"Turing patterns in network-organized activator–inhibitor systems".

Hiroya Nakao ^{1, 2} and  Alexander S. Mikhailov ³

¹ Department of Physics, Kyoto University, Kyoto 606-8502, Japan
² JST, CREST, Kyoto 606-8502, Japan
³ Department of Physical Chemistry, Fritz Haber Institute of the Max Planck Society, Faradayweg 4-6, 14195 Berlin, Germany

Correspondence to: Hiroya Nakao ^{1, 2} e-mail: nakao@ton.scphys.kyoto-u.ac.jp

Correspondence to: Alexander S. Mikhailov ³ e-mail: mikhailov@fhi-berlin.mpg.de 

Turing instability in activator–inhibitor systems provides a paradigm of non-equilibrium self-organization; it has been extensively investigated for biological and chemical processes. Turing instability should also be possible in networks, and general mathematical methods for its treatment have been formulated previously. However, only examples of regular lattices and small networks were explicitly considered. Here we study Turing patterns in large random networks, which reveal striking differences from the classical behaviour. The initial linear instability leads to spontaneous differentiation of the network nodes into activator-rich and activator-poor groups. The emerging Turing patterns become furthermore strongly reshaped at the subsequent nonlinear stage. Multiple coexisting stationary states and hysteresis effects are observed. This peculiar behaviour can be understood in the framework of a mean-field theory. Our results offer a new perspective on self-organization phenomena in systems organized as complex networks. Potential applications include ecological metapopulations, synthetic ecosystems, cellular networks of early biological morphogenesis, and networks of coupled chemical nanoreactors.

Supplementary Information:
http://www.nature.com/nphys/journal/vaop/ncurrent/suppinfo/nphys1651_S1.html

Reaction–diffusion systems support a wealth of complex self-organized patterns, such as stationary dissipative structures, travelling fronts and pulses, rotating spiral waves, or chemical turbulence 1, 2, 3, 4, 5, 6. Within the last decade, attention has been brought to a class of models representing their network analogues, where the interacting species occupy network nodes and are diffusively transported across the links 7, 8, 9, 10, 11. Such models typically arise when ecological metapopulations with dispersal connections between habitats are considered 12, 13, 14, 15, 16 or spreading of infections through transportation networks is investigated 17, 18, 19, 20, 21. They can also correspond to networks of diffusively coupled chemical reactors or biological cells 8, 9, 10, 11. Network architecture makes the analysis of self-organization difficult, and therefore it has so far been largely restricted to such kinds of non-equilibrium pattern formation as epidemic spreading 19, 20, 21 or synchronization 22, 23, 24. More complex forms of network self-organization are, however, also possible.

In 1952, Turing showed 1 that differences in the diffusion constants of activator and inhibitor species can bring about destabilization of the uniform state and lead to spontaneous emergence of periodic spatial patterns. The Turing patterns can emerge in autocatalytic chemical reactions with inhibition 2, 3, 4, in processes of biological morphogenesis 25, 26, 27, 28, 29, and in ecosystems 30, 31, 32, 33. They provide a classical example of complex non-equilibrium self-organization.

As early as 1971, Othmer and Scriven 8 pointed out that Turing instability can occur in network-organized systems and may play an important role in the early stages of biological morphogenesis, as morphogens diffuse over a network of intercellular connections. They have proposed a general mathematical framework for the analysis of such network instability, which has been subsequently explored 9, 10, 11. The examples of specific applications of the theory were, however, limited to regular lattices 8, 9 or small networks 10, 11.

In studies of network phenomena, characteristic statistical features of collective dynamics were first revealed when large unstructured random networks, such as the Erdös–Rényi or scale-free networks 34, 35, 36, were considered, for which powerful analytical methods, for example, the mean-field approximation 19, 20, 21, 22, 23, 24, can be applied. Detailed statistical investigations of the emerging stationary Turing patterns in such large random networks thus need to be performed and this is the aim of our present work.

