HEAT DENATURATION STUDIES OF RAT LIVER MITOCHONDRIAL DNA : A Denaturation Map and Changes in Molecular Configurations

The effect of progressive denaturation of open circular molecules (component II) and supercoiled covalently closed circular molecules (component I) of rat liver mitochondrial DNA has been followed by heating in the presence of formaldehyde and examination in the electron microscope. After heating at 49°C, two, three, or four regions of strand separation were visible in 25% of the component II molecules. Comparisons of the patterns of distribution of these regions in individual molecules indicated that they occurred at at least three specific positions around the molecule. Also, these regions, which were assumed to be rich in adenine and thymine, were within a segment which was less than 50% of the length of the molecule. After heating at 50°C, up to 14 regions of strand separation were observed, but when comparisons were made no clear groupings were found. At 51°C, component II molecules were completely separated into a single-stranded circle and a single-stranded linear piece of similar length. Strand separation was accompanied by shortening of the molecule. At 70°C, single-stranded circles had a mean length of 2.7 µ, compared with 5.0 µ for native molecules. Progressive heating of component I molecules resulted first in conversion to an open circle (I') and then to a second supercoiled form (I'). Visualization of further denaturation products of component I was prevented by crosslinking of the molecule by formaldehyde at high temperatures.     

Gap filling and not replication fork progression is the rate-limiting step in the replication of UV-damaged simian virus 40 DNA.

We have analyzed the structural characteristics of simian virus 40 replicative intermediate DNA produced after UV irradiation and the kinetics of conversion of this intermediate DNA into form I DNA. Replicative intermediate DNA isolated at 30 or 60 min after UV irradiation consists primarily of two species of molecules that sediment in neutral sucrose gradients as either Cairns theta structures or relaxed monomeric circles. Replication forks on the Cairns intermediate DNA are symmetrically located with respect to the origin of replication, ruling out the possibility of asymmetric pauses or blocks to replication fork progression at damage sites. The relaxed circles contain at least one randomly located discontinuity in the daughter strand. Pulse-chase experiments demonstrated that a UV fluence-dependent fraction of the Cairns intermediate DNA progresses through the relaxed circular intermediate before being converted to completed form I molecules. Disappearance of Cairns intermediate DNA occurs at the same rate in irradiated and unirradiated cells, whereas completion of the relaxed circular intermediate DNA occurs at a slow rate, relatively independent of UV fluence. These data support a model for replication of UV-damaged DNA in which replication rapidly continues past damage sites via a gap formation event.     

Processive action of T4 endonuclease V on ultraviolet-irradiated DNA.

The action of the dimer-specific endonuclease V of bacteriophage T4 was studied on UV-irradiated, covalently-closed circular DNa. Form I ColE1 DNA preparations containing average dimer frequencies ranging from 2.5 to 35 pyrimidine dimers per molecule were treated with T4 endonuclease V and analysed by agarose gel electrophoresis. At all dimer frequencies examined, the production of form III DNA was linear with time and the double-strand scissions were made randomly on the ColE1 DNA genome. Since the observed fraction of form III DNA increased with increasing dimer frequency but the initial rate of loss of form I decreased with increasing dimer frequency, it was postulated that multiple single-strand scissions could be produced in a subset of the DNA population while some DNA molecules contained no scissions. When DNA containing an average of 25 dimers per circle was incubated with limiting enzyme concentrations, scissions appeared at most if not all dimmer sites in some molecules before additional strand scissions were produced in other DNA molecules. The results support a processive model for the interaction of T4 endonuclease V with UV-irradiated DNA.     

Physical map of the DNA of bacteriophage tf of Pseudomonas putida

A physical map has been constructed for P. putida bacteriophage tf DNA containing single-strand breaks (nicks). Localization of cleavage sites for EcoRI, HindIII, HpaI ClaI, BamHI, SalI, XbaI and XhoI restriction endonucleases was determined. Position of single-strand breaks was mapped by electrophoretic analysis of denatured tf DNA and electron microscopy of partially denatured DNA samples. The tf genome is characterized by the presence of two classes of nicks differing in the frequency of their presence in population of bacteriophage DNA molecules.     

