INTRODUCTION
Recent years, Bulik et al. (2005) quantified the contribution of defective ribosomal products to antigen production by a modelbased computational analysis. Malonga et al. (2006) proposed a model for proteinRNA interaction to study transfer RNA binding to human serum albumin. Whitehead et al. (2006) constructed a physiological response mode to understand cellular responses to gamma radiation, based on integrated analysis of temporal changes in global mRNA and protein abundance along with proteinDNA interactions and evolutionarily conserved functional associations. By analyzing the interactions between micro RNAs and a human cellular signaling network, Cui et al. (2006) found that microRNAs predominantly target positive regulatory motifs, but less frequently target negative regulatory motifs.
However, to our knowledge, questions how a large ribosomal subunit recognize a complex constructed with a small ribosomal subunit and an initiator tRNA bound on an initiation codon on an mRNA and how a triplet nucleotides (codon) at A site in a ribosome and on an mRNA basepairs a sequence of three complementary nucleotides (anticodon) of a particular tRNA, beyond lengths of chemical bonds, have not been answered in a perspective of informatics.
Present objectives of this study are to develop and propose informatics models
of recognitions between a large ribosomal subunit and a complex constructed
with a small ribosomal subunit and an initiator tRNA bound on an initiation
codon on an mRNA and between basepairs of a triplet nucleotides (codon) at
A site in a ribosome and on an mRNA and a sequence of three complementary nucleotides
(anticodon) of a particular tRNA, beyond lengths of chemical bonds, for a natural
protein synthesis, based on published molecular biological data (Riddle and
Carbon, 1973; Stöffler and Whittman, 1977; Lake, 1985; Alberts et al.,
2002) and our published concepts and methods (Cheng and Zou, 2003, 2006, 2007).
Therefore, we theoretically answer the above questions in a view of informatics.
MATERIALS AND METHODS
Modeling Informative Recognition (IR) Between a Large Ribosomal Subunit
and a Complex Constructed with a Small Ribosomal Subunit and an Initiator tRNA
Bound on an Initiation Codon on an mRNA
The protoplasm has been considered as an electrolyte with an uneven charge
distribution and the natural cellular electric field has been considered as
quasi static in our previous studies (Cheng and Zou, 2003, 2006, 2007). This
study was conducted in our institute from 2006 to 2007. We use the same consideration
to propose our new models of an Informative Recognition between a complex (an
informative sender) constructed with a small ribosomal subunit and an initiator
tRNA bound on an initiation codon on an mRNA and a large ribosomal subunit (an
informative receiver) beyond lengths of chemical bonds, for a natural protein
synthesis (Fig. 1). We estimate a low layer of Informative
Intensity (II), at point P (x, y, z) in a Cartesian coordinate system, with
a Coulomb's Electric Field Intensity (EFI) that is a multiplication of charge
unit dq_{s} (r_{s}), at a point P_{s} (x_{s},
y_{s}, z_{s}), of a sender, a medium function M_{EF}
(rr_{s}) and a transmitting function T_{EF} (rr_{s}),
where, r is a position vector from the origin to P, r_{s }is a position
vector from the origin to P_{s} in or on the sender. rr_{s}
is a distance between P and P_{s} and ε (rr_{s}) is a
permitivity function of vector rr_{s}:

(1) 

(2) 

Fig. 1: 
An informative recognition between a large ribosomal subunit
and a complex constructed with a small ribosomal subunit and an initiator
tRNA bound on an initiation codon on an assumed mRNA in a Cartesian coordinate
system. The complex is considered as an informative sender with an assumed
net charge Q_{sn }(<0) and the large ribosomal subunit is considered
as an informative receiver with an assumed net charge Q_{rn }(>0),
respectively. The draw is not in a real scale 

(3) 
Then, we estimate a high layer of Informative Intensity (II) with a convolution
of a production of a medium and a transmitting functions and a total charge
distribution Q_{s} (r_{s}) on or in the complex,

(4) 
Where * means a convolution mathematically. Obviously, an integration of Eq. 4 means an Informative Flux (IF) as well as an Electric Field Flux (EFF).
We estimate a middle layer of Informative Response Intensity (IRI) with an
electric field force F_{dq} (r_{r}), based on Coulomb's law,

(5) 
Where, dq_{r} (r_{r}) is an integral unit of a receiver's total charge distribution Q_{r} (r_{r}). r_{r }is a position vector from the origin to a point P_{r} (x_{r}, y_{r}, z_{r}) on or in a large ribosomal subunit (Fig. 1).
Finally, we estimate a high layer of Informative Response Intensity (IRI) in
terms of a total electric field force F_{t},

