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Bilaterally symmetric facial morphology simulated by diffusion-controlled chemical precipitation in gel
Chemical Physics Letters 556 (2013) 315–319
Contents lists available at SciVerse ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Bilaterally symmetric facial morphology simulated by diffusion-controlled chemical precipitation in gel John Petruska a, Laura M. Barge b,⇑ a b
Molecular and Computational Biology, Department of Biological Sciences, University of Southern California, 1050 Child’s Way, Los Angeles, CA 90089, USA Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
a r t i c l e
i n f o
Article history: Received 9 October 2012 In final form 19 December 2012 Available online 27 December 2012
a b s t r a c t Reactions controlled by diffusion create self-organizing periodic patterns in chemical systems and play a key role in biological pattern formation through diffusion-generated morphogen gradients. To better understand the organizing ability of diffusion-controlled assembly, we investigated the formation of bilaterally symmetric morphologies by simple inorganic precipitation reactions in neutral agarose gel. Our results reveal that bilaterally symmetric ‘face-like’ deposits of insoluble products reproducibly form in gel, by reactions governed by the properties and concentrations of soluble reactants placed symmetrically relative to a midline and by the temporal and spatial distributions arising by diffusion from initial times and positions of reactant placement. Ó 2013 Published by Elsevier B.V.
1. Introduction In developmental biology, gradients of diffusible biochemicals called morphogens control cell growth and differentiation by binding to cell-membrane receptors in complex biochemical signaling pathways that regulate cellular gene expression and resultant products [1,2]. Diffusion-controlled biochemical reactions are thought to play a key role in the development of many biological patterns [3], e.g., periodic segmentation in Drosophilia embryos, limb segmentation in vertebrates [4], and striped or spotted patterns in feather or hair growth [5,6]. In the case of vertebrate skeletal growth and facial features, bilateral symmetry seems to require retinoic acid, a vitamin A-derived amphipathic molecule able to diffuse through cell membranes [7–9]. Perhaps such a morphogen can stimulate the combination of intracellular and extracellular activities needed for fibroblasts to abundantly produce and secrete the triple-helical protein, collagen, which aggregates (i.e. precipitates) in extracellular space to form the connective tissue fibers of skeleton and skin. How collagen fiber production is regulated to achieve bilateral symmetry in the whole body plan has yet to be determined. Symmetric patterns can arise in simple chemical precipitation systems when soluble reactants, such as inorganic anions and cations, move only by diffusion while forming insoluble ionic combinations (precipitates) in an aqueous gel. The formation of an insoluble precipitate occurs when the combination of interacting anion and cation concentrations exceeds a certain threshold (the solubility product), whereupon precipitation may spontaneously ⇑ Corresponding author. E-mail address: [email protected] (L.M. Barge). 0009-2614/$ - see front matter Ó 2013 Published by Elsevier B.V. http://dx.doi.org/10.1016/j.cplett.2012.12.041
yield crystals or organized particulate deposits, such as periodic (Liesegang) bands or rings, held by the gel fibrous network [10–12]. Previously we have shown that periodic banding in agarose gel, observed for inorganic precipitates such as silver chromate or dichromate, is caused by soluble ionic impurities that can be removed by extracting agarose powder with pure water [13]. In the resultant neutral agarose gel, we can study the precipitation properties of inorganic ions in the absence of ionic impurities that induce the periodic banding observed in commercial agarose [13] and animal gelatin [13–16]. By using water-extracted agarose to avoid the effects of ionic impurities, we have begun to examine how diffusion-controlled patterns of ionic precipitation in neutral agarose gel depend on (i) the choice of ionic reactants and their concentrations, and (ii) where and when each reactant is introduced in the system. In this Letter we illustrate some examples of bilaterally symmetric ‘facial’ patterns formed by diffusion-controlled precipitation of inorganic ions in a thin layer of neutral agarose gel formed in a standard Petri dish. Such a gel allows anionic (a) and cationic (c) reactants to diffuse freely in two dimensions, while holding in place the insoluble (ac) products formed. Bilateral symmetry of insoluble product deposition is achieved in a reproducible fashion simply by using diffusion to regulate the ionic reactant concentrations as a function of distance and time from initial sites of highest concentration symmetrically placed with respect to a midline. 2. Experimental Gels of neutral agarose (0.5% by weight) were prepared by using electrophoresis grade agarose powder (Bio Rad), which was extracted with ultrapure water to remove ionic impurities [13],
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before being dissolved with stirring in hot water or aqueous solution at 99–100 °C. In each case, a 10-ml aliquot of hot agarose solution was transferred to a Petri dish (100 10 mm) on a level plate warmer (70 °C) and kept there for 10–15 min before slowly cooling to room temperature, in order to eliminate any pouringinduced effects in the gel. After cooling, gels were stored in a cold room at 4 °C in the dark to avoid light-induced conversion of Ag+ ion to Ag metal (photographic effect). To obtain the bilaterally symmetric diffusion-controlled morphologies shown here (Fig. 1), we used localized and extended competition on the midline, between two anionic reactants, a and b, competing to form an insoluble precipitate with symmetrically placed cationic reactant c (Fig. 1A and D, respectively). It should be noted that each Petri dish of gel was placed on top of a graph paper template showing the positions of drops to be added, to ensure accurate geometry for bilateral symmetry.
