Abstract
What steers evolution? The answers are not clear at cellular and molecular levels in a perspective of biomedical infophysics today.
In this article, we define memory as stored information (SI) that can be remembered and recalled to respond to other memories or information; a cell as a memory unit; DNA genes, mRNA, proteins and other cellular components as sub-memory units.
Correspondently, we define inherited memories (IM) as that obtained through genetic procedure (e.g., cellular fertilization, division or proliferation) and acquired memories (AM) as that obtained from the extra cellular environments (e.g., external DNA, RNA, proteins or other components); the memory intensity (MI) as stored information intensity (SII), such as the electric field intensity (EFI) and the gravitational field intensity (GFI); memory response intensity (MRI) as stored information response intensity (SIRI), such as forces or energies.
We define three types of sub-cellular memories: the static are stored in genes (sets) in DNA strands, the dynamic are stored in RNA (sets) and the functional are stored in proteins (sets). We think memories include spatial and temporal fields or virtual particles, such as the electric (major), magnetic (minor) and the gravitational (inconsiderable), as well as the structured matters (represented with charges and masses).
We classify cellular stabilities as inner and external cellular stabilities. We define, inner cellular stability as inheritance fidelity of DNA genome in divided cells, external cellular stability as contact inhibition of divided cells; a complete stability means the both inner and external stabilities are satisfied; controllability as that normal parent cells are divided into normal children cells; convergence as that the final divided cells become the differentiated and (or) apoptosis (programmed death) or necrosis. The programmed death is electromagnetically or mostly electrically encoded.
Based on the definitions, our previous works and published data, we propose our memory and control models of Evo-Geno and Evo-Devo (evolutionary genome and evolutionary development) of species. We assume the correspondent environments (including nutrients) in the two reference frames of Evo-Geno and Evo-Devo are (almost) the same or similar and the correspondent memory sets are also (almost) the same or similar. Therefore, we hypothesize; the recalling orders of cellular memory sets during human Evo-Devo are the same as the remembering orders of cellular memory sets during human Evo-Geno. I.e., the first remembered memory set is first recalled; the second remembered memory set is second recalled; and the last remembered memory set is last recalled; for the transcription and the expression. The cells memories remember the orders.
Introduction
What steers evolution? All the theories trying to answer this question involves three aspects of pattern, mechanism and process of evolution [1-2]. In 1828, Von Baer reported, I have two small embryos preserved in alcohol, that I forget to label. At present, I am unable to determine the genus to which they belong. This could be the first connection of both embryo pattern and genus development together. It could be the start of Development Biology. Then Karl Ernst Von Baer proposed four principles, Von Baer' s law [3], but refused natural selection proposed by Darwin (main) and Wallace (only) [1].
Then Ernst Haeckel formulated his controversial theory as "Ontogeny recapitulates phylogeny" in 1866 [4-6], based on the comparison between embryonic developments of different species and the theory of the evolution [6-11]. The notion later became simply known as the recapitulation theory.
It is no credible evolutionary mechanism in 1866, post-origin pattern recapitulation: quite wrong to turn into pattern into a law [1]. From 1980 to present, it has been Modern Era of evolution. In 1980s, it was time of Evodevo, evolutionary developmental biology (genetics) taxa phyla. Evolution now has been studied on three levels [2]: at gene level, by mutation; at organism level, by repatterning; at population level, through selection. Gene studies have showed: the deflection of a developmental trajectory over all or any part of its course caused by mutation in one or more of the genes that help to control the direction that the trajectory takes. Co-option: the evolutionary process in which something (often a gene or group of interacted genes) that starts off with a particular role and ends up acquiring a new role either as well as or instead of its original one [1]. That means an existing gene for a new function is easier than producing a new gene [2].
However, what is between pattern and mechanism? The process is also a big question. In this paper, we reexamined the Ernst Hackle's controversial theory "Ontogeny recapitulates phylogeny". We agree he was wrong to turn into pattern into a law. But it is interesting to questions: why are there these patterns? Why are the patterns similar to at embryo stages and different from in adults? What mechanisms are behind these patterns? How to form these patterns? What are relationships between the genome variation, phylogenetic (specie) evolution and ontogenetic development? The answers are not clear at cellular and molecular levels in a perspective of biomedical infophysics today, although many significant models have been proposed to describe regulation, differentiation, or interaction with the environment [12-20].
