FPGA Computing in Modern Bioinformatics - Parallel Computing for Bioinformatics and Computational Biology - page 728

three-dimensional atom coordinates of each atom. The coordinates are given in Å
and measure the absolute distance of the atom to a three-dimensional origin. The
origin is located at one corner of the three-dimensional space which leads to the
fact that all coordinate values are positive and no negative values are needed for the
protein structure representation. The precision of the given coordinates is limited to
three positions after the decimal point. This precision is sufficient for the calculation
and enables that the coordinates can be processed as a fix-point representation. The
three-dimensional space is limited to a cube with 65.535Å dimension on each axis.
This space limitation is introduced, because the protein structures with the lowest
energy usually form a compact structure rather than a stretched structure across the
three-dimensional space. The used atom coordinate values are defined as:

Atom coordinates x , y , z =[

]

0, 65.535 Å (28.4)

This atom coordinate representation is sufficient for the calculation and has the advan-
tage that all coordinate values can be stored and processed as 16-bit data words.
Another important point is that the fix-point representation of the coordinates enables
a less resource intensive implementation of the necessary mathematical operations.
The second analysis examines these mathematical operations and the dependency
of the individual operations. Looking at the vector sum calculation the needed oper-
ations are defined by the formula and the 16-bit input data words. No optimization
can be applied for this step. The result of the vector sum calculation is afterwards
compared against the minimum and maximum values to determine if the atom pair
contributes an energy term to the total energy or not. Knowing that the implementa-
tion of a square root operation in hardware requires lots of resources and limits the
throughput of the complete computation, an optimized algorithmwould eliminate the
square root operation if possible.
This square root operation can be eliminated, because the computed distance value
is solely used for the comparison of the minimum and maximum values. Therefore
the square root operation can be eliminated if in return the comparison values are
adjusted accordingly. This optimization of the complete algorithmwill save resources
in the FPGA architecture and even more important it makes the complete parallel
architecture more efficient and faster.
Another more general aspect of the complete implementation is its flexible usage.
The biologist should be able to set and change the used energy values which are
used for the comparison. This modification of the energy values has to be taken into
account when the parallel architecture is designed. The required flexibility of the
parallel architecture must be combined with the requirement of an efficient and fast
execution. Therefore energy values are stored within a so called lookup table to fulfil
these flexibility and performance aspects. This lookup table is a memory block which
stores the energy values that are assigned to specific atom distances. The lookup table
is loaded with user values to provide the flexibility in the energy value, and on the
other hand, an access to the stored energy values can be performed with every clock
cycle when a protein structure is processed by the architecture.