Locating Interrupted Hydrogen Bonding in the Secondary Structure of PM2 Circular DNA by Comparative Denaturation Mapping

Previous studies with HCHO have revealed a reaction with superhelical DNA that strongly suggests that this DNA consists of small regions of interrupted secondary structure. To map these sites in PM2 DNA, the following set of experiments was performed using electron microscopy. (i) A denaturation map of nicked form II was obtained using Inman's alkaline-HCHO conditions. (ii) The superhelical form I was reacted with HCHO at 30 C until equilibrium was achieved at the interrupted sites (3.6% reactivity). The excess HCHO was removed rapidly and X-ray treatment was employed to nick these prereacted molecules. These form II molecules containing HCHO (form II HCHO) were also subjected to denaturation mapping. It would be expected that the HCHO-unpaired regions would serve as induction sites for the propagation of melting. Hence, depending on the location of the induction sites; we would anticipate either the creation of new regions of melting or a normal denaturation map shifted to lower pH values. Comparison of the development of progressive denaturation of form II and form II HCHO reveals that the latter is the case. The denaturation maps of form II are highly organized patterns of adenine-thymine (AT)-rich regions, with a total of five regions at extreme pH conditions. There are six highly organized regions for form II HCHO, i.e., smaller adjacent loops, at low denaturation conditions where no denaturation is seen for form II. These coalesce into the pattern for form II containing four of five A-T-rich regions observed for form II. Hence we conclude that the regions of altered hydrogen bonding in superhelical PM2 DNA are four to six in number and they map in the A-T-rich regions of the DNA.     

Adriamycin-mediated introduction of a limited number of single-strand breaks into supercoiled DNA

It was reported previously that Adriamycin converts form I covalently closed circular, supercoiled bacteriophage PM2 DNA to the relaxed circular form II DNA; no form III linear DNA was produced as a result of the extracellular action of Adriamycin in the presence of NADH-dehydrogenase. When form II DNA, produced by the action of Adriamycin, was treated with the BAL 31 nuclease, a single sharp DNA band after agarose gel electrophoresis indicated the presence of only full-length linear form III DNA. As one of its activities, the BAL 31 nuclease introduces a single-strand break in the complementary strand opposite a preexisting single-strand break. When form II DNA, produced by the action of gamma irradiation, was reacted with the BAL enzyme, the resulting linear DNA molecules exhibited a broad range of molecular weights, indicating the presence of many single-strand breaks in the substrate form II DNA. When the Adriamycin-produced form II DNA was treated with restriction endonucleases that cleave PM2 DNA at a single site, either with or without pretreatment with the BAL enzyme, the formation of only full-length linear DNA was observed. Thus, the drug is capable of introducing one or only a very limited number of single-strand breaks into supercoiled DNA; furthermore, these breaks are introduced at random sites along the DNA molecules.     

A vaccinia virus DNase preparation which cross-links superhelical DNA.

Multiple DNA-dependent enzyme activities have been detected in highly purified preparations of a single-strand-specific nuclease from vaccinia virus. These enzyme preparations were extensively purified and characterized by using superhelical DNAs as substrates. In particular, the nuclease activity was monitored by the extent of conversion of supercoiled closed duplex DNA (DNA I) to nicked circular DNA (DNA II), which could subsequently be converted to duplex linear DNA (DNA III) by prolonged incubation with the enzyme. DNA species which were not substrates for the enzyme included relaxed closed duplex DNA, DNA II which had been prepared by nuclease S1 treatment or by photochemical nicking of DNA I, and DNA III. With plasmid pSM1 DNA as substrate, the extent of cleavage of DNA I to DNA II was found to increase with superhelix density above a threshold value of about -0.06. The linear reaction products were examined by gel electrophoresis after restriction enzyme digestion of the DNAs from plasmids pSM1 and pBR322 and of the viral DNAs from bacteriophage phi X174 (replicative form) and simian virus 40, and the map coordinate locations of the scissions were determined. These products were further examined by electron microscopy and by gel electrophoresis under denaturing conditions. Electron micrographs taken under partially denaturing conditions revealed molecules with terminal loops or hairpins such as would result from the introduction of cross-links at the cutting sites. These species exhibited snapback renaturation. The denaturing gel electrophoresis experiments revealed the appearance of new bands at locations consistent with terminal cross-linking. With pSM1 and pBR322 DNAs, this band was shown to contain DNA that was approximately twice the length of a linear single strand. The terminal regions of the cross-linked linear duplex reaction products were sensitive to nuclease S1 but insensitive to proteinase K, suggesting that the structure is a hairpin loop not maintained by a protein linker. A similar structure is found in mature vaccinia virus DNA.     

