How to Model Toxicity Pathways

a modern integrated electronic circuit chip easily contains 1 billion transistors, which can be practically simulated in a circuit design computer program. intracellular biochemical circuits contain a finite set of interacting molecular components, about 20 000 to 30 000 genes, their transcriptomic and proteomic products, and small-molecule metabolites. in theory, toxicity pathways, which are subsets of the entire intracellular biochemical networks, can be computed. Mapping these pathways is an ongoing scientific effort. With the ever-improving, modern high-throughput, and high-content omic analytic tools, we are moving closer to the day that all the molecular components, their interactions, component concentrations, and interacting strength are known.

these toxicity pathways will be modeled as dynamic systems, where RNAs, proteins, and metabolites are treated as dependent state variables, and their rates of change are governed by coupled differential equations. To come up with these equations, we need to draw on the types of biochemical interactions specific to the participating molecular components, which define the quantitative characteristics of the interactions and regulations. Elementary molecule-molecule interactions proceed on the principle of mass action (the rate of which is proportional to the concentrations of reactants). Certain combinations of these linear interactions can give us highly non-linear signaling properties. These small combined circuit structures are called network motifs.39 They appear in biochemical networks repeatedly at frequencies higher than random combinations of reactions. Common network motifs include ultrasensitive response motifs, feedback loops, and feedforward loops (Figure 8.2). Logically connected network motifs constitute larger biochemical pathways or networks underpinning cellular-level functions, such as cell cycle progression, differentiation, stress response and homeostasis, and apoptosis.40-42

Signal amplification is an essential feature of signal propagation through biochemical networks. Amplification is required to compensate for attenuation of signals as they move along the pathways. it also provides properties needed for emergent, non-trivial behaviors. A suite of ultrasensitive response


Network motifs, including positive feedback, negative feedback, coherent and incoherent feedforward, and their dynamical functions

Figure 8.2 Network motifs, including positive feedback, negative feedback, coherent and incoherent feedforward, and their dynamical functions.

motifs, discovered over the past few decades, can amplify small percentage changes in input biochemical signals to larger percentage changes in output signals. These motifs include positive cooperative binding, homo-mul- timerization, multi-step signaling, zero-order covalent modification cycle, and molecular titration.36,43-4S On a global input-output plot, ultrasensitive responses provided by these motifs usually appear as sigmoidal curves that can be approximated by a Hill equation. The Hill coefficient represents the degree of signal amplification. Multiple ultrasensitive response motifs can be further combined into more complex network motifs to get a higher degree of amplification. An example is the mitogen-activated protein kinase cascade.46

Although these ultrasensitive motifs can operate alone to amplify signals, they are usually embedded in feedback or feedforward network motifs to support more complex cellular behaviors. Positive feedback loops are the prototypical network structure necessary for irreversible switch-like behaviors. This is seen with cell differentiation in lineage specification and cell cycle progression through distinct phases. It is also seen in other cellular processes involving binary decision making based on whether the input signal surpass a threshold or not.42 For instance, in B-lymphocyte terminal differentiation, a bistable circuit, comprising coupled transcriptional feedback loops involving multiple transcriptional repressors, operates to mediate the irreversible transition of B-cells into antibody-secreting plasma cells.47 Environmental immunotoxicant TCDD, acting via the aryl hydrocarbon receptor, can perturb this feedback circuit and suppress B-cell differentiation.

Negative feedback loops are a prototype network motif structure necessary for adaptation and homeostasis. It is a well-conserved motif operating in cellular stress responses to a variety of stressors.3541 these stress response pathways normally involve a sensor protein detecting cellular state changes, a transcription factor, and a suite of genes induced by the transcription factor to counteract the perturbed cellular state. For instance, in oxidative stress response, Keapl is the sensor molecule detecting cellular redox state changes. The altered function of Keapl as an E3 ligase adaptor protein then results in Nrf2 activation through protein stabilization. Nrf2 then translocates into the nucleus where it induces a number of antioxidant or related genes to bring the altered redox state back to normal.48 Ultrasensitive motifs are invariably embedded in these negative feedback loops to sufficiently amplify signals to induce stress genes to levels high enough to normalize the perturbed cellular state. Negative feedback is an inherently nonlinear motif that can generate superlinearly shaped (concave downward) or threshold dose responses.48 Post-translational feedback activation of stress proteins in the absence of transcriptional alteration of stress genes might be important for cells to adapt to low level and transient stresses.49 When this post-translational adaptation is saturated and transcriptional control is invoked, cellular and even apical adversity will likely result.50

Feedforward loops are another network motif structure that can mediate cellular adaptation. This requires an “incoherent” feedforward loop, where the two arms of the loop regulate a common target molecule in opposite directions. In oxidative stress response, a number of chemical oxidants can directly modify the sensor molecule Keapl. The signaling path from a chemical oxidant to Keapl, Nrf2, antioxidant genes, and finally to reactive oxygen species (ROS) forms the negative feedforward arm of the feedforward loop.48 The positive arm is from chemical oxidants to ROS, in which ROS production is increased by chemical oxidants. This incoherent forward loop can generate three different types of dose responses (superlinear, threshold, or hormetic) in the low-dose region, depending on the signaling strength of the feedforward arms.51

In the toxicology and risk assessment field, debates on whether biological systems have a threshold or not in response to external perturbations have been ongoing. Statistical arguments surrounding response data have been of little help. Such data can only support but not prove the existence of thresholds in the low-dose region where biological and measurement variability tend to dominate. Additional evidence supporting thresholds has to come from mechanistic studies where the underlying toxicity pathway being perturbed is expected to produce a threshold or threshold-like behaviors. Most of the common network motif structures that inherently produce threshold responses are summarized in a review article.38 These motifs include, in addition to the feedback and feedforward structures discussed above, a small number of bifurcation motifs (transcritical bifurcation and supercritical pitchfork bifurcations). Many biological examples are associated with these threshold motifs. Knowledge of the underlying network structure of toxicity pathways being perturbed will help better describe the shape of the dose-response curve in the low-dose region, reducing the uncertainty of whether or not there is a threshold.

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