Activator–inhibitor systems on networks:

Activator–inhibitor systems in classical continuous media are described by:

where u(x,t) and v(x,t) are local densities of the activator and inhibitor species. Functions f(u,v) and g(u,v) specify local dynamics of the activator, which autocatalytically enhances its own production, and of the inhibitor, which suppresses the activator growth. D_act and D_inh are the diffusion constants of activator and inhibitor species. The Turing instability 1  sets in as the ratio D_inh/D_act of the two diffusion constants is increased and exceeds a threshold. It leads to spontaneous development of alternating activator-rich and activator-poor domains from the uniform background. The activator and the inhibitor may represent two different chemical species 2, 3, 4. In ecological models, the activator typically corresponds to the prey and the inhibitor to the predator 5, 16, 30, 32.

In our study, we consider the network analogue of model (1) where activator and inhibitor species occupy discrete nodes of a network and are diffusively transported over links connecting them. The links may represent diffusive connections between chemical reactors or dispersal of ecospecies from one habitat to another. The topology of a network with N nodes is defined by a symmetric adjacency matrix whose elements A_{i j} take A_{i j}=1 if the nodes i and j ( i, ,j =1,…,N ) are connected ( i not = j ) and A_{i j} = 0 otherwise.  The degree (number of connections) of node i is given by:

For convenience, we always sort network nodes { i } in decreasing order of their degrees { k_i } so that the condition k₁>k₂>...k_N holds. Diffusive transport of species into a certain node i is given by the sum of incoming fluxes to node i from other connected nodes { j }, where the fluxes are proportional to the concentration difference between the nodes (Fick’s law). By introducing the network Laplacian matrix, L_{i j}=A_{i j} - k_id_{i j}, the diffusive flux of species u to node i is expressed as:

and similarly for v (see Methods section). Generally, diffusional mobilities of species u and v on a network are different.

Equations describing network-organized activator–inhibitor systems are thus given by:

for i=1,…,N. Now f(u,v) and g(u,v) represent the local activator–inhibitor dynamics on individual nodes and satisfy several conditions given in the Methods section. We denote the diffusional mobility of the activator species as e(=D_act) and that of the inhibitor species as se(=D_inh), where s=D_inh/D_act is the ratio between them. The considered systems have a uniform stationary state (u, v), where f (u,v)=0, and g(u,v)=0. This uniform state can become unstable because of the Turing instability.

As a particular example of an activator–inhibitor network system, the Mimura–Murray model 30 of prey–predator populations on scale-free random networks is used in the main text (see Methods section). In the Supplementary Information, results for the Brusselator model 2 and Erdös–Rényi random networks are also given.

The Turing instability:

The Turing instability is revealed through linear stability analysis of the uniform stationary state with respect to non-uniform perturbations. In the classical case of continuous media 1, non-uniform perturbations are decomposed into a set of spatial Fourier modes representing plane waves with different wavenumbers. As noticed by Othmer and Scriven 8, the roles of plane waves and wavenumbers are played in networks by eigenvectors and eigenvalues  (a=1,…,N) of their Laplacian matrices (see Methods section) 37, 38, 39, 40.

Introducing small perturbations ( du_i, dv_i ) to the uniform state and substituting into equations (2), a set of coupled linearized differential equations is obtained. By expanding the perturbations over a set of Laplacian eigenvectors and eigenvalues of their Laplacian matrices (see Methods section), the linear growth ratel_a of each mode is determined from a characteristic equation (see Methods section). The ath mode is unstable when Re l_a is positive. The Turing instability occurs 8, 9, 10, 11 when one of the modes (that is, the critical mode) begins to grow. At the instability threshold, Re l_a=0 for some a=a_c and Re l_a<0  for all other modes.

