Figure 1.
Simple three-element CMAP configurations.
Depictions of the configurations, with the concepts in boxes and their influences represented by green arrows (positive) and bar-headed red connectors (negative), are shown on the left of each panel. All configurations have the requirement that concept 1 transiently activates concept 3. F denotes fitness index for corresponding configuration. On the right of each panel, the time-courses of the concept values are shown: red, C1; blue, C2; and dark green, C3. A: only feed-forward reactions are allowed; B: a feedback from C2 to C1 is allowed; C: a case where no interactions between C1 and C2 are allowed; D: there are no limitations on the connections. (See Illustration of the Method.)
Figure 2.
CMAP of cortical oscillations for hypotheses generation.
The scheme is derived from the original CMAP paper [15] to describe the phenomenon of cortical oscillations [24]. The red connectors depict the inhibitory influences that are characterized by negative weights while the green arrows represent activation characterized by positive weights. The black dotted connectors reflect the unknown causal influences being tested in this work: they can be activation (green) or inhibition (red). The shadowed boxes indicate ‘self-inhibitions’ for a corresponding concept Ci where wii<0. The colored dashed connectors can be characterized by corresponding sign of weight or be non-existent during testing. The red half-circle connected to the inhibitory influence between MLC-pho and p-MLC depicts the second order interaction between the product (p-MLC) and the enzyme (MLC-pho). (For explanations of higher order interactions see Materials and Methods).
Table 1.
Results of hypothesis generation1.
Figure 3.
Distribution of weights for selected causal influences for different hypotheses.
Distribution of weights for hypotheses 4 and 5 for four causal influences. Top row: hypothesis 4; bottom row: hypothesis 5. All histograms are normalized by the total number of occurrences.
Figure 4.
Distribution of weights for selected causal influences for different set sizes.
Distribution of weights for hypothesis 5 for four causal influences as a function of set size. K = 3 (upper row), 5 (middle row), 7 (bottom row). All histograms are normalized by the total number of occurrences.
Figure 5.
Results of in silico experiments to test the effect of reducing cytoplasmic free calcium according to Hypotheses 4 and 5 (see text).
The bar graphs represent the portion of weight sets that produced an increase in oscillation period (green) or a decrease in oscillation period (red) or cessation of oscillations (black) when the value of calcium self-inhibition weight (wCaCa<0) was decreased by 0.4 from the initial value for each set with the constraint that the final weight value could not be less than −0.9. Weight sets that already had the minimum value of −0.9 (maximum ‘self-inhibition’) were excluded from simulations. All initial weight sets were taken from the Monte Carlo simulations.