What Can Systems Biology Do for You?

2. Correlation Models

Though they often are considered distinct, most biological pathways talk to each other. Take, for instance, tumor necrosis factor (TNF) and epidermal growth factor (EGF) signaling. Peter Sorger at Harvard Medical School and colleagues recently published a pair of papers on these two pathways, the first of which used correlation modeling to identify those intracellular signals that most tightly correlated with TNF signaling.1 (The second used kinetic modeling.)

A correlation model renders a pathway at a relatively granular level, without necessarily considering each element explicitly. As a result, it can be built with little a priori knowledge of the pathway components.

Suppose for instance, that you know ligand levels, that some intracellular molecule is phosphorylated, and the resulting phenotype. "If your model has gaps like that you can use correlation modeling ... you can have black boxes between the stages," says Hamid Bolouri at the Institute for Systems Biology in Seattle.

Correlation models use data types similar to those for kinetic models. But, says Sorger, the difference is in its density: "Kinetic modeling requires a greater density of data." Correlation modeling can also more easily accommodate heterogeneous data such as biochemical levels, activities, and phenotypes, he adds. "Kinetic modeling, being more local, cannot easily predict phenotype." The tradeoff, says Bolouri, is that while correlation models "can make good predictions from incomplete data ... the model is not mechanistic."

Nevertheless, correlation models can reveal unexpected insights. "EGF receptor activation was as tightly correlated with TNF as it was with EGF treatment," says Sorger. "That seems nuts, until you realize that as soon as you add TNF, the cell releases an EGF-like ligand in the first of a four-step autocrine cascade."

3. Logical Models

Logical models describe biological processes as a series of simple Boolean logic gates: If X and not Y then Z, and so on. Reka Albert at Pennsylvania State University and her colleagues used this to model the behavior of plant stomata - the pores on plant leaves that allow carbon dioxide in and oxygen out.

"We have about 100 components in our network," she says, "and about half of them are unknown." Given that lack of knowledge, and the dearth of information describing how these components interact, Albert's group developed a logical model to simulate the pathway.2

"Because there is almost no quantitative or kinetic information available for the components and interactions, we assumed two states for each component," she explains - on or off, or active or inactive. One of the components of the model, for instance, was "actin cytoskeleton reorganization," whose Boolean rule was "cytosolic calcium OR NOT RAC1."

Though intuitive and relatively simple to construct (assuming you have some mechanistic knowledge of your pathway) such models have several drawbacks. Biological components typically do not follow Boolean behavior. In addition, with no kinetic data inputs, the models can identify the important components but not the concentrations to which they correspond.

Still, logical models can yield benefits. Albert's team was able to use its model of stomata behavior to predict accurately the effect of intracellular pH on the process. "We tested that experimentally and found good qualitative agreement."

4. Kinetic Modeling

Kinetic models seek to describe the temporal and spatial behavior of every component in the system individually, using differential equations. Sorger says that they represent the pinnacle of complexity in computational modeling. "With kinetics, you require the most knowledge." John Tyson at Virginia Polytechnic Institute and State University uses kinetic modeling in his work on cell-cycle oscillation.

Data that can be factored into the model include: mutant phenotypes; how proteins interact, are activated, and are degraded; and how fast things change. In the case of the cell-cycle oscillator, the literature is awash in data, Tyson says, but consolidating that information into a simple set of rules was out of the question. "It's impossible to figure out intuitively how all these components will work together," he says. "The network is too complicated, with too many contradictory signals."

Untangling these signals can provide unexpected insights into the so-called emergent behaviors of complex systems. These are properties that are only apparent in the context of the whole system. The cell-cycle oscillator, for example, does nothing dramatic for a time, until some critical threshold is attained, and suddenly there's a burst of activity. Then everything quiets down and the cycle begins again. "These threshold events are nonlinear, and simple linear models don't capture them," Bolouri says.

But in the absence of data, simple linear models sometimes are required. Indeed, Tyson's work on the cell-cycle oscillator has been marked by a long series of refinements along the continuum of model complexity.

"When we first started modeling the cell cycle, we didn't know all the parts," says Tyson. "We built a detailed kinetic model of part of the cycle, and used a simple Boolean model for the rest, where we had no detail." Thus with refinements they've been able to fill the gaps.

"Modeling is a way to refine your understanding of the molecular basis of cell physiology," he says, "a way to determine the implications of what you're thinking. A kinetic model can often tell you where your thinking is wrong and how to fix it. "

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