Archives of Molecular Medicine and Genetics (AMMG)

RASER Model of Single-Molecule Enzyme Catalysis and Its Application to the Ribosome Structure and Function



Sungchul Ji1*


1Department of Pharmacology and Toxicology, Ernest Mario School of Pharmacy, Rutgers University, Piscataway, N.J. USA


*Corresponding Author:Sungchul Ji, Department of Pharmacology and Toxicology, Ernest Mario School of Pharmacy, Rutgers University, Piscataway, N.J. USA, TEL:609-240-4833 ; FAX:609-240-4833 ;E-mail:sji.conformon@gmail.com


Citation:Sungchul Ji (2017) RASER Model of Single-Molecule Enzyme Catalysis and Its Application to the Ribosome Structure and Function. Arch Mol Med & Gen 1:104.


Copyright: : © 2017 Sungchul Ji, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited


Received date:December 15, 2017; Accepted date:January 04, 2018; Published date:January 04, 2018


Introduction

In the article published in 1998 entitled “The Cell as a Collection of Protein Machines: Preparing the Next Generation of Molecular Biologists”, B. Alberts (1998) [1] made the following remarkable statement which is as true today as when it was printed two decades ago:


“Proteins make up most of the dry mass of a cell. But instead of a cell dominated by randomly colliding individual protein molecules, we now know that nearly every major process in a cell is carried out by assemblies of 10 or more protein molecules. And, as it carries out its biological functions, each of these protein assemblies interacts with several other large complexes of proteins. Indeed, the entire cell can be viewed as a factory that cantains an elaborate network of interlocking assembly lines, each of which is composed of a set of large protein machines.”


This statement contains the following key ideas:


(1) The cell is a system of molecular machines (also called protein machines).


(2) Every major cell process is carried out by assemblies of 10 or more molecular machines.


(3) Cell biological functions are carried out by a network of molecular machine assemblies that interact with one another.


In other words, Alberts is distinguishing three levels of organization of protein machines in the cell:


(i) individual molecular machines (also called enzymes, protein machines),


(ii) assemblies of molecular machines, and


(iii) networks of molecular machine assemblies.


For the convenience of discussions, I am suggesting here that we refer to the above conjecture as the Alberts’ “molecular machine network doctrine of the cell” or the AMNDC.


The AMNDC embodies a hierarchical structure reminiscent of the three linguistic structures indicated in bold letters in the last column of Table 1. This is consistent with the hypothesis that cells use a molecular language which is isomorphic (i.e, similar in structure) with the human language [2,3]. As evident in the second column of Table 1, there are plethora of terms used to describe the various organizational components of cell metabolism that are largely confined to the first two levels (see the first column of Table 1) and do not distinguish between the organizational levels II and III. But we have recently found a quantitative method referred to as the Planck-Shannon (PS) space that can distinguish molecular sentences (as points in the PS space; see Table 2 e) and molecular texts (as lines in the PS space; see Table 2 e). Based on these considerations (i.e., the cell language-human language isomorphism and the Planck-Shannon space), I am recommending here for the first time that cell metabolism be divided into three levels of (i) molecular machines (MM), (ii) metabolic pathways (MP), and (iii) networks of metabolic pathways (NMP).


Table 1: A recommended unification of the terminologies in cell metabolism.


Level of Organization Common terms now in use Recommended terms Cell-linguistic analogs [Evidence] (Ji, 2017c)18
I Molecular machines (MMs)19 Protein machines1 Molecular machines (MM) (Molecular words) Words (to denote) [long tailed-histograms of turnover times] (see Figure 1 (g))
II Metabolic pathways (MPs)c Assemblies1 of MMs Metabolons20 Hyperstructures21 Metabolic modules22 Metabolic machines23 Metabolic fields24 Metabolic pathways (MP) (Molecular sentences) Sentences (to decide) [long-tailed histograms of mRNA levels encoded by genes] (see Table 2 e)
III Assemblies1 of MPs Metabolons20 Hyperstructures21 Metabolic modules22 Metabolic machines23 Metabolic fields24 Networks of metabolic pathways (NMP) (Molecular texts) Texts (to reason/compute) [linear correlations in the Planck-Shannon space] (see Table 2 e and f)

19(Ji, 1991).

