Proteins as Semiconductor devices
Yuichi Tokita1
11

Advanced Materials Laboratories, Sony Corporation, Japan

Introduction

Bioelectronics is one of the most promising technologies forthe next generation, because bio-materials have excellent
characters which cannot be realized by the silicon devices.
Actually, biosensors have been already commercialized byenzymes. Recently, bio battery (biofuel cell) evolving from thebiosensor has been actively developed by various groups with us[1]. It is however difficult to truly open up the bioelectronics
world, without understanding the ET behaviour in bio-materials,
especially in protein. Thus we tried to investigate the ET inprotein by using a precise wave function calculated from awhole structure of protein (zinc-substituted cytochromes c andb562: Zn-cyts c and b562) [2, 3].
Attempting to understand the photoinduced ET mechanism,
we have calculated an all-electron wave function for the groundstate of Zn-cyts c and b562 on the basis of DFT. Gouterman’s 4orbitals are assigned on the basis of the excited states ofchromophore model for Zn-porphine complex calculated withthe time-dependent DFT method. ET rates between each 4orbitals and other MOs were estimated using Fermi’s golden
rule.
ki→f = 2/ħ×|Hfi|2(Efi) (1)where Hfi is the electronic coupling matrix elements, Efi is theMO energy difference between final and initial states, and  isthe delta-function. In Zn-cyt c, it appeared that the two occupied
MOs of the 4-orbitals show exclusively higher ET rate from/toparticular MOs that localize on outermost amino acid residues,
whereas ET rates involving the two unoccupied MOs of the 4orbitals are much slower. On the other hand the two unoccupied
MOs of the 4-orbitals show much higher ET rate from/toparticular MOs in Zn-cyt b562. These results imply that theintramolecular ETs in photoexcited Zn-cyt c or b562 aregoverned by the hole transfer through occupied or unoccupied
MOs, respectively. This description may also comprehend both
Dutton’s model and Gray’s model. According to the Hfi analyses,
the Hfi values around the 4-orbitals region are almost
homogeneous and their influences on ET rate constants should
be relatively small. Hence, if the δ(Efi) effect is small, the ET
rate will be well-described with Dutton’s model where a mass ofpeptides can be treated as a continuous medium. On the otherhand, the Gray model is rather preferable when the effect ofδ(Efi) is not negligible.
The couplings of MOs between zinc porphyrin core andspecific amino acid residues on the protein surface have been
demonstrated in Zn-cyts c and b562 immobilized on an Au
electrode via SAM. The voltage dependence of the photocurrent
appeared to be ohmic behavior like a photoconductor in Zn-cyt cand to be rectifying behavior like a photodiode in Zn-cyt b562,
which strongly support the intramolecular ET mechanism in Zncyts c and b562 proposed on the basis of the theoretical
calculations.
2Calculations

we computed the all-electron wavefunction of Zn-cyts c andb562 by using Protein DF. For the excited states, we performed atime-dependent DFT (TDDFT) calculation of the chromophoremodel (CM) consisting of Zn-porphine with the two axial
ligands and we have assigned molecular orbitals (MOs)
responsible for the excited states of Zn-cyts c and b562.
2.1