For localized competition (Fig. 1A), the agarose was dissolved in a hot solution of anionic reactant a (3 mM potassium chromate or potassium dichromate). After this gel containing uniformly distributed a had cooled to 4 °C, competing anionic reactant b was added as a 50 ll drop of 0.3 M potassium iodide, placed on spot marked b on the midline (Fig. 1A). Then a 50 ll drop of 4.0 M silver nitrate solution was placed at each of the two spots marked c, equidistant from the midline. For extended competition (Fig. 1D), the agarose gel was prepared without any added chemical and cooled to 4 °C, before placing a 50 ll drop of 0.3 M potassium chromate or dichromate at each of the two positions marked a on the midline and a 50 ll drop of 0.3 M potassium iodide at each of the two b positions on the same midline. These drops were allowed to diffuse into the gel for 5 days in the dark at 4 °C, to create bilaterally symmetric concentration gradients of chromate (or dichromate) and iodide within the gel. Then a 50 ll drop of 4 M silver nitrate was carefully placed at each of the two spots marked c, equidistant from the midline (Fig. 1D). In each experimental setup, after the silver nitrate drops were added, the gel was kept for at least three more days at 4 °C in the dark, before being photographed. As silver ions diffused into the gels, the following reactions occurred to produce insoluble precipitates (;) with the chromate, or dichromate, and iodide anions: þ 2 2Agþ þ CrO2 4 ! Ag2 CrO4 #, or 2Ag þ Cr2 O7 ! Ag2 Cr2 O7 #, and Agþ þ I ! AgI #. 3. Results 3.1. Facial morphologies formed by bilaterally symmetric diffusioncontrolled precipitation The two ‘eyes’ in our simulated facial morphologies (Fig. 1) are defined by the equidistant placement, relative to the midline, of two small (50 ll) drops of concentrated reactant c, in the form of colorless silver cation (Ag+) at 4 M concentration, as its highly soluble silver nitrate salt (AgNO3). These drops are added only after all the anionic reactants (a and b) have been placed to define ‘face with nose’ centered on the midline, as indicated in Figure 1A and D. As reactant a for ‘face’ formation, we chose the colored anion 2 of chromate (CrO2 4 ) or dichromate (Cr2 O7 ), which might be viewed as a colored mimic of the dominant but colorless phosphate or pyrophosphate anion in biology. As reactant b that competes with a for ‘nose’ formation, we chose the colorless iodide anion (I), also as potassium salt, after finding that chloride (Cl) and bromide (Br) gave less satisfactory results (data not shown). The results shown here (Fig. 1B, C, E and F) clearly reveal that even simple chemical precipitation reactions between inorganic ions, when controlled by diffusion from symmetric reactant arrangements, can produce insoluble product morphologies resembling those made by complex biological organisms.
Figure 1. Experimental setups and resulting diffusion-controlled precipitation patterns obtained with one cationic reactant and two competing anionic reactants. (A) First experimental setup, where colored anionic reactant a (potassium chromate or dichromate) was uniformly distributed in the agarose gel at low concentration, before a drop of competing colorless anionic reactant b (potassium iodide) at higher concentration was placed at one spot marked by a dot on the gel, along with two symmetrically placed drops of colorless cationic reactant c (silver nitrate) at even higher concentration. (B and C) are the resultant diffusion-controlled precipitation patterns for colored silver chromate and dichromate, respectively. (D) The second experimental setup, starting with plain agarose gel with alternating drops of reactants a and b at equal concentration placed as indicated by dots and allowed to diffuse for 5 days to create diffusion gradients of a and b before drops of reactant c were added in the same two symmetric locations. These produced the very different precipitation patterns (E) and (F) for colored silver chromate and dichromate, respectively. (The concentrations and volumes of the a–c drops are detailed in the Section 2).
3.2. Morphologies formed with localized competition on the midline In our first experimental setup (Fig. 1A), used to obtain the results in Figure 1B and C, anionic reactant a was uniformly distributed at low concentration (3 mM) in the hot agarose gel solution before a 10 ml aliquot was pipetted into a Petri dish and then covered on a plate warmer. After the gel had been cooled slowly to 4 °C, anionic reactant b and cationic reactant c were carefully placed as 50 ll drops on top of the solidified gel, as indicated by the dots in Figure 1A. The covered gel was then kept in the dark at 4 °C for at least two days to obtain complete diffusion-controlled precipitation of both silver iodide and silver chromate or dichromate.
