Towards a collective biology of the gene

J. theor. Biol. (1987) 126, 127-136

Towards a Collective Biology o f the Gene JULIAN C HELA-FLORESt

International Centre for Theoretical Physics, Trieste, Italy and Physics Department, Universidad Simon Bolivar, Caracas, Venezuela (Received 19 December 1985, and in finalform 17 November 1986) Two features of heterochromatin: heteropycnosis (high values of chromatin condensation), and repressed genetic expression, force upon us the use of cooperative variables, rather than molecular ones. In particular a "repressor" hypothesis is formulated, in which a useful parameter is clearly identified. This enables us to discuss the synchronized repression of a large number, n, of genes (as in the case of the Burr body, in which n is larger than 100). The hypothesis is documented with phenomena known to occur in active chromatin. Possible tests are suggested.

1. Ideas and Concepts (A) INTRODUCTION

A satisfactory answer is still awaited to the question of why h u m a n females do not code for twice as many proteins controlled by a given locus on the X-chromosomes as c o m p a r e d to males. In other words, the origin of such "dosage compensation" of the X-chromosomes is still a puzzle (Sharat-Chandra, 1986). However, several important contributions come from the work on human sex chromosomes (Barr, 1959), on abnormalities in relation to D N A replication (Yunis, 1965), and in heterochromatization (Brown, 1966). First of all, early experiments ( G r u m b a c h et aL, 1963) found that five individuals with extra X-chromosomes have one X which replicates with the majority of the complement, while others replicate late. This implies that the late replicating Xchromosomes are heteropycnotic (i.e. they are in a highly condensed state) in interphase, and perhaps more significantly, that their genetic expression is repressed. A second contribution (Lyon, 1961) has been to establish a relationship between D N A condensation and metabolic inactivation of an X - c h r o m o s o m e (Xi, inactivated), out of the two available in normal females (the active one is denoted by Xa). This "'silencing" of the X~-chromosome occurs early in embryogenesis and is remarkable since there are over one hundred loci on this chromosome, which measures some 154 million nucleotide pairs. The Xi's are the Barr bodies, which are seen adhering to the nuclear m e m b r a n e of many cells (Barr, 1959). A third experimental observation throwing some light on the question of the silencing of X~ is the work on the reactivation of X-chromosomes (X~ ~ X~), which is known to occur during ontogeny of oocytes, since the asynchronous D N A synthesis (which characterizes the silent human X-chromosome), in fact switches on to early D N A replication (Migeon et al., 1986). t Also at Instituto Internacional de Estudios Avanzados, IDEA, Caracas, Venezuela. 127 0022-5193/87/100127 + 10 $03.00/0

O 1987 Academic Press Inc. (London) Ltd

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The above remarks lead to some unanswered questions, prominent amongst which are: (i) What is the mechanism of X-chromosome repression? (ii) Why does Xi replicate asynchronously, i.e., later than the Xa chromosome, as well as the autosomes? We feel that some of the above mentioned facts may help to answer these questions, provided they are interpreted with the help of quantum mechanics. However, since this important subject has not been called upon in molecular genetics at present, we pause to introduce the background against which some progress may be possible (preliminary results on the question of trisomy in humans are an encouraging sign that quantum mechanics may indeed lend some support to research in genetics (Chela-Flores, 1986)). (B) M O L E C U L A R

BIOLOGY

IS B A S E D O N M I C R O S C O P I C

QUANTUM

MECHANICS

The seminal contribution of deciphering the detailed chemical nature of B-DNA (Watson & Crick, 1953) requires concepts of quantum mechanics which lie entirely within the domain of atomic and molecular physics, typically of microscopic nature (atomic orbitals, chemical bonds). The essential aspects of these concepts were well understood in the 1930's; in fact, the very influential summary of research on the chemical bond was first published in 1939 (Pauling, 1960). Parallel to these developments, at about the same time, London took an important step forward by pointing out that some quantum modes may be macroscopically o c c u p i e d - - a phenomenon sometimes referred to as "condensation" (London, 1938; Chela-Flores, 1975, and references therein). Since that time several phenomena have been understood as manifestations of macroscopic quantum mechanics (MQM): the helium superfluids, superconductivity in metals and alloys, neutron star interiors, the spectra of even-even nuclei, the Josephson effect, and the quantized Hall effect. In all of these phenomena a common feature is the stability of the ground state. In spite of these significant contributions, present efforts in molecular biology are confined within the bounds of microscopic quantum mechanics (mQM). A special point requires further attention: these works in MQM show that nature seems to grant condensed matter the capacity to stabilize its ground state by a variety of mechanisms. The essential point is not what the nature of the mechanism really is; not even which are the particular excitations; but, rather, the underlying t h e m e - with relevance to genetics--is that there is an intrinsic impediment to deplete the ground state. We shall illustrate this specific point in the context of a hypothesis in which the ground state of a whole chromosome (Xi) will make use of such an impediment in order to repress gene expression and thereby provide a mechanism for achieving the necessary dosage compensation for all the somatic cells of female mammals beyond the third week of gestation. The rest of this work is laid out as follows: In section 2 a case is presented for the usefulness of the concept of a "gap parameter" when applied in the context of the living state, rather than in its normal quantum mechanical application in the solid or liquid states. We argue that this