Figure 1 shows the growth rate l as a function of L for the Mimura–Murray model on a scale-free random network. Three curves, corresponding to different ratios s of diffusion constants (below, at and above the instability threshold), are displayed for e=0.06. Critical curves for two other values of e are also shown. The Turing instability becomes possible for s>s_c. The dispersion curve l=F(eL) first touches the horizontal axis at L=L_c and the Laplacian mode f^ac  possessing the Laplacian eigenvalue La_c that is closest to L_c, becomes critical. Note that the Laplacian spectrum of a network is discrete and, therefore, the instability actually occurs only when one of the respective points on the dispersion curve crosses the horizontal axis.

Figure 1: Linear stability analysis.

Figure 1 : Linear stability analysis.

Linear growth rates L_a of Laplacian modes a=1,…,N for the Mimura–Murray model on a scale-free network (N=200 nodes and mean degree (k=10) are plotted as functions of the Laplacian eigenvalues L_a for the critical ratio of diffusion constants s=15.5~s_c.

Three curves corresponding to three values of the diffusional mobility e=0.425, 0.165 and 0.060 are shown. For comparison, curves with s=15.0 and s=16.0 are also drawn for e=0.060. Critical modes are indicated for each value of e. The critical modes and the corresponding Laplacian eigenvalues are a_c=15, L_c= -3.62 for e=0.425, a_c=135, L_c= -9.32 for e=0.165, and a_c=190, L_c= -25.3 for e=0.060.

The above results are analogous to those holding for continuous media (see ref. 6). The critical ratio s_cin the networks is the same as in the classical case. The Laplacian eigenvalue L_c of the critical network mode corresponds to -q_c², where q_c is the critical wave number in the continuous media. Despite such formal analogies, properties of Turing patterns in large random networks are very different from their classical counterparts, as demonstrated in the following sections.

Critical Turing modes in large random networks

When a Turing pattern starts to grow after slightly exceeding the instability threshold, the activator and inhibitor distributions in this pattern are determined by the critical Laplacian eigenvector as du_i, dv_i af^a_c). Therefore, to understand the organization of growing Turing patterns, the properties of Laplacian eigenvectors should be considered.

As an example, Fig. 2a,b display critical eigenvectors of a scale-free network for two different values of the diffusion constant e. The same eigenvectors are shown graphically in Fig. 2c,d. In the chosen representation, network nodes with larger degrees (hubs) are located in the centre and the nodes with lower degrees in the periphery of the graph. The nodes are coloured red when f_i(^ac)>0.1 (for example, the activator concentration is significantly increased), blue when f_i(a_c)<0.1 (significantly decreased), and yellow for -0.1<f_i(ac)<0.1 (no significant change).

Figure 2: Critical Turing modes of a scale-free network.

Figure 2 : Critical Turing modes of a scale-free network.

The network size is N=200 and the mean degree is {k}=10.

a,b, Critical eigenvectors s_c=190 (a) and s_c=15 (b) plotted against the node index i. Node degrees k_i are shown by green stepwise curves. Node indices {i} are sorted according to their degrees { k_i }.

c,d, The same critical eigenvectors s_c=190 (c), and s_c=15 (d), displayed graphically on the network.

It is clearly seen that spontaneous differentiation of nodes takes place—the distinguishing feature of the Turing instability. However, it affects only a fraction of all nodes. The differentiated nodes, with significant deviations of the activation level, tend to have close degrees. When diffusional mobility e is small, only a subset of hub nodes undergoes differentiation (Fig. 2a,c). If e is large, differentiated nodes have just a few links (Fig. 2b,d). Thus, correlation between the characteristic degrees of the differentiated nodes and the diffusional mobility exists. This behaviour is general and is related to the effect of localization of Laplacian eigenvectors.