1(Alberts, 1998)

c(Metabolic pathways, https://en.wikipedia.org/wiki/Metabolic_pathway)

20(Srere, 1987)

21(Noris, et al., 1999)

22(Hartwell, 1999)

23(Holcombe, 1991)

24(Welch and Smith, 1990)


Isomorphism between cell and human languages

There may be two complementary aspects to the isomorphism between cell language (cellese) and human language (humanese) [4] (Ji, 1999) -- the qualitative and the quantitaive. References [2,4,5] discuss the qualitative similarity (or qualitative functor, to borrow the category-theoretic idiom) and Table 2 below lists the quantitative similarities (or quantitative functor [6,7]. It is surprising to find that both cellese and humanese obey the same pair mathematical equations: Planckian Distribution Equation (PDE) was derived from physics [8,9] and the Menzerath-Altmann law (https://en.wikipedia.org/wiki/Menzerath%27s_law) was derived from linguistics but they are indistinguishable as far as their ability to fit long-tailed histograms generated from biology (not shown) or linguistics (see the right column in Table 2). Therefore, it seems reasonable to conclude that these observations provide both the qualitative and quantiative evidence supporting the validity of the isomorphism postulate between cellese and humanese [2-5].


Once a long-tailed histogram is fitted into PDE, two numbers can be generated from the PDE – (i) the Planckain information of the second kind, IPS, and (ii) the Shannon entropy (H). IPS is defined by Eq. (1):


IPS = - log2 ((µ – mode)/σ) (1)


where µ and σ are the mean and the standard deviation of the long-tailed histogram under consideration. The Plankian information of the first kind, IPF, was defined as the binary logarithm of the ratio of the Area Under the Curve (AUC) of PDE over the AUC of the associated Gaussian –like equation (GLE) [10].


The Shannon entropy is calculated based on Eqs. (2) and (3):


H = -Σ pi log2 pi (2)


where pi is the probability of observing the ith event or entity calculated as


pi = yi / Σyi (3)


where yi is the frequency of the ith event of entity and the index I runs from 1 to n, the total number of events or entities.


The information encoded in PDE parameter values of a long-tailed histogram can be visualized as a point in what is referred to as the Planck-Shannon space (see Table 2 e and f). When two groups of 10 sets each of the mRNA levels are chosen from the budding yeast transcriptome measured by Garcia-Martinez et al [11], one group having metabolic functions and the other not, the Planck-Shannon plots produced a linear correlation for the former (see Table 2 e) but not for the latter (see Table 2 f). Since each point in Table 2 e represents a long-tailed histogram of a metabolic pathway, the ten points forming a correlated line indicates that the Planck-Shannon space can recognize the third level of metabolic organizations as predicted in the last row of Table 1. That is, the Planck-Shannon space can distinguish molecular sentences (or metabolic pathways) as individual points, regardless of whether or not correlated with one another and molecular texts as linearly correlated points three or more in number.


Table 2: The Planckian Distribution Equation (PDE) and the Menzerath-Altmann Law (MAL) connect the cell and human languages. Adopted from (Ji, 2017a) [10].


Cell Language (Cellese) Human Langauge (Humanese)


Table 2

Planckian Distribution Equation (PDE): Role of Standing (or Resonance) Waves in Material Organizations in the Universe.