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MQM parameter occurs in chromosomes by means of biochemical modification in the chromatin molecular components. These suggestions are formalized, in section 3, in terms o f a "repressor hypothesis", in which the gap, or repressor parameter A, is introduced; some support is given in section 4. In section 5 the closely related hypothesis of Lyon (1961) is discussed in terms of A. Some tests of the repressor hypothesis are suggested. Finally, the work concludes in section 6 by pointing out the main advantages of collective, rather than molecular genetics.

2. Potential Use of New Macroscopic Quantum Mechanical Concepts in Genetics (A) T H E T R A N S L A T I O N

PROCESS

RESPONSES

REQUIRES

A PROGRAMMED

SET OF CHROMOSOME

IN THE FORM OF EXCITATIONS

Multiple steps are needed in order to translate the coded information from the DNA codons into proteins: these are assembled in the cytoplasm on ribosome sites, by the action of aminoacylated tRNAs, which induce the elongation of polypeptides into full proteins. The translation process, summarized in the standard genetic code, requires that chromosomes may respond to the inflow of the available metabolic energy Em by various physiological changes. It may be instructive to illustrate some specific examples of such changes in the components of chromatin (histones and DNA; the role ofnon-histone chromatin proteins, such as methylases and highly mobile groups, HMG, are omitted, for simplicity): (i) Acetylation of histones This process renders the template more accessible to external factors (Karp, 1984). There are some enzymes in nuclei (acetylases and deacetylases) capable of adding or removing acetyl groups from the amino group of a given lysine residue of the core histones. The net effect of acetylation is to neutralize the positive charge of the lysine residue, thereby decreasing the coupling of histone and DNA: this is an example o f what we call in this paper a decrease in density p of chromatin; the more frequent expression "'decrease in D N A condensation" is not often used, so as to avoid confusing the reader with the quantum mechanical concept of condensation (cf. section 1 above). Such a decrease of chromatin density, therefore, prepares the chromosome for enzymatic action, as for example the action of RNA polymerase, or DNAase I, II, or III. It is also well known that hormones that induce an increment of genetic activity underlie an associated increment in the level of histone acetylation. We may then conclude that the evidence arising from histone acetylation suggests a relationship between a decrease in chromatin density and an increase in genetic expression. (ii) Ubiquination of histones The extent of ubiquinated H2A histones (uH2A) varies with the state ofchromatin, with high levels in regions undergoing active transcription (these levels may reach

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up to 10% of the H2A molecules of the cell). Ubiquitin is a 76 amino acid protein (Bond & Schlesinger, 1985). uH2A disappears during each mitosis, as the chromosomes increase their density, i.e. as they condense. (iii) Methylation o f a given base in a D N A molecule This biochemical process consists of modifications of chromatin by the addition of a methyl (--CH3) group to a given DNA base. This yields an inverse proportionality between the extent of methylation of a gene and its activity in transcription (Felsenfeld & McGee, 1982). However, this result is only clear for housekeeping genes, but methylation within genes that are expressed in a tissue specific manner, has no evident mechanisms that the genome uses for regulating gene expression, the general trend (at least in housekeeping genes) being that undermethylation facilitates gene expression.

