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Abstract

In Human, Odors are detected by a large family of Olfactory Receptors (ORs) proteins. A sequence of Human ORs database has been proposed by D. Lancet et al. (2000, 2006) based on divergence of evolutionary model. In our earlier work, we have reckoned many important features (viz. Fractal dimension of Indicator matrix, DNA walk, Hurst exponent of 2-adic and 4-adic representations, codon compositions) of DNA sequences and their corresponding amino acid sequences of human ORs and also after making local changes we have calculated the same and found significant quantitative variations between the original and edited sequences. But it is a fact that two same sequences may function different and two different sequences may function same due their specific protein structure. So for complete understanding the effect of mutation we need to study the structure of proteins of those DNA sequences. In this article, an effort has been made to understand the effect of local mutations in the amino acid sequences as well as their tertiary protein structures of Human ORs. The significant changes are resulted through the present analysis through Fractals and standard Bioinformatics tools.

Key words

human olfactory receptors (ORs), protein sequences, fractal dimension & protein structure

Introduction

ORs is the basis for the sense of smell, and they constitute the largest gene super family in the Human genome [1]. In Human genome, there are about 25000 protein-coding genes and out of which only 700 approximately ORs present [2,3]. However, these genes are more complex, with more alternative splicing generation of larger number of protein products.

Mutation is a biological process which are essentially an arbitrary insertion/ deletion/ replacement in the genomic DNA sequences. Effect of mutations occur in enzymes that do not function, abnormal protein structure or changes in protein conformation that result in a non-functioning or differently functioning protein.

In our earlier work, we have taken a class of human ORs sequences and their mutated sequences which are analyzed using Fractal we have been able to understand effect of edition (mutation) in DNA level. Some of the sequences are entirely been tracked out as per fractal observations and some of them still in the ranges. But through these analysis what we have lost to conclude is that whether they are at all functioning or malfunctioning. Essentially only syntactical changes in DNA are being encountered. So for complete understanding the effect of mutation we need to study the structure of proteins of those DNA sequences.

In this article, we have deciphered a quantitative details of effect of local mutation in protein through fractal analysis and standard Bioinformatics¹.

Current state of the art and review of fundamentals

Point mutations in a protein sequence may result in a change or loss of the native structure, which in turn may cause a change or loss of function [4], and ultimately yields different phenotypes. In addition to the natural variations among the individuals, researchers frequently introduce single amino acid residue replacements by misdirected mutagenesis in the laboratory to explore structural and functional features of proteins.

Experimental exploration of different positions in a protein structure with various residue types is a time consuming and expensive process. Such an exploration is generally facilitated by three dimensional (3D) modeling of side-chain mutations [5-9]. While the modeling of a single side chain in a given atomic environment seems to be one of the easiest of all protein structure prediction problems, it is still unsolved [10]. Seemingly insignificant change of a side-chain may lead to a significant change or loss of protein function [11]. This observation implies that side-chain conformation prediction is useful only if it is highly accurate, which makes it a challenging problem. Two simplifications are frequently applied in the modeling of side-chain conformations. First, amino acid residue replacements often leave the backbone conformation almost unchanged [12]. As a consequence, many algorithms x the backbone during the search for the best side-chain conformations. Second, it was observed that most side-chains in high-resolution crystallographic structures can be represented by a limited number of conformers that comply with stereo chemical and energetic constraints [13]. This observation motivated Ponder and Richards to develop the first library of side-chain rotamers for the 17 types of residues with dihedral angle degrees of freedom in their side-chains, based on 10 high-resolution protein structures determined by X-ray crystallography [14].

¹ Data Used: We have taken a list of OR sequences of namely OR13G1, OR10K1, OR10T2, ,OR10R2, OR6Y1, OR10K2, OR2T1, OR2T4, OR2T5, OR2T6, OR6P1, OR10Z1, OR6K2, OR6K3, OR6K6, OR6N1, OR2L2, OR6N2, OR2L8, OR5AX1, OR5AY1, OR2G2, OR6F1, OR2G3, OR5AV10, OR11L1, OR10J1, OR2T3, OR1C1 and OR10J5 from OR database .

However, it seems difficult to directly apply traditional pattern matching algorithms [15-17] to 3D protein structure data. There are several qualitative bio-physical/chemical techniques through which we can analyze protein structures [18].

There are several methods to analyse and to compare tertiary protein structures. A method for matching curves that accommodates large and small deformations was implemented by Karp and Rabin [19]. This method preserves geometric similarities in the case of small deformation, and decreases geometric constraints when large deformations occur.