In 2008, the author noticed the similarity between the blackbody radiation spectrum at 5000 °K (see Figure 1 (c)) and the histograms of single-molecule enzyme turnover times reported by Lu, Xun and Xie [12] (see the blue curve in Figure 1 (g)). This motivated the author to ‘generalized’ the Planck’s blackbody radiation formula, Eq. (4) in Figure 1, by replacing the universal constants and temperature with 4 or later 3 free parameters as shown in Eqs. (5) and (6), respectively, resulting in the so-called Planckian Distribution Equation (PDE), Eq. (5) or (6). PDE was also referred to as BRE (Blackbody Radiation-like Equation) before the term PDE was coined in analogy to the Gaussian Distribution Equation (GDE) [10]. These two equations are equivalent and can be mutually transformed using the equalities, (7), (8) and (9). As evident in Figures 1 (f) and (g), PDE (or BRE) fits both the blackbody radiation spectrum and the single-molecule enzyme kinetic histogram. PDE has been found to fit many other long tailed histograms generated in the fields of protein folding (Figure 1 (h)), whole-cell RNA metabolism (Figure 1 (i)), T-cell receptor diversity [10], 7-mer DNA frequency distribution (Table 2 a), protein length frequency distribution (Table 2 c), word length frequency distribution in a speech (Table 2 b), sentence length frequency distribution in private letters (Table 2 d), decision time histogram [10], US annual income distributions in 1996 and 2013 [10], and the polarized microwave background radiations [10].


Figure 1
Figure 1

In order to account for the unexpected universality of PDE fitting almost all long tailed histograms examined so far (over 100), it was postulated, based on the physical interpretations of the two terms in PDE (see Figure 1 (d)), that all the observed regularities (or organizations) in the Universe that produce long-tailed histograms are the results of the standing (or resonance) waves generated by the input of energy into the system of oscillators under consideration (see Figure 2) just as an input to the Chladni plate (https://www.youtube.com/watch?v=wvJAgrUBF4w) generates energy-dependent patterns of particle distributions on its surface, the patterns being the visible examples of material organizations driven by standing (or resonance) waves of the vibrating plate.


Figure 2
Figure 2

RASER Model of Single-Molecule Enzyme Catalysis

The fitting of the single-molecule enzyme turnover histogram into PDE, Figure 1 (g), ), indicates that the free energy content of an enzyme molecule may be quantized (see Figure 3 below), just as the fitting of the blackbody radiation spectra of atoms into the Planck’s radiation equation implied the quantization of the electronic energy of atoms (https://en.wikipedia.org/wiki/Bohr_model).


Figure 3
Figure 3

Once it is accepted that the free energy content of an enzyme molecule is quantized (Figure 3) as evidenced by the PDE fitting of the single-molecule enzyme kinetic data (see Figure 1 (g)), it is relatively easy to find similarities between laser and enzymic catalysis as depicted in Figure 4.


RASER is an acronym derived from Rate Amplification based on the Substrate-Enhanced reaction Rates, in analogy to laser, or Light Amplification based on Stimulated Emission of Radiation. There is the possibility that, just as the blackbody radiation equation of Planck was found to apply to the single-molecule enzyme turnover times of cholesterol oxidase [5], so the subatomic mechanisms underlying the phenomenon of laser may apply (analogically) to the molecular mechanism of enzyme action, as proposed in Figure 4 (b).


In the mechanism of laser (Figure 4 (a)), the input of “pumping” photons, hν1, causes the electrons of the atoms constituting the laser medium (e.g., ruby crystal) to undergo the transition from the ground state energy level to the excited state energy level (see the 1 to 2 arrow). The excited state is short-lived and loses some of its energy as heat and undergo a transition to a lower energy level called “metastable” state (see the 2 to 3 arrow, Figure 4 (a)). Sate 3 is more stable than State 2 but still much more unstable than the ground state (see 1). When there are enough number of electrons in the metastable/excited state (thus creating the so-called “population inversion”), the arrival of triggering photons, hν2, induces the de-excitation of electrons from the metastable excited state to the ground state (see the 3 to 1 arrow), accompanied by the emission of photons identical to the triggering photons, hν2, but larger in number than the original triggering photons leading to light amplification. The emitted photons are “coherent” in that they are identical with respect to (i) amplitude, (ii) frequency, and (iii) phase.


Unlike electrons in atoms that are all in the lowest-energy ground state before absorbing photons, enzymes appear to exist in different ground states to begin with, before thermal excitation (i.e., before absorbing thermal energy), as indicated by the four solid bars in Figure 4 (b), which is enabled by the quantization of the Gibbs free energy levels of enzymes indicated by the observation that the single-molecule enzyme turnover times of cholesterol oxidase fit PDE as demonstrated in Figure 1 (g).