In 1859, Charles Darwin published his book of evolution? The Origin of Specie By Means of Nature Selection. He understood that adaptation was essence of evolution [11].
In 1953, Watson JD and Crick FH proposed molecular structure of nucleic acids that is a base of genome [21-22].
In our previous studies of biomedical infophysics [23], we modeled the inherited information: replication, transcription [24-25] and expression of genes [26-27]; and the acquired information: long and short terms of memories stored in proteins or other ionic objects [28], by studying exchanges of cellular information, energy and matters with the extra cellular environments. We also modeled cell division and proliferation [29-33], and pronuclear movements in fused eggs of fertilization [34]. These models are involved in nature adaptation and selection at molecular or cellular level with classic or quantum statistical mechanics, Newtonian mechanics and electromagnetism. The polymerases work like statistical and mechanical filters to select adapted particles for the replication, transcription or expression.
Additionally, we defined information as an attribute (property) of an object. The object can be ether actual (rest mass and size are not equal to 0) or virtual (rest mass and size are equal to 0; e.g. a photon). The attribute can be ether a form or content. The form can be ether a behavior or a pattern (or structure) data. The behavior can be ether active (a method) or reactive (an event). The pattern data can be ether spatial (frequency) or temporal (frequency). The content can be a children object, an element or a component. We also consider both mass and charge as important properties or attributes of matter and specific or special information of an object [23].
To associate information, energy and matter originally and systematically, we defined our information framework [23] as the following:
Information Intensity (II): a strength of information, e.g., electromagnetic field (EMF) intensity (EMFI), electric field (EF) intensity (EFI), magnetic field (MF) intensity (MFI) or gravitational field (GF) intensity (GFI).
Information Response Intensity (IRI): strength to respond to information intensity, e.g., interactive forces (or energies).
Positive, Negative or 0 Information Recognition (IR): the interactive force (or energy) between two objects is respectively repulsive, attractive or 0.
We think information is, stored in structured (moving) matters (attributes: charges or masses) (senders or producers), transmitted with II in a media (an information transmitter) on events, following an information transmitting function (method) and recognized or responded with IRI by other structured matters (receivers or responders) on events.
Because EMF or EF play much more important roles than GF in most biomedical cases, we often investigate EMF or EF signal (object) to elucidate our information framework and ignore GF.
Continuing our previous works, in this article, we propose our memory and control models of Evo-Geno and Evo-Devo (evolutionary genome and evolutionary development) of species, biological cellular and sub-cellular memories, remembering, recalling, addressing, accessing and controlling the memories. We derive equations to describe related fertilization, division and proliferation of cells, production and reduction of genes. We model the optimum control of biomedical information flow and the optimum path for a cellular component motion too. We also compare models of the simplest and the most complex eukaryotic division, proliferation and differentiation: dictyostelium discoideum and human cells [35-36], in a perspective of Evo-Geno and Evo-Devo.
Methods
We use electromagnetism, cellular and molecular biology; transformations or mappings of events and 4 dimensional (4D) space - time coordinates [37] from human Evo-Geno reference frame to Evo-Devo reference frame; discrete mathematics [38] and numerical analysis [39]; computer science; Newtonian mechanics; analytic mechanics ; and the modern adaptive and selective control theory [40-44].
Our models in this paper are based on published biomedical data [35-36, 46-49] and infophysics [23-34, 45].
Models
3.1 Memories of Evo-Geno and Evo-Devo of Species
In this article, we continue our previous works of information framework [23-34]. We define, memory as stored information (SI) that can be remembered and recalled to respond to other memories or information; a cell as a memory unit; DNA genes, mRNA, proteins and other cellular components as sub-memory units. The same as information, memories include spatial and temporal fields (virtual particles), such as the electric (virtual photons, major), the magnetic (minor) and the gravitational (gravitons, inconsiderable), as well as the structured matters (represented with charges and masses).
Correspondently, we define inherited memories (IM) as that obtained through genetic procedure (e.g., cellular fertilization (fusion), division or proliferation) and acquired memories (AM) as that obtained from the extra (cellular) environments (e.g., external DNA, RNA or proteins); the memory intensity (MI) as stored information intensity (SII), such as the electric field intensity (EFI) or virtual photons and the gravitational field intensity (GFI) or gravitons; memory response intensity (MRI) as stored information response intensity (SIRI), such as forces or energies.
