Gene nature Very hydrophilic br Medium
2.2. Realization of electrical network for gene using amino FITC-Dextran string model
Amino acids are cascaded with each other to form the gene primary structure, as shown in Fig. 1. Likewise, the n numbers of amino acid circuit models are cascaded in the series using 1st Foster topology (Daryanani and Resh, 1969) to model electrical network of gene. This network is converted into an equivalent electrical gene circuit and the impedances of amino acid circuits are replaced by equivalent im-pedance Zneq of gene. The length of amino acid string determines the number of cascaded electrical circuit for specific gene.
For amino acid chain of length three, the electrical circuit is ob-tained by attaching three amino acids in series. The equivalent im-pedance for amino acid chain length two to arbitrary length n is
Zb + ZSC
Zeq = Zeq
2.3. Realization of gene sensor transfer function model
The gene network is excited by AC signal and responses are mea-sured across load resistance RL. This network is transformed into Laplace domain network which is known as gene sensor as in Fig. 1. The voltage source is denoted by Vin(s) and the equivalent impedance by Zn(s) where n denotes the number of amino acids in the gene; s is La-place frequency given by jω, where ω is 2π times the frequency and j is square root of −1. The output voltage Vout(s) induced across the load and the sensor transfer function for gene are expressed as follows, Vout (s ) = Vin (s ). RL
The transfer function G between output and input of the sensor is the ratio of two polynomials of degree n. For an amino acid chain of length four, the numerator and denominator of the corresponding system model transfer function are both polynomials of degree four. Since Gn is a function of Ri, Ci, Li, RL and Gn-1, and ratio of two poly-nomials, recurrence relation between numerator as well as denominator polynomials of Gn and Gn-1 can be obtained.
For pure hydrophobic gene i.e. gene composed of hydrophobic re-sidues only, the recurrence relations are as follows:
where GnHb = NnHb/DnHb, NnHb and DnHb are numerator and denominator polynomials of degree n, and Rn, Ln are the respective resistance and inductance values of the nth amino acid in the pure hydrophobic gene chain.
Similarly, for pure hydrophilic gene the recurrence relations are as follows:
where NnHp and DnHp are numerator and denominator polynomials of degree n, and Rn, Cn are the resistance and capacitance values of the nth
Healthy Homo sapiens genes.
Gene nature Gene length range Gene ID Gene name Block length
Hydrophobic > 450 ATBFRUCT1 Glycosyl hydrolases family 32 protein 541
ATCWINV1 Beta-fructofuranosidase 537
GLB1 Galactosidase beta 1 678
KDM1A Lysine demethylase 1A 686
MYO1C Myosin IC 725
cmeC Multidrug eﬄux pump protein CmeC 479
TTHA1135 ba3-type cytochrome C oxidase polypeptide I 568
acrB Multidrug eﬄux system protein 1057
ECK0456 Multidrug eﬄux pump subunit AcrB 1057
spr1652 Cell wall surface anchor family protein 648
FSHMD1A Facioscapulohumeral muscular dystrophy 1A 802
bamA Outer membrane protein assembly factor BamA 532
Measured phase values (deg) for Homo sapiens's genes.
Gene type Gene ID Frequency in Hz
amino acid in the pure hydrophilic gene chain. Resistance Rn is same for all hydrophobic and hydrophilic amino acids.
Now the recurrence relations for gene chain consists of hydrophobic and hydrophilic residues both, are as follows:
where Gn = Nn/Dn, Nn and Dn are the polynomials of degree n for both hydrophilic and hydrophobic genes. Therefore using these expressions, the transfer function can easily be computed for the electrical system model of amino acid chain of any arbitrary length.