One of the main aims of current biology is to understand the origin of the molecular organization that underlies the complex dynamic architecture of cellular life. Here, we present an overview of the main sources of biomolecular order and complexity spanning from the most elementary levels of molecular activity to the emergence of cellular systemic behaviors. First, we have addressed the dissipative self-organization, the principal source of molecular order in the cell. Intensive studies over the last four decades have demonstrated that self-organization is central to understand enzyme activity under cellular conditions, functional coordination between enzymatic reactions, the emergence of dissipative metabolic networks (DMN), and molecular rhythms. The second fundamental source of order is molecular information processing. Studies on effective connectivity based on transfer entropy (TE) have made possible the quantification in bits of biomolecular information flows in DMN. This information processing enables efficient self-regulatory control of metabolism. As a consequence of both main sources of order, systemic functional structures emerge in the cell; in fact, quantitative analyses with DMN have revealed that the basic units of life display a global enzymatic structure that seems to be an essential characteristic of the systemic functional metabolism. This global metabolic structure has been verified experimentally in both prokaryotic and eukaryotic cells. Here, we also discuss how the study of systemic DMN, using Artificial Intelligence and advanced tools of Statistic Mechanics, has shown the emergence of Hopfield-like dynamics characterized by exhibiting associative memory. We have recently confirmed this thesis by testing associative conditioning behavior in individual amoeba cells. In these Pavlovian-like experiments, several hundreds of cells could learn new systemic migratory behaviors and remember them over long periods relative to their cell cycle, forgetting them later. Such associative process seems to correspond to an epigenetic memory. The cellular capacity of learning new adaptive systemic behaviors represents a fundamental evolutionary mechanism for cell adaptation. The cell is a highly self-organized dynamic molecular system that constitutes the basic fundamental unit of all known life forms.A breakthrough has been made in the knowledge of the cellular molecular components and understanding the basic mechanisms of many of their interactions. However, we still do not know many of the essential aspects of the highly self-ordered dynamics that characterize the biochemical life of cells.All molecular components of cells exhibit complex chemical transformations shaping an extreme super complex system, where simultaneously the concentrations of millions of ions and molecules change permanently following high-ordered patterns, structured in space and in time.The consequences of these incessant self-organized and self-regulated dynamics of reactive molecular transformations are adequate cellular growth, the development of all physiological processes to maintain its functional structures, continuous adaptation to the environment, and, lastly, mitosis. Alterations in these self-organized dynamics lead to different pathologies and, on certain occasions, the dynamic order collapses and cell dies.The limitations in the study of cellular molecular dynamics by traditional methods have been compensated by the efforts of quantitative sciences applied to Biology, especially Systems Biology. Physical-mathematical approaches are making possible to understand the principles underlying the complex cellular molecular dynamics adequately, so concepts such as self-organized dissipative structures, self-regulation, the emergence of functional properties, systemic attractors, and information processing, are part of the new landscape of contemporary biology.In light of these quantitative advances, each cell is not a mere molecular aggregate but a super complex dynamic system where highly self-ordered dissipative patterns, the main source of molecular order in the cell, do emerge together with self-regulatory behaviors originated by biomolecular information processing, another fundamental source of organization in the cell.Here, we present an overview of the main sources of biomolecular order and complexity that underline the molecular dynamics of cells. These sources span from the most elementary levels of molecular activity to the emergence of systemic behaviors.-In the “The Dynamics Originated by the Molecular Turnover and the Role of the Enzymes in These Super Complex Dynamics” section, we have approached two fundamental issues: the dynamics originated by the molecular turnover of cells and the role of the enzymes in these super complex dynamics.All molecular components of the cell are synthesized and degraded continually following sophisticated interdependent processes that defy the human intellect. This continuous molecular turnover is produced by a super complex dynamic system formed by millions of biochemical reactions, which occur continuously at every moment of cellular life. The continuous recycling and incessant chemical transformations, that encompass practically all molecules, shape a critical scenario, only in which cellular life is possible .The super complex dynamics originated by this huge molecular turnover constitute the fundamental systemic characteristic of all basic life units.The specialists of the life sciences and those of the quantitative sciences, attracted by the biological fact, should adequately understand the fundamental molecular dynamics of the cell, and the surprising magnitude that they reach at a global level.Numerous works have been carried out on molecular recycling, mainly of proteins . HoweverAll reactive molecular transformations occurring in the cell are essentially chemical reactions, that is, modifications on how atoms are bonded. Practically, all these dynamics of chemical changes in the cell are mediated by enzymes, the most extraordinary macromolecular nanomachines, responsible for breaking and joining covalent bonds, the fundamental chemical bonds in biological molecules. Through their ability to decrease the bond activation energy, enzymes permanently modify the way atoms are bonded, making possible the accelerated creation and destruction of molecules. Accordingly, enzymes are fundamental and essential molecules for metabolic life. They are the main focus of attention of this review.metabolic dynamics (which means activities developed by enzymes), it is not possible to properly understand what a cell is, nor the essential elements that underlie in its self-ordered and self-regulated functionality.Without understanding the meaning and magnitude of the dynamic molecular turnover that occurs in all living cells, as well as the fundamental role of enzymes in these permanent -Section “Dissipative Self-Organization of Enzymatic Activities, the Main Source of Molecular Organization in the Cell” addresses the dissipative self-organization of enzymatic activities, the main source of molecular organization in the cell.Enzymes are responsible for molecular recycling processes shaping multienzyme complexes , which carry out their activity with autonomy between them playing distinctive and essential roles in cellular physiology. When a multienzyme complex operates far enough from equilibrium dissipative self-organization can emerge , 2014.Here, we show the main enzymatic dissipative structures: biomolecular oscillations (metabolic rhythms). Even though self-organized structures are very diverse, and we also cover other different dissipative patterns including circadian rhythms, birhythmicity, multi-stability, and spatial traveling waves.Numerous physical-mathematical analyses of enzymatic pathways have contributed to a better understanding of the emergence of self-organized processes. They are essential to research the main source of molecular organization in the cell. Most of these functional biochemical studies have been carried out using systems of differential equations e.g., the Krebs cycle , the amiThe dissipative structures that emerge in self-organized multi-enzymatic complexes constitute one of the most genuine properties of cells, and the rigorous knowledge of their nature and significance is an essential element in the comprehension of the biological fact at its most basic and elementary levels.-Dissipative metabolic networks (DMN) and the emergence of the systemic metabolic structure (SMS) are covered in the “Dissipative Metabolic Networks and the Emergence of the Systemic Metabolic Structure” section.Enzymes form basic functional metabolic subsystems (multienzyme complexes) for turnover activities where dissipative patterns emerge. At a higher level of complexity, they shape different DMN, which originate the emergence of the SMS at a global level.Saccharomyces cerevisiae, Helicobacter pylori, and Escherichia coli  at a systemic level, taking into account the self-organized behavior, DMN was created in 1999 . Essentihia coli .Adenylate energy system constitutes another global process responsible for the functional enzymatic integration in the SMS at a global level. A primary systemic ratio between ATP, ADP, and AMP concentrations was proposed by Atkinson  to calcuCellular energy quantification shows that almost all organisms keep their AEC within narrow values under growth conditions, more specifically between 0.7 and 0.95, despite the extreme complex fluctuations in the adenine nucleotide concentrations.Further quantitative studies have shown that each cell is a complex non-linearly open system in which there is not a specific energy value that is conserved, but rather dynamic forms of energy change . Specifi-The “Enzymatic Information Processing, the Second Leading Source of Molecular Order in the Cell” section of this review deals with enzymatic information processing: the second fundamental source of molecular order in the cell.Enzyme activity during molecular turnover not only originates the emergence of high self-organized dissipative patterns, structured in space and time, but is also capable of producing complex self-regulatory behavior by information processing which highly increases the functional complexity of cellular system. The sophisticated cycles of construction and destruction of the molecular components could not be accomplished adequately without this source of new information, order, and organization.The first quantitative work on the processing of molecular information in bits, in a multi-enzymatic complex, was performed in 2012 in the yeast glycolysis , one of On the other hand, a dynamic structure of information processing appears in the DMN when TE is considered under systemic activity . AccordiAlong with these works, different biological examples are displayed in the text showing that unicellular organisms possess a complex self-regulatory behavior originated by biomolecular information processing, the second fundamental source of organization in the cell.