We define three types of sub-cellular memories: the static, the dynamic and the functional (or working). The static are stored in genes (sets) in DNA strands, and they are and remain almost the same for most cells as long as the cells are normal. The dynamic are stored in RNA (sets) and (at least) not completely the same for different cells and the averaged life span is from 10 minutes to two days for mammals. The functional are stored in proteins (sets), and they are the major working memories. Different cells or proteins have different functions [35–36].
Complex memories often occur, such as ribosome and nucleosome. Fig.1 illustrates our models of the static and (or) the functional memories (intensities or response intensities); Fig. 2. is about the dynamic and (or) the functional memories, based on molecular data [35-36], the above definitions and our previous published biomedical infophysics models [29–33].
Cellular memory components (objects) are mostly remembered, recognized or interacted with the memory response intensities (MRI). The remembrance or recognition can be positive, negative and 0 based on the forces or energies [23-28].
A cell inherits its parent(s) memories and exchanges information, energy and matters with its environments and dynamically produce the functional memories (proteins) to remember where, when, how and what to do. At a cellular level, a cell works like a microcomputer; at a sub-cellular level, cellular plasma woks like central processing units (CPU); at a molecular level, proteins, especially, the polymerases, work like adders. A cell and its components conform themselves to build up an optimum space – time electromagnetic fields or memory intensities (MI) with their limited charges to perform the most useful and efficient functions, such as replication, transcription and expression of genes. The information processing is mostly based on electromagnetism, such as Maxwell equations and Poynting theorem, as well as signal theory, such as auto and cross correlation, filtering of frequencies or energies [23-28].
We think the electromagnetic fields intensity (EMI), especially the electric field intensity (EFI) are major instruction signals and play the most important roles in addressing, controlling and accessing the cellular and sub-cellular memories; and the addressing (including selecting), controlling and accessing (i.e., data) buses are combined or mixed into one working bus: intra or extra cellular fluids (electrolytes). Therefore the working mode is efficient, simple and elegant.
Equations 1 to 4 and Fig. 3 and Fig. 4 show how the memories are located and addressed (or selected), controlled and accessed in a perspective of computer science, electromagnetism and Newtonian mechanics [23, 28]. The methods are equivalent to Hamiltonian principle and analytic mechanics, see section 3.5. The cellular EFI Et(r, f, b, t), mechanical and viscous forces locate, address, control and access the cellular and sub cellular memories. The components are either electric or induced electrically, and naturally locate at or move to the most stable and ordered states. If they are in unordered and or unstable states, abnormal embryonic development could occur. For a fertilized egg, the divided multiple units (a fate map [35]) of cellular plasma contain specific and initial (or early) components, such as proteins (regulators, hormones, growth factors, enzymes) and RNAs for the specific and initial (or early) divisions or cleavages, determine the future cellular differentiations and functions, see Fig.3. We think the modeling principle is suitable to other biological cells too.
We define some instruction addressing of biological signals. Immediate addressing is direct, the signal instruction itself contains the target memory address, such as ion channel currents of Ca++, Na+, K+, …, the ion signals immediate perform some function after they interact their targets. Registering addressing is indirect, the signal instruction itself does not contain the target memory address, but some registers do, such as gene regulators and RNA polymerase II contain the target memory address for beginning sites of mRNA transcription, where we define some cellular components as registers.
The memories interact or exchange information, energy or matter with the extra and intra environments. The working buses are respectively the continuum in the intra and extra cellular fluids (electrolyte media) and the discrete transports in the cellular membrane; and they are the combination of data, control and address buses. Usually, DNA and RNA are equivalent to read only memories (ROM); proteins are equivalent to random access memories (RAM) [23, 28]. A chromosome is equivalent to a database or data warehouse. See Fig. 4.
A mitochondrion is equivalent to a power plant that provides energies for the cellular activities. It also releases cytochrome C to induce cellular apoptosis [35-36].
