Transcription polymerase-catalyzed emergence of novel RNA replicons

A general RNA-templated RNA extension activity of E. coli RNA polymerase

Multisubunit "DNA-dependent" RNA polymerases (RNAPs) have noncanonical RNA-directed RNA synthesis activity; this allows the synthesis of complementary RNA from RNA templates. Such noncanonical RNAP activities are biologically significant, serving RNA pathogens such as hepatitis delta virus (HDV) and contributing to cellular gene regulation. Despite the broad biological implications of these processes, our understanding of the underlying RNAP mechanisms remains incomplete. Using Escherichia coli RNAP, a multisubunit RNAP, as a model, we describe here the general RNA-templated RNA extension activity of that enzyme. Our data argue that the 3' end of an added RNA template can fold back and pair with upstream bases in the template, creating an intramolecular primer:template duplex as short as 1-2 base pairs. The RNAP then extends this intramolecular duplex, incorporating nucleotides complementary to the template. RNA-templated RNA extension occurred in minutes and did not appear to be suppressed by the presence of a promoter-containing DNA template. Excepting oligonucleotides implicitly designed to prevent any possibility of 3' end self-priming, every RNA template we tested could be extended by the enzyme, highlighting the general nature of this reaction. These data define a general activity of a cellular RNAP. Unrestricted, this activity could contribute to the emergence and replication of RNA-based agents such as HDV and viroids; if highly regulated, the activity could limit these same elements.

A review of advances in in vitro RNA preparation by ssRNAP

In vitro transcription (IVT) based on single-subunit RNA polymerase (ssRNAP) has enhanced the widespread application of RNA drugs in the biomedical field, showcasing unprecedented potential for disease prevention and treatment. While the classical enzyme T7 RNA polymerase (T7 RNAP) has driven significant progress in RNA production, several challenges persist. These challenges include the selectivity of the initiation nucleotide, low incorporation efficiency of modified nucleotides, limited processivity on certain templates, heterogeneity at the 3' end of RNA products, and high level of double-stranded RNA (dsRNA) byproducts. No review has systematically addressed the efforts to overcome these challenges. To fill this gap, we reviewed recent advances in engineering T7 RNAP variants and the discovery of novel ssRNAPs aimed at addressing the shortcomings of T7 RNAP. We also discussed the underlying mechanisms of ssRNAP-mediated byproduct formation, strategies to mitigate dsRNA production using modified nucleotides, and for the first time to sorted out the application of artificial intelligence in IVT. Overall, this review summarizes the advances in RNA synthesis via IVT and provides potential strategies for improving RNA products. We believe that ssRNAPs with more excellent performance will be on the stage of RNA synthesis in the near future to meet the growing demands of both scientific research and pharmaceutical industry.

DragonRNA: Generality of DNA-primed RNA-extension activities by DNA-directed RNA polymerases

RNA polymerases (RNAPs) transcribe DNA into RNA. Several RNAPs, including from bacteriophages Sp6 and T7, Escherichia coli, and wheat germ, had been shown to add ribonucleotides to DNA 3' ends. Mitochondria have their own RNAPs (mtRNAPs). Examining reaction products of RNAPs acting on DNA molecules with free 3' ends, we found yeast and human mtRNAP preparations exhibit a robust activity of extending DNA 3' ends with ribonucleotides. The resulting molecules are serial DNA→RNA chains with the input DNA on the 5' end and extended RNA on the 3' end. Such chains were produced from a wide variety of DNA oligonucleotide inputs with short complementarity in the sequence to the DNA 3' end with the sequence of the RNA portion complementary to the input DNA. We provide a set of fluorescence-based assays for facile detection of such products and show that this activity is a general property of diverse RNAPs, including phage RNAPs and multi-subunit E. coli RNAP. These results support a model in which DNA serves as both primer and template, with extension beginning when the 3' end of the DNA is elongated with a ribonucleotide. As this DNA→RNA class of molecule remains unnamed, we propose the name DragonRNA.