Characterization and localization of the naturally occurring cross-links in vaccinia virus DNA

The vaccinia virus genome is a single, linear, duplex DNA molecule whose complementary strands are naturally cross-linked. The molecular weight has been determined by contour length measurements from electron micrographs to be 122 ± 2.2 × 10⁶. Denaturation mapping techniques indicate that the nucleotide sequence arrangement of the DNA is unique. Two forms of cross-linked vaccinia DNA were observed in alkaline sucrose gradients. The relative S-values of the two cross-linked species were appropriate for a single-stranded circle and a linear single strand, each with a molecular weight twice that expected for an intact, linear, complementary strand of vaccinia DNA. The fraction of sheared vaccinia DNA able to “snap back” after denaturation suggested a minimum of two crosslinks per molecule. Full-length single-stranded circles were observed in the electron microscope after denaturation of vaccinia DNA. Partial denaturation produced single-stranded loops at the ends of all full-length molecules. Exposure of native vaccinia DNA to a single strand-specific endonuclease isolated from vaccinia virions caused disruption of the cross-links, as assayed by alkaline sedimentation, and produced free single-strand ends when partially denatured DNA was observed in the electron microscope. We conclude that vaccinia DNA contains two cross-links, one at or near (within 50 nucleotides) each end in a region of single-stranded DNA. Two models for the cross-links are presented.     

Evidence for supercoiled hepatitis B virus DNA in chimpanzee liver and serum Dane particles: possible implications in persistent HBV infection

In chimpanzee hepatitis B virus (HBV) carriers, the mechanism of viral persistence has been examined by analyzing viral DNA molecules in liver and serum. Chimpanzee liver DNA contained two extrachromosomal HBV DNA molecules migrating on hybridization blots at 4.0 kb and 2.3 kb. There was no evidence for integration of HBV DNA into the host genome. The extrachromosomal molecules were distinct from Dane particle DNA and were converted to linear 3.25 kb full-length double-stranded HBV DNA on digestion with Eco RI. Nucleases S1 and Bal 31 converted "2.3 kb" HBV DNA to 3.25 kb via an intermediate of "4.0 kb" apparent length. The HBV DNA molecule that migrated at 2.3 kb represents a supercoiled form I of the HBV genome, and the molecule that migrated at 4.0 kb represents a full-length "nicked," relaxed circular form II. Evidence for supercoiled HBV DNA in serum Dane particles was obtained by production of form II molecules upon digestion with nuclease S1 or Bal 31. It is proposed that most Dane particles represent interfering noninfectious virus containing partially double-stranded DNA circles and that particles containing supercoiled HBV DNA may represent infectious hepatitis B virus.     

Comparison of the fine structure of mitochondrial DNA from Saccharomyces cerevisiae and S. carlsbergensis: electron microscopy of partially denatured molecules.

Denaturation-maps of mitochondrial DNA from Saccharomyces cerevisiae and S. carlsbergensis have been derived from electron microscopic observations of partially denatured complete circular molecules and large fragments of these circles. The mitochondrial DNA from the two species differ by 6% in total length, but seems from the maps to contain some regions of apparent close homology. The cleavage pattern of the two DNAs by the restriction endonuclease EcoRI is compared by gel electrophoresis.     

Sedimentation and intrinsic viscosity behavior of PM2 bacteriophage DNA in alkaline solution