Oscillation of cellular electric charges or filed and vibration of cellular membrane produce periodic exchanges of information, energy and matters across the cellular membrane by the membrane transporters. The oscillation and the vibration are approximately synchronous and work like a crystal clock for the cellular microcomputer as well as like a biological clock [23, 28, 45].
Based on the definitions, our previous works [23-34] and published data [35-36], we propose our memory and control models of Evo-Geno and Evo-Devo of species, using transformations or mappings of sets of cellular memories, events and the related environments in correspondent 4 dimensional (4D) spatial and temporal coordinates from human Evo-Geno reference frame to human Evo-Devo reference fame, see Fig. 5. We agree with that the species evolution is the genome evolution (Evo-Geno) [35]. Significant variations of germ chromosomes (genome) play important roles in production of new species.
Within our transformations or mappings, we assume the correspondent environments (including nutrients) in the two reference frames are (almost) the same or similar and correspondent memory sets are also (almost) the same or similar. Evo-Devo is serialized in order of Evo-Geno.
Let a cellular event set e’ of remembering memories occur in environments of 4D space – time reference frame coordinates: t’, x’, y’, z’, during human Evo-Geno, see Fig. 5. We map the event set and the related environment to a cellular event set e of recalling memories in correspondent environments of 4D space - time reference frame coordinates: t, x, y, z, during human Evo-Devo. The mapping between human 8th week embryo and the chimpanzee is based on the published data of the brain capacities [46, 47]. The mapping between a today’s human child of 3 years old and homo sapiens in the middle stone age is based on the published data of the language abilities [48]. The mapping between today’s a human child of 6 years old and a homo sapiens in the bronze age is based on the published data of the writing abilities [49]. Other mappings are based on published data between forms (patterns) of the embryos [4-11, 35]. From the figure, we can see about 1.4 billion years of Evo-Geno from a eukaryote to chimpanzee (human’s closest species) only maps about 8 early weeks of human Evo-Devo. The most significant differences between human and animals are located in the evolutions of the brains. It is well known that human brains are developing until about 21 years old after the birth.
We approximate the mapping relation R(t, t’) or time transformation as equation 5. Obviously, the time duration of Evo-Devo is relative and contracted compared with that of Evo-Geno.
Because the spatial difference, in the two frames, is not significant compared with the temporal difference, we approximate the spatial transformations or mappings to be invariant to simplify our models.
Fig. 6 illustrates our assumed regulations (regulatory bindings), transcriptions and expressions of cellular memory sets, during human Evo-Devo. If we replace the subscript letters with the correspondent capital and map the time coordinate from t to t’, we obtain similar results during Evo-Geno, see the mappings in Fig. 5. The serial procedures ensure the necessary regulators must preexist before transcribing the target gene sets during Evo-Devo as well as during Evo-Geno. For instance, the required regulators, transcribed Ra and inherited or inserted Ra,i, must preexist at the fish age before transcribing the target gene sets at the amphibian age.
Therefore, we hypothesize, the recalling orders of cellular memory sets during human Evo-Devo are the same as the remembering orders of cellular memory sets during human Evo-Geno. I.e., the first remembered memory set is first recalled; the second remembered memory set is second recalled; and the last remembered memory set is last recalled; for the transcription and the expression. The cells memories remember the orders. See Fig. 7. Of cause, it follows the dissipative structure theory [50] that the organisms evolve more and more in orders, i.e., more negative entropy; some genes are not transcribed and expressed if they are inhibited.
3.2 Division (Cleavage), Differentiation, Fertilization (Fusion) of Cells
We think the cellular and sub-cellular memories are absolutely variant and relatively covariant (variance with the same or similar patterns). We consider every cell as a memory (holder, or retainer): cells inherit memories from their parents and acquire memories from their environments to build up and hold their memories for their children cells. The memories are most electric in nature. The electric forces play an important role in positioning the cleavage plane of mitosis or amitosis [23, 29-30].
In the topic of gene transcription and expression, the functional memories are mostly regulators, repressors and polymerases. The memories remember where, when, how and what (genes) to transcribe and to express.
