### Five Point Circle for the Triangular Form of Double Reciprocal (Lineweaver-Burk) Plot in Enzyme Biochemistry

#### Abstract

The nine circle in geometry desrve significance of correlation with circumscribed circle, inscribed circle and the Euler line for a triangle. The nine significant concyclic points on the circle recognized by the triangle include: the midpoint of each side of the triangle; the foot point of each altitude and the midpoint of the line segment from each vertex of the triangle to the orthocenter (where the three altitudes meet; these line segments lie on their respective altitudes). The present attempt is dealing with utilization of principle of “Nine point circle” in understanding the concept of relations between the concentration of substrate [S] and the velocity (v) of enzyme controlled reactions in biochemistry. The steps of the attempt include: determination of mid points of three sides of the triangular form of double reciprocal plot; foot point of each line segment forming the altitude of a triangular form of double reciprocal plot; the midpoint of the line segment from each vertex of the triangle to the point representing the orthocenter of the triangular form of double reciprocal plot and determination of center for expected circle in triangular form of double reciprocal plot.

Significant feature of triangular form of double reciprocal (Lineweaver-Burk) plot in present attempt is right angled triangle. The mid points of the three sides of triangular form of double reciprocal (Lineweaver-Burk) plot are easy for location. Being a right angle triangle, the orthocenter of triangular form of double reciprocal (Lineweaver-Burk) plot in present attempt coincides with the vertex at the right angle. The right angled vertex of triangular form is serving not only as the orthocenter, but also as the foot point for the base segment and the height segment. The segment perpendicular to real form of double reciprocal (Lineweaver-Burk) plot and passing through the right angled vertex give the third altitude foot point. The mid point of base segment and height segment constitute the mid point of the segment passing from vertex to the orthocenter. The five significant points resulted on circle include: B, D, E, F and G. The x and y co-ordinates of point “B” are: 1 and (1÷Vmax) respectively. The x and y co-ordinates of point “D” are: [(1÷2)] and [(Km+2) ÷ 2Vmax)] respectively. The x and y co-ordinates of point “E” are: [(1÷1)] and [(Km+2) ÷ 2Vmax)] respectively. The x and y co-ordinates of point “F” are: (1÷2) and (1÷Vmax) respectively. The x and y co-ordinates of point “G” are: [(Vmax^{2}) ÷ (Vmax^{2}+Km^{2}] and [Km(Vmax^{2}+Km)+Vmax^{2}]÷ [(Vmax^{2}+Km^{2})Vmax] respectively. Therefore, the resulted circle is titled as, “Five Point Circle for the Triangular Form of Double Reciprocal (Lineweaver-Burk) Plot in Enzyme Biochemistry”.

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