The approach is based on the computation of a set of geodesic paths connecting the curves. These two curves are defined as a source area and a destination area that can have an arbitrary number of connected components and different topologies.

In the present work, in understanding local mutation effect(s) on protein structures and functions, fractal geometric techniques have been employed [20]. We took a list of human olfactory receptors amino acid sequences and corresponding protein structures for this study. Before entering into the main work. Let us have a very brief look into fractals.

Fractal and fractal dimension

Our artificial world can be described easily through Euclidean geometric shapes. But there are many things in nature. Such as shape of cloud, geometry of lightening etc. could not be described through Euclidean geometry [21]. Many mathematicians descended the challenge for a fair enough description of natural objects. But after a long period in 1975, B. Mandelbrot took the challenge and gave the birth of a new geometry to describe nature which is known to us as Fractal Geometry in short Fractal. The precise definition of "Fractal" according to Benoit Mandelbrot is as a set for which the Hausdroff Besicovitch dimension strictly exceeds the topological dimension. To gain a quantitative insight of Fractal, some fractal parameters, namely Fractal dimension, Hurst exponent, succolarity, lacunarity etc. is also introduced in the literature. A brief discussion follows about one of the well-known methods of calculating fractal dimension, namely Box-Counting method [22].

Box-counting method

This method computes the number of cells required to entirely cover an object, with grids of cells of varying size. Practically, this is performed by superimposing regular grids over an object and by counting the number of occupied cells. The logarithm of N(r), the number of occupied cells, versus the logarithm of 1/r, where r is the size of one cell, gives a line whose gradient corresponds to the box dimension.

Methods and results

Here we took thirty two protein sequences of Human ORs and their corresponding tertiary protein structures through Protein Structure Prediction Server ((PS)²) server [23].

Methods

After DNA sequence taken from ORDB [2] we have calculated the number of A,T,C and G occurrence in a single DNA sequence which has given in Tables 2 and 3, then we have edited the sequence to get a new sequence, after finding the position of each sequence. Before and after local editing in the sequences the detail account of frequencies of singletone nucleotide and polytone nucleotides is given in the Table 1. Using Bioinformatics toolbox of Matlab, we have determined the some of the graphs of fundamental protein properties, namely % of accessible residues (AR), Buried resides (BR), Alpha helix (Chou & Fasman) (AH), Amino acid composition (%)) (AC), Beta sheet (Chou & Fasman) (BS), Beta turn (Chou & Fasman) (BT), Coil (Deleage & Roux) (C), Hydrophobicity (Aboderin) (H), codon frequencies (CF) [24,25]. Corresponding to each of such graph we have evaluated the fractal dimension using the fractal analysis tools [21]. We have also found the 3D structure of those original and edited sequences. Then we have calculated the fractal dimension of the 3D protein structures given in Table 4 and compared both the FD value through DaliLite Pairwise comparison of protein structures to nd the Z-scores [26] and then find the difference between these two values [27-31].

Table 1. Details of protein Sequence Mutation where in from column we have no. of consecutive current nucleotides and in to column no. of edited nucleotides along with their Position has mentioned.