We use capital C to denote a cell memory set that is composed with sub-memory sets: chromosomes (genome), RNAs, proteins, other components (such as ATP, glucose, inorganic ions, …) in cellular plasma, et al. Because the components, genes, mRNAs, polymerases and general factor proteins, such as activators, (master) gene regulators and repressors, et al., are most important to transcription and expression [35-36] during human Evo-Geno and Evo-Devo, we focus on the components, genes, mRNA and proteins in the sets and omit others to simplify our models. We represent the generations of cells in an iterative algorithm of numerical analysis [39] and terms of discrete mathematics [38], see equations from 6 to 33.
There are totally 2k descendents after k divisions (cleavages). All sets of divided cells and their components should be in an ordered relation and usually satisfy stability, controllability and convergence.
We classify cellular stabilities as inner and external cellular stabilities. We define, inner cellular stability as inheritance fidelity of DNA genome in divided cells, external cellular stability as contact inhibition of divided cells; a complete stability means the both inner and external stabilities are satisfied; controllability as that normal parent cells are divided into normal children cells; convergence as that the final divided cells become the differentiated and (or) apoptosis (programmed death) or necrosis.
The programmed death is electromagnetically or mostly electrically encoded. The division or proliferation procedure continue until the final cells become the differentiated and (or) apoptosis. Nutrients and environments play important roles in cellular fertilization (fusion), differentiation or proliferation.
We think, in nature: the complete stability is equivalent to the controllability; normal differentiated mature neuron and red blood cells are convergent; normal epitheliums are stable or controllable; tumor or cancer cells are not stable, nor controllable and nor convergent. We think one of major problem for a tumor or cancer cell is that it can not synthesize enough related proteins in time to perform contacting inhibitions, i.e., when speeds of the translating proteins for essential and sufficient contacting inhibition are slower than that of replicating DNA, tumors or cancers could happen.
The published data of the miss pairing probability of DNA synthesis is from 10-6 to 10-9 [35]. The mutation is a source to induce tumor or cancer cells as well as to produce new genes. According to our previous quasi quantum statistical mechanical studies [23-25] to parametrically fit the published data, encoding error is normal and natural, 100% fidelity of DNA replication is abnormal and unnatural [24]; divisible cells finally become tumor or cancer cells if they are not apoptosis (programmed death), see Fig. 8. Therefore, apoptosis is one way to prevent or to cure the diseases.
See Fig. 8: (a) is a simplified illustration of maintain and production of human phylogeny at cellular level (Evo-Geno); (b) is a simplified illustration of maintain and reproduction (life cycle) of a human at cellular level during Evo-Devo. We classify biological cells as the germ cells and nutrient cells. When ontogenetic developments are normally complete, the subjects become adults and have reproductive capabilities. At a cellular level, it means mature germ cells genetically obtain rebirthing functions for themselves and nutrient cells. After successful fertilization (equation 33a), the next generation occurs. Obviously, germ calls and fertilized eggs are the most important cells to maintain and to produce species, nutrient cells help or support germ cells to accomplish the continuation of lives.
Mutation of DNA is natural and must happen as long as cellular proliferations occur according to our previous quantum mechanical analysis [23-25]. Therefore, when the mutation reaches a threshold, a cancer or a tumor naturally and must occur.
3.3 Production and Reduction of Genes
In the same way as the above, we can describe a formula to produce or to reduce a gene (static memories) in DNA strands. See equation 34.
If a new gene (set) for a new species is produced in germ cells, mostly during meiosis, in an Evo-Geno reference frame coordinate system, the new gene (set) can be transcribed and expressed in the decedent generations in an Evo-Devo reference frame coordinate system when the essential and sufficient conditions are satisfied. If the new species is adaptive to the environments, it will be naturally selected to survive.
3.4 Optimal Control of the Inherited Memory (Information) Flows
Fig. 9 illustrates our models of optimal control of the inherited memory (information) flows: from the static DNA to the dynamic mRNA (a) and from the dynamic mRNA to the functional proteins (b), in a view of biomedical infophysics. The memories (information) flows are involved in interaction between the inherited and the acquired memories (information) and are controlled with adaptation and selection at nuclear (a) and cellular (b) levels. Where, the adaptation is equivalent to the optimization; the selection is equivalent to the robustness: to attract specific (complementary) particles and to repulse the others, to minimize the encoding (memory) errors. We believe the nervous, endocrine, cardiac vascular, meridian and lymphatic systems play important roles in the interactions, the cellular and nuclear regulation with the plasma, especially the proteins (functional memories) such as polymerases and regulators, play important roles. We assume the physics equations of the adaptation and the selection are mostly classic or quantum statistical mechanics. The polymerases for the replication, transcription and expression mechanically filter the particles [24-27].