PEGylated Multimeric RNA Nanoparticles for siRNA Delivery in Traumatic Brain Injury

Traumatic brain injury (TBI) impacts millions of people globally, however currently there are no approved therapeutics that address long-term brain health. In order to create a technology that is relevant for siRNA delivery in TBI after systemic administration, sub-100 nm nanoparticles with rolling circle transcription (RCT) are synthesized and isolated in order improve payload delivery into the injured brain. Unlike conventional RCT-based RNA particles, in this method, sub-100 nm RNA nanoparticles (RNPs) are isolated. To enhance RNP pharmacokinetics, RNPs are synthesized with modified bases in order to graft polyethylene glycol (PEG) to the RNPs. PEGylated RNPs (PEG-RNPs) do not significantly impact their knockdown activity in vitro and lead to longer blood half-life after systemic administration and greater accumulation into the injured brain in a mouse model of TBI. In order to demonstrate RNA interference (RNAi) activity of RNPs, knockdown of the inflammatory cytokine TNF-α in injured brain tissue after systemic administration of RNPs in a mouse model of TBI is demonstrated. In summary, small sub-100 nm multimeric RNA nanoparticles are synthesized and isolated that can be modified using accessible chemistry in order to create a technology suitable for systemic RNAi therapy for TBI.

Intergenerational transport of double-stranded RNA in C. elegans can limit heritable epigenetic changes

RNAs in circulation carry sequence-specific regulatory information between cells in plant, animal, and host-pathogen systems. Such RNA can cross generational boundaries, as evidenced by somatic double-stranded RNA (dsRNA) in the nematode Caenorhabditis elegans silencing genes of matching sequence in progeny. Here we dissect the intergenerational path taken by dsRNA from parental circulation and discover that cytosolic import through the dsRNA importer SID-1 in the parental germline and/or developing progeny varies with developmental time and dsRNA substrates. Loss of SID-1 enhances initiation of heritable RNA silencing within the germline and causes changes in the expression of the sid-1-dependent gene sdg-1 that last for more than 100 generations after restoration of SID-1. The SDG-1 protein is enriched in perinuclear germ granules required for heritable RNA silencing but is expressed from a retrotransposon targeted by such silencing. This auto-inhibitory loop suggests how retrotransposons could persist by hosting genes that regulate their own silencing.

The Possible Crystallization Process in the Origin of Bacteria, Archaea, Viruses, and Mobile Elements

We propose a hypothesis for the simultaneous emergence of bacteria, archaea, viruses, and mobile elements by sequential and concrete biochemical pathways. The emergence process can be considered analogous to crystallization, where genetic and biochemical systems stabilize as organisms evolve from their common ancestor, the LUCA, which was a non-free-living pool of single operon type genomes including double-stranded (ds) DNA at an ancient submarine alkaline vent. Each dsDNA operon was transcribed by different systems in σ, TFIIB, or TBP genomes. Double-stranded DNA operons can fuse and stabilize through the action of specific transcription systems, leading to differentiation between the Bacteria (σ genome) and Archaea (TBP genome) domains. Error catastrophe can be overcome by the parallel gain of DNA replication and DNA repair mechanisms in both genomes. Enlarged DNA enabled efficient local biochemical reactions. Both genomes independently recruited lipids to facilitate reactions by forming coacervates at the chamber of the vent. Bilayer lipid membrane formation, proto-cell formation with a permeable membrane, proto-cell division, and the evolution of membrane-associated biochemistry are presented in detail. Simultaneous crystallization of systems in non-free-living bacteria and non-free-living archaea triggered the co-crystallization of primitive viruses and mobile elements. An arms race between non-free-living cells and primitive viruses finally led to free-living cells with a cell wall and mature viruses.

The RNA Revolution in the Central Molecular Biology Dogma Evolution

Human genome projects in the 1990s identified about 20,000 protein-coding sequences. We are now in the RNA revolution, propelled by the realization that genes determine phenotype beyond the foundational central molecular biology dogma, stating that inherited linear pieces of DNA are transcribed to RNAs and translated into proteins. Crucially, over 95% of the genome, initially considered junk DNA between protein-coding genes, encodes essential, functionally diverse non-protein-coding RNAs, raising the gene count by at least one order of magnitude. Most inherited phenotype-determining changes in DNA are in regulatory areas that control RNA and regulatory sequences. RNAs can directly or indirectly determine phenotypes by regulating protein and RNA function, transferring information within and between organisms, and generating DNA. RNAs also exhibit high structural, functional, and biomolecular interaction plasticity and are modified via editing, methylation, glycosylation, and other mechanisms, which bestow them with diverse intra- and extracellular functions without altering the underlying DNA. RNA is, therefore, currently considered the primary determinant of cellular to populational functional diversity, disease-linked and biomolecular structural variations, and cell function regulation. As demonstrated by RNA-based coronavirus vaccines' success, RNA technology is transforming medicine, agriculture, and industry, as did the advent of recombinant DNA technology in the 1980s.