-Finally, in the “Hopfield-Type Systemic Attractors in Dissipative Metabolic Networks. Cellular Systemic Behaviors” section, the emergence of Hopfield-type systemic attractors in DMN is analyzed. It is necessary to underline that these attractors allow the cellular metabolic structure (CMS) to behave as an individual and complete integral system. As a consequence, cellular systemic behaviors occur.The emergence of Hopfield-type dynamics was quantitatively observed using advanced tools of Statistic Mechanics and techniques of Artificial Intelligence in complex enzymatic dynamics . HopfielAmoeba proteus sp. and Metamoeba leningradensis sp.) showed associative learning behaviors , the self-regulation of metabolic dynamics (molecular information processing), and the emergence of the cellular systemic properties (Hopfield-like dynamics). All these issues are essential to correctly understand what a cell is.To help life scientists who are unfamiliar with quantitative sciences understand these fundamental multidisciplinary issues, we have not used mathematical formulations here. Besides, we have reinforced the fundamental ideas with a considerable number of biological examples.Systems Biology is being increasingly used as an appropriate methodology to address dynamic metabolic processes and the higher-level properties emerging in the cell from interactions between its elementary molecular parts, forming complex self-organized and self-regulated structures, from basic enzymatic activities to complex cellular adaptive behavior.Systems biology is fundamental to understand the functional architecture of the most complex, sophisticated, and overwhelming molecular system known in nature, the living cell.Cells are dynamic metabolic reactors in which millions of biochemical reactions, tightly interrelated and integrated into sophisticated networks, shape the most complex molecular system in nature.All molecular components of the cell are in a dynamic state of reactive transformations. The proteome, lipidome, glycome, metabolome, and transcriptome are synthesized and degraded continually in all cell types see .Not only molecules but also cellular structures are subjected to cycles of construction and destruction. For instance, the endoplasmic reticulum, the largest endomembrane system, exhibits a permanent turnover; the cytoskeleton is another molecular dynamic system that undergoes continuous reorganization through the synthesis and degradation of its structural elements during the cell cycle; the mitochondria are dynamic organelles that are incessantly undergoing fusion, fission, and molecular destruction; the peroxisome turnover also takes place by autophagy-related mechanism; also, cellular membranes are highly reactive dynamic structures in non-stop recycling, so, in 30 min, an active cell such as a macrophage recycles by endocytosis and exocytosis an amount of plasma membrane that equals its complete plasma membrane see .From a molecular perspective, each cell is in a permanent state of self-construction and self-destruction. This is the fundamental systemic characteristic of all basic units of life. The continuous molecular recycling that defines the systemic cellular functionality relies on a super complex dynamic system formed by millions and millions of biochemical reactions which occur continuously, at every moment of the cellular life.metabolism  and anabolic processes . These anabolic and catabolic reactions ensure molecular recycling in the cell.Enzymes are the biomolecules that perform the most important biological cellular functions. Unlike the rest of the biomolecules, enzymes are not passive. They are the only ones that can carry out a catalytic activity, transforming some molecules into others and developing complex interrelated reactive dynamics . These biocatalysts are responsible for the formation of all the ATP in the cell, DNA synthesis, apoptosis, mitosis, cytoskeleton organization, DNA repair, alternative splicing, chromosome regulation, gene expression, post-translational modifications, Golgi apparatus activity, etc. In short, all the main activities in the cell are mediated by enzymes. They constitute the fundamental elements of all essential physiological processes, which allow a cell to grow, multiply, and adapt to the external medium. However, being biologically essential, many issues of enzyme activities remain poorly understood which warrant further investigation.There are a lot of important biomolecules in the cell, such as ATP, nucleotides, lipids, structural proteins, etc., but enzymes constitute the unique active biomolecules with the capacity to reordering the atoms, i.e., the ability to transform some molecules into others creating or destroying bonds between atoms.catalytic specificity. However, the enzymatic functionality, the set of different patterns of activity carried out by every enzyme, cannot be predicted from the primary structure alone. Enzymes are not rigid molecular structures; they have complex dynamic conformations and are continuously undergoing a wide range of conformational fluctuations which modify their catalytic activities. Even in the native state, an enzyme exhibits a range of complex interconverting conformations driven by thermodynamic fluctuations . The time of diffusion between successive catalytic steps is minimized. This non-covalent direct transfer process of metabolic intermediates originates faster catalysis, making the catalysis more efficient in the multienzyme sets  in such a way that all the substrate and product concentrations spontaneously start to oscillate along time , see All metabolite concentrations of multienzyme sets that exhibit dissipative self-organization processes present transitions between complex oscillations and quasi-steady states under cellular conditions . The qua2 . These endogenous autonomous oscillators can adapt their internal metabolism to changes in the external environment  during 24-h day/night cycles . CircadiCircadian transcription-translation cycles are intertwined with different metabolic activities and respiratory oscillations, which ensures the systematic coordination and integration of cellular physiological processes .–1 for calcium waves; Lastly, a fundamental type of dissipative structure in cells is the spatial traveling waves which consist of three-dimensional self-organized coherent oscillation of metabolite concentrations that propagates progressively across the intracellular medium, reminiscent of a wave moving across water. These wave pulses of biochemical activity, moving through subcellular domains over large intracellular distances, are too fast .All modular metabolic networks that shape the cell can be considered as discrete dynamic sets, which perform relatively autonomous activities with specific and coherent enzymatic functionalities. Several scientific works have demonstrated that these elemental networks shape specialized modular units showing the genuine segregation of the metabolic activity . SegregaDissipative multienzyme complexes can also be considered fundamental modular networks , 2014. Imetabolic segregation, catalytic activities present another essential property of organization: systemic metabolic integration.Aside from the Biocatalytic sets organized into distinct basic modular networks are functionally integrated with the cell through global coordination resulting from the concerted metabolic actions of the different specialized biochemical activities as a whole .functional segregation expresses the partial interdependence of specialized metabolic nets , functional connectivity , and effective connectivity , see an example in A significant number of experimental and numerical works have shown that basic units of life exhibit complex self-regulatory behaviors originated by biomolecular information processing, the second essential source of order and organization in cells.According to the Information Theory, TE permits quantifying, in bits, the information of biomolecular patterns see . The infTE ≤ 1.00 (with mean ± SD = 0.79 ± 0.12), which suggests highly effective connectivity in the dissipative multienzyme subsystem. The analysis also indicated that the flows of functional connectivity (contained in the different metabolite patterns) change in all catalytic transitions studied , and it occurred with the emergence of complex quasiperiodic patterns. The phosphofructokinase (E2) was the principal source of molecular information in the system, and the pyruvate kinase worked as a sink, which corresponds to a functional target; the irreversible enzyme hexokinase appeared with a flow close to zero and less constrained .In summary, as a whole, the glycolytic pathway operates as a molecular information processing system, which at every moment redefines metabolic information flows that make each irreversible enzyme evolve with well-defined catalytic activities, under different inputs of glucose concentrations. The glycolytic metabolic subsystem behaves as a catalytic unit highly self-organized (dissipative processes) and self-regulated against the external changes of glucose input concentrations (molecular information processing). Each irreversible enzyme carries out three informative operations simultaneously: molecular information reception, molecular information integration, and source of new informative molecular flows. Thus, the dissipative multienzyme subsystems exhibit, at any time, precise sets of molecular instruction fluxes, and, as a result, each multienzyme complex shows specific and well-defined metabolic activities that permanently self-regulate the system. These dissipative multienzyme complexes can be considered the most fundamental units to accomplish the processing of molecular information in the cell .To understand how different multienzyme complexes functionally operate together, TE was applied for the study of the catalytic activities of DMNs . In thisSMS was observed under these external conditions, i.e., MSb12 was permanently active working as the metabolic core, the other subsystems presented on-off shifting states, and MSb15 was inactive . Even more, the network adapted its metabolic activity to the new environmental situation (a single stimulus) through its structural and flux plasticity , exhibiting both metabolic structural plasticity  and metabolic flux plasticity ; this type of global self-regulation has been observed in several unicellular organisms . There are multiple functional stable states for a DMN.Second, due to self-organized and self-regulated processes in the DMN, systemic attractors  emerge and globally govern the network. All enzymatic dynamics are stabilized in these systemic attractors. Multiple attractors  define the complex landscape on which the systemic enzymatic dynamics rely. As a consequence of the attractor dynamics, the metabolic system works as a fully integrated and individual entity.Third, “the systemic attractors that emerge in the system correspond to Hopfield-like dynamics which can store metabolic information patterns . The bioIn sort, Hopfield-like metabolic attractors store systemic enzymatic dynamics which may be properly recovered from external stimuli. Metabolic dynamics are systemically governed by these metabolic attractors which modulate the enzymatic activities, change the connections among dissipative multienzyme associations, and stably store these dynamic connections.The study with Hopfield networks  quantitaThe principles of associative memory were discovered at the beginning of the 20th century by Nobel Laureate Ivan Pavlov in his classic studies with dogs, which opened up a new paradigm in behavioral sciences.In all organisms with a nervous