3.5 Optimum Path of Cellular Component Motion
We think the variation principle of least action of analytical mechanics is more understandable to elucidate states of natural adaptation and selection of the evolution at cellular and sub-cellular levels. Therefore, we use the (extended Hamiltonian) variation principle of minimum action [40], extended Lagrange functions [41], the related constraint (or state) equations and the modern adaptive and selective control theory [42-44] to construct our models of cellular component motions. See equations from 35 to 39. The methods are equivalent to that of computer science and Newtonian mechanics [23, 28], see section 3.1.
Fig. 10 illustrates, with the principle of least action with free ends constrain, an optimum path of that an RNA polymerase II is binding a beginning site on DNA with gene regulators. The functional memories (regulatory proteins) remember where, when, how and what (static memories: genes) to bind and to transcribe (dynamic memories: mRNA). We draw only three possible paths in the figure for a clear illustration. The middle path is our assumed selected one. Models in this section and our previous published models of genetic information flow [23-27] describe natural variation, adaptation and selection of evolution at cellular and (or) sub-cellular levels.
3.6 Comparison of Eukaryotic Reproduction, Proliferation and Differentiation between Amoeba and Human
Fig. 11 illustrates the simplest eukaryotic (dictyostelium discoideum) reproduction, proliferation and differentiation, and interaction with natural environments. The eukaryotes aggregate together when nutrients are rare. Surface of the aggregated cells is much smaller than that of discrete ones. Based on equation 39, therefore, to aggregate can save a lot of heat; it is benefit to survive for the species in the wild and hard environments.
Fig. 12 illustrates the most complex eukaryotic (human cells) reproduction, proliferation and differentiation, and interaction with environments. The environments are often inside (at least partially) human bodies. The environments inside human bodies are optimum, for the cells, to obtain sufficient nutrients and consistent states, such as temperature.
We approximately consider the model in Fig. 11 is involved in event sets of remembered memories and related coordinates in a human Evo-Geno reference frame and the model in Fig. 12 is involved in event sets of recalling memories and related coordinates in a human Evo-Devo reference frame. There are correspondent mappings between the two frames, see Fig. 5.
Discussion
We believe our models in this investigation are helpful to understand the mechanisms of cellular or biological memories as well as evolutionary genome and developments. Therefore, our models are meaningful to prevent or to cure related diseases.
Concepts of memory and information are different, but they are related. Which concept to use depends on research topics. In this investigation, we use the concept of memory because we respectively focus on remembering and recalling information of genome during Evo-Geno and Evo-Devo. In our previous studies [23-34], we used the concept of information because we focused on encoding, decoding, filtering, transmission, transformation or interaction of signals or informative objects.
The static and the dynamic memories have also some functions, even the functions are weaker than that of the functional. The concepts of the memories have meanings of remembrance as well as information.
We think a variable structure control model [42] is also suitable to sliding and binding of polymerases on DNA or mRNA. However, we think the model is too simple to describe the spatial and temporal pattern recognition, adaptation and selection; oppositely, our model in this paper is more suitable for this study. We also consider the structure concept includes the conformation concept in this paper.
In this investigation, we introduce some important concepts of Einstein’s relativity into our models. Such as natural laws are invariant or covariant in deferent reference frame, space - time transformations (mappings), 4D reference frame coordinate systems, time contraction, conservation [37]. However, the concepts in our models are not exactly the same as that of the relativity.
We can only propose our models and model the state equations in formula today. Future study could be quantitative.
Conclusion
Our models of Evo-Geno and Evo-Devo demonstrate the recalling orders of cellular memory sets during human Evo-Devo are the same as the remembering orders of cellular memory sets during human Evo-Geno. I.e., the first remembered memory set is first recalled; the second remembered memory set is second recalled; and the last remembered memory set is last recalled; for the transcription and the expression. The cells memories remember the orders.
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Correspondence
E-mail: kangcheng.1@netzero.net and huaz1@netzero.net. The both authors make the same contribution.
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Selves
Competing Interests
none
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