## 4 Results  
By using the Pareto ranking, the most important node in the network is found to be CD81. (See Figure S1 for Pareto ranking of control patients.) A Gibbs Homology network at threshold 32 in which CD81 has the highest Betti centrality is shown in Figure 3 (highlighted in yellow) and the nearest-neighbor nodes with smaller, though important Gibbs energies, are shown highlighted in green. Figure 2: Genes having the most impact on dropping Gibbs homology network complexity (threshold = 32), with counts corresponding to the number of patients having the particular gene as target. Importantly, CD81 is a transmembrane protein that has tissue specific expression in various tissues including: tonsil, cerebral cortex, lymph node, smooth muscle, and reproductive tissues [35]. Shown in mice, CD81 regulates neuron-induced astrocytic differentiation [36]. Three alleles of the mice CD81 in seven genetic backgrounds were associated to abnormal brain development, hematopoietic system, and/or immune cells development and behavior [37]. In CD81-null mice, astrocyte and microglia cell numbers were upregulated, which lead to a 30% increase in brain size [38]. However, in human patients, deficiency of CD81 proteins was only associated to defected B cells [39]. As shown in mice and rats, expression of CD81 gene was up-regulated after seizure in three hippocampal cell layers: DGCL, CA1 pyr, and CA3 pyr [40,41]. In addition, the gene coding for the CD81 protein was recognized as a tumor-suppressor gene [42]. The second most frequent protein in the Pareto ranking of Betti centrality nodes is HSP90 AA1 (heat shock protein 90 alpha family class A member 1). It is a stress induced isoform of the molecular chaperone Hsp90. In human, the gene has ubiquitous expression in brain and testis and 25 other tissues [43]. The expression of HSP90 AA1 is known to be elevated when cellular stress is present, including in leukemia, several types of cancer, T cell under certain stimulation, and individuals suffering from chronic obstructive pulmonary disease (COPD) [44]. In rats, it was found that HSP90 protein levels in piriform cortex decreased after status epileptic. The degradation was related to neuronal vulnerability to status epilepticts insult [45]. The third most frequent protein, excluding ribosomal proteins, according to the Pareto ranking of Betti centrality nodes is EEF1A1 (eukaryotic translation elongation factor 1, alpha 1). It plays an important role in the cellular translation process. Although EEF1A1 was not associated with neurological diseases, its isoform EEF1A2 was identified to be related. The two proteins are 92% similar in their amino acid sequences but exhibit non-overlapping expression patterns [46]. The difference in functions that the two isoforms perform might be due to post-translational modifications [47]. In wild-type mice, expression of A2 takes over from A1 starting at 21 days after birth; at the same time, a deletion or biallelic mutation of EEF1A2 gene was found responsible for the early-onset neurological  
Figure 3: CD81 (yellow) and its nearest neighbors in the PPI network labeled in green. abnormalities and early death in mice [48; 49]. In human patients, EEFTA2 missense mutation was associated to early-onset epilepsy, severe intellectual disabilities and specific subtle facial dysmorphic features [50; 51; 52]. TUBA1A (Tubulin Alpha 1a) is one of the components that make up the cytoskeleton. In particular, together with beta tubulin, it forms a stable tubulin heterodimer that is a building block of microtubules. Microtubules play key roles in mitosis of dividing cells where they form mitotic spindles. In non-dividing cells such as neurons, microtubules form parallel bundles in axons and dendrites providing pathways for axoplasmic transport. Tubulin's gene is overexpressed in the brain's spinal cord and other tissues [53].