  Due to structural and functional abnormalities or genetic variations and
mutations, there may be dysfunctional molecules within an intracellular
signaling network that do not allow the network to correctly regulate its
output molecules, such as transcription factors. This disruption in signaling
interrupts normal cellular functions and may eventually develop some
pathological conditions. In this paper, computation capacity of signaling
networks is introduced as a fundamental limit on signaling capability and
performance of such networks. The computation capacity measures the maximum
number of computable inputs, that is, the maximum number of input values for
which the correct functional output values can be recovered from the erroneous
network outputs, when the network contains some dysfunctional molecules. This
contrasts with the conventional communication capacity that measures instead
the maximum number of input values that can be correctly distinguished based on
the erroneous network outputs.
  The computation capacity is higher than the communication capacity, if the
network response function is not a one-to-one function of the input signals. By
explicitly incorporating the effect of signaling errors that result in the
network dysfunction, the computation capacity provides more information about
the network and its malfunction. Two examples of signaling networks are studied
here, one regulating caspase3 and another regulating NFkB, for which
computation and communication capacities are analyzed. Higher computation
capacities are observed for both networks. One biological implication of this
finding is that signaling networks may have more capacity than that specified
by the conventional communication capacity metric. The effect of feedback is
also studied. In summary, this paper reports findings on a new fundamental
feature of the signaling capability of cell signaling networks.