(6) 
where, r_{r}r_{s} is a distance between P_{s} and P_{r}, the distance is greater than a distance of any chemical bond.
Modeling Informative Recognition (IR) Between Codon and Anticodon Basepairs
at A Site in a Ribosome and on an mRNA:
Figure 2 illustrates our quantum mechanics model of Informative
Recognition, in a Cartesian coordinate system, when an incoming aminoacyl tRNA
(anticodon: AAC) is basepairing with a codon (UUG) at A site bound with a ribosome
that moves along an assumed mRNA template strand in the elongation (+y direction)
of a protein synthesis. An amino acid of a peptidyl tRNA at P site has been
linked in the peptide chain. We assume the incoming aminoacyl tRNA (an informative
receiver) has a quantum wave function Ψ with a free state, the complex
(an informative sender) constructed with a codon at A site and a ribosome forms
a potential energy function to attract a complementary aminoacyl tRNA and to
repulse other aminoacyl tRNA. V and L were defined respectively, for a convenient
calculation, as an effective constant height and length of a potential energy
function in our previous studies (Cheng and Zou, 2003). We assume L is about
a size of a ribosome in x direction (greater than a distance of any chemical
bond). When the height is a barrier (V>0), well (V<0) or plain (V = 0),
the interactive force F between the incoming aminoacyl tRNA and the complex
is repulsive, attractive or zero, respectively and its absolute value is proportional
to the height, based on Ehrenfest theorem in quantum mechanics:

(7) 
Where, V (x) is a potential energy function.

Fig. 2: 
In a cartesian coordinate system, a ribosome and a codon
at A site on an assumed mRNA constructs a complex (an informative sender)
and a potential energy function V(x) that, respectively attracts (V<0)
or repulses (V>0) a complementary or the other aminoacyl tRNA (an informative
receiver). Assumed effective constant heights of a barrier (V>0), a plain
(V = 0) and a well (V<0) are plotted for a comparison. The drawing is
not in a real scale 
RESULTS AND DISCUSSION
We defined a positive, negative or zero Informative Recognition when the interactive
force is repulsive, attractive, or zero, respectively (Cheng and Zou, 2006,
2007). Based on the concepts, our modeling results in this paper show a large
ribosomal subunit and a complex constructed with a small ribosomal subunit and
an initiator tRNA bound on an initiation codon on an mRNA have a negative Informative
Recognition, Eq. (5) and (6) involve Newtonian
dynamic movements, Eq. (6) makes a final decision, for a large
ribosomal subunit, to hug, to leave or to ignore the complex.
According to our quantum mechanics model in this article (Fig. 2 and Eq. 7), normal complementary basepairs of the codon and the anticodon have negative Informative Recognitions because their interactive forces are attractive; the other basepairs (not shown in the figure) have positive Informative Recognitions because their interactive forces are repulsive. A previous study reported a probability of wrong basepairs is about 1/10000 (Kirkwood et al., 1986), We estimate a constant barrier height of a potential energy function of our quantum mechanics model using our published method (Cheng and Zou, 2003), the height is about 0.28 eV at a temperature of 37°C. Therefore, we correlate a constant barrier height of a potential energy function and a probability of a wrong basepair.
The significant findings of this research are using Coulomb's law to estimate an informative recognition between a large ribosomal subunit and a complex constructed with a small ribosomal subunit and an initiator tRNA bound on an initiation codon on an mRNA and using Ehrenfest theorem to approximately represent informative recognition between basepairs of the codon and the anticodon, for protein translation. Our modeling results complete our original objectives.
In the special expression of (quasi) electrostatics, we think it is more informative
to present an intensity or a force of Coulomb's electric field with a convolution,
Eq. 4 and 6, than with a common integration,
because it is very convenient to apply a Fourier Transform to obtain some information
in frequency domain and it is very elegant to perform signal (informative) processing
in future. In the special expression of quantum mechanics, we, respectively
consider the wave function Ψ and the gradient of the wave function Ψ
of Schrödinger equation as Potential Intensity and Field Intensity of information
and matter and their integrations as corresponding Fluxes. We also believe,
the principles of our models have general meanings because can be translated
in other fields, such as magnetism, acoustics or ultrasonics and hydrodynamics.
Moreover, our models in this study combine biochemistry, informatics and physics
more organically than our previous works as well as they support from each other.
The limitation of the models is to obtain the distributions of electric charges and permittivities or to measure the data of quantum mechanics in real world environments today.
ACKNOWLEDGMENT
We thank Miss Vivien Cheng for helpful suggestions and comments for this publication.