let [Formula: see text] be an integer such that [Formula: see text]. A [Formula: see text]-value of a sequence [Formula: see text] of elements of a finite metric space [Formula: see text] is an element [Formula: see text] for which [Formula: see text] is minimum. The [Formula: see text] function whose domain is the set of all finite sequences on [Formula: see text], and defined by [Formula: see text] is a [Formula: see text]-value of [Formula: see text] is called the [Formula: see text] function on [Formula: see text]. In this note, an axiomatic characterization of the [Formula: see text] function on finite Boolean lattices is presented.

A median of a sequence π = (x 1 , x 2 , . . . , x k ) of elements of a finite metric space (X, d)The function Median with domain the set of all finite sequences on X and defined by Med(π) = {x : x is a median of π} is called the median function on X. In this paper, the median function on finite Boolean lattices is axiomatically characterized via location functions.

Computational models of network-driven processes have become a standard to explain cellular systems-level behavior and predict cellular responses to perturbations. Modern models can span a broad range of biochemical reactions and species that, in principle, comprise the complexity of dynamic cellular processes. Visualization plays a central role in the analysis of biochemical network processes to identify patterns that arise from model dynamics and perform model exploratory analysis. However, most existing visualization tools are limited in their capabilities to facilitate mechanism exploration of large, dynamic, and complex models. Here, we present PyViPR, a visualization tool that provides researchers static and dynamic representations of biochemical network processes within a Python-based Literate Programming environment. PyViPR embeds network visualizations on Jupyter notebooks, thus facilitating integration with Python modeling, simulation, and analysis workflows. To present the capabilities of PyViPR, we explore execution mechanisms of extrinsic apoptosis in HeLa cells. We show how community-detection algorithms can identify groups of molecular species that represent key biological regulatory functions and simplify the apoptosis network by placing those groups into interactively collapsible nodes. We then show how dynamic execution of a signal, under different kinetic parameter sets that fit the experimental data equally well, exhibit significantly different signal-execution modes in mitochondrial outer-membrane permeabilization -the point of no return in extrinsic apoptosis execution. Therefore, PyViPR aids the conceptual understanding of dynamic network processes and accelerates hypothesis generation for further testing and validation.1 Cellular processes are controlled by networks of biomolecular interactions that process 2 signals and trigger a response [1-3]. These molecular networks give rise to nonlinear 3 dynamic processes that are difficult to explain and predict using reductionist 4 methods [4]. Mathematical models of cellular signaling pathways have become 5 commonplace in order to gain insights and describe the molecular mechanisms that 6 control cellular processes [5][6][7]. In general, these models continue to grow in size and 7 complexity, which makes the exploration of network structure and dynamics increasingly 8 challenging. Visualization tools comprise one effective way to explore network processes 9 and acquire conceptual insights about signal-execution mechanisms. In addition, 10 visualization tools can facilitate detection of execution patterns, and aid in hypothesis 11 generation for experimental validation. However, to the best of our knowledge, most 12 tools focus on static network representations of models without strategies to deal with 13 June 3, 2019 1/17 increasingly complex models, and generally lack support to visualize model dynamics. 14 Therefore, there is a need for novel tools that provide viable visualizations of large 15 models as well as support for intuitive visualiza...