Effective Synthesis of mRNA during In Vitro Transcription with Fewer Impurities Produced

The remarkable efficacy of COVID-19 vaccines has established mRNA as a highly promising biomedical technology. However, the adequate application of mRNA therapeutics necessitates additional measures to mitigate the inherent immunogenicity, which is predominantly caused by dsRNA. As a byproduct of the in vitro transcription of mRNA, dsRNA was reported to be originated through several distinct mechanisms, including the extension of 3' loop-back hairpins, the extension of hybridized abortive transcripts, and promoter-independent transcription. The intricate mechanisms involved pose a dilemma as the reduction in dsRNA results in a concomitant decrease in other critical quality attributes of mRNA. Here, we demonstrate that the promoter binding motifs of T7 RNA polymerase directly impact the production of promoter-independent transcription-based dsRNA. Specifically, the G753A mutation significantly reduces the formation of dsRNA byproducts, which can further combine with modified nucleotides to enhance the effectiveness of dsRNA mitigation and with previously reported high-integrity mutation K389A to minimize side effects. Accordingly, the present study reports a cost-effective approach to synthesize high-purity, less immunostimulatory mRNA by using an engineered T7 RNA polymerase mutant.

DNA-terminus-dependent transcription by T7 RNA polymerase and its C-helix mutants

The remarkable success of messenger RNA (mRNA)-based vaccines has underscored their potential as a novel biotechnology platform for vaccine development and therapeutic protein delivery. However, the single-subunit RNA polymerase from bacteriophage T7 widely used for in vitro transcription is well known to generate double-stranded RNA (dsRNA) by-products that strongly stimulate the mammalian innate immune response. The dsRNA was reported to be originated from self-templated RNA extension or promoter-independent transcription. Here, we identified that the primary source of the full-length dsRNA during in vitro transcription is the DNA-terminus-initiated transcription by T7 RNA polymerase. Guanosines or cytosines at the end of DNA templates enhance the DNA-terminus-initiated transcription. Moreover, we found that aromatic residues located at position 47 in the C-helix lead to a significant reduction in the production of full-length dsRNA. As a result, the mRNA synthesized using the T7 RNA polymerase G47W mutant exhibits higher expression efficiency and lower immunogenicity compared to the mRNA produced using the wild-type T7 RNA polymerase.

Cellular roadmaps of viroid infection

Viroids are single-stranded circular noncoding RNAs that infect plants. According to the International Committee on Taxonomy of Viruses, there are 44 viroids known to date. Notably, more than 20 000 distinct viroid-like RNA sequences have recently been identified in existing sequencing datasets, suggesting an unprecedented complexity in biological roles of viroids and viroid-like RNAs. Interestingly, a human pathogen, hepatitis delta virus (HDV), also replicates via a rolling circle mechanism like viroids. Therefore, knowledge of viroid infection is informative for research on HDV and other viroid-like RNAs reported from various organisms. Here, we summarize recent advancements in understanding viroid shuttling among subcellular compartments for completing replication cycles, emphasizing regulatory roles of RNA motifs and structural dynamics in diverse biological processes. We also compare the knowledge of viroid intracellular trafficking with known pathways governing cellular RNA movement in cells. Future investigations on regulatory RNA structures and cognate factors in regulating viroid subcellular trafficking and replication will likely provide new insights into RNA structure-function relationships and facilitate the development of strategies controlling RNA localization and function in cells.

Viroids: Non-Coding Circular RNAs Able to Autonomously Replicate and Infect Higher Plants

Viroids are a unique type of infectious agent, exclusively composed of a relatively small (246-430 nt), highly base-paired, circular, non-coding RNA. Despite the small size and non-coding nature, the more-than-thirty currently known viroid species infectious of higher plants are able to autonomously replicate and move systemically through the host, thereby inducing disease in some plants. After recalling viroid discovery back in the late 60s and early 70s of last century and discussing current hypotheses about their evolutionary origin, this article reviews our current knowledge about these peculiar infectious agents. We describe the highly base-paired viroid molecules that fold in rod-like or branched structures and viroid taxonomic classification in two families, Pospiviroidae and Avsunviroidae, likely gathering nuclear and chloroplastic viroids, respectively. We review current knowledge about viroid replication through RNA-to-RNA rolling-circle mechanisms in which host factors, notably RNA transporters, RNA polymerases, RNases, and RNA ligases, are involved. Systemic movement through the infected plant, plant-to-plant transmission and host range are also discussed. Finally, we focus on the mechanisms of viroid pathogenesis, in which RNA silencing has acquired remarkable importance, and also for the initiation of potential biotechnological applications of viroid molecules.