As has recently been shown 40, Laplacian eigenvectors in large unstructured random networks with broad degree distributions tend to localize on subsets of nodes with close degrees. The localization effect for a scale-free network is illustrated in Fig. 3. Here, all nodes are divided into groups with equal degrees k. For each k and a chosen Laplacian eigenvalue L, the number of ‘differentiated’ nodes with f_i^(s)=0.1 or f_i^(s)= -0.1 in the respective eigenvector is counted. The density diagrams in Fig. 3 display the relative numbers of such nodes as functions of the Laplacian eigenvalue L and the degree k. One can see that differentiated nodes are approximately located along the diagonal of the density map. The localization effect is more pronounced for the larger network. Thus, each Laplacian eigenvector has a charactertic localization.

Moreover, this characteristic degree is approximately equal to the negative of the respective eigenvalue, so that a simple relationship k_a ~  -L_a holds for a scale-free network.

Figure 3: Localization of Laplacian eigenvectors in scale-free networks.

Figure 3 : Localization of Laplacian eigenvectors in scale-free networks.

The network size and the mean degree are N=200, k=10 (a), and N=1,000, k=20 (b).

Density distribution of differentiated nodes in each subset of nodes with equal degrees k is shown for the entire set  Lof Laplacian eigenvectors.

monotonously increasing function of the negative of the critical Laplacian eigenvalue,  - L_sc, and thus a decreasing function of the diffusional mobility e.

Turing patterns:

The initial exponential growth is followed by a nonlinear process leading to the formation of stationary Turing patterns. We have investigated nonlinear evolution of the system and properties of asymptotic stationary patterns by numerical simulations. Figure 4 presents typical results, obtained for intermediate diffusional mobility (e=0.12) and slightly above the instability threshold (s=15.6), for the Mimura–Murray model on a random scale-free network of size N=1,000 and mean degree { k }=20. The nodes are sorted in the order of their degrees, as shown in Fig. 4d.

Figure 4: Nonlinear evolution and a stationary Turing pattern.

Figure 4 : Nonlinear evolution and a stationary Turing pattern.

The Mimura–Murray model with parameters e = 0.12 and s =15.6 on a scale-free network of size N = 1,000 and mean degree { k } = 20. Nodes are ordered according to their degrees.

a, The critical mode (the Laplacian eigenvector with s_c=422).

b, The activator pattern at the early evolution stage (t=200).

c, The stationary activator pattern at the late stage (t=1,500).

d, Dependence of the degree on the node index.

Starting from almost uniform initial conditions with small perturbations, exponential growth is observed at the early stage. The activator pattern at this stage, Fig. 4b, is similar to the critical mode, Fig. 4a, where the deviations result from the contributions from neighbouring modes that are already excited to some extent. Later on, however, strong nonlinear effects develop, and the final stationary pattern, Fig. 4c, becomes very different from the one determined by the critical mode.

Observing the nonlinear development, we notice that some nodes get progressively kicked off the main group near the destabilized uniform solution in this process (see Supplementary Video). Eventually, in the asymptotic stationary state, the nodes become separated into two groups. The separation occurs only for the nodes with relatively small degrees, whereas the nodes with high degrees do not differentiate.

Our numerical investigations furthermore reveal that the outcome of nonlinear evolution depends sensitively on the initial conditions. Different Turing patterns are possible at the same parameter values and strong hysteresis effects are observed. As an example, Fig. 5a shows how the amplitude of the stationary Turing pattern, defined as:

varies under gradual variation of the parameter s in the upward or downward directions. Stationary patterns observed at points P, Q, and R in Fig. 5a are shown in Fig. 5b.

Figure 5: Hysteresis and multistability.

Figure 5 : Hysteresis and multistability.

The Mimura–Murray model with parameters e = 0.12 and s = 15.6 on a scale-free network of size N=1,000 and mean degree { k} =20.

a, Amplitude A of the Turing pattern versus the diffusion ratio s; variation directions of s are indicated by arrows. The inset shows the blow-up near R.

b, Stationary Turing patterns at the parameter points   P (s=17.0),   Q (s=13.5) and   R (s=12.8).