	Protein Name: OR10K1			Protein Name: OR6Y1			Protein Name: OR2T4
Edited	From	To	Position	From	To	Position	From	To	Position
	1T	1G	34	4T	4G	557	4G	4C	841
	1C	1G	7	4T	4C	106	4T	4A	644
	3T	3A	83
	Protein Name: OR1C1			Protein Name: OR2G2			Protein Name: OR2G3
Edited	From	To	Position	From	To	Position	From	To	Position
	4T	4A	766	4T	4A	775	4T	4G	96
	3T	3A	92	3C	3A	884	5C	5G	861
	3T	3C	107	2C	2A	139	3T	3C	833
	Protein Name: OR2L2			Protein Name: OR2L8			Protein Name: OR2T1
Edited	From	To	Position	From	To	Position	From	To	Position
	5T	5A	147	4T	4G	344	4G	4C	126
	5T	5C	606	2T	2G	9	4G	4A	287
	4A	4G	5	2C	2G	9	5C	5G	485
	Protein Name: OR2T3			Protein Name: OR2T5			Protein Name: OR2T6
Edited	From	To	Position	From	To	Position	From	To	Position
	4T	4G	527	5T	5A	334	5T	5A	539
	5C	5G	503	4C	4G	792	4G	4A	772
	4C	4T	890	3C	3A	155
	4C	4A	653	2C	2A	5
	3C	3A	338
	Protein Name: OR5AT1			Protein Name: OR5AV1P			Protein Name: OR5AX1
Edited	From	To	Position	From	To	Position	From	To	Position
	5C	5G	851	5T	5G	144	5T	5G	533
	5A	5T	56	3T	3C	60	5T	5A	719
	4T	4A	636	3G	3C	20
	3T	3C	760
	3T	3A	177
	3T	3G	303
	2T	2G	536
	Protein Name: OR5AY1			Protein Name: OR5BF1			Protein Name: OR6F1
Edited	From	To	Position	From	To	Position	From	To	Position
	5T	5A	504	4T	4G	720	5C	5G	520
	4G	4A	284	1C	1G	88	4C	4G	25
				3T	3G	28	3T	3G	34
	Protein Name: OR6K2			Protein Name: OR6K3			Protein Name: OR6K6
Edited	From	To	Position	From	To	Position	From	To	Position
	4T	4G	759	4T	4C	96	4T	4G	823
	4C	4G	878	4A	G	715	4T	4A	701
	3T	3G	309				3T	3G	156
							2C	2A	15
							2G	2A	901
	Protein Name: OR6N1			Protein Name: OR6N2			Protein Name: OR6P1
Edited	From	To	Position	From	To	Position	From	To	Position
	3T	3G	427	4G	4A	680	4C	4T	555
	4T	4A	608	4T	4C	726	5T	5C	491
	4C	G	520	2T	2G	28	5T	5A	184
							1C	1G	183
							1T	1G	75
	Protein Name: OR10J1			Protein Name: OR10J5			Protein Name: OR10K2
Edited	From	To	Position	From	To	Position	From	To	Position
	4T	4G	38	5T	5G	629	5T	5G	725
	4T	4A	722	4T	4A	249	3T	3A	280
	3C	3A	78	3T	3G	880
	Protein Name: OR10R2			Protein Name: OR10T2			Protein Name: OR10Z1
Edited	From	To	Position	From	To	Position	From	To	Position
	4T	4G	753	5T	5C	316	4T	4A	497
	4A	4C	187	4T	4G	229	4G	41	709
	3T	3G	677	3T	3A	500
	2T	2A	10	2C	2A	691
	Protein Name: OR11L1			Protein Name: OR13G1
Edited	From	To	Position	From	To	Position	From	To	Position
	4C	4A	403	4T	4C	170
	3T	3G	90	3T	3A	634
	2C	2A	626	2T	2A	402

Table 2.

