It is well understood that the CREB protein is highly involved in neuronal mechanisms underlying memory and learning in mammalian brain, and deficiencies in CREB activity can result in transition to certain pathological conditions. In this paper, we use some published experimental data, along with a neuronal system composed of the Izhikevich neuron model, to characterize how CREB abnormalities can alter neuronal signals and the system behavior. The abnormal data are extracted from intracellular recordings collected from the neurons of transgenic mice expressing VP16-CREB - a constitutively active form of CREB - whereas the normal data are obtained from the wild-type mice neurons. Upon estimating the neuron model parameters from the experimental data, we observe that the model exhibits good fit to both normal and abnormal data, for various synaptic input currents. To study the effect of CREB abnormalities on the considered neuronal system, we use the information theoretic redundancy parameter. It basically measures - for the system output neuron - the amount of spike count information overlap that exists between the states of the stimulus currents injected to the input neurons. Our analysis reveals a noticeable increase in the information redundancy, when CREB behaves abnormally. This finding motivates further exploration of the biological implications of the information redundancy in neuronal systems, and its use as a parameter to model abnormalities in CREB and perhaps other important transcription factors involved in learning and memory.