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Figure 1B shows the results obtained when the uniformly distributed reactant a was 3 mM chromate (K2CrO4) and Figure 1C, when a was 3 mM dichromate (K2Cr2O7) instead. In each case, the competing anionic reactant b was applied as a 50 ll drop of 0.3 M iodide (KI) to define the ‘nose’ position. Also, in each case, the two symmetrically placed drops of cationic reactant c, defining the two ‘eye’ positions, were each 50 ll of 4 M AgNO3. Therefore in each experiment the diffusing Ag+ ions were at sufficiently high concentration to act as morphogens in precipitating silver chromate or dichromate (2Agþ þ CrO2 or 2Agþ þ 4 ! Ag2 CrO4 #, Cr2 O2 ! Ag Cr O #), not only in the ‘eye’ region, but also every2 7 2 7 where else in the gel, including the ‘nose’ region where silver iodide precipitation (Ag+ + I ? AgI;) competed with silver chromate or dichromate precipitation to shape the nose morphology. As we see in Figure 1B and C, a sharply defined zone of precipitation roughly triangular in shape is formed in this region and a ‘nose-like’ morphology appears in this region over a period of time (about 48 h). In the case of Figure 1B, the silver chromate is precipitated in very fine particles outside the nose region, while in Figure 1C the crystals of silver dichromate are much more conspicuous. In both cases, crystals are no longer apparent in the nose region where iodide is competing with chromate for the silver, and the triangular shape of this region is defined by the diffusion of silver ions from two bilaterally symmetric locations. 3.3. Morphologies formed with extended competition in chemical gradients In our second experimental setup, shown in Figure 1D, we started with a 0.5% agarose gel devoid of any added chemicals. Instead of using a uniform distribution of chromate or dichromate, we created gradients of chromate or dichromate alternating with iodide, prior to addition of the silver nitrate. Gradients were created by placing alternating drops of competing anionic reactants, a and b, evenly spaced on the midline (Fig. 1D). In this case the gradient was allowed to form over a period of several days before cationic reactant c (silver nitrate) was added as two symmetrically placed drops in the same positions and same concentration as before. Figure 1E and F show the results for the two cases: a as chromate and dichromate, respectively. Comparing Figure 1B and E, we see the strong effect on morphology of having a gradient of chromate and iodide anions competing for silver cations instead of having a uniform distribution of chromate with competing iodide restricted to a ‘nose-like’ domain. The same is true for the comparison of Figure 1C and F, for dichromate instead of chromate. By creating concentration gradients of the competing a and b reactants, we not only observe (Fig. 1E and F) a dramatic change in both eye and nose morphology, but also no longer see any evidence of the crystalline structures observed in Figure 1B and C. The experimental setup in Figure 1A gives similar nose morphologies with a as chromate (Fig. 1B) or dichromate (Fig. 1C), but the setup in Figure 1D gives very different nose as well as eye morphologies, as seen in Figure 1E and F. In the case of chromate (Fig. 1E) there is a sharp boundary around the ‘eyes’ and ‘nose’ regions, and the ‘forehead’ above the eyes is very different from the ‘mouth’ region below the nose. In contrast, the dichromate case (Fig. 1F) yields more diffuse boundaries and less difference between the ‘forehead’ and ‘mouth’ regions. 4. Discussion In this Letter we present experimental examples of reproducible bilaterally symmetric morphologies resulting from competing precipitation reactions in a diffusion-controlled system, starting
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with very simple initial conditions. Rather than introducing a complex template of localized sources for the outer reactant, as Grzybowski and colleagues have done in a wet stamping technique [14–17], we chose to focus on systems where there are only two sources of the outer reactant located symmetrically about a midline to simulate bilaterally symmetric pattern formation – a hallmark of biology. As a diffusion medium we used neutral agarose gel (electrophoresis-grade agarose purified by successive extractions with deionized-and-distilled water). Such a gel contains little or no soluble ionic components, in contrast to the gelatin used by the majority of previous workers. Gelatin is often being used without taking into account that its soluble organic ions can induce periodic banding in inorganic precipitates, especially silver chromate and dichromate [13]. Since gelatin is primarily used in the wet stamping technique [14–16], it is likely that the soluble organic components of gelatin are responsible for the periodic banding patterns observed, rather than the precipitation reactions themselves [13].