		(Before) Protein Name: OR10K1										(After)Protein Name: OR10K1
occurrences	1		2	3	4	5	6	7		8	1		2	3	4	5	6	7		8
A	116	28		4	0	1	0	0		0	116	29		4	0	1	0	0		0
T	172	41		13	1	0	0	0		0	173	40		12	1	0	0	0		0
G	98	23		5	1	0	0	0		0	98	24		5	1	0	0	0		0
C	138	54		12	2	0	0	0		0	138	54		12	2	0	0	0		0
Total number of Characters : 957											Total number of Characters : 957
		(Before) Protein Name: OR6Y1											(After)Protein Name: OR6Y1
occurrences	1		2	3	4	5	6	7		8	1		2	3	4	5	6	7		8
A	145	25		5	1	0	0	0		0	145	25		5	1	0	0	0		0
T	164	39		10	4	1	1	0		0	164	39		10	2	1	1	0		0
G	107	29		4	2	0	0	0		0	107	29		4	3	0	0	0		0
C	143	56		6	1	0	0	0		0	143	55		6	1	0	1	0		0
Total number of Characters : 994											Total number of Characters : 994
		(Before) Protein Name: OR2T4											(After)Protein Name: OR2T4
occurrences	1		2	3	4	5	6	7		8	1		2	3	4	5	6	7		8
A	142	24		3	0	2	0	0		0	141	24		3	0	3	0	0		0
T	189	26		9	2	3	0	0		0	189	26		9	1	3	0	0		0
G	104	33		9	0	1	0	0		0	104	33		9	1	1	0	0		0
C	129	60		6	4	1	0	0		0	129	60		6	3	1	0	0		0
Total number of Characters : 1009											Total number of Characters : 1009
		(Before) Protein Name: OR10Z1										(After)Protein Name: OR10Z1
occurrences	1		2	3	4	5	6	7		8	1		2	3	4	5	6	7		8
A	138	14		3	0	0	0	0		0	136	14		3	0	2	0	0		0
T	162	39		8	4	0	0	1		0	162	39		8	3	0	0	1		0
G	106	24		10	3	0	0	1		0	106	24		10	2	0	0	1		0
C	129	53		8	1	1	1	0		0	129	53		8	1	1	1	0		0
Total number of Characters : 957											Total number of Characters : 957
		(Before) Protein Name: OR6N2											(After)Protein Name: OR6N2
occurrences	1		2	3	4	5	6	7		8	1		2	3	4	5	6	7		8
A	129	30		6	1	1	0	0		0	129	30		6	1	1	0	0		0
T	155	45		14	4	1	0	0		0	155	44		14	4	1	0	0		0
G	104	29		4	2	0	0	0		0	103	29		5	1	0	0	0		0
C	135	44		6	1	0	0	0		0	134	44		6	1	0	0	0		0
Total number of Characters : 970											Total number of Characters : 970
		(Before) Protein Name: OR5BF1										(After)Protein Name: OR5BF1
occurrences	1		2	3	4	5	6	7		8	1		2	3	4	5	6	7		8
A	135	21		4	2	0	0	0		0	135	21		4	2	0	0	0		0
T	165	35		11	4	1	1	0		1	165	35		10	3	1	1	0		1
G	103	32		3	0	1	0	0		0	104	32		4	1	1	0	0		0
C	140	40		9	2	0	0	0		0	139	40		9	2	0	0	0		0
Total number of Characters : 954											Total number of Characters : 954
	(Before) Protein Name: OR5AV1P											(After)Protein Name: OR5AV1P
occurrences	1		2	3	4	5	6	7		8	1		2	3	4	5	6	7		8
A	128	26		4	1	1	0	0		0	128	26		4	1	1	0	0		0
T	149	40		10	3	5	1	0		0	149	40		9	3	4	1	0		0
G	96	26		6	1	0	0	0		0	96	26		5	1	0	1	0		0
C	110	32		3	3	1	1	0		0	110	32		5	3	1	1	0		0
Total number of Characters : 896											Total number of Characters : 896
		(Before) Protein Name: OR5AT1										(After)Protein Name: OR5AT1
occurrences	1		2	3	4	5	6	7		8	1		2	3	4	5	6	7		8
A	124	24		8	1	2	0	0		0	122	24		8	2	2	0	0		0
T	148	48		20	5	0	0	0		0	146	47		17	4	0	0	1		0
G	102	21		3	3	0	0	0		0	101	22		4	3	0	1	0		0
C	133	33		5	1	2	0	0		0	132	32		5	1	1	1	0		0
Total number of Characters : 945											Total number of Characters : 945
		(Before) Protein Name: OR11L1										(After)Protein Name: OR11L1
occurrences	1		2	3	4	5	6	7		8	1		2	3	4	5	6	7		8
A	126	19		6	1	0	0	0		0	125	20		6	1	1	0	0		0
T	164	35		11	3	0	0	1		0	165	35		11	2	0	0	1		0
G	111	33		5	3	0	0	0		0	111	33		6	3	0	0	0		0
C	126	60		8	5	0	0	0		0	126	59		8	4	0	0	0		0
Total number of Characters : 985											Total number of Characters : 985
		(Before) Protein Name: OR6K6											(After)Protein Name: OR6K6
occurrences	1		2	3	4	5	6	7		8	1		2	3	4	5	6	7		8
A	132	19		6	0	1	0	0		0	132	19		6	2	1	0	0		0
T	147	39		11	5	2	1	0		0	147	39		10	3	2	1	0		0
G	108	31		6	0	0	0	0		0	106	30		6	1	1	0	0		0
C	115	54		6	2	0	0	0		0	115	53		6	2	0	0	0		0
Total number of Characters : 942											Total number of Characters : 942
		(Before) Protein Name: OR2T6											(After)Protein Name: OR2T6
occurrences	1		2	3	4	5	6	7		8	1		2	3	4	5	6	7		8
A	131	19		6	2	0	0	0		0	130	19		6	3	1	0	0		0
T	163	31		7	2	2	0	0		0	163	31		7	2	1	0	0		0
G	98	27		6	7	1	0	0		0	98	27		6	6	1	0	0		0
C	137	40		9	2	2	0	0		0	137	40		9	2	2	0	0		0
Total number of Characters : 942											Total number of Characters : 942
		(Before) Protein Name: OR2G2										(After)Protein Name: OR2G2
occurrences	1		2	3	4	5	6	7		8	1		2	3	4	5	6	7		8
A	132	21		7	1	0	0	0		0	129	20		7	2	2	0	0		0
T	161	33		13	5	1	0	0		0	161	33		13	4	1	0	0		0
G	109	30		9	3	0	0	0		0	109	30		9	3	0	0	0		0
C	117	45		14	1	0	0	0		0	117	44		13	1	0	0	0		0
Total number of Characters : 970											Total number of Characters : 970
		(Before) Protein Name: OR2T3											(After)Protein Name: OR2T3
occurrences	1		2	3	4	5	6	7		8	1		2	3	4	5	6	7		8
A	139	17		3	1	0	0	0		0	137	17		3	3	2	0	1		0
T	172	21		7	4	0	1	0		0	171	21		7	3	0	2	0		0
G	126	24		9	0	0	0	0		0	125	24		9	0	2	0	0		0
C	137	54		11	3	4	0	0		0	137	54		10	3	1	0	0		0
Total number of Characters : 973											Total number of Characters : 973