(B) T R A N S C R I P T I O N : T I l E F I R S T S T E P I N T H E T R A N S L A T I O N O F T H E G E N E T I C M E S S A G E

The main insight provided by studies of D N A sequences which are rich in unmethylated dinucleotides CpG, the so called CpG-rich islands (Bird, 1986), is that methylation may be a secondary event following primary inactivation by other mechanisms, serving in this manner to imprint inactivity. Many inactive genes reactivate simply by artificial demethylation. This, in turn, suggests that methylation is an impediment to transcription, although the way in which this occurs remains unknown. These biochemical processes illustrate that there is a correlation between them and gene expression, which is worth pursuing. This we propose to do by introducing collective variables, so that some aspects of gene expression may be addressed without having first to decide which specific biochemical modification of one of the chromatin components is of primary, or secondary importance.

(C) T O W A R D S A C O L L E C T I V E B I O L O G Y O F T R A N S C R I P T I O N

We are thus led to suggest that inactivity of genes may be viewed to some advantage not only by questioning the molecular detail of the specific biochemical modification of the chromatin component, but rather by focussing attention on the process of DNA condensation itself. This remark may be clarified as follows: In their homeostatic equilibrium chromosomes adopt specific conformations, which we call their "ground state". Such conformations require a certain amount of energy in order to change the tertiary structure of the histones, or DNA. We can express this situation by stating that before the chromatin components can rearrange themselves (so as to favour, or inhibit gene expression), a certain minimum amount of metabolic energy--a threshold energy A--must be reached. The changes in tertiary structure of the histones (as well as non-histone proteins), and DNA lead to a change of chromosome structure, which we call a "chromosome excitation" or an excitation in the chromosome ground state.

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This completes the phenomenological picture of chromosome responses to the multiple metabolic pathways to which it is subjected. The dynamical changes which are evident in microphotographs of the various stages of meiosis or mitosis may be expressed by saying that the lowest excitation (i.e. the change in conformation achieved by the minimum amount of metabolic energy required in order to overcome the energy threshold A), is separated from the chromosome ground state by an energy gap, or repressor parameter A. As an illustration we may point out that one of the processes contributing towards the gap, or repressor parameter, is the activation of demethylases, for which a finite amount of energy is required in order to switch on an inactive (hypermethylated) gene. However, other factors may be relevant as, for instance, the finite amount of energy required to activate acetylases, hence decreasing the D N A condensation. This, in turn, has the effect of lowering A. Further contributions to A could arise from, for example, ubiquination or phosphorylation. The potential use of the repressor p a r a m e t e r - - a new macroscopic quantum mechanical concept in the context of genetics--will be evident when we return to the problem of the mechanisms underlying the two aspects of heterochromatin: heteropycnosis and genetic repressed expression; we turn our attention to this topic in the following section.

3. The Repressor Hypothesis: Physical Basis for Chromosome Dynamics (A) F O R M U L A T I O N

OF THE HYPOTHESIS

When a large number o f genes are involved in the process of inhibition of gene expression (as in the case of the silencing of the X-chromosome: Xa~X~), or in active chromatin (as in the case of the lampbrush chromosome in amphibians, or the reactivation of the silent X-chromosome: X~ ~ Xa, early in the blastoderm stage of embryogenesis), we assume that: (i) There is an energy threshold A--the repressor parameter beneath which chromatin is silent, i.e. gene expression is inhibited. (ii) The repressor parameter depends on the heteropycnotic nature of chromatin (i.e. on the chromatin density p or, in other words, on the degree of D N A condensation).

(B) P R E L I M I N A R Y

DISCUSSION OF THE HYPOTHESIS

As we have seen above, the specific molecular mechanism by means of which transcription is inhibited is not known; in fact, several factors may be relevant, some playing a primary role, and some playing a secondary role. There are distinct advantages in discussing gene inactivation, in terms of the total energy threshold required for the induction of changes in tertiary structure of the chromatin components. Previous experience in physics demonstrates the non-trivial consequences of selecting the appropriate collective variables (Chela-Flores, 1975). The differences

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between living matter, benefiting from a continuous supply of (metabolic) energy-such as the chromosomes--and condensed matter in its solid or liquid states, should not alter the fact that collective variables may, in principle be an asset, at least in the early genes (Chela-Flores, 1985). Part (ii) of the hypothesis was suggested by the Lyon Hypothesis. This aspect will be discussed in section 5(a). The departure from the work of Lyon will be appreciated in section 5(c), when gene expression will be extended from the early stages of embryogenesis to the later stages of neuron differentiation.