It is possible that, when an enzyme molecule absorbs enough thermal energy through Brownian motions, it is excited to the transition state lasting only for a short period of time, probably 10-14 to 10-12 seconds, the periods of chemical bond vibrations. The thermally excited enzyme is thought to undergo a transition to a more stable state called the “metastable” or “activated” state probably lasting up to 10-9 seconds. It appears that the metastable/activated state can be deactivated in two ways – (i) spontaneously (as in “spontaneous emission” in laser), and (ii) induced by substrate binding (as in “induced emission”). It is possible that during spontaneous deactivation of the active/metastable state of an enzyme, the excess energy is released as uncoordinated and random infrared photons (i.e., as heat), whereas, during the substrate-induced deactivation, the excess energy of the enzyme-substrate complex is released in a coordinated manner via, e.g., the synchronization of local enzyme processes [5], resulting in catalysis, just as the triggering photon-induced de-activation of population-inverted electrons in atoms results in the amplification of emitted photons as laser.


Figure 4
Figure 4

The enzyme catalytic mechanism proposed in Figure 8.5 (b) is referred to as the SID-TEM-TOF mechanism because it embodies the following three key processes [8,9]:


(i) Substrate- or Stimuli-Induced Deactivation in Step 4,


(ii) Thermally Excited Metastable state in the 1 to 2 and 2 to 3 steps


(iii) leading TO Function i.e., catalysis, in the 3 to 1 Step.


It is here postulated that the SID-TEM-TOF mechanism described here underlies many so-called Planckian processes defined as the physicochemical or social processes generating long-tailed histograms that fit PDE) [8,9] (and their records/results) that obey the Planckian distribution equation, Eqs. (5) or (6).

A Resonance Model of the Structure and function of Ribosomes.

Unlike in the transcriptional steps in gene expression where the same kinds of molecules, i.e., the nucleic acids, DNA and RNA, directly interact (or contact or touch each other) via the Watson-Crick base-paring mechanism, in the translational step, there is no direct interaction between mRNA and amino acids, but rather their interactions are mediated by tRNA which recognizes mRNA at its anti-codon arm and amino acids at its 3'-acceptor stem, about 60 Ǻ away (see the blue region in the mechanism of translation


shown at https://www.quora.com/Why-are-ribosomes-so-important-in-plant-cells). The universality of the wave-particle duality demonstrated in [10] suggests that the tripartite coupling among codon, anticodon, and amino acid in the ribosome-mRNA-tRNA complex may be mediated by resonant vibrations or standing waves (also called resonance or resonant waves) (see Figure 5 (c), (d) and (e)) generated within the complex, just as the vibrational patterns located at distant regions on the Chladni (1756-1827) plate are coordinated via resonance (https://www.youtube.com/watch?v=wvJAgrUBF4w).


Figure 5
Figure 5

The Chladni plate is an ideal model for illustrating the role of resonance in molecular biology. At a given resonance frequency, the particles on remote regions of the Chaldni plate are coordinated without any direct interactions between them and yet form ordered patterns. This is similar to what happens in the ribosome system when a peptide molecule is synthesized; i.e, different components of the ribosome-mRNA-tRNA complex execute their motions that are so coordinated as to achieve the peptide synthesis. The ribosome and the Chladni plate are compared at several levels in Table 1.


Table 3: The ribosome-Chladni plate comparison.


Chladni plate Ribosome
1. Vibrating system metal plate ribosome + mRNA + tRNA complex
2. Objects being organized sand particles codons, anticodons, aminoacyl residues
3. Scale macroscopic microscopic (also called molecular)
4. Source of energy driving the organization electricity/sound waves thermal energy paid back by the free energy of chemical reactions without violating the Second Law [7]
5. Common principle obeyed Fourier theorem Fourier theorem

The idea of using the Chladni plate (see Figure 5 (e)) as a molecular model of the protein synthesis in the ribosome occurred to this author while preparing for the keynote lecture, "RASER model of single-molecule enzyme catalysis", that I presented at the 8th International Conference on Proteomics and Bioinformatics, held in Osaka, Japan, in May, 2017 (see Figure 5 (g)). I formulated this idea before I realized that J. Franck and his group was working on the mechanism of protein synthesis in the ribosome along based on a similar approach [13] (i.e., the wave approach to molecular biology [10], for which he shared the Nobel Prize in Chemistry this year ( https://www.nobelprize.org/nobel_prizes/chemistry/laureates/2017/).