The sedimentation coefficient and intrinsic viscosity of nicked and closed circular PM2 bacteriophage DNA have been measured as a function of pH in the alkaline region. A gradual increase in the sidimentation coefficient, and a corresponding decrease in the intrinsic viscosity, are observed for the superhelical (closed) circle in the pH region from 10.5 to about 10.9. This has been tentatively interpreted in terms of the known dependence of sedimentation coefficient upon the number of superhelical turns. At slightly higher pH values, the curve passes through the minimum (sedimentation coefficient) and maximum (intrinsic viscosity) expected when the superhelical turns present at neutral pH are unwound by partial alkaline denaturation. Sedimentation studies of the relaxed (nicked) circular species have revealed the existence of DNA forms in the pH region from 11.27 to 11.37 which sediment considerably faster than the closed circle in the same pH region. These have been identified as partially denatured nicked circles, in which varying fractions of the duplex structure have undergone alkaline denaturation, but strand separation has not yet occurred. Varying fractions of a slower species, either undenatured or completely denatured nicked circles, are also observed in some of these experiments. A corresponding result is observed in the intrinsic viscosity vs. pH curve. When nicked circular PM2 DNA is exposed to various alkaline pH's, rapidly neutralized, and sedimented at neutral pH, the expected sharp transition from native to denatured (strand-separated) molecules is seen. However, a very narrow pH range is noted in which native and denatured forms coexist in a single experiment. The above experiments carried out upon the closed form also reveal a narrow pH range in which the bulk of the transition from native closed circles to the collapsed cyclic coil takes place, in acccord with an earlier study on a different DNA. This transition is shown never to be completely effected, however, as there is a fraction (7–8%)of the closed circles which renature to the native form, regardless of the alkaline pH employed. This same phenomenon was not observed in the case of artificially closed λb₂b₅c DNA circles. Possible explanations for some of the above results are discussed.     

Site specificity of bleomycin-mediated single-strand scissions and alkali-labile damage in duplex DNA.

Form II PM2 DNA, which contained bleomycin-mediated single-strand breaks, was purified and treated with the extracellular endonuclease from Alteromonas BAL 31. This enzyme cleaves the phosphodiester backbone opposite a single-strand break to yield a double-strand break. The locations of these double-strand breaks were determined relative to the cleavage sites produced by the restriction enzyme HindIII. The experimental procedure was as follows. Form I PM2 DNA was treated with bleomycin to produce alkali-labile bonds. These were hydrolyzed by alkali treatment and the DNA, now containing single-strand breaks, was purified and treated with the BAL 31 enzyme and the HindIII enzyme to determine the positions of the original alkali-labile bonds. It was found that the single-strand breaks and alkali-labile bonds were introduced at preferred sites on the PM2 genome, since electrophoretic analyses of the DNA after the HindIII digestion revealed DNA bands of discrete sizes. The molecular weights of the DNA fragments produced by these treatments indicate that single-strand breaks and alkali-labile bonds occur at the same sites as those previously determined for direct double-strand scissions introduced by bleomycin at neutral pH. Some of the specific sites of double-strand scissions mediated by bleomycin at neutral pH (Lloyd et al., 1978b) are also shown here to be relatively more reactive than other sites when the DNA contains superhelical turns.     

Extracellular nucleases of Pseudomonas BAL 31. I. Characterization of single strand-specific deoxyriboendonuclease and double-strand deoxyriboexonuclease activities.

The culture medium of Pseudomonas BAL 31 contains endonuclease activities which are highly specific for single-stranged DNA and for the single-stranded or weakly hydrogen-bonded regions in supercoiled closed circular DNA. Exposure of nicked DNA to the culture medium results in cleavage of the strang opposite the sites of preexisting single-strand scissions. At least some of the linear duplex molecules derived by cleavage of supercoiled closed circular molecules contain short single-stranded ends. Single-strand scissions are not introduced into intact, linear duplex DNA or unsupercoiled covalently closed circular DNA. Under these same reaction conditions, 0X174 phage DNA is extensively degraded and PM2 form I DNA is quantitatively converted to PM2 form III linear duplexes. Prolonged exposure of this linear duplex DNA to the concentrated culture medium reveals the presence of a double-strand exonuclease activity that progressively reduces the average length of the linear duplex. These nuclease activities persist at ionic strengths up to 4 M and are not eliminated in the presence of 5% sodium dodecyl sulfate. Calcium and magnesium ion are both required for optimal activity. Although the absence of magnesium ion reduces the activities, the absence of calcium ion irreversibly eliminates all the activities.     

Studies on Circular Deoxyribonucleic Acid I. Isolation of Bovine Papilloma Virus and Characterization of Its Deoxyribonucleic Acid

A simple method is described for the isolation of bovine papilloma virus and its deoxyribonucleic acid (DNA). As found with other representatives of this virus group, this DNA preparation contains two components, I and II, as shown by sedimentation and electron microscopic studies. Component I is a fast-sedimenting, twisted, circular DNA molecule and represents usually 70 to 90% of the DNA in the mixture. The direction of the twist in the superstructure is right-handed. Component II originates from I by one or more single-strand breaks and is the "relaxed" circular from of the viral DNA.     