4.1. Diffusion-controlled pattern formation in neutral agarose The patterns formed by inorganic precipitates in neutral agarose are highly reproducible given the same set of initial conditions, as revealed by the striking maintenance of bilateral symmetry in our simple diffusion-controlled chemical precipitation experiments. Chemical diffusion obeys Fick’s laws for describing the concentration at any point as a function of distance and time, in terms of a diffusion constant. In our work we ensured that the gel was uniform by keeping the Petri dish of gel on a plate warmer for at least 10–15 min before it was allowed to cool slowly, in order to minimize any asymmetry or distortions caused by pouring. We also made sure the plates were horizontal so the thickness of the gel would be the same at every point. By specifying the initial conditions accurately, the concentration of reactants and insoluble products at every position can then be reproduced accurately. This enables resultant (insoluble) product structures to be defined in two (and possibly 3) dimensions by defining initial reactant conditions in small areas, e.g., placing a small drop of reactant at a specific site. In reaction-diffusion systems, the geometry of reactant placement [18] along with the chemical conditions such as electrolyte concentration and pH [19–21] can affect the resulting precipitation pattern. Precipitation in the form of crystals or small colloidal particles can be considered as an assembly process of soluble reactive units (e.g. inorganic ions) that form insoluble products held in place by the gel fibers. In our simple system, we chose silver cation (Ag+) at high enough concentration to precipitate all the anions placed in or on the gel. The silver cation therefore behaves like a morphogen, since it is at sufficiently high concentration to diffuse throughout the entire gel and precipitate all of the anionic components, which may be viewed as behaving like morphogen receptors. The fact that the patterns we obtained are bilaterally symmetric is a good indication of the reproducibility of patterns formed by diffusioncontrolled product formation. As seen in Figure 1B and C, at each of the two points where we added the silver cation in a concentrated drop, we obtained a dense precipitate of silver chromate (Fig. 1B) or silver dichromate (Fig. 1C). This silver precipitate formed in a circular shape of limited size in the place where the drop made direct contact with the gel. Where silver came in contact with chromate or dichromate alone, the precipitate was densely packed at the point of highest silver concentration, but beyond that point we observed crystalline growth with clear spaces between the crystals.
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4.2. Inhibition of silver chromate/silver dichromate crystal growth by iodide When the silver reached the area where iodide was present along with chromate or dichromate as a consequence of diffusion, there was no visual evidence of typical silver chromate or dichromate crystal growth, suggesting that iodide was inhibiting crystal growth. There was a sharp boundary that marked the leading edge of the iodide diffusion front, separating the ‘nose’ region from the region which contained chromate or dichromate alone without iodide. Within this bounded region we could see changes in deposition that gave rise to structures resembling the shape of a nose (Fig. 1B and C). When we alternated drops of chromate (or dichromate) and iodide on the midline and allowed them to mix together by diffusion to create a gradient ranging from chromate at the top to iodide at the bottom, before adding the silver ion (Fig. 1D), no crystal growth was seen at any point within the various structures that were formed (Fig. 1E and F), indicating that iodide ion inhibits crystal growth of both silver chromate and dichromate. (It should be noted that silver iodide on its own produces very fine colloidal particles of precipitate.) The resultant patterns in Figure 1E and F reveal the complex changes in morphology obtained simply by changing the initial arrangement of the reactants in space and time. 4.3. Specification of initial conditions In this simple chemical experiment, there are four independent variables that need to be specified in order to reproduce the results. We can simply term these as ‘What?’, ‘How much?’, ‘Where?’, and ‘When?’. ‘What’ refers to the choice of chemicals being used to create the gradients and precipitated products in the morphology. This condition is approximately the same in all of our experiments, since all contain colorless silver cation reacting with colorless iodide anion competing with colored chromate or dichromate anion. However, as can be seen by comparing the silver chromate results (Fig. 1B and E) with silver dichromate results (Fig. 1C and F), a change in only one reactant (chromate replaced by dichromate) can dramatically alter the diffusion-controlled precipitation pattern. In our two experimental setups (Fig. 1A and D), we used the same three chemical reactants and similar but not identical total amounts of each reactant, i.e., ‘What’ and ‘How much’ were only slightly changed. However, between Figure 1A and D, the ‘Where’ and ‘When’ components were changed significantly. The ‘Where’ and ‘When’ components of reaction-diffusion systems refer to the geometry and timing of initial reactant placement, and it has been shown in previous work that the geometry of reactants can affect precipitation patterns through interference of reaction fronts [18]. The ‘What’ and ‘How much’ components refer to the chemical conditions of the experiment: for example, the pH of the gel can affect the solubility of precipitating compounds (as shown in aluminum hydroxide reaction–diffusion experiments [20–21]), and in the case of chromate/dichromate where relative abundances of these precipitating ions are pH dependent