Assembly of Biologically Functional Structures by Nucleic Acid Templating: Implementation of a Strategy to Overcome Inhibition by Template Excess

Delivery of therapeutic molecules to pathogenic cells is often hampered by unintended toxicity to normal cells. In principle, this problem can be circumvented if the therapeutic effector molecule is split into two inactive components, and only assembled on or within the target cell itself. Such an in situ process can be realized by exploiting target-specific molecules as templates to direct proximity-enhanced assembly. Modified nucleic acids carrying inert precursor fragments can be designed to co-hybridize on a target-specific template nucleic acid, such that the enforced proximity accelerates assembly of a functional molecule for antibody recognition. We demonstrate the in vitro feasibility of this adaptation of nucleic acid-templated synthesis (NATS) using oligonucleotides bearing modified peptides (“haplomers”), for templated assembly of a mimotope recognized by the therapeutic antibody trastuzumab. Enforced proximity promotes mimotope assembly via traceless native chemical ligation. Nevertheless, titration of participating haplomers through template excess is a potential limitation of trimolecular NATS. In order to overcome this problem, we devised a strategy where haplomer hybridization can only occur in the presence of target, without being subject to titration effects. This generalizable NATS modification may find future applications in enabling directed targeting of pathological cells.

A scenario for the emergence of protoviroids in the RNA world and for their further evolution into viroids and viroid-like RNAs by modular recombinations and mutations

Viroids are tiny, circular, and noncoding RNAs that are able to replicate and systemically infect plants. The smallest known pathogens, viroids have been proposed to represent survivors from the RNA world that likely preceded the cellular world currently dominating life on the earth. Although the small, circular, and compact nature of viroid genomes, some of which are also endowed with catalytic activity mediated by hammerhead ribozymes, support this proposal, the lack of feasible evolutionary routes and the identification of hammerhead ribozymes in a large number of DNA genomes of organisms along the tree of life have led some to question such a proposal. Here, we reassess the origin and subsequent evolution of viroids by complementing phylogenetic reconstructions with molecular data, including the primary and higher-order structure of the genomic RNAs, their replication, and recombination mechanisms and selected biological information. Features of some viroid-like RNAs found in plants, animals, and possibly fungi are also considered. The resulting evolutionary scenario supports the emergence of protoviroids in the RNA world, mainly as replicative modules, followed by a further increase in genome complexity based on module/domain shuffling and combination and mutation. Such a modular evolutionary scenario would have facilitated the inclusion in the protoviroid genomes of complex RNA structures (or coding sequences, as in the case of hepatitis delta virus and delta-like agents), likely needed for their adaptation from the RNA world to a life based on cells, thus generating the ancestors of current infectious viroids and viroid-like RNAs. Other noninfectious viroid-like RNAs, such as retroviroid-like RNA elements and retrozymes, could also be derived from protoviroids if their reverse transcription and integration into viral or eukaryotic DNA, respectively, are considered as a possible key step in their evolution. Comparison of evidence supporting a general and modular evolutionary model for viroids and viroid-like RNAs with that favoring alternative scenarios provides reasonable reasons to keep alive the hypothesis that these small RNA pathogens may be relics of a precellular world.

Viroids and Viroid-like Circular RNAs: Do They Descend from Primordial Replicators?