Table 3. Detail no. of nucleotides (A, T, C, and G) consecutively present before and after mutation occurs, along with total no. of nucleotides present in the given amino acid sequences.

		(Before) Protein Name: OR6F1										(After)Protein Name: OR6F1
occurrences	1		2	3	4	5	6	7	8	1		2	3	4	5	6	7	8
A	128	14		7	2	0	0	0	0	128	14		7	2	0	0	0	0
T	157	31		10	4	1	0	0	0	157	31		10	4	1	0	0	0
G	113	34		5	1	0	0	0	0	111	33		5	1	1	0	0	1
C	142	42		7	3	2	0	0	0	142	42		7	2	1	0	0	0
Total number of Characters : 942										Total number of Characters : 942
		(Before) Protein Name: OR10J1									(After)Protein Name: OR10J1
occurrences	1		2	3	4	5	6	7	8	1		2	3	4	5	6	7	8
A	142	27		5	1	0	0	0	0	141	27		5	3	0	0	0	0
T	152	39		6	4	1	1	0	0	152	39		6	2	1	1	0	0
G	121	22		7	0	1	0	0	0	120	22		7	0	2	0	0	0
C	130	38		9	2	1	0	0	0	130	38		8	2	1	0	0	0
Total number of Characters : 945										Total number of Characters : 945
		(Before) Protein Name: OR10K2									(After)Protein Name: OR10K2
occurrences	1		2	3	4	5	6	7	8	1		2	3	4	5	6	7	8
A	125	23		4	1	0	0	0	0	124	23		4	2	0	0	0	0
T	171	45		13	1	2	0	0	0	171	45		12	1	1	0	0	0
G	100	21		8	1	0	0	0	0	100	21		8	1	1	0	0	0
C	142	47		7	2	0	0	0	0	142	47		7	2	0	0	0	0
Total number of Characters : 954										Total number of Characters : 954
		(Before) Protein Name: OR6K2										(After)Protein Name: OR6K2
occurrences	1		2	3	4	5	6	7	8	1		2	3	4	5	6	7	8
A	144	20		4	1	0	1	0	0	144	20		4	1	0	1	0	0
T	156	48		17	4	0	0	1	0	156	48		16	3	0	0	1	0
G	123	26		3	0	0	0	0	0	123	26		4	2	0	0	0	0
C	132	43		7	3	1	0	0	0	132	43		7	2	1	0	0	0
Total number of Characters : 991										Total number of Characters : 991
	(Before) Protein Name: OR5AX1										(After)Protein Name: OR5AX1
occurrences	1		2	3	4	5	6	7	8	1		2	3	4	5	6	7	8
A	130	30		6	2	0	0	0	0	130	30		6	2	1	0	0	0
T	155	45		15	5	4	0	0	0	155	45		15	5	2	0	0	0
G	98	30		2	1	0	0	0	0	97	30		2	1	0	1	0	0
C	118	40		7	1	0	0	0	0	118	40		7	1	1	0	0	0
Total number of Characters : 960										Total number of Characters : 960
		(Before) Protein Name: OR5AY1									(After)Protein Name: OR5AY1
occurrences	1		2	3	4	5	6	7	8	1		2	3	4	5	6	7	8
A	127	23		5	1	0	0	0	0	126	22		5	2	0	0	0	1
T	177	41		10	3	2	0	0	0	177	41		10	3	1	0	0	0
G	135	21		4	4	0	0	0	0	135	21		4	3	0	0	0	0
C	138	39		3	1	1	0	0	0	138	39		3	1	1	0	0	0
Total number of Characters : 960										Total number of Characters : 960
		(Before) Protein Name: OR2T1										(After)Protein Name: OR2T1
occurrences	1		2	3	4	5	6	7	8	1		2	3	4	5	6	7	8
A	139	21		7	0	0	0	0	0	139	21		7	1	0	0	0	0
T	144	41		13	2	1	0	0	0	144	41		13	2	1	0	0	0
G	110	27		9	5	0	0	0	0	110	27		9	3	1	0	0	0
C	118	51		11	0	2	0	0	0	118	51		11	1	1	0	0	0
Total number of Characters : 973										Total number of Characters : 973
		(Before) Protein Name: OR1C1										(After)Protein Name: OR1C1
occurrences	1		2	3	4	5	6	7	8	1		2	3	4	5	6	7	8
A	134	22		2	1	0	1	0	0	133	22		3	1	1	1	0	0
T	166	37		13	3	1	0	0	0	166	37		11	2	1	0	0	0
G	122	22		4	2	0	0	0	0	122	22		4	2	0	0	0	0
C	145	43		4	3	1	1	0	0	145	43		5	3	1	1	0	0
Total number of Characters : 960										Total number of Characters : 960
		(Before) Protein Name: OR2G3									(After)Protein Name: OR2G3
occurrences	1		2	3	4	5	6	7	8	1		2	3	4	5	6	7	8
A	122	28		9	1	0	0	0	0	122	28		9	1	0	0	0	0
T	154	38		12	3	1	1	0	0	154	38		11	2	1	1	0	0
G	84	37		6	0	0	0	0	0	84	37		6	1	1	0	0	0
C	138	38		7	2	2	0	0	0	138	38		8	2	1	0	0	0
Total number of Characters : 945										Total number of Characters : 945
		(Before) Protein Name: OR6K3										(After)Protein Name: OR6K3
occurrences	1		2	3	4	5	6	7	8	1		2	3	4	5	6	7	8
A	140	25		4	3	1	1	0	0	140	25		4	2	1	1	0	0
T	148	45		12	5	1	0	0	0	148	45		12	4	1	0	0	0
G	104	28		2	1	0	0	0	0	104	27		2	1	0	1	0	0
C	132	38		11	1	0	1	0	0	130	38		11	1	0	2	0	0
Total number of Characters : 963										Total number of Characters : 963
		(Before) Protein Name: OR2L2										(After)Protein Name: OR2L2
occurrences	1		2	3	4	5	6	7	8	1		2	3	4	5	6	7	8
A	144	25		6	4	0	0	0	0	144	25		6	3	1	0	0	0
T	158	41		10	2	3	1	0	0	158	41		9	2	1	1	0	0
G	107	19		5	1	1	0	0	0	107	18		6	1	1	1	0	0
C	129	38		9	2	0	0	0	0	129	38		9	2	1	0	0	0
Total number of Characters : 954										Total number of Characters : 954