There are several components in what is here referred to as the "resonance model of the ribosome structure and function' (RMRSF):


(i) The ribosome and its associated RNA's and proteins are a system of molecular oscillators that obey the Fourier theorem (see Figure 5 (a)), i.e., all the wave patterns, both traveling and standing (see Figure 5 (b)) of the system can be constructed from the linear combinations of the vibrational motions of all the chemical bonds [14],


(ii) the standing waves in the ribosome system are determined by the geometrical (or conformational) shape (or topology) and the energy content of the system, and


(iii) the chemical (i.e., peptide bond formaton) and mechanical events (i.e., translocation of the tRNA from the A site to the P site, etc.) taking place at the anti-codon arm and the 3'-acceptor stem (see Figure 5 (f)) are 'coupled' or 'coordinated' through the resonance mechanism, just as are the motions of the sand particles located in distant regions on the Chladni plate, or just as the vibrational motions of the tuning forks (see Figure 5 (c)) are coupled to the vibrational motions of the water column by resonance thereby exchanging both energy and information between them. The resonance model of the ribosome structure and function depicted in Figure 5 is based on the simiarilties and differences between the ribosome and the Chaladni plate summarized in Tale 3.


It may be noted that my vibrational approach to enzymology/molecular biology dates back to 1974 [15] when I concluded as follows:


" An ordinary enzyme possesses 10^3 to 10^4 vibrational degress of freedom, as compared to 3 each for the translational and rotational degrees of freedom. It is therefore reasonalble to assume that the vibrational motions of individual bonds in the enzyme will be far more important in enzyme catalysis than the translational or rotatioal motions of the enzyme as a whole. Given all the vibrational frequencies of the individual bonds in an enzyme, as well as their three-dimensional arrangements, we can in principle deduce the thermodynamic and catalytic properties of the enzyme under any conditions."


The resonance mechanism of coupling proposed in Figure 5 between the aminoacyl group at the 3' acceptor stem and the anticodon at the opposite side of the ribosome about 60 Ǻ away is consistent with the conclusion reached by Petoukhov that genes in DNA can be viewed as oscillators that couple to one another via resonance [16]. One of the reasons that Petoukhov came to invoke the resonance mechanism is that many of the regularities found in the genetic codes and DNA sequences (e.g., Chargaff's parity rules [17] obey the tensor multiplication rules of matrices widely used in engineering and physics to analyze vibrational mechanics. Thus, it is clear that Petoukhov's resonance approach to modeling genetic structures [16,17] indirectly supports the resonance coupling mechanism postulated for the transfer of genetic information from the codons of mRNA to the amino acyl residues of tRNA as briefly summarized in Figure 5 above [26-28].


Conclusions

The fitting of the single-molecule enzyme turnover histograms to the Planckian Distribution Equation (PDE) derived in 2008 from the blackbody radiation equation discovered by M. Planck in 1900 opened up an unprecedented avenue of research concerning the molecular mechanism of enzyme catalysis, i.e., the possible role of standing waves or resonance and the possible analogy between laser and enzyme catalysis. This in turn led to the possible role of resonance in the coupling between the anti-codons and the amino acyl groups on the opposite sites of tRNA molecule about 60 Ǻ apart, thus removing the mystery behind the coupling between genes and amino acids during protein synthesis. The resonance-based mechanism of information transfer from genes on DNA to proteins mediated by t-RNA is consistent with by the recent findings of [16,17] who was able to generate the 64 genetic codons staring from the four letters of the gentic alphabet using the mathematical techniwu of tensor multiplicaitons of matrices of the genetic alphabet, the same method widely used in studying resonance phenomena in physics and engineering.


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