system, associative learning and memory are essential cognitive characteristics that allow obtaining critical information for adaptation and survival, mastering new behaviors through the association of diverse stimuli. These characteristics are ubiquitous in numerous species from mollusks to humans, but until now they have never been observed in individual cells.A. proteus and M. leningradensis were analyzed under an associative conditioning setting , the DC electric field and the peptide related to the nutrition of amoeba, placed at the positive pole, some amoebae seem to relate these stimuli (anode and peptide), and subsequent control tests showed that most of the conditioned They acquired a new persistent pattern of cellular motion, described by the move toward the anode , insteadThese experiments, in which a single cell links two different simultaneous stimuli thus developing a new behavior, are the first published evidence that an associative Pavlovian-like memory is present in single cells .Cellular conditioning may be necessary for critical functions, for example, the regulation of migration. Locomotion movements are fundamental not only to survive and avoid predators, but also in individual cells of multicellular organisms to carry out essential life processes like embryogenesis, organogenesis, immune response, tissue repair, and others. Several severe health conditions, such as cancer, vascular and heart diseases, and intellectual disability, may develop as the consequences of inaccurate control of this systemic motility property. Such migratory cellular abilities are also present in the metastatic process of cancer .In this review, we have mainly approached four aspects that characterize cellular functioning: the role of dynamic molecular processes, the mechanisms implicated in self-organization (dissipative structures) and the self-regulation of metabolic dynamics (molecular information processing), and the emergence of the cellular systemic properties.More specifically, the work focuses on the main principles that govern enzymatic activity, under complex dynamic conditions prevailing inside the cell, which are crucial to elucidate the structural and functional architecture of basic units of life.The scope of Systems Biology applied here is based on integrating concepts and knowledge in Biochemistry, Enzymology, Molecular and Cell Biology, and other biological sciences. We also discussed the results of quantitative research, analyzed by application of physical-mathematical tools such as statistical mechanics, differential calculus, discrete mathematics, artificial intelligence, computing, and others. Nevertheless, favoring the didactic purpose of the review we did not use the mathematical formulations.The following paragraphs add some conclusive examples and summarize the main aspects of this review in an integrative way.Strictly speaking from a biochemical viewpoint, the cell is a complex molecular reactor, extremely self-organized in a sophisticated manner, and in a permanent biomolecular recycling status (section “The Dynamics Originated by the Molecular Turnover and the Role of the Enzymes in These Super Complex Dynamics”).Millions of biochemical reactions happen simultaneously in every basic unit of life at any time. This process of reactive transformations also includes subcellular structures. Nothing is inert, all the molecules and structures that make up each cell undergo complex chemical transformations see . Notice The cell is an extremely complex and dynamic system; the endless molecular turnover, which characterizes it, modifies the chemical composition of the whole reactor every second and, as a consequence, the concentration patterns of ions and molecules change permanently over time. These continuous cycles of synthesis and destruction, and incessant chemical molecular transformations shape the essential scenario in which cellular life is possible. When this dynamic process of molecular turnover collapses, the cell dies. This is the main systemic characteristic of all living unicellular organisms.The consequences of self-regulated turnover dynamics are adequate cellular growth, the development of all physiological processes to maintain its functional structures, continuous adaptation to the environment, and mitosis.in vitro or in silico, has failed so far. In every cell, molecular synthesis and destruction are compensated and harmonized between them, following complex and unrepeatable reactive patterns, whose laws and defining principles are still unknown.The highly complex organization of cellular turnover dynamics defies the human intellect. Any attempt to synthetically reproduce this global molecular turnover, either Enzymes are fundamental molecules for metabolic life. Molecular reactive transformations are essentially chemical reactions, modifications on how atoms are bonded. Practically, all reactive transformations in the cell are mediated by enzymes, extraordinary macromolecular nanomachines responsible for breaking and joining covalent bonds, the fundamental chemical links in biological molecules (section “The Dynamics Originated by the Molecular Turnover and the Role of the Enzymes in These Super Complex Dynamics”). Cellular life would be impossible without enzymes; they are key protagonists in all reactive and physiological processes in the cell.active macromolecules responsible for the chemical work. Through their ability to decrease the activation energy of bonds, enzymes permanently modify how atoms are bonded, making possible the accelerated creation and destruction of molecules.Unlike other cellular molecules, enzymes are Catalytic enzymatic activities are termed metabolic processes. There are two basic types of enzymatic reactions, catabolism (implicated in molecule destruction) and anabolism (implicated in molecule synthesis). Together, these enzymatic activities are called cellular metabolism. In short, the cell is a complex enzyme-mediated metabolic system where reactive molecular transformations of synthesis and destruction happen unceasingly mediated by catalytic activities.Reactive cellular processes have little to do with the Chemistry of Equilibrium. The fundamental characteristic of cellular biochemistry is that the catalytic reactions, considered globally, occurs far from the Thermodynamic Equilibrium. Under these particular conditions, irreversible enzymatic processes raise the spontaneous emergence of self-organized dissipative structures .Different catalytic mechanisms allow processes far from Thermodynamic Equilibrium, and one of the most important is the non-linear enzyme kinetics of many irreversible enzymes with allosteric regulation , 2007.Two principal types of self-organized dissipative structures emerge in the cell, temporal molecular rhythms, and spatial waves. In temporal rhythms, molecular concentrations fluctuate over time in an oscillatory manner . Every cSo, the cell is a metabolic system in which self-construction and self-destruction occur following complex catalytic rhythms, mainly coordinated by spatial molecular waves.The self-organized dissipative structures were discovered by Nobel Laureate Ilya Prigogine , and themetabolic segregation and systemic metabolic integration, operating simultaneously (section “Dissipative Metabolic Networks and the Emergence of the Systemic Metabolic Structure”).At the cellular level, enzymatic activity dramatically depends on the collective functional structure of catalytic processes which is defined by the two fundamental principles that connect the main forms of enzyme organization in the cell: Enzymes do not work independently of each other in the cellular molecular crowding, but instead shape different types of multienzyme associations, grouped by their metabolic tasks and catalytic roles. Thus all chemical reactions that occur in living cells are segregated functionally .Moreover, these catalytic complexes interact reversibly with structural proteins and membranes originating thermodynamically open microcompartments, in which molecular rhythms can regulate the efficiency of the enzymatic reactions involved .Metabolic Subsystem was suggested in 1999 to refer to these self-organized multienzyme sets in which complex quasi-steady-state behavior and molecular oscillations may emerge spontaneously inside the cell (The term the cell . These dthe cell  representhe cell .systemic metabolic integration) forming a very complex dynamic super-system, the CMS. Such global structure was observed for the first time in 1999 by analyzing DMN through numerical studies .The dissipative multienzyme complexes permanently send information through metabolite patterns between their different enzyme components. As a result of the overall process, these enzymatic assemblies operate as basic molecular information processing units . Thus, eCMS behaves as a self-regulated dynamic entity that permanently sends specific regulatory signals to multi-enzyme complexes make them evolve in well-defined and precise metabolic activities by information processing, see On the other hand, a complex parallel super-system of information processing appears in the metabolic networks when the systemic activity is considered . CMS behPhysarum polycephalum is a paradigmatic example of the emergence of complex cellular behaviors mediated by information processing in unicellular organisms. This microorganism can discover the minimum-length option between two distant points in a labyrinth . Besides, the information generated in these processes highly increases the complexity of cellular system. abyrinth . Note thabyrinth . P. polyutrients ; 2004b.  NP-hard . This mu NP-hard . During  happens . It has  happens . Recentllearning . Molecullearning .Efficient information processing is impossible without memory (section “Hopfield-Type Systemic Attractors in Dissipative Metabolic Networks. Cellular Systemic Behaviors”). The presence of Hopfield-like dynamics characterized by associative memory in dissipative enzymatic networks was numerically verified in 2013 . Such a A. proteus and M. leningradensis  amoebae. This research also allowed the quantification of the importance of the nucleus during the cellular migration  in cells and cytoplasts matches with the Pavlovian-like dynamic memory (44 min on average)” ” .The nucleus has been classically considered an essential element governing cell movement, nevertheless direct quantitative evidence was lacking. The migratory analysis of enucleated and non-enucleated amoebae described above  also demCMS exists , to research the mechanism behind the emergence of the omplexes . The funThe high redundancy of the enzymes (with an increased number of copies) and the consequent multiplicity of dissipative self-organized multienzyme complexes that prevail inside the cell would determine the spontaneous formation of the SMS.CMS.A continuous process of molecular synthesis and destruction represents thousands of metabolic reactions that happen permanently and simultaneously in the cell, ensuring the emergence, robustness, and stability of the The only possible scenario for cellular life is a dynamic system in permanent self-construction and self-destruction process that guarantee the functionality of a high number of dissipative self-organized multienzyme complexes. There is no other alternative. This sophisticated and massive dynamics of endless molecular transformations encompasses the whole metabolic system and constitutes the most critical dynamic property, essential and definitory, of cellular life.metabole meaning “change” or “transformation.” This word reflects exactly the essential characteristic of the basic units of life. Rather than a molecular genotheque (box of genes) in evolution, the cell could be considered a singular dynamic metabolic unit capable to self-organize and self-regulate in an endless process of molecular turnover.The word “metabolism” comes from the Greek de novo.”