As s was increased starting from the uniform initial condition, the Turing instability took place at s=s_c with the amplitude A suddenly jumping up to a high value that corresponds to appearance of a kicked-off group. If s was further increased, the amplitude A grew. Starting to decrease s, we did not however observe a drop down at s=s_c. Instead, a punctuated decrease in the amplitude A, which is characterized by many relatively small steps, was found. Reversing the direction of change of the parameter s at different points, many coexisting solution branches could be identified. The characteristics of Turing patterns vary with their amplitudes. When A is close to zero (point R in Fig. 5a), only a few kicked-off nodes remain in the system. Such localized Turing patterns, with only a small number of destabilized nodes, are found below the Turing instability threshold, s<s_c, and can coexist with the linearly stable uniform state.

To understand the properties of the developed Turing patterns above the instability boundary (s>s_c), one can use the mean-field approximation, similar to that previously employed for epidemic spreading models and coupled oscillators on large unstructured random networks  7, 19, 20, 21, 22, 23, 24, 41. In this approximation, detailed interactions of each network element with its neighbouring nodes are neglected and the element is coupled to certain global mean fields collectively determined by the entire system. The coupling strength to the global mean fields is proportional to the number of links connecting an element to the rest of the network. This approximation enables us to fit the whole stationary Turing pattern using the bifurcation diagram of an individual activator–inhibitor element coupled to global mean fields, when their values are known (see Methods section and Supplementary Information).

In Fig. 6, we compare the computed Turing patterns with the mean-field results using the values of the global mean fields yielded by direct numerical simulations. The stationary Turing patterns are well fitted by stable branches of the individual elements, although scattering of numerical data gets enhanced near the branching points. In the Supplementary Information, a similar analysis is performed for the Brusselator and for Erdös–Rényi networks. The Brusselator has a different bifurcation diagram in the presence of external fields. Nonetheless, a good agreement with the predictions of the mean-field theory is again found.

Figure 6: Stationary Turing patterns compared with the mean-field bifurcation diagrams.

Figure 6 : Stationary Turing patterns compared with the mean-field bifurcation diagrams.

The Mimura–Murray model on a scale-free network of size N=1,000 and mean degree { k }=20. The diffusion ratio is s=15.6 (a), and s=30 (b).

The diffusional mobility e = 0.12 is fixed. Crosses show computed Turing patterns. Blue curves (dots) indicate stable branches and light-blue curves (dots) correspond to unstable branches of a single activator–inhibitor system coupled to the global mean fields. See Supplementary Information for details.

Thus, fully developed network Turing patterns are essentially explained by the bifurcation diagrams of a single node coupled to the global mean fields, with the coupling strength determined by the degree of the respective network node. The mean-field theory is generally not applicable for localized Turing patterns below the Turing instability threshold.

Discussion:

The fingerprint property of the classical Turing instability in continuous media is the spontaneous formation of periodic stationary patterns. Our investigations of the Turing problem for large random networks have revealed that, whereas the bifurcation remains essentially the same, properties of emergent patterns are very different. In networks, the critical Turing mode is approximately localized on a subset of nodes with their degrees close to some characteristic value controlled by the mobility of species. The final stationary patterns deviate strongly from the critical mode. Multistability, that is, coexistence of a number of different stationary patterns for the same parameter values, is typically found and hysteresis phenomena are observed. As we have shown, fully developed network Turing patterns above the instability threshold can be well understood within the mean-field approximation.

The origins of such difference lie in the statistical structural properties of network-organized systems. The diameters of random networks are typically small (at most L=lnN for random scale-free networks 42). Because of their small diameters, diffusional mixing in such systems is fast, explaining why the mean-field approximation works so well there. For comparison, a d-dimensional cubic lattice with N nodes has a diameter of about L=N^1/d. Thus, a lattice with the same number N of nodes and a comparable diameter L should have a high dimension d >> than 1. Large random networks are thus structurally much closer to high-dimensional lattices or globally coupled systems than to the lattices with a few dimensions. Because of their small diameters, Turing patterns with alternating domains cannot exist in such systems, and only several domains (clusters) may be present there, as indeed seen by us for the considered networks. Note that spontaneous differentiation of elements into two groups has been previously observed in studies of globally coupled activator–inhibitor systems 43, 44.