Table 4. Fractal Dimension of 3D Structures Before and After Mutation of nucleotides (A, T, C, G) of the Protein Sequences

Protin Name	Fractal Value (Before)	Fractal Value After	Di erence
OR13G1	1.18132	1.06183	0.11949
OR10K1	1.04287	1.09353	0.05066
OR10T2	1.10484	1.16372	0.05888
OR10R2	1.16588	1.1053	0.06058
OR6Y1	1.07644	0.93621	0.14023
OR10K2	1.06859	1.12591	0.05732
OR2T1	1.21768	1.22402	0.00634
0R2T4	1.03177	1.14265	0.11088
OR2T5	1.20664	1.19132	0.01532
OR2T6	1.23737	1.20839	0.02898
OR6P1	1.11079	0.93621	0.17458
OR10Z1	1.12791	1.00266	0.12525
OR6K2	1.03983	1.05646	0.01663
OR6K3	1.04208	1.03747	0.00461
OR6K6	1.03636	0.93444	0.10192
OR6N1	1.10593	1.04295	0.06298
OR2L2	0.97866	1.20928	0.23062
OR6N2	1.20545	1.18611	0.01934
OR2L8	0.96544	0.98279	0.01735
OR5BF1	1.09345	1.06988	0.02357
OR5AX1	1.17028	1.14738	0.0229
OR5AY1	1.23445	1.17678	0.05767
OR2G2	1.14891	1.0137	0.13521
OR6F1	1.05202	1.07362	0.0216
OR2G3	1.06231	0.98389	0.07842
OR5AV1	1.02043	0.96039	0.06004
OR11L1	1.18718	1.04259	0.14459
OR10J1	1.1283	1.08652	0.04178
OR2T3	1.06912	0.98635	0.08277
OR1C1	1.0842	1.04096	0.04324
OR10J5	1.11492	1.17187	0.05695

Results

In this section, we have selected some of OR proteins through which we have studied the effect of local mutation in protein properties as stated above. We have given the accessible residue and alpha helix properties of OR2T6 amino acid sequence before and after mutation in Figures 1 and 2. We have also other amino acid sequences detail has given in Tables 1-3. We have evaluated their fractal dimension of each of its properties. We have given the 3D structure of OR2T6 sequence after and before mutation in Figure 3, also marked the changes in 3D structure of before and after mutation. We have also generated 3D structure of each of the amino acid sequence, and also evaluate the fractional dimension of each of the structures before and after mutation.