Zn-cyt c
The horse heart Zn-cyt c contains 104 amino acid residues
and one c-type Zn-protoporphyrin. The protoporphyrin is boundcovalently to polypeptide (apo-protein) of Zn-cyt c via thioether
bonds between two vinyl side chains and Cys14 and Cys17.
Residues His18 and Met80 form the fifth and sixth axial ligandsof zinc- protoporphyrin, respectively. The numbers of atoms
and electrons are 1764 and 6590, respectively.
The coordinate of Zn-cyt c (horse heart) was obtained fromthe protein data bank as 1m60. A molecular mechanics
calculation was performed using the Generalized Born method(dielectric constant is 80) with Discovery Studio Modeling 1.5(force field: CHARMm) to relax local structure distortions, inthe state that the structure of Zn-protoporphyrin was fixed. At
the neutralization, Na+ and Cl- ions were placed around theanionic and cationic residues, respectively. For an anionic
residue where a Na+ ion could not be placed for steric reason, ahydrogen atom was added to the carbonyl oxygen with 0.96Å
fixed bond length in the direction of the nearest hydrogen ofwater molecule. Whereas for a cationic residue where Cl- ion
could not be placed for steric reason, the hydrogen nearest to anoxygen of water molecules was removed. 5258 water molecules(TIP3) were placed around the protein. In order to relax the Na+and Cl- ions, all water molecules and Na+ and Cl- ions weresubjected to a molecular mechanics energy minimum
calculation under a fixed coordinate of the protein structure. Inthe DFT calculation, the TIP3 water molecules were removed
and Na+ and Cl- ions were treated as point charges +1 and -1,respectively.
The all-electron calculation of Zn-cyt c was carried out by
using the Gaussian-based DFT program, proteinDF with VWN
functional and sg-1 grid, following the method for native
cytochrome c reported by Sato et al [4]. The basis and auxiliary
function sets used are listed in Table 1. The effective initial
guess was constructed using quasi-canonical localized orbitals(QCLOs). Firstly, we decomposed Zn-cyt c into Znprotoporphyrin and apo-protein. The apo-protein was further
decomposed into single amino acid fragments, 1, 2 …104residues. The ordinary all-electron calculations were performed
for the 104 molecules. Then, all-electron calculations of the 102
tri-peptide fragments, 1-3, 2-4, 3-5…102-104 were carried out.
In this step, the initial electron density was estimated from thecorresponding electron density expanded by using the auxiliary
functions for each single residue in the results of the previousstep. The calculated canonical MOs of the tri-peptides werethen localized on each atom and the QCLOs for the fragment
defined by main chain or side chain regions were then obtained.
Iterating this type of elongation procedure, we prepared fifteen
peptides of the apo-protein: 1-7, 6-14, 13-19, 18-24, 22-30, 2937, 36-44, 43-51, 50-58, 57-65, 64-72, 71-80, 80-86, 85-95, and94-104.
The Zn-protoporphyrin part was built up through anotherelongation pathway. We computed a chromophore model (CM)consisting of Zn-porphine, 5-ethylimidazole for His18 andmethyl propyl sulfide for Met80. The geometric data of theseelements were derived from the computational structure of Zncyt c constructed above. We replaced all side chains ofprotoporphyrin with hydrogen atoms to make Zn-porphine. 5ethylimidazole, methyl propyl sulfide and Zn-porphine werecalculated separately, then the model was expanded to the Znprotoporphyrin complex containing Zn-cyt c and its surrounding
small peptides, 13-19 and 79-81.
All side chains ofprotoporphyrin were introduced, and Cys14, Cys17 and two
vinyl side chains were connected via thioether bonds. Finally
we combined the results of the Zn-protoporphyrin complex andthe other parts of apo-protein, and carried out the all-electroncalculation of Zn-cyt c. This calculation includes 1764 atoms,6590 electrons and 8786 MOs.
The excited states calculation of chromophore in Zn-cyt cwas performed by using the TDDFT method with the Gaussian
03 (Rev.B03) program package. The basis sets and thefunctional are the same as those of the all-electron calculation ofZn-cyt c. The model structure was adopted to the CM describedabove. The symmetry is C1 and ten excited states of CM werecalculated.

residues. The difference in MO energy levels of eachcorresponding 4-orbitals between the two systems are almost in
the same extent, +2.34 eV, though the average energy shift fromZn-cyt c to Zn-cyt b562 is +1.38 eV. Hence the relative energy
level of 4-orbitals against protein bands consisting of MOs
localized on amino acid residues is very different between thetwo proteins. In Zn-cyt b562, the unoccupied 4-orbitals (MOs3326 and 3329) locate in the lower region of the protein’sconduction band, whereas such an overlap is not found in Zn-cytc. On the other hand, the occupied 4-orbitals (MOs 3302 and3304) are placed at a shallow position in the higher valenceband of Zn-cyt b562. In comparison to Zn-cyt c, the MOs withholes and the valence band with amino acid character are more
weakly coupled in Zn-cyt b562. These electronic structure
differences between the two proteins dictate the molecularsemiconductor nature of the proteins.
Table 1. Calculated ET parameters for Zn-cyt b562 and Zn-cyt c
MO Pairs