There is, however, a further important aspect   distinguishing complex networks from high-dimensional lattices and globally coupled systems , namely, strong degree heterogeneity. It plays a significant role in problems involving network diffusion. Indeed, under the same concentration gradients across the links, a node with a higher number of links receives a larger incoming flux from the neighbouring nodes and also more strongly influences the rest of the system. Approximate localization of the Laplacian eigenvectors on the subsets of nodes with close degrees is characteristic for such networks 40. It is also known that the exact localization of Laplacian eigenvectors can occur on networks 11. However, it is only possible for networks having special structures and, typically, it would not be found in large random networks.

In contrast to scale-free networks, all nodes in an Erdös–Rényi network become statistically identical in the infinite-size limit and the heterogeneity disappears 7. Therefore, Turing patterns in such networks should tend to become uniformly random in this limit, similar to those in globally coupled systems 43, 44. Note, however, that significant heterogeneity and, thus, localization are still found by us for Erdös–Rényi networks with about a thousand of nodes, viewed as large in typical biological or ecological applications.

Turing instability may be realized experimentally using networks of coupled chemical reactors 10. Recent progress in nanofluidics allows one to construct even microscopical biomimetic reactors, down to the nanoscale, and couple many of them into complex networks 45. The original study by Othmer and Scriven 8 has been motivated by an observation that, in the early stages of biological morphogenesis, an embryo should represent a multicellular network rather than a continuous reaction–diffusion medium. Indeed, the contact network of biological cells in the developing embryo of Caenorhabditis elegans has been determined 46, 47 and much experimental evidence for the presence of activator–inhibitor mechanisms in biological morphogenesis has been gathered 26, 27, 28, 29. Turing instability may occur in cellular networks under the same conditions as those for continuous biological media.

There has long been discussion about the possibility of classical Turing patterns in spatially extended ecological systems. Recently, it has been shown that the conditions needed for the Turing instability in predator–prey ecosystems can be generally satisfied and, therefore, Turing patterns should represent a characteristic form of ecological self-organization 31, 32, 33. There is a broad class of ecological systems which represent networks 12, 13, 14, 15, 16. The nodes of such a network are individual habitat patches (such as trees or lakes), and diffusive coupling between them results from dispersal connections between the habitats. Complex networks of connections between the habitats can develop (see, for example, refs 13, 14, 15). Often, predators are more mobile than the prey, thus favouring the Turing instability. Similar behaviour may be expected in epidemiology where infected individuals are autocatalytically reproducing and the number of available susceptible individuals may get reduced, decreasing the reproduction efficiency 5. Spreading of infections over air transportation networks has been actively discussed 7, 17, 18.

Taking into account that preconditions for the Turing instability are satisfied by a broad class of biological and ecological systems, it is very possible that such an instability has already been observed in experiments. However, it would be difficult to tell, by looking at species distribution, whether a particular observed complex pattern is a result of an intrinsic Turing instability or it is a consequence of heterogeneity in the local properties of the nodes. In this situation, an efficient strategy may be to focus not merely on the observation of complex patterns, but to investigate how such patterns respond to various perturbations and parameter variations. Such a strategy has recently been successfully followed to prove the existence of the classical Turing instability in the patterns of skin colouring in fish 48, 49. If an observed pattern is the result of the Turing mechanism, it should develop spontaneously when the conditions are changed. Only a subset of network nodes which have similar degrees should undergo differentiation initially and this subset would change for the same network if the mobilities of species or other parameters are varied. After a perturbation, a different stable stationary pattern should generally be established.