Figure 1. Protein Properties of OR2T6 protein sequence ORs

Figure 2. Edited Protein Properties of OR2T6 protein sequence ORs

Figure 3. Change in structure of OR2T6 protein sequence before and after mutation

Discussion

In the previous section a set of 32 OR sequences has been experimented through Fractal dimensional analysis. Mainly we are intended to observe the similarities or dissimilarities in the original and edited (mutated) OR sequences. We have found out the fractal dimension of the different graphs and their corresponding fractal dimension of the protein properties as mentioned earlier.

It is obvious that if the percentage of Accessible Residues (AR) is less than the percentage of Buried Residues (BR) must be higher as these two protein properties are complementary to each other. Accordingly, the other protein properties also get affected due to the decrement of percentage of AR in an OR protein. In other words, all such protein properties are interlinked for a protein. This particular detail has been wide-opened in the Table 1.

Here we have considered 13 OR sequences out of those 31 sequences for which a detail analysis has been made in the Tables 5 and 6.

Table 5. AR - Accessible residue BR- Buried residue Properties AA - Amino Acid AH - Alpha Helix properties

		AR			BR			AH			AA
protein	A	B	R	A	B	R	A	B	R	A	B	R
OR10K1	1.94359	1.94361	B=A	1.94266	1.94331	B<A	1.9427	1.94318	B<A	1.94289	1.94358	B<A
OR10Z1	1.94373	1.94284	B>A	1.94281	1.9432	B<A	1.94253	1.94298	B<A	1.94331	1.94303	B>A
OR2G3	1.94264	1.94372	B<A	1.94283	1.94315	B<A	1.94266	1.94299	B<A	1.94247	1.94366	B<A
OR2T6	1.94346	1.9431    B>A		1.94263	1.94317	B<A	1.94314	1.94269	B<A	1.94324	1.94299	B>A
OR2T1	1.94293	1.9433    B<A		1.9426	1.94308	B>A	1.94179	1.94269	B<A	1.94325	1.9431	B<A
OR6N2	1.94274	1.9436    B<A		1.94265	1.94324	B<A	1.94367	1.94326	B>A	1.94284	1.94389	B<A
OR6P1	1.9431	1.94313	B=A	1.94232	1.94333	B<A	1.94303	1.94297	B=A	1.94215	1.94378	B<A
OR13G1	1.94248	1.94283	B<A	1.94251	1.9434    B<A		1.94319	1.94306	B<A	1.94325	1.94259	B>A
OR6K2	1.94279	1.94315	B<A	1.9424	1.94309	B<A	1.9431	1.94336	B<A	1.94282	1.94355	B<A
OR2T5	1.94302	1.94346	B<A	1.94248	1.94357	B<A	1.9427	1.9432	B<A	1.94292	1.94342	B<A
OR10J5	1.94305	1.94333	B<A	1.94182	1.94332	B<A	1.94294	1.94341	B<A	1.94331	1.9435	B<A
OR6Y1	1.94263	1.94321	B<A	1.94215	1.94283	B<A	1.94279	1.94317	B<A	1.94237	1.94334	B<A
OR1C1	1.94271	1.94321	B<A	1.94173	1.94304	B<A	1.94244	1.94273	B<A	1.94225	1.94333	B<A

Table 6. BS- Beta sheet BT-Beta turn HPC - Hydrophobicity coil, codon properties, and A, B , R used for After , Before and Result respectively