Viroids are a unique class of plant pathogens that consist of small circular RNA molecules, between 220 and 450 nucleotides in size. Viroids encode no proteins and are the smallest known infectious agents. Viroids replicate via the rolling circle mechanism, producing multimeric intermediates which are cleaved to unit length either by ribozymes formed from both polarities of the viroid genomic RNA or by coopted host RNAses. Many viroid-like small circular RNAs are satellites of plant RNA viruses. Ribozyviruses, represented by human hepatitis delta virus, are larger viroid-like circular RNAs that additionally encode the viral nucleocapsid protein. It has been proposed that viroids are direct descendants of primordial RNA replicons that were present in the hypothetical RNA world. We argue, however, that much later origin of viroids, possibly, from recently discovered mobile genetic elements known as retrozymes, is a far more parsimonious evolutionary scenario. Nevertheless, viroids and viroid-like circular RNAs are minimal replicators that are likely to be close to the theoretical lower limit of replicator size and arguably comprise the paradigm for replicator emergence. Thus, although viroid-like replicators are unlikely to be direct descendants of primordial RNA replicators, the study of the diversity and evolution of these ultimate genetic parasites can yield insights into the earliest stages of the evolution of life.

Psychrophilic phage VSW-3 RNA polymerase reduces both terminal and full-length dsRNA byproducts in in vitro transcription

RNA research and applications are underpinned by in vitro transcription (IVT), but RNA impurities resulting from the enzymatic reagents severely impede downstream applications. To improve the stability and purity of synthesized RNA, we have characterized a novel single-subunit RNA polymerase (RNAP) encoded by the psychrophilic phage VSW-3 from a plateau lake. The VSW-3 RNAP is capable of carrying out in vitro RNA synthesis at low temperatures (4-25°C). Compared to routinely used T7 RNAP, VSW-3 RNAP provides a similar yield of transcripts but is insensitive to class II transcription terminators and synthesizes RNA without redundant 3'-cis extensions. More importantly, through dot-blot detection with the J2 monoclonal antibody, we found that the RNA products synthesized by VSW-3 RNAP contained a much lower amount of double-stranded RNA byproducts (dsRNA), which are produced by transcription from both directions and are significant in T7 RNAP IVT products. Taken together, the VSW-3 RNAP almost eliminates both terminal loop-back dsRNA and full-length dsRNA in IVT and thus is especially advantageous for producing RNA for in vivo use.

An RNA-Based Theory of Natural Universal Computation

Life is confronted with computation problems in a variety of domains including animal behavior, single-cell behavior, and embryonic development. Yet we currently do not know of a naturally existing biological system that is capable of universal computation, i.e., Turing-equivalent in scope. Generic finite-dimensional dynamical systems (which encompass most models of neural networks, intracellular signaling cascades, and gene regulatory networks) fall short of universal computation, but are assumed to be capable of explaining cognition and development. I present a class of models that bridge two concepts from distant fields: combinatory logic (or, equivalently, lambda calculus) and RNA molecular biology. A set of basic RNA editing rules can make it possible to compute any computable function with identical algorithmic complexity to that of Turing machines. The models do not assume extraordinarily complex molecular machinery or any processes that radically differ from what we already know to occur in cells. Distinct independent enzymes can mediate each of the rules and RNA molecules solve the problem of parenthesis matching through their secondary structure. In the most plausible of these models all of the editing rules can be implemented with merely cleavage and ligation operations at fixed positions relative to predefined motifs. This demonstrates that universal computation is well within the reach of molecular biology. It is therefore reasonable to assume that life has evolved - or possibly began with - a universal computer that yet remains to be discovered. The variety of seemingly unrelated computational problems across many scales can potentially be solved using the same RNA-based computation system. Experimental validation of this theory may immensely impact our understanding of memory, cognition, development, disease, evolution, and the early stages of life.

A single mutation attenuates both the transcription termination and RNA-dependent RNA polymerase activity of T7 RNA polymerase

Transcription termination is one of the least understood processes of gene expression. As the prototype model for transcription studies, the single-subunit T7 RNA polymerase (RNAP) is known to respond to two types of termination signals, but the mechanism underlying such termination, especially the specific elements of the polymerase involved, is still unclear, due to a lack of knowledge with respect to the structure of the termination complex. Here we applied phage-assisted continuous evolution to obtain variants of T7 RNAP that can bypass the typical class I T7 terminator with stem-loop structure. Through in vivo selection and in vitro characterization, we discovered a single mutation (S43Y) that significantly decreased the termination efficiency of T7 RNAP at all transcription terminators tested. Coincidently, the S43Y mutation almost eliminates the RNA-dependent RNAP (RdRp) activity of T7 RNAP without impeding the major DNA-dependent RNAP (DdRp) activity of the enzyme. S43 is located in a hinge region and regulates the transformation between transcription initiation and elongation of T7 RNAP. Steady-state kinetics analysis and an RNA binding assay indicate that the S43Y mutation increases the transcription efficiency while weakening RNA binding of the enzyme. As an enzymatic reagent for in vitro transcription, the T7 RNAP S43Y mutant reduces the undesired termination in run-off RNA synthesis and produces RNA with higher terminal homogeneity.