“Metabolism can be considered the largest known source of molecular complexity in nature” . RoughlyCMS. “Through the structural and functional complexities, the metabolic evolution has developed a large diversity of biochemical organizational forms, ranging from sophisticated bacterial metabolism, via the complex enzymatic networks, characteristic of protists, to the extraordinary structures and processes derived from the multicellular eukaryotic organization, such as embryogenesis or the neural networks present in higher mammals. The millions of living metabolic species represent the inexhaustible source of complexity developed by the dynamic forces of the cellular metabolism” (Across the millennia, many adaptive molecular mechanisms have been acquired in the biological evolution by the abolism” .Every unicellular organism results from the direct and uninterrupted transmission of this extraordinary and singular metabolic organization. Over millions of years, sophisticated metabolic dynamics have evolved to originate complex biological supracellular structures, reproducing at different scales the singular intrinsic organization enclosed in itself … up to become self-aware.ID, LM, MF, JC-P, JL, and IM performed the analysis and design of the research mapping. LM involved in main funding. All authors wrote the manuscript and agreed with its submission. IM conceived, designed, and directed the investigation.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


This study constructs a comprehensive index to effectively judge the optimal number of topics in the LDA topic model. Based on the requirements for selecting the number of topics, a comprehensive judgment index of perplexity, isolation, stability, and coincidence is constructed to select the number of topics. This method provides four advantages to selecting the optimal number of topics: (1) good predictive ability, (2) high isolation between topics, (3) no duplicate topics, and (4) repeatability. First, we use three general datasets to compare our proposed method with existing methods, and the results show that the optimal topic number selection method has better selection results. Then, we collected the patent policies of various provinces and cities in China  as datasets. By using the optimal topic number selection method proposed in this study, we can classify patent policies well. From a text mining perspective, topics in a text corpus can be viewed as probability distributions of terms present in the corpus or clusters that define weights for those terms ,2. The LHowever, the LDA topic model has a problem that it does not give the optimal number of topics for the text itself, and the exact number of topics needs to be determined by the model user in other ways . The detSome studies have shown that the effectiveness of topic classification in LDA models is closely related to the selection of the number of topics. If the number of topics selected is too small, the meaning under each topic will be too broad; if the number of topics selected is too large, it will lead to an over-clustering of data, producing useless topics or topics with too much similarity. To address this issue, Blei et al. 2003) proposed a perplexity model to determine the quality of topic models with different numbers of topics  proposed. He et aDoc 1 = Doc 2 = Doc 3 = Doc 4 = .Then, we use a toy example to show the differences and problems of the most commonly used methods of perplexity, JS divergence, and coherence. Assume that the following four documents are available for LDA training:Test1 = Test2 = .The two test set documents are:k set from two to four, and the “topic-word” probabilities are calculated for different numbers of topics, as shown in First, the LDA model is used to train four documents with the number of topics With human intuition, the training set can be divided into two topics, animals {dog, cat, pig} and fruits {apple, pear}. We use the top two words in the probability ranking to determine the content of the topic. As can be seen from When the number of topics is three, the first two words in Topic1 are “apple” and “pear”, which can be judged as a fruit topic. The first two words in Topic2 are “dog” and “cat”, which can be judged as an animals topic. The first two words in Topic3 are also animal-related, “dog” and “pig”.When the number of topics is four, the first two words in Topic1 are ‘apple’ and ‘dog’, and the content of the topic cannot be determined. The first two words in Topic2 are animal-related, ‘dog’ and ‘cat’, which can be judged as an animals topic. The first two words in Topic3 are ‘apple’ and ‘dog’, and the content of the topic cannot be determined. The first two words in Topic4 are fruit-related, ‘apple’ and ‘pear’, which can be judged as a fruit topic.It can be seen that the LDA model with two topics is the most consistent with human intuition. In contrast, the LDA model with three topics has two animal-related repetitive topics, and the LDA model with four topics has two unknown topics that cannot be distinguished.Second, the topic probabilities of the test set documents are calculated for the LDA model with different numbers of topics. Combining the “topic-word” probability in When the number of topics is three, the probability that the content of Test1 belongs to Topic1 Fruit is 0.5932, the probability that it belongs to Topic2 Animals is 0.3182, and the probability that it belongs to Topic3 Animals is 0.0885. The probability that the content of Test2 belongs to Topic1 Fruit is 0.1151, the probability that it belongs to Topic2 Animals is 0.7711, and the probability that it belongs to Topic3 Animals is 0.1138.When the number of topics is four, the probability that the content of Test1 belongs to Topic1 Unknown topic is 0.0655, the probability that it belongs to Topic2 Animals is 0.3075, the probability that it belongs to Topic3 Unknown topic is 0.0632, and the probability that it belongs to Topic4 Fruit is 0.5637. The probability that the content of Test2 belongs to Topic1 Unknown topic is 0.0842, the probability of belonging to Topic2 Animals is 0.7476, the probability of belonging to Topic3 Unknown topic is 0.0837, and the probability of belonging to Topic4 Fruit topic is 0.0845.It is also clear from the topic determination of the test set documents by the LDA models with different numbers of topics that the “document-topic” probability obtained by the model with two topics is most consistent with our intuitive judgment. The LDA models with three and four topics produce duplicate and unknown topics, which interfere with the topic probability of the test documents and affect our judgment of the topic content of the documents.From the above analysis, it can be seen that the LDA model with two topics is most consistent with our intuitive judgment. Since this toy example is too simple, it is not difficult to manually select the optimal number of topics, but for a large number of documents, it will be very difficult to judge manually. Next, we will use different methods to select topics for this toy example to see whether the existing methods can select the optimal LDA model.Third, the number of topics for the LDA model was selected using the perplexity, JS divergence, coherence, and stability methods as well as our proposed optimal topic number selection method. Since the toy example has fewer words and texts, with only two words related to fruits and three words related to animals, the coherence, stability method, and our proposed optimal topic number selection method were calculated by using the top two words ranked for each topic to indicate the topic meaning. The calculation results are shown in The perplexity method considers the predictive ability of the model for documents. The principle is that if most of the words in a document are the top words in the probability ranking of the topics generated by LDA, then the prediction of the topic to which the document belongs is more accurate. On the contrary, it is difficult to determine the topic of the document. Therefore, the lower the perplexity, the better the prediction ability of the model. From The JS divergence method considers that the topics generated by a topic model should be well differentiated from each other, and JS divergence is a measure of the difference in word-probability distributions between topics to determine whether a topic model is good or bad. Therefore, for JS divergence, the greater the difference in the distribution of “topic-word” probabilities among topics, the better the topic generation model. The coherence method considers the coherence of semantic information in the model, that is, the conditional likelihood is estimated for the combination of words for which the document contains the first n of the topic words at the same time. Therefore, for the coherence method, the higher the probability that the words with the highest topic ranking can appear in a document at the same time, the better the classification effect of the model. From The optimal number of topics selection method we propose adds the judgment of model stability and coincidence based on the consideration of the predictive ability and topic isolation of the model, as shown in This toy example shows that both the perplexity method and the JS divergence method select the number of topics to be four, which is the maximum number of topics for our training of this small sample. The selection results of these two methods are not consistent with our intuitive judgment. From By analyzing the existing studies, it can be seen that although the LDA model can generate topics well by the probability distribution of words, it cannot give an optimal judgment about the number of topics to be selected. Most of the existing studies perform topic number selection from a certain feature that a good topic classification model should have. For example, the perplexity method considers that a good topic classification model should be able to effectively classify unknown documents outside the training set. The JS divergence or JS divergence approach considers that the less similar the content among the topics classified, the better the topic classification model. Both the coherence method and the stability method proposed by Greene judge the goodness of the topic classification by the similarity of the words within the same topic in the model. Although these existing topic selection methods are not comprehensive for topic classification, they also provide a good basis for us to think about how to judge whether a topic classification model is good or not.Based on the existing studies, it is known that a better topic selection model should have the following characteristics: (1) The topic model has certain predictive ability; i.e., the model can classify the unknown input corpus well. (2) There