One goal of systems biology is to expose what is obscure in the obvious, that is, what unexpected properties emerge when biological parts are combined to form systems. In this study, we constructed a model of the oxygen sensor in the Sre1 regulatory pathway to investigate how its components work together to create a hypoxic response. We framed the model structure according to our prior knowledge and then selected parameters that yielded simulated results consistent with a variety of experimental observations. The model structure was rich enough to make this possible, suggesting that our knowledge of the system covers the essential interactions that drive the hypoxic response. We then used the model to investigate two ways that the prolyl hydroxylase Ofd1 regulates the transcription factor Sre1N in an oxygen-dependent manner. Although these two regulatory functions are not easily separable in vivo, we removed them from the model individually to determine what each contributes to the overall performance of the system. We found that the Ofd1 function of blocking Sre1N binding to DNA is essential to achieve oxygen-dependent Sre1N regulation. The second Ofd1 function of accelerating Sre1N degradation is essential for the pathway to recover quickly, as observed when oxygen is restored after a period of hypoxia.
Ofd1 represents a novel paradigm for an oxygen sensor in that a single protein regulates both inhibition and degradation of a hypoxic transcription factor. In contrast, these functions are performed independently by two enzymes in the HIF system, the other major paradigm for oxygen sensing in eukaryotes. The dual mechanisms of action of Ofd1 are described by our six-state model, in which Ofd1 can be unbound, bound to Nro1, or bound to Sre1N, oxygenated or nonoxygenated. This amounts to a competitive setup in which Sre1N competes with Nro1 to bind to Ofd1; the relative affinity of Ofd1 for the two is modulated by oxygen. This regulation-through-variable-competition motif is also found in the HIF system, in which HIFα competes with ARD proteins for access to FIH, and the terms of this competition depend on available oxygen (Cockman et al., 2009
). The HIF system involves enzymes (FIH, PHDs) modifying substrates (HIFα, ARD proteins) and has been modeled as such (Kohn et al., 2004
; Qutub and Popel, 2006
; Dayan et al., 2009
; Schmierer et al., 2010
). In contrast, Ofd1 is known to bind both Sre1N and Nro1 (Lee et al., 2009
) but is not known to enzymatically modify either, and Ofd1 enzyme activity is not required for it to inhibit DNA binding or accelerate degradation of Sre1N (Hughes and Espenshade, 2008
; Lee et al., 2011
). Accordingly, our model describes the binding and unbinding of Ofd1 without assuming enzymatic activity, and this is sufficient to replicate the observed behavior of the Sre1 pathway (). Thus Ofd1 serves as the central point of a simpler version of the HIF system.
By combining the six-state model of Ofd1 with models of Sre1N-dependent sre1N+
transcription and oxygen-dependent ofd1+
transcription, our model shows how a complex system of biological control logic responds to low oxygen by producing an order-of-magnitude increase in a hypoxic transcription factor. This system can be considered a feedforward mechanism with respect to the metabolic pathways it regulates, as it senses an environmental disturbance that would alter the function of those pathways (low oxygen) and acts preemptively to compensate. Embedded in this feedforward mechanism is the positive feedback of Sre1N on its own production, which has been shown to be necessary for strong Sre1N up-regulation (Hughes et al., 2009
). Moreover, although we approximated Ofd1 production in the model as a function of oxygen, ofd1+
is a known target gene of Sre1N (Todd et al., 2006
), and thus the increased production of Ofd1 at low oxygen can be considered a negative feedback path within the larger feedforward mechanism. Our model predicts that in sre1N
cells subjected to hypoxia, this negative feedback path is responsible for the fall in Sre1N after its increase (). We conjecture that this Sre1N overshoot allows a faster response to hypoxia in the same way that overshoots in man-made control systems allow faster responses to changing inputs. The effect of this negative feedback path is unknown in wild-type cells, which combine the control logic described here with the additional negative feedback of ergosterol repressing Sre1 transport and cleavage (Porter et al., 2010
). However, on the basis of our results here, we surmise that this hidden negative feedback path may play a previously unappreciated role in the wild-type hypoxic response, suggesting a course for further experimentation.
In addition to this testable prediction about the effect of Ofd1 production, our model makes the prediction that the oxygen threshold for increasing Sre1N can be tuned by adjusting levels of Nro1 (). This is yet another resemblance to the HIF system, in which ARD proteins are predicted to play a similar role in tuning the oxygen threshold for HIFα up-regulation (Cockman et al., 2009
; Schmierer et al., 2010
). Although we assumed a constant concentration of Nro1 for modeling purposes, this mechanism could be a means by which other processes in the cell influence the Sre1 pathway through changing Nro1 levels or activity. Furthermore, this mechanism could facilitate evolutionary adaptation, providing a way of retuning the system in response to selective pressure without fundamentally changing its structure. Validating the predicted effect experimentally and looking deeper into the physiological role of Nro1 are interesting matters for future investigation.
In developing the model presented here, we used an exhaustive parameter search method, which constrained the space of plausible model parameters by identifying those consistent with a variety of observations about the function of Ofd1 in the Sre1 pathway (Materials and Methods). This method, while computationally intensive, has several important features that made it appropriate for identifying the parameters of this model. First, it thoroughly explores the parameter space, unlike optimization-based parameter search methods, which can get “stuck” in one region of the parameter space and miss better solutions in other regions. To be thorough, the exhaustive method requires a sufficiently fine grid for sampling the parameter space. Second, the exhaustive method circumvents problems with model identifiability by providing an entire set of solutions consistent with observations. For this model, the difficulty of obtaining reliable measurements at very low oxygen levels created an identifiability problem that affected the parameters KXNF and kdXNF, which govern Sre1N–Ofd1 binding and degradation in the absence of oxygen. Although these parameters were poorly constrained (), we were still able to draw conclusions from the model by examining what was uniformly true for all consistent parameter sets. Third, the exhaustive method can easily incorporate data from other models that have a known relationship to the model being identified. In this case, we incorporated data from several strains of yeast undergoing several types of treatment into the model identification process (Materials and Methods).
Although the model presented here describes the sre1N
strain of S. pombe
, it is directly applicable to understanding wild-type yeast, as the sre1N
mutation simply bypasses the machinery for ergosterol-dependent Sre1 cleavage in S. pombe
. Less directly, this model may be applicable to understanding SREBP pathways in other species of fungi, many of which are natural permutations of that in S. pombe
(Bien and Espenshade, 2010
). One known limitation of the model is that it does not accurately describe the cellular responses to long-term hypoxia or highly anoxic conditions (); one can imagine that such extreme stimuli would generate responses well beyond that of Ofd1. Nevertheless, the model is still relevant under such conditions to describe the Ofd1-generated component of the hypoxic response.
Overall, the model presented here advances our understanding of the Ofd1 oxygen sensor in the S. pombe
SREBP pathway from qualitative to quantitative. Physiologically, this sensor functions in tandem with an ergosterol sensor (Porter et al., 2010
) to control ergosterol production along with other processes affected by hypoxia. Present studies focus on modeling this multiple-input, multiple-output control system to better understand regulation in this larger network. Ultimately, this model may be useful for understanding OGFOD1, the orthologue of Ofd1 in mammalian cells, which is involved in hypoxic signaling for cell death (Saito et al., 2010
) and stress responses (Wehner et al., 2010
). It remains to be seen whether OGFOD1 mediates a general hypoxic response in the manner of Ofd1, but our model provides a starting point for understanding quantitatively how such a response would work.