4. Facts Found From Experiments

(A) THEORY VERSUS EXPERIMENTS Some further data found from experiments in fact strengthen the proposal of a collective approach to genetics. We delay until later the formulation o f the underlying quantum mechanical-microscopic--theory o f the dynamics of the excitations that give rise to the repressor parameter. At present it is perhaps sufficient to remain at the phenomenological level, i.e., we restrict ourselves to studying the insights that the questions formulated in terms of the repressor parameter allows us to answer. The theoretical study of the specific excitations (unknown at present) giving rise to A is to be undertaken in a separate work, since the methods of quantum statistical mechanics may throw some light on the fundamental question of the temperature dependence of A. Relevant, and exciting, experimental work on heat shock proteins (Munro & Pelham, 1985) might then, in principle, be brought within the scope o f the repressor hypothesis, and hence of the collective genetic approach.

(B) F U R T H E R

ILLUSTRATIONS

OF CHROMOSOME

DYNAMICS

Besides the histone-DNA rearrangements during genetic expression (cf. section 2(A)), there are some further examples of changes in D N A condensation, which are observed in a variety of organisms. Prominent amongst these are: (i) lnterphase chromosome in eukaryotes D N A molecules in eukaryotes may be of the order of 1 cm. They are condensed in the nuclei with the help of histones into a nuclesome N. In particular, the H1 histone stabilizes the arrangements of the Ns into a helical coil of diameter of the order o f 30 nm (Ayala & Kiger, 1984). A second coiling takes place forming a tube of order 200 nm, thus providing small values of chromatin density (p small). (ii) Metaphase chromatid in eukaryotes A larger coil of order 600 nm is formed, leading to high values o f chromatin density (p large).

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(iii) Prokaryotic chromosomes There are circular DNA molecules with circumference of the order of 10 7 ./~. This should be compared with the size of E. coli, which is some 2 x 104 ,~ long and has a diameter of 8 x 103 A. This demonstrates that D N A must be in a highly condensed state (p large). (iv) Meiosis During meiosis I (actually in prophase I) there is a stage called the diplotene, in which a striking reduction in chromatin condensation (p small) is observed (Kimball, 1984).

(C) S O M E S U G G E S T E D

PROPERTIES

From the work in section 1 on the X-chromosomes of female mammals nuclei. Once this change occurs early cell maintain that state (Morishima et

OF THE REPRESSOR

PARAMETER

Barr body, we known that one of the two remains condensed in somatic interphase in embryogenesis, the descendants of each al., 1962). This leads us to the property:

(i) The anomalies introduced by a change in the repressor parameter are faithfully inherited

This property is remarkable, for it shows that no irreversible change of structure has occurred (and passed on to progeny). The change has rather been in the dynamics of the chromatin excitations, which in turn are reflected in variations in the repressor parameter. A second guiding line is also inferred from experiment: heterochromatin, at least in the Barr body, replicates very late in the S-phase of each cell cycle (Morishima et al., 1962). From this observation we propose the identification of a new feature of collective genetics: (ii) The repressor parameter acts as an inhibitor to replication On the other hand, we may further clarify the significance of this work by summarising what we learnt in section 2 (A): (iii) The repressor parameter may be interpreted as an inhibition factor to gene expression

5. Discussion (A) LOCAL AND COLLECTIVE

CONTROL

OF GENE

EXPRESSION

At this stage it is convenient to recall that the local (i.e. restricted to a few genes) control of gene expression is well understood (Jacob & Monod, 1961). This operon theory shares with ours the feature that control is achieved at the level of transcription, excluding the possibility that the main input to genetic regulation is delayed in a eukaryotic cell to a later level: RNA processing of the primary RNA transcript;

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during transport from the nucleus to the cytoplasm; or even during the translation of the mature mRNA by the ribosomes into the amino acid chain of a protein. (B) T H E L Y O N H Y P O T H E S I S

As already stated in section I(A), a relationship between metabolic inactivation of X~ and D N A condensation (i.e., p large) was suggested some time ago (Lyon, 1961). This may be understood as follows: In the diplotene (cf. section 4(B)iV), chromatin is highly active in RNA synthesis, motored by abundant metabolic energy. This tends to decrease the DNA condensation (i.e. to lower the density p) in a remarkable way by expanding to an enormous extent. In the extreme case in amphibians, this leads to the lampbrush chromosomes--already mentioned in section 3(A). From this typical behaviour we infer that low levels of metabolic energy may not be sufficient to ensure the lowering of p in order to guarantee full RNA synthesis. Thus, insufficiency of metabolic energy will underlie large values of p and, according to the repressor hypothesis, this will be recognised in large values of the repressor parameter. On the other hand, larger values of the repressor parameter imply an enhancement in the repression of possible excitations from the ground state (the reader is advised to return to section 2(c) for the elementary introduction of our quantum mechanical terminology). Thus, all the conformational changes that must be driven by enzymes, so as to accomplish normal transcription will consequently also be reduced. In the extreme case this will lead to inactivation. This applies to heterochromatization in general, but, in particular, it applies to heterochromatization of the X~-chromosome. This provides an understanding of the Lyon hypothesis. (C) TESTING