should be a certain degree of isolation between different topics generated by the model; i.e., the occurrence of duplicate topics is avoided. (3) The words within each topic generated by the topic model are correct. (4) The generated model is robust; i.e., the data from the same source consistently generated similar solutions. Based on these characteristics, this study proposes a comprehensive method for determining the optimal number of LDA topics. There is no research to select the number of topics for LDA models from a comprehensive perspective, and most of the existing methods are one-time tests, which make it difficult to ensure that the models can be reliably and stably implemented repeatedly. In view of the limitations of existing studies, this paper will propose a comprehensive method for judging the optimal LDA topic number based on the above four characteristics that a good topic model should have.Latent Dirichlet Allocation (LDA) is a document topic generation model proposed by Blei et al. (2003) after introducing the Dirichlet distribution based on Probabilistic Latent Semantic Analysis (PLSA). LDA is a classical model for generating Bayesian probability models, which is based on the assumption that documents are generated from multiple topics according to a certain random probability distribution, and each topic is composed of words according to a random probability distribution. Thus, a document is a collection of topics with different probabilities, and a topic is a collection of words with different probabilities. The LDA topic model calculates the probability of the conditional distribution (posterior distribution) of the hidden variables given the observed variables by using the joint distribution. The observed variable is the set of words and the hidden variable is the topic, whose probability map model is shown in The joint distribution of the observed and hidden variables corresponding to the generation process of the LDA model is shown in Equation (1).kth topic. The proportion of that topic in the dth document is kth topic in the dth document. The set of topics contained in the dth document is nth word in the dth document belongs. The set of all words in the dth document is denoted nth word in the dth document. nth word of the document corresponds to the topic to which it belongs when the topic is determined, and nth word of the document belongs and the word.The concatenated symbol in Equation (1) describes the dependence of the random variables. Here, M is the size of the test corpus, dth text , and Perplexity is calculated as follows.Existing studies found that although the perplexity can judge the predictive ability of the topic training model to a certain extent, when the number of topics is selected by the perplexity, the number of topics selected is often too large and does not converge, and similar topics are likely to appear, resulting in a low discrimination of topics. Therefore, this study further judges the number of topics by the inter-topic similarity of the training model to improve the accuracy.The isolation of the topic model is usually calculated using either the Kullback–Leibler divergence (JS divergence) or the Jensen–Shannon divergence (JS divergence). Since the JS divergence does not satisfy the symmetry and triangular inequality , the JS P and Q, the more similar they are, the smaller the JS divergence, and the more isolated they are, the larger the JS divergence value. JS divergence is calculated by the following formula.The JS divergence formula is based on the deformation of the JS divergence formula. JS divergence is also called relative entropy; for two probability distributions P and Q will give different results, so the JS scattering formula after adjusting to symmetry is as follows.Since the JS divergence formula is asymmetric, swapping the positions of P and Q are the same, the JS divergence takes a value of 0.The JS divergence takes a value between 0 and 1. When the distributions of k. Then, the test set text is used as the input of the model to get the word probability distribution of the test set corresponding to k topics, and the average probability of each word is calculated based on the probability distribution of words corresponding to different topics. Finally, the standard deviation of the JS distance between the word probability distribution of each topic and the average probability distribution is calculated as the isolation degree when the number of topics is k. The calculation formula is as follows.ith topic and k topics.In the calculation, first, the data are divided into training and test sets, and the training set text is used to complete the training of the LDA model under the given number of topics The stability of a clustering algorithm is expressed as the ability of this algorithm to consistently produce similar solutions for data originating from the same source . Greene t words of that topic, where t is less than the total number of words. This substitution not only makes the similarity between topics comparable but also greatly reduces the computational effort. In this study, the Jaccard index was used to calculate the similarity of word ranking lists for each pair of topics. An average Jaccard index (AJ index) was defined to calculate the word ranking, since it has a large impact on the meaning of the topic. The AJ index calculates the average of the word similarity for each pair of topics ranked from 1 to t. The calculation is as follows.Topic model algorithms usually take the ranking of words under each topic as their output. In the LDA model, these words are ranked based on the probability distribution of the words under the topic. Assume that the two topic lists are d words of the topic at the selected vocabulary depth of t. The AJ index calculation is a symmetric calculation method that reflects both the degree of vocabulary relatedness of the two topics and the similarity of the ranking of the words.In the above equation, d words for two topics t equal to 5.As an example, As shown in k topics are k optimal consistent combinations is summed and averaged, which is the stability of the subject set Assume that two different sets containing The An example is given below. Suppose there are two topic sets S1 and S2 that both contain three topics.The set of topics for s1 is:The set of topics for s2 is:Then, the The optimal coherence combination is:The stability of Three situations may occur when using the training model with the test model for stability measurement: (1) In the coherence combination of the training model and the test model, there are no repeatedly selected topics in the test model, as follows.(2) In the coherence combination of the training model and the test model, there are repeatedly selected topics in the test model, and there are some topics that are not selected, as follows.(3) In the coherence combination of training and testing models, there exists a certain training topic that appears to have the same maximum AJ value as the topics of more than two testing models, as follows.An optimal topic classification should be such that every topic word sequence under the training model corresponds to every topic word sequence under the test model. There are two cases that result in the topics of the training model and the test model not corresponding exactly. The first is that since the sampled dataset is smaller than the overall dataset, in some sampling, it may result in the topics trained in the training set not corresponding exactly to the test model. The second one is that when the number of topics in the test model is too large, it is easy to generate similar duplicate topics, which leads to the same value when calculating the stability of the training and test models. However, this aspect is mostly lacked in the existing studies. In order to improve the accuracy of the model stability measurement and make its applicability more complete, in this study, we add a consideration of whether the training model and the test model completely coincide in terms of topic connotation to the model stability measurement.The combination of the maximum coherence of the sets c denotes the number of topics in the test model and the training model that coincide, and k denotes the number of topics.In the above equation, As an example, let two sets of topics that both contain three topics, and the model similarity measures of training model The optimal coherence combination is,In the second case, in the coherent combination of the training model and the test model, there are duplicate selected topics in the test model, and there are some topics that are not selected.The optimal coherence combination isThe test model has two occurrences of In the third case, there is a coherent combination of training and test models in which a certain training topic has the same maximum AJ value as more than two test model topics.The optimal coherence combination isThe test model has one occurrence of The value of model coincidence is greater than or equal to 1. When the value of model coincidence is 1, it means that the subjects of the training model and the test model can completely coincide, and the larger the value of coincidence means that the coincidence of the training model and the test model is worse. As in the case of model stability measurement, this study obtains multiple model coincidence values through multiple sampling training and finally averages them to obtain the average coincidence value as a basis for judgment.A reliable topic model should have three characteristics: first, the model has a good predictive capability, which means the model has low perplexity; second, there is a certain degree of isolation between different topics to avoid the appearance of duplicate topics, which means the similarity between topics is low; third, the model has a high stability, which means the model is repeatable. Fourth, the directionality of the topics of the model is unique and reliable, which means that the model has a low degree of coincidence.Existing studies have found that selecting the number of topics by the perplexity value often leads to the selection of too large a number of topics. In this study, the perplexity of the topic model is combined with the model isolation, stability, and the coincidence index proposed in this study to obtain a better number of topics by cyclically training and testing the model. It is important to note that here, since usually, the calculated values of the perplexity method are much larger than several other metrics. In order to avoid the influence bias among the indicators, we take the logarithm of the perplexity when using our proposed method. The final topic superiority scores are defined as follows.k topic superiority scores of the k. The calculation steps are shown in To calculate the degree of model stability for different topic numbers k, first, an initial topic model is generated based on the complete dataset, and this model for the complete data is also the test model for the subsequent calculation of topic consistency, which is defined as The calculation steps are as follows:Step 1: The complete document set n (after data cleaning) is trained by the LDA model to generate topic test models with different numbers of topics Step 2: Samples are drawn from the complete document set n with a sampling rate of Step 