11			BS			BT			Coil			HPC			codons
	protein	A	B	R	A	B	R	A	B	R	A	B	R	A	B	R
	OR10K1	1.94326	1.94386	B<A	1.94292	1.94295	B=A	1.9447	1.94411	A>B	1.9428	1.94275	B<A	1.94279	1.94336	B<A
	OR10Z1	1.94289	1.94243	B>A	1.94337	1.94271	B>A	1.94379	1.94409	B<A	1.94266	1.94276	B<A	1.94319	1.942298	B>A
	OR2G3	1.94239	1.94389	B<A	1.94295	1.94247	B>A	1.94407	1.94395	B>A	1.94263	1.94239	B>A	1.94278	1.94331	B<A
	OR2T6	1.94233	1.9439	B<A	1.94289	1.94252	B>A	1.94407	1.94398	B=A	1.94289	1.94305	B<A	1.94307	1.94279	B>A
	OR2T1	1.94279	1.94307	B<A	1.94216	1.94254	B<A	1.94374	1.94401	B<A	1.94267	1.94299	B<A	1.94319	1.94302	B>A
	OR6N2	1.94281	1.94385	B<A	1.94367	1.94291	B>A	1.94423	1.94408	B>A	1.943	1.94276	B>A	1.94238	1.94295	B<A
	OR6P1	1.94243	1.94387	B<A	1.94305	1.94279	B>A	1.94407	1.94414	B<A	1.944266	1.94276	B<A	1.94231	1.94362	B<A
	OR13G1	1.94236	1.94273	B<A	1.94336	1.94327	B>A	1.94409	1.94444	B<A	1.9425	1.94307	B>A	1.94359	1.94289	B>A
	OR6K2	1.94289	1.94243	B>A	1.9427	1.94261	B>A	1.94379	1.94412	B<A	1.94253	1.94278	B<A	1.94284	1.94331	B<A
	OR2T5	1.94287	1.9432	B<A	1.94303	1.94268	B>A	1.94407	1.94405	B=A	1.9428	1.94316	B<A	1.94242	1.94321	B<A
	OR10J5	1.94231	1.94381	B<A	1.94289	1.9428	B=A	1.94417	1.944	B>A	1.94187	1.94323	B<A	1.94315	1.94352	B<A
	OR6Y1	1.94273	1.94373	B<A	1.9426	1.94367	B>A	1.944	1.94389	B>A	1.94334	1.94281	B>A	1.94263	1.94281	B<A
	OR1C1	1.94246	1.94389	B<A	1.94296	1.94256	B>A	1.94413	1.94408	B=A	1.94211	1.94259	B<A	1.94179	1.94361	B<A

Let us illustrate the above fact by taking one example.

In case of OR2T6, the mutated sequence differs from the original OR2T6 in two positions at 539 and 772 of the sequence. The poly-string of 5Ts has been changed into 5As in the position 539 in the edited sequence and in position 772, 4Gs has been changed into 4As. Consequently the frequency of 1As is decreases by 1, 4As increased by 1, 5As increased by 1, 5Ts decreased by 1 and 4Gs decreased by 1 ,but the other frequencies of poly-strings has been remain unchanged even though the above changes in the poly-string frequencies of 5Ts and 4Gs.

As a result, the Fra2021 Copyright OAT. All rights reserv Residues (AR) in the mutated sequences is less than that of the original OR2T6. As a result, the FD of Buried Residues (BR) for the mutated OR2T6 is greater than that of the original, the FD of Alpha helix is greater than the and even after mutation the FD coil are almost same as it was in original OR2T6 whereas the FD of Amino Acid Composition (AA), Codon frequency (C) and Beta Turn (BT) of the mutated OR2T6 is less than that of the OR2T6. The FD of Beta Sheet and Hydrophobicity (HPC) is greater than that of the original OR2T6. Also the tertiary structures of the protein for the OR2T6 and corresponding edited sequence have been changed. The fractal dimension of those tertiary structure of proteins are 1:23737 and 1:20839 respectively.

Conclusion

In this study, we have considered a few OR sequences to understand the local mutation in the protein level. The detail account of poly-string frequencies have been made for each of the ORs and corresponding edited sequences. We then saw the effect of those local changes in poly-string frequency through the protein properties and tertiary structure of the protein of each of the ORs and edited sequences. As we illustrated through the example of OR2T 6 and its edited sequence in the discussion, we found that the edited sequence is almost same with the original OR2T 6 in the sense of ordering of the nucleotide bases except for the frequency change in case of 1As, 4As, 5As, 5Ts and 4Gs. Here we have found that the edited sequence of OR2T 6 is almost sequentially similar and also the tertiary structure is almost similar to the original tertiary structure of the protein OR2T6. Hence, it is our strong conviction that these kinds of mutation can be allowed in making the function of OR2T6 un-altered. Of course, the biological experiment is left to make us assured about its original functionality of OR2T6. Similar kind of analysis is also applicable for the other sequences in accordance with the change and their effect in protein properties and their tertiary structures.

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