Action of Escherichia coli P1 restriction endonuclease on simian virus 40 DNA

The P1 restriction endonuclease (EcoP1) prepared from a P1 lysogen of Escherichia coli makes one double-strand break in simian virus (SV40) DNA. In the presence of cofactors S-adenosylmethionine and ATP the enzyme cleaves 70% of the closed circular SV40 DNA molecules once to produce unit-length linear molecules and renders the remaining 30% resistant to further cleavage. No molecules were found by electron microscopy or by gel electrophoresis that were cleaved more than once. It would appear that the double-strand break is made by two nearly simultaneous single-strand breaks, since no circular DNA molecules containing one single-strand break were found as intermediates during the cleavage reaction. The EcoP1 endonuclease-cleaved linear SV40 DNA molecules are not cleaved at a unique site, as shown by the generation of about 65% circular molecules after denaturation and renaturation. These EcoP1 endonuclease-cleaved, renatured circular molecules are resistant to further cleavage by EcoP1 endonuclease.The EcoP1 endonuclease cleavage sites on SV40 DNA were mapped relative to the partial denaturation map and to the EcoRI and HpaII restriction endonuclease cleavage sites. These maps suggest there are a minimum of four unique but widely spaced cleavage sites at 0.09, 0.19, 0.52, and 0.66 SV40 units relative to the EcoRI site. The frequency of cleavage at any particular site differs from that at another site. If S-adenosylmethionine is omitted from the enzyme reaction mix, SV40 DNA is cleaved into several fragments.An average of 4.6 ± 1 methyl groups are transferred to SV40 DNA from S-adenosylmethionine during the course of a normal reaction containing the cofactors. Under conditions which optimize this methylation, 7 ± 1 methyl groups can be transferred to DNA. This methylation protects most of the molecules from further cleavage. The methyl groups were mapped relative to the Hemophilus influenzae restriction endonuclease fragments. The A fragment receives three to four methyl groups and the B and G fragments each receive one to two methyl groups. These fragments correspond to those in which cleavage sites are located.     

Pisum sativum endonuclease. Studies on substrate specificity and possible use as a biochemical tool

An endonuclease purified from germinating pea (Pisum sativum) seeds has been shown to catalyze the hydrolysis of heat-denatured single-stranded DNA. Since P. sativum endonuclease shows appreciable activity in the presence of DNA destabilizing agents and, unlike many similar endonucleases, significant activity at neutral pH, it is a potentially valuable tool for studies of the secondary structure of nucleic acids. The residual hydrolysis of duplex DNA is directed towards partially denatured, A,T-rich areas in native DNA. The rate of hydrolysis of deoxypolynucleotides was in the order poly(dT) greater than denatured DNA greater than poly(dA) greater than poly(dA-dT) = native DNA. Neither poly(dC), poly(dG) nor poly(dC).poly(dG) were attacked by the enzyme. Supercoiled, covalently closed circular phage PM2 form I DNA is converted to singly hit nicked circular form II and doubly hit linear from III duplexes. Prolonged treatment with enzyme does not further cleave the linear form III DNA. Addition of increasing concentrations of NaCl in the incubation mixture suppresses the conversion of form I to form II, but not the conversion of form II to form III, which is enhanced with the increasing ionic strength. The enzymatically relaxed circular form, I degree, obtained by unwinding of supercoiled DNA with a DNA-relaxing protein, is resistant to the action of the enzyme. Molecules with intermediate superhelix densities do not serve as substrates. The sites of cleavage of P. sativum endonuclease in PM2 DNA occur within regions that are readily denaturable in a topologically constrained superhelical molecule.     

Simian Virus 40 Deoxyribonucleic Acid Synthesis: Analysis by Gel Electrophoresis

An agarose-gel electrophoresis technique has been developed to study simian virus 40 deoxyribonucleic acid (DNA) synthesis. Superhelical DNA I, relaxed DNA II, and replicative intermediate (RI) molecules were clearly resolved from one another for analytical purposes. Moreover, the RI molecules could be identified as early or late forms on the basis of their electrophoretic migration in relation to that of DNA II. The technique has been utilized to study the kinetics of simian virus 40 DNA synthesis in pulse and in pulse-chase experiments. The average time required to complete the replication of prelabeled RI molecules and to convert them into DNA I was approximately 10 min under the experimental conditions employed.     