It has already been demonstrated 50 that synthetic predator–prey ecosystems can be experimentally designed. If such a system is distributed over a number of habitats with artificial dispersal connections between the habitats and, moreover, if the rates of dispersal for the predator and the prey species can be independently controlled, this would present a clear set-up for the experimental investigations of Turing patterns in ecological networks.

Methods:

Equation (3) has a single stable fixed point when b = 0 (that is, e = 0), and, as b is increased, this system typically undergoes a saddle-node bifurcation that gives rise to a new stable fixed point.

In Fig. 6, we have computed stationary Turing patterns of the Mimura–Murray model by numerical integration of equation (2), and determined the respective global mean fields H^(u) and H^(v) at s=15.6 and s=30. Substituting these computed global mean fields into equation (3), bifurcation diagrams of a single node have been obtained. Each node i in the network is characterized by its degree k_i, so that it possesses a certain value of the bifurcation parameter, b=ek_i. Therefore, the obtained bifurcation diagrams can be projected onto the Turing pattern as shown in Fig. 6. See Supplementary Information for more details.

This work was supported by the Volkswagen Foundation, Germany, and by the MEXT, Japan (Global COE Program ‘The Next Generation of Physics, Spun from Universality and Emergence’ and Kakenhi Grant No. 19760253).

Author Contributions:

Both authors designed the study, carried out the analysis, and contributed to writing the paper. H.N. performed numerical simulations.

Competing interests statement
The authors declare no competing financial interests.

Received 23 December 2008; Accepted 15 March 2010; Published online 25 April 2010.

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This extremely detailed and perceptive formulation by Hiroya Nakao and Alexander Mikhailov of the molecular principles of tissue self-organization now raises new questions about the presence of similar mechanisms during the progression and metastasis of vertebrate neoplasms. Such questions have already been raised in the fields of cell de-differetiation and entropic gain as observed within human neoplasms, and may now be further correlated with the tumor responses noted after therapy with effective RNA therapy of diverse neoplasms.

1. Frenster JH, "Medical Systems Biology".

2. Frenster JH, "Human Throughput Systems".

3. Markert CL,  "Neoplasia: A Disease of Cell Differetiation".

4. Mishra PJ,  and Merlino G,  "MicroRNA reexpression as differentiation therapy in cancer".

5. Taulli R, Bersani F, Foglizzo V, Linari A, Vigna E, Ladanyi M, Tuschl T, and Ponzetto C,
"The muscle-specific microRNA miR-206 blocks human rhabdomyosarcoma growth in xenotransplanted mice by promoting myogenic differentiation".

1. Each cell retains all of its embryonic genes for a lifetime.

2. Controls for embryonic genes are often absent in adults.

3. Uncontrolled embryonic genes can replicate wildly.

4.  Replicating genes participate in  intra-cellular competition.

5.  The basis for gene competition is selective transcription.

6.  MicroRNAs can reprogram embryomic transcription.

7.  Gene reprogramming can produce normal phenotypes.

8.  Normal phenotypes can by-pass chromosomal lesions.

9.  MicroRNA therapy may need to be permanent.

10. Transplantation of microRNAs could be preferred.

http://www.embryomas.net/

1. Pathways within cell genomes involve a flow of information.

2. Information can flow by direct contact or by third parties.

3. Direct contact within whole genomes is difficult to regulate.

4. DNA-DNA direct contects are influenced by agents.

5. Nuclear agents include hydrophilic ionic and hydrophobic conforming ligands.

6. Third parties within genomes involve RNAs and proteins.

7.  RNAs and proteins are easy to regulate or reverse.

8.  Information can be shared, lost, or transformed.

9. System information can be hidden during system isolation.

10.  Local information can be permanently lost during system entropy.

http://www.embryomas.net/

Links to Current Research in Euchromatin:
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A Brief History of Activator RNA:

"Ultrastructural Probes of Active DNA Sites, and the RNA Activators of DNA".
(PowerPoint Presentation).

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