THE REPRESSOR

HYPOTHESIS

The Lyon hypothesis was an important contribution towards gaining a deeper insight into the genetics of developmental biology. As we have already seen in previous sections, heteropycnosis of the Xi-chromosome and gene silencing are assumed to be intimately related at the blastoderm stage in embryogenesis. In contrast to this time-tested hypothesis, in our own approach we have not restricted ourselves to the early stages of development but, rather, that the dynamics o f chromosome excitations may in general be approached profitably in terms of collective genetics. These arguments suggest looking at chromatin structure in various cells, so as to understand the mechanisms for shortening, or lengthening, of linker D N A (as the reader may recall, "linker" DNA is a variable length of DNA which connects adjacent histone cores). A general trend should emerge: chromosome actively engaging in RNA transcription should evidence relaxation of the coupling of histone cores and linker DNA. For example, at later stages of development, in fact at the end of cell differentiation in cortex neurons (which occurs well before birth in humans), increments in the repressor parameter would signal an underlying reduction of gene expression, for

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terminally differentiated neurons. In separate works we propose to discuss these aspects of collective neurogenetics, including experiments performed so far. However, such a discussion lies beyond the scope of this paper.

6. Conclusions By introducing collective genetics in order to supplement standard molecular genetics, we have benefited from a physically motivated hypothesis--well tested in the context of embryogenesis. It has been pointed out, in previous sections, that the main feature of this work is that specific molecular processes (such as the addition of methyl or acetyl groups to chromatin macromolecules) need not be considered in detail. Specific molecular processes would now be considered as contributing towards the overall repressor parameter A. In other words, the general trend of inhibition, or expression, is governed by the collective variable A. Following these lines we have avoided detailed knowledge of macromolecular structure in our discussion of gene expression. This approach is particularly well suited to gene regulation when a very large number of genes are involved. In the long run this may be the most attractive aspect of collective genetics. In this respect we may recall that difficulties have been pointed out regarding the proposal of sequencing the rest of the human genome (Dulbecco, 1986). This underlines the importance of not limiting studies of genetics to molecular biology, since the hurdles to the direct sequencing are many (Robertson, 1986). Our preliminary results suggest a way towards some progress, which is independent of the detailed structural information contained in the complete cellular genome. Useful discussions at earlier stages of this research project are greatfully acknowledged with Professors Tadashi Arai, Antonio Borsellino, Luigi Cavalli-Sforza, Mukunda Das, Fawzi El Fiki, Zygmunt Galdzicki, Norman March, Sergio Mascarenhas, Peter Mbaeyi, Mohan Sapru, Obaid Siddiqi and Fernando Vericat. The author would also like to thank Professor Abdus Salem, the International Atomic Energy Agency and UNESCO for hospitality at the International Centre for Theoretical Physics, Trieste. Finally, thanks are due to ICTP for financial support that made it possible to carry out the present work. REFERENCES AYALA, F. J. & KIGER, JR, J. A. (1984). Modern Genetics, 2nd ed. p. 109. Menlo Park, California: Benjamin/Cummings. BARR, M+ L. (I959). Science 130, 679. BIRD, A. P. (1986). Nature 321,209. BOND, U. & SCHLESINGER, M. J+ (1985). Mol. Cell Biol. 5, 949. BROWN, S. W. (1966). Science 151, 417. CHELA-FLORES,J. (1975). J. Low Temp. Phys. 21,307. CHELA-FLORES,J. (1985). J- theor. Biol. 117, 107. CHELA-FLORES,J. (1986). Modelling chromain Fibers: Insights into Genetic Disorders. In: Proc. Fifth Intern. Conf. on Mechanics in Medicine and Biology, pp+ 333-336. Universith degli Studi di Bologna, Italy+ 1-5 July. DI-ILBECCO,R. (1986). Science 231, 1055.

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