The Cilioprotist Cytoskeleton , a Model for Understanding How Cell Architecture and Pattern Are Specified: Recent Discoveries from Ciliates and Comparable Model Systems

The cytoskeletons of eukaryotic, cilioprotist microorganisms are complex, highly patterned, and diverse, reflecting the varied and elaborate swimming, feeding, reproductive, and sensory behaviors of the multitude of cilioprotist species that inhabit the aquatic environment. In the past 10-20 years, many new discoveries and technologies have helped to advance our understanding of how cytoskeletal organelles are assembled in many different eukaryotic model systems, in relation to the construction and modification of overall cellular architecture and function. Microtubule organizing centers, particularly basal bodies and centrioles, have continued to reveal their central roles in architectural engineering of the eukaryotic cell, including in the cilioprotists. This review calls attention to (1) published resources that illuminate what is known of the cilioprotist cytoskeleton; (2) recent studies on cilioprotists and other model organisms that raise specific questions regarding whether basal body- and centriole-associated nucleic acids, both DNA and RNA, should continue to be considered when seeking to employ cilioprotists as model systems for cytoskeletal research; and (3) new, mainly imaging, technologies that have already proven useful for, but also promise to enhance, future cytoskeletal research on cilioprotists.

An essential role for the piRNA pathway in regulating the ribosomal RNA pool in C. elegans

Piwi-interacting RNAs (piRNAs) are RNA effectors with key roles in maintaining genome integrity and promoting fertility in metazoans. In Caenorhabditis elegans loss of piRNAs leads to a transgenerational sterility phenotype. The plethora of piRNAs and their ability to silence transcripts with imperfect complementarity have raised several (non-exclusive) models for the underlying drivers of sterility. Here, we report the extranuclear and transferable nature of the sterility driver, its suppression via mutations disrupting the endogenous RNAi and poly-uridylation machinery, and copy-number amplification at the ribosomal DNA locus. In piRNA-deficient animals, several small interfering RNA (siRNA) populations become increasingly overabundant in the generations preceding loss of germline function, including ribosomal siRNAs (risiRNAs). A concomitant increase in uridylated sense rRNA fragments suggests that poly-uridylation may potentiate RNAi-mediated gene silencing of rRNAs. We conclude that loss of the piRNA machinery allows for unchecked amplification of siRNA populations, originating from abundant highly structured RNAs, to deleterious levels.

Insertions of codons encoding basic amino acids in H7 hemagglutinins of influenza A viruses occur by recombination with RNA at hotspots near snoRNA binding sites

The presence of multiple basic amino acids in the protease cleavage site of the hemagglutinin (HA) protein is the main molecular determinant of virulence of highly pathogenic avian influenza (HPAI) viruses. Recombination of HA RNA with other RNA molecules of host or virus origin is a dominant mechanism of multibasic cleavage site (MBCS) acquisition for H7 subtype HA. Using alignments of HA RNA sequences from documented cases of MBCS insertion due to recombination, we show that such recombination with host RNAs is most likely to occur at particular hotspots in ribosomal RNAs (rRNAs), transfer RNAs (tRNAs), and viral RNAs. The locations of these hotspots in highly abundant RNAs indicate that RNA recombination is facilitated by the binding of small nucleolar RNA (snoRNA) near the recombination points.

On Catalytic Kinetics of Enzymes

Classical enzyme kinetic theories are summarized and linked with modern discoveries here. The sequential catalytic events along time axis by enzyme are analyzed at the molecular level, and by using master equations, this writing tries to connect the microscopic molecular behavior of enzyme to kinetic data (like velocity and catalytic coefficient k) obtained in experiment: 1/k = t equals to the sum of the times taken by the constituent individual steps. The relationships between catalytic coefficient k, catalytic rate or velocity, the amount of time taken by each step and physical or biochemical conditions of the system are discussed, and the perspective and hypothetic equations proposed here regarding diffusion, conformational change, chemical conversion, product release steps and the whole catalytic cycle provide an interpretation of previous experimental observations and can be testified by future experiments.