Electron microscopic identification of supercoiled regions in complex DNA structures

When intracellular lambda replicative intermediates (theta structures) are intercalated with psoralen and then irradiated with long wavelength ultraviolet light (u.v.), interstrand crosslinks are produced. After purification and denaturation of these theta structures, a global difference in denaturation can be observed by electron microscopy; parental sections are essentially native whereas daughter segments are highly denatured. This difference can be explained if parental sections are covalently continuous (and therefore able to supercoil) and daughter segments are not. Due to the higher thermal stability of supercoiled DNA, parental DNA will remain native while daughter sections will denature. Because these structures are crosslinked, the thermal treatment does not lead to dissociation of the highly denatured daughter strands. Experiments with simple negatively supercoiled plasmid circles support the above conclusions. When circles are crosslinked with psoralen-u.v. and then denatured, they remain native because of the higher thermal stability of covalently closed structures. If the circles are linearized before heating but after the psoralen-u.v. treatment, the thermal stability effect is eliminated and the molecules become highly denatured. In this case, however, the crosslinking density is found to be higher than in samples linearized before psoralen-u.v. treatment. This, therefore, shows that crosslinking density also reflects the superhelical state of the molecule at the time of psoralen-u.v. treatment. Two different properties can be used to discriminate between supercoiled and covalently discontinuous domains in complex DNA structures. First, supercoiled regions remain native while covalently discontinuous segments denature following a thermal treatment. This effect requires that covalent continuity exists up to and during the heating treatment. Second, because negative superhelicity enhances psoralen intercalation, crosslinking density is higher in these regions. Even if supercoiled domains are destroyed after the psoralen-u.v. treatment, the imprint of superhelicity is retained and can be recognized as a higher than normal crosslinking density.     

Nuclease TT1 from Thermus thermophilus HB8 has an endonuclease activity preferential to circular DNAs.

Homogeneously purified nuclease TT1 from Thermus thermophilus HB8 is known as an exonuclease to produce 5'-mononucleotides. Besides the exonuclease activity, nuclease TT1 also possesses endonuclease activity preferential to superhelical (form I) and single-stranded circular DNA. Although the rate of cleavage is slower than that of form I, covalently closed circular DNA (form I') is also cleaved. Form I DNA was nicked to yield relaxed circles (form II) first, and was then nicked at the opposite site to yield unit length linear DNA (form III) which was subsequently hydrolyzed to 5'-mononucleotides exonucleolytically. Both endo- and exo-nuclease activities co-migrate on polyacrylamide gels. The general properties of the endonuclease activity are very similar to those of the exonuclease activity. The temperature optimum for endonuclease activity was 85 degrees C. The pH-optimum was in pH-range from 7.5-9.1. The enzyme was active over a wide range of Mg2+ concentrations (2.5-125 mM), and was inhibited by EDTA. A linear substrate such as (dT)8 was a competitive inhibitor for this endonuclease activity.     

The properties of native and denatured DNA in buoyant rubidium trichloroacetate at neutral pH

Aqueous RbTCA is generally suitable as a buoyant solvent for both native and denatured DNA at neutral pH and room temperature. Native PM-2 DNA II, for example, is buoyant at 3.29 M salt, 25 degrees C; whereas the denatured strands band together at 4.52 M. Two properties of the solvent make this system uniquely useful for separations based upon the extent of secondary structure. First, the melting transition temperature for chemically unaltered DNA is depressed to room temperature or below. Second, the buoyant density increase accompanying denaturation is extraordinarily large, 174 mg/ml for PM-2 DNA II. This value is three times that found in aqueous NaI and ten times that for CsCl. The properties of the RbTCA buoyant solvent presented here include the compositional and buoyant density gradients and the buoyant density dependence upon base composition. The DNA remains chemically unaltered after exposure to RbTCA as shown by the absence of strand scissions for closed circular DNA and by the unimpaired biological activity in transformation assays. Intact virion DNA may be isolated by direct banding of whole virions in RbTCA gradients without prior phenol extraction. Strongly complexed or covalently bound proteins may be detected by their association with the buoyant polymer in the denaturing density gradient.