Hfi (eV)Zn-cyt b562

3302_3300-8.52×10-1-4.41×10-2

1.57×1017

3304_3307-1-1+1.11×10

4.15×1016-1-2

5.66×1016-3

1.39×1018-2

3.46×1017

3326_3325

Zn-cyt b562
Calculation of Zn-cyt b562 was performed according toabove method. The Zn-cyt b562 contains 106 amino acid residues
and one b-type Zn-protoporphyrin. Residues His102 and Met7
form the fifth and sixth axial ligands of Zn-protoporphyrin,respectively. The coordinate of cyt b562 was obtained from theprotein data bank as 256B and Zn-cyt b562 structure was madeby substituting Zn for Fe. This calculation includes 1722 atoms,
6628 electrons and 8758 MOs.

2.23Conclusion

The intramolecular ET rate constants of photoexcited Zn-cytb562 were estimated from [Eq. (1)] by using each and related tothe Gouterman’s 4-orbitals. As is seen in the case with Zn-cyt c,distinct ET rates for specific couples of MOs in Zn-cyt b562 areobserved. Dominant intramolecular ET rate constants for each
Gouterman’s 4-orbital of Zn-cyt b562 and Zn-cyt c aresummarized in Table 1. In Zn-cyt b562, the rate constants
between unoccupied MOs are one order of magnitude larger
than those between the occupied MOs. The two unoccupied
MOs are localized on the outermost amino acid residues around
Gly70 (MO3331) and Pro56 (MO3332), respectively, which arelocated on the opposite side of the protein-SAM interface andexposed to the solution (Scheme 1, Figure 2a, Figure S2, Table
S2). On the other hand, the two occupied MOs are localized on
the Glu18 (MO3300) and Asp50 (MO3307), respectively, andboth reside on the electrode-contact side. Hence the majormechanism of ET in the photoexcited Zn-cyt b562 is “electrontransfer (ET) in the conduction band” through two-states
coupling between unoccupied MOs, showing that thephotoexcited Zn-cyt b562 is an n-type semiconductor. This isquite different from Zn-cyt c where “hole-transfer (HT) in thevalence band” between occupied MOs dominates. This protein
is a p-type semiconductor, even though the “dopant” is the sameas in Zn-cyt b562.
Why is one protein n-type and the other p-typesemiconductor? We analyzed the ground state electronicstructures of both proteins. MO energies of Zn-cyt b562 are
generally higher, compared to those of Zn-cyt c, which reflects
difference in charge of the two proteins: Zn-cyt b562 and Zn-cytc have negative (isoelectric point, pI = 5.5) and positive (pI =9.6) charges in pH 7.0, respectively. Importantly, the effect of
the negative charge of Zn-cyt b562 to its 4-orbitals energies are
more prominent than the other porphyrin MOs assigned toporphyrin () orbitals and the MOs localized on amino acid-1

Proteins

Zn-cyt cEfi (eV)-6.94×10-5.71×1003329_3331+1.15×103329_3332-1-7.33×10ki→f (sec )-5.50×10+9.11×10+1.48×10

3268_3270-1-3.51×10-2+2.27×10

5.17×1016

3272_3271-6.15×10-2-9.24×10-5

3.91×1017

3297_3296-4.91×10-2-1.59×10-2

1.45×1015

3299_3298-2-1

7.42×1014+9.40×10-1.14×10

Acknowledgements
We thank Harry B. Gray and Jay R. Winkler (Caltech)for helpful discussions and comments.
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