3: Calculate the stability of the test model Step 4: Calculate the isolation of models under different numbers of topics by using the Step 5: Calculate the perplexity of models under different numbers of topics by using the remaining Step 6: Calculate the topic superiority index under different numbers of topics by using the stability, coincidence, isolation, and perplexity obtained from Steps 3 to 5.Step 7: Repeat Steps 2 to 6 to obtain the topic superiority index of the τ test and test models, and calculate the average topic superiority index under different numbers of topics.Step 8: The number of topics corresponding to the smallest average topic superiority index is taken as the optimal number of topics.This section uses three datasets, 20news_groups , WOS_469We use the same data pre-processing approach for different datasets. Before training the LDA model on the documents, the text information of all documents is firstly processed for word splitting and stop word removal. We used the Lemminflect package  in Pythok. The number of topics trained for the 20new_groups dataset ranges from five to 30. The number of topics trained for the WOS_46986 dataset ranges from two to 20. The number of topics trained for the AG_news dataset ranges from two to 20. The hyperparameter α indicates the sparsity of topics in the document, that is, the set of topics in which the document is expected to contain most of the topics; the larger the α, the greater the number of topics that can be contained in the document. β indicates the sparsity of words in the topics, the smaller β indicates the non-uniform distribution of words within the topics. According to Hagen (2018), when the number of topics is not very large, different initializations do not have a significant impact on topic variation [β in all LDA training models as dynamic variables related to the number of topics, which is In this study, we use the Gensim package  in Pythoariation . This stt words with the highest probability of each topic were selected to represent that topic, and the values of t were taken as 20, 50, 80, and 100. When calculating the stability of the model, the first step is to select the number of words that represent each topic. According to the formula for calculating the stability, it is known that the lower ranked words have less influence on the final calculation result, but the more words there are, the larger the calculation volume is, so it is not necessary to include all the topic words in the calculation. Existing studies have not reached a consensus on how many words should be selected to represent a topic . Take thAs can be seen from In this section, we compare the optimal topic number selection method proposed in this paper with the several commonly used topic number selection methods such as perplexity, JS divergence, coherence, and HDP  by using three different datasets, which are 20news_groups, WOS_46986, and AG_news. Among these methods, the smaller the value of both the optimal topic score and the perplexity score we propose, the better the classification of the topic model. In contrast, the larger the JS divergence and coherence scores, the better the classification of the topic model. Teh et al. (2006), on the other hand, improved the original LDA model by proposing Markov chain Monte Carlo algorithms for posterior inference in hierarchical Dirichlet process mixtures and describe applications to problems in information retrieval and text modeling .In addition, we use an LDA model based on the word-embedding approach to further validate the applicability of our proposed method. Regarding the processing of the LDA model for the word-embedding approach, we use the word-embedding data provided by Pennington et al. (2014), which are named GloVe . For comThe JS divergence and coherence scores are between 0 and 1. Compared with them, the topic superiority score and perplexity scores have larger values. To better show the differences in topic number selection of different methods in the figure, we normalize the topic superiority score and perplexity scores. The results of different topic selection methods are shown in As can be seen in The optimal number of topics selected by the perplexity method is 8. The model perplexity score tends to increase in the range of topics selected from eight to 15, and it again shows a significant downward trend between topics selected from 15 to 30. Although the optimal number of topics selected by the perplexity method is eight in the range of five to 30, the trend of a sharp decrease in the perplexity score as the number of topics rises cannot be ignored. Later, we will apply a real example of patent policy to test the perplexity method and find that the perplexity score decreases as the number of topics increases, which also proves this point.The JS divergence method shows an increasing and non-converging trend in the scores calculated in the interval from five to 30 topics, so the optimal number of topics chosen for this method in this interval is 30.The calculated score of the coherence method is relatively smooth in the interval from five to 30 topics, and the optimal number of topics selected is seven, but it also has a low peak at 15 topics.We used the Tomotopy package  in PythoThe optimal number of topics derived from our proposed method in the word-embedding LDA model is 25. In the range of topics from five to 25, the calculated scores show a significant decreasing trend.From the above analysis, it can be seen that the score curve obtained by our proposed optimal topic number selection method is closest to the U-shape, and therefore, the optimal value is most likely to exist. The optimal topic number obtained on the use of the word-embedding LDA model is closest to the original value. In contrast, other topic number selection methods may have the following problems.First, the perplexity method has the possibility that the calculated score decreases as the number of topics increases, leading to the final inability to select the optimal number of topics.Second, the scores obtained by the JS divergence method increase with the number of topics, which makes it difficult to converge, and it also suffers from the problem that the final number of selected topics is too large.Third, the score curve calculated by the coherence method is too smooth, and multiple optimal values may appear.Fourth, when selecting the number of topics for the 20news_groups dataset, we found that the number of topics selected by the HDP method was too large. However, the HDP method is an improvement of the original LDA training model by mapping the text vector to the topic feature space to obtain a three-layer model of document–topic–feature items, and then, the optimal topics can be trained automatically. We find that there are still two problems in the application of the HDP method. The features that a reasonable topic classification should satisfy are not fully considered, such as the four features mentioned in our method. This leads to the fact that the optimal number of topics derived from the HDP method may be very different from the actual number of topics. In addition, the HDP method is difficult to be applied to other improved LDA models or some other text classification models constructed based on word and topic distributions because it is an improvement of the training process of the original LDA model.According to the results of selecting the number of topics in the 20news_groups dataset, it can be seen that the number of topics selected by our proposed method is closest to the original 20 topics. If the number of topics selected is too large, it may lead to too much subdivision of topics and too much similarity between topics, while if the number of subjects selected is too small, it may lead to some topics that should be separated being merged.To further verify the effectiveness of our proposed optimal topic number selection method, this section uses the T-SNE package  in Pythow in the topic z. z in the mth document md. Therefore, the generation probability of a document containing n word vectors W is shown in Equation (12).According to the LDA document generation formula, the generation probability of each word in each document is shown in Equation (11).k, which is After training the LDA model on the original test set of 20news_groups data in the previous section, we have obtained the “topic-word” probability distribution for these datasets with different number of topics i. mth document after removing the words with subscript i. For the test set, m belongs. Finally, the “document-topic” probability of the test document can be calculated based on the statistics of the topics corresponding to each word after multiple sampling.In this paper, we use the Gibbs Sampling approach, which is commonly used in LDA models, to estimate the “document-topic” probability, as shown in Equation (13).The specific steps are as follows.z to each word w in this document. Set the initial value of the hyperparameter α. In this paper, the initial value of α is set to 1/k.Step1: Select one of the documents m in the test set and assign a random topic number z is estimated using the Gibbs Sampling method, and then, the topic number corresponding to each word is updated.Step2: The probability of each word corresponding to topic Step2.1: Estimation of the current topic distribution of document m, which is m corresponds to the currently assigned topic, that is, Step2.2: Calculate the probability that each word in document Step2.3: The topics to which each word belongs are reassigned according to the current topic probability Step3: Repeat Step2 until Gibbs Sampling convergence reaches a steady state, that is, the estimate of m is obtained by counting the frequency distribution of the topic to which each word in document m belongs.Step4: The “document-topic” probability distribution of document Step5: Repeat Step1 to Step4 for each document in the test set to obtain the “document-topic” probability for each document.Each document in the training and test sets is represented by a k-dimensional “document-topic” probability distribution, which is used to draw a topic clustering map of the documents. To better compare the clustering effect of the documents in the training and test sets, we first use a binary variable to label the documents as training or test documents, respectively. Then, the documents in the training and test sets are clustered together based on the k-dimensional “document-topic” probability distribution of each document. Finally, the clustering graphs of the documents in the training set and test set are displayed separately according to the document IDs. This enables the borders of the clustering graphs of the training and test sets to be consistent, allowing us to distinguish the performance of the topic models in the training and test sets more clearly. This processing allows the distribution of the clusters in the training and test sets to be consistent across the range, allowing us to analyze the performance of the topic models on both the training and test sets more clearly.Among the original topics in the 20news_groups dataset, some of them have widely different content , while others have more similar content . In this section, we compare the clustering effect of documents with similar content and the clustering effect of documents with more different content.First, we select documents with large differences in topic content for clustering comparison, which are documents under the four original topics of alt.atheism, comp.sys.mac.hardware, rec.sport.hockey, and sci.space. We compare the clustering of the training and test set documents under 13 topics (LDA) and 25 topics (word-embedding LDA) selected by our proposed optimal topic selection method, 8 topics selected by the perplexity method , 30 topics selected by the JS divergence method, and 59 topics selected by the HDP method, as shown in From From From Then, we would like to further observe the clustering effect of the LDA model for documents with more similar topics under different topic number selection methods. We have selected the documents under the four original topics comp.sys.mac.hardware, comp.windows.x, rec.sport.baseball, and rec.sport.hockey. The documents under these four original classes were chosen because comp.sys.mac.hardware and comp.windows.x both belong to the computer domain, and rec.sport.baseball and rec.sport.hockey both belong to the sports domain, as shown in From From From As can be seen in Finally, the performance of our proposed optimal topic number selection method on the word-embedding LDA model will be verified. In addition to choosing documents from the same original categories as before for comparison, we added a categorical comparison of documents from four topics: comp.graphics, comp.sys.mac.hardware, rec.autos, and sci.space.From From As can be seen from From In this section, we use the WOS_46986 dataset to compare the optimal topic number selection method proposed in this paper with several commonly used methods: the perplexity selection method, JS divergence selection method, and coherence selection method. We also include the results of the optimal topic number selection method applied to the word-embedding LDA model for the comparison. The topic model scores of different topic selection methods are shown in As can be seen in However, in the application of the word-embedding LDA model, the trend of the score curves calculated by the optimal topic number selection method in the WOS_46986 dataset is slightly different from that in the 20news_groups dataset. In the 20news_groups dataset, the score curve shows a clear downward trend in the range of five to 25 topics. In the WOS_46986 dataset, the score curve shows a decreasing trend in the range of two to five topics, an increasing trend in the range of five to 10 topics, and a decreasing trend again after the number of topics is greater than 10. There are two possible reasons for this discrepancy. First, the documents in the WOS_46986 dataset have relatively concentrated word expressions. Second, the original WOS_46986 dataset has further divided each topic into multiple subdomains under the seven main categories. The word-embedding method allows the words of each document to form more associative relationships on the subdomains, thus enabling further segmentation of the subdomains when the number of topics is further increased.Among the original topics of the WOS_46986 dataset, there are some topics with large differences in document content, such as documents under the original topics of ECE, Psychology, and Biochemistry. There are also some topics with some overlap in document content, such as documents under the original topics Medical and Biochemistry, and documents under the original topics ECE  and CS (Computer Science).First, we selected three topics with large differences in content for clustering comparison, which are documents under the original topics of ECE , Psychology, and Biochemistry. We compare the clustering of the training and test set documents under seven topics (LDA) and five topics (word-embedding LDA) selected by our proposed optimal topic selection method, and 20 topics selected by the JS divergence method. The number of topics selected by the perplexity method is nine, which is basically the same as the number of topics selected by the optimal topic selection method, so we only use the LDA training model with seven topics for analysis, as shown in From From From Next, we further observe the classification effect of the LDA model for documents with more similar topic content under different numbers of topics. We selected documents under the original categories of CS, ECE, Medical, and Biochemistry. Among them, there are many documents with overlapping contents in CS and ECE topics, and some documents with overlapping contents in Medical and Biochemistry topics.From From From In this section, we use the AG_news dataset to compare the optimal topic number selection method proposed in this paper with several commonly used methods: the perplexity selection method, JS divergence selection method, and coherence selection method. We also include the results of the optimal topic number selection method applied to the word-embedding LDA model for the comparison. The topic model scores of different topic selection methods are shown in As can be seen in The AG_news dataset includes four original themes: world, sports, business, and sci/tech. These four topics cover a wide range of content. Even for documents under the same topic, the content varies greatly. In this section, we compare the clustering effects of the LDA model with four topics and the word-embedding LDA model with 11 topics selected by the optimal topic number selection method, as well as the clustering effects of the LDA model with 10 topics selected by the perplexity method. The number of topics selected by the coherence method is three, which is basically the same as the number of topics selected by the optimal topic selection method, so we only use the LDA training model with four topics for analysis. The JS divergency method still suffers from the problem that the number of selected topics is too large, so its clustering effect is similar to that of the 20new_groups and WOS_46986 datasets, and we do not repeat the demonstration in this section.Combining Combining Combining The experimental environment is a computer with Windows 10 Home Edition operating system, Intel (R) Core (TM) i7-11700 CPU, 2.50GHz, and 16GB RAM. We use different data sizes to compare the time consumption of different methods. The different data sizes are shown in As shown in X-axis coordinate. Second, the longer the average text length, the more time it takes. For example, although the word-embedding LDA model for the AG_news dataset has a larger bag-of-words size than the word-embedding dataset of 20news_groups and has the largest number of documents, its training time consumption is relatively small. Third, the larger the bag-of-words size, the more time consuming in the training, as can be seen from the comparison results of the red and black lines in The training speed of the LDA model is related to several factors. First, the larger the number of topics trained, the more time it takes. As shown in The next discussion is the computational time consumption of different topic number selection methods for different data sizes. First, the computation time of the four dimensions of our proposed optimal topic number selection method is shown in It can be seen from The time consumptions shown in As can be seen from From the above, it is clear that although our proposed method is constructed to consider reasonable topic selection from four indicators, while several other methods consider only one aspect of topic classification, the time consumed of our proposed method is in the middle level in terms of the time consumed for one-time computation. In addition, it should be noted that if we want to obtain a more reliable optimal number of topic selection, we also need to perform multiple sampling, which will increase the computational time consumption of the optimal topic selection method.In summary, our proposed optimal topic number selection method has several advantages. First, in terms of the number of topics selected, the optimal topic number selection method can better select the appropriate number of topics for the LDA model. Compared with several other topic number selection methods, the optimal number of topics derived from our method is closest to the real number of topics. In our example, the number of topics selected by the perplexity method and the coherence method is much smaller than the real number of topics. The optimal number of topics selected by the JS divergence method is at the maximum boundary of the topic selection interval, which makes us skeptical about whether this selected number of topics is optimal. The optimal number of topics selected by the HDP method is much larger than the true number of topics.Second, from the score curves, the score curve of the number of topics derived from our proposed optimal topic number selection method is closest to a U-shaped curve, which makes it possible to find the optimal extreme value point in the score curve. On the one hand, the score curve derived from the perplexity method has an optimal point at the position where the number of topics is small. However, when the number of topics exceeds a certain threshold, the perplexity value decreases sharply with the increase in the number of topics, so the perplexity method may have the problem that the larger the number of topics selected, the lower the perplexity value, and the curve is difficult to converge. The topic number score curve derived from the coherence method presents a smooth fluctuating state, and the state of this curve is less reliable than the U-shaped curve obtained by the optimal topic number selection method in finding the optimal value. The curves derived from the JS divergence method, on the other hand, exhibit the problem of failure to converge as the number of topics increases.Third, from the clustering graphs under different topic numbers, the optimal topic number selection method and the perplexity method are able to classify documents with large differences in content clearly. The optimal number of topics selected by the JS divergence method is large, and there is the problem of overclassifying content that is originally the same topic. The HDP method selects the largest number of topics, which leads it to divide the original same topic content into multiple subclasses, similar to the state of model overfitting in the training set, which leads the model to fail to perform good classification in the test set instead. For documents with small differences in content, the LDA topic model selected by the optimal number of topics selection method and the JS divergence method can classify those documents that are similar in content but still have some differences better, but it is difficult to achieve good classification for documents with too similar content. In the example of this paper, the number of topics selected by the perplexity method is too small, making it impossible to classify documents with similar content. Although the number of topics selected by the HDP method is larger, it is still unable to effectively divide documents with similar topics and suffers from the problem of topic over division. In addition, the HDP method is difficult to apply to other topic classification models since it is an improvement of the LDA model.Fourth, although the number of topics selected by our proposed optimal topic number selection method cannot be exactly equal to the real number of topics, and there is the problem of difficulty in classifying topics for documents with similar content, this problem is in fact due to the original defect of the LDA model. The purpose of our proposed method is to evaluate LDA training models with different numbers of topics and to select the optimal one from them. It has been demonstrated by the above examples that this method can do this. However, our optimal topic number selection method does not change the defects of the original LDA topic model. If the original LDA model is unable to classify similar documents in any case, then our optimal topic number selection method is unable to do so, either. We use an improved word-embedding LDA model to further validate the applicability of our proposed method. It turns out that our proposed method is also applicable to this improved LDA model. Since the word-embedding method can compensate for the problem that the original document word expressions are too sparse to be clustered, it makes the final selected word-embedding LDA model have better clustering effect than the original LDA model.In the subsequent sections, we will also use Chinese patent policy texts as real cases for LDA topic classification, and use our proposed optimal topic number selection method for topic division and calculation as further validation.The policy texts involved in this study are obtained from the Wolters Kluwer Information Database and Peking University Law Database. The scope of collection is patent policy texts from all provinces and cities in China . Since some patent policies are included in other policy texts, in order to collect patent policies as extensively as possible, this study retrieved all policy texts with one of the following keywords in the title: patent, intellectual property, science and technology, innovation, and all policy texts with the word patent in the full text in the two databases. After removing duplicate texts and texts with less than 20 words of content, there were 9286 valid patent policy texts remaining, ranging from 1982 to 2018. As shown in Before conducting text analysis, the 9286 policy texts are first pre-processed. The steps are as follows:Step 1: Split words. Use Python’s Jieba package  to splitStep 2: Merge synonyms. For example, the names of universities are combined into universities; the names of banks are combined into banks; award rankings and grades are combined into award grades; technology parks with regional names are unified, etc.Step 3: Remove stop words. Punctuation, graphics, non-Chinese characters, auxiliary words, and words with a word frequency less than or equal to 10 are removed. Due to the wide range of policies collected in this study, some policies also contain topics that are not related to patents or technologies. In order to avoid producing unnecessary topics during LDA model training, this study also removes this part of irrelevant words. The final number of valid words obtained is 13,309.k. Then, the ratio of the training set and test set is set as 8:2, where 80% of the documents from all policy texts are randomly selected as the training set and the remaining 20% are selected as the test set for 30 times. In this part, the first t words with the highest probability of each topic were selected to represent that topic, and the values of t were taken as 20, 50, 80, and 100. The specific training process is consistent with that described in As can be seen from Finally, the perplexity, isolation, stability, and coincidence of the model are calculated according to the steps in The values calculated by the different topic selection methods are normalized as shown in As can be seen from The results of the optimal number of topics based on isolation, perplexity, and the method proposed in this study are compared as shown in The optimal numbers of topics selected in terms of perplexity and JS divergence are both 70, and the words and probabilities under each topic are shown in (1)Patent creation policies. The management of patent-creating activities is an important function of the State Intellectual Property Office (SIPO), i.e., the examination and granting of patent rights. The target of the patent creation policy is mainly the creators of patents, including enterprises, research institutes, universities, and individual inventors. There are four main aspects of the patent creation policy: one is to encourage inventions and patent applications through awards and various prizes, the second is to encourage inventions and creations by means of title evaluation or high-tech evaluation, the third is to encourage the declaration of subject projects in key technical fields, and the fourth is the introduction of innovative talents.(2)Patent utilization policies. Patent utilization is a key step to realize the value of intellectual property rights (IPR). The current patent utilization policy focuses on promoting the industrialization and commercialization of patent achievements. Its policy targets are mainly the creators and users of patents.(3)Patent protection policies. Starting from 2014, many regional judicial systems in China have established dedicated IP courts for handling IP-related legal disputes. Meanwhile, special IPR actions conducted by the SIPO and local IPR bureaus as the leading units have also made progress in many aspects, strengthening the fight against IPR infringement through administrative protection means and further optimizing the IPR legal, market, and cultural environments. China’s IPR protection policy is currently facing many reforms, including enhancing the statutory means of IPR enforcement, optimizing IPR enforcement procedures, reforming comprehensive IPR administrative enforcement, and broadening IPR dispute resolution channels.(4)Patent management policies. The patent management policies are public policies that guide and regulate the IP management activities of power holders from the government level. They include upgrading the IP management level of patent rights holders, certification of IP consistent enterprises, management of project and personnel titles, etc. IP management activities are actions exercised by IPR subjects, and the policies are mainly guiding and encouraging policies, whose core objective is to enhance the IP management level of rights holders.(5)Patent service policies. Patent services are an important way to facilitate a good interface between patent creation, utilization, protection, and management. The content of patent service policies is encapsulated in the links of patent creation, utilization, protection, and management, and it transfers patent services originally provided by rights holders and government departments to third-party institutions in the market. A major shift in China’s current patent policy is to establish and improve the patent service industry system. Typical patent service businesses include public platforms for patent education and operation, patent information and intelligence, patent legal services, patent financial services, patent personnel training, and technology consulting. Promoting the formation of an industrial chain covering the whole process of patent creation, utilization, protection, and management in a competitive market environment is the main policy objective of patent service policy.In order to better verify the accuracy of the model proposed in this study, we invited 20 experts to classify the patent policy topics, which were finally divided into five major types of patent creation policies, patent utilization policies, patent protection policies, patent management policies, and patent service policies, including 19 sub-categories and 55 policy topics.The topic contents obtained by the three methods were refined, summarized, and divided into 55 subclasses under five major categories. Then, the accuracy rates under different topics number selection methods were calculated according to the classification results, as shown in In this study, we propose the coincidence index based on the perplexity, isolation, and stability, and construct a method for optimal topic number selection of the LDA model. The method is a comprehensive evaluation of the optimal number of topics based on four aspects: the topic model has high predictiveness, there are no duplicate topics among individual topics, the model has repeatability, and each topic has high explanatory power, which is more accurate than the existing methods of judging the optimal number of topics by perplexity or isolation. It can help analysts perform effective and accurate topic extraction in a large amount of text.To better verify the feasibility of the method proposed in this study, our proposed optimal topic selection method is compared with several commonly used methods using three generic datasets, 20news_groups, WOS_46986, and AG_news, in the empirical part. It is found that our proposed optimal topic selection method has better topics selection results. In addition, we use the real data of the patent policies of each province and city in China  for further verification and analysis. According to the method proposed in this study, 54 topics are finally obtained. Compared with the results of the experts’ classification of patent policies into 5 major categories, 19 sub-categories and 55 subclasses, 49 topics of the 54 topics selected in this study can correspond to the experts’ classification, and the remaining five for the corresponding topics can also match with the sub-categories. Although the topic selection method in this study is applied to the LDA model, the principle can be extended to other topic models.The method proposed in this study to determine the optimal number of topics for LDA has some practicality; especially when dealing with a large number of texts and a large number of topic classifications, the method has high accuracy and reliability. However, there are still some limitations in this study. First, during the experiment, we found that the deletion of stop words will have an impact on the distribution of words under each topic, and different researchers may have different treatments on the stop words, resulting in subjective bias, which can be improved and studied in the future. Second, some lexical information was not considered in this study for text processing and topic generation, but this information may affect the connotation of the topics, so lexicality and word-associated meanings can also be considered in future studies. Third, due to the natural drawback of the original LDA topic model, it cannot divide well for topics that are too similar. This leads to the fact that even though we were able to pick a relatively optimal number of topics, we did not achieve a result that is consistent with the true number of topics. Therefore, we also validate the use of our proposed method on the word-embedding LDA model, and it turns out that the optimal topic number selection method is also applicable. Since the word-embedding LDA model is better for topic classification, our final selected model is also able to better classify documents by topics. We also found through the literature collection that many works have been done by scholars in improving the accuracy of LDA topic models: for example, the Gaussian LDA model proposed by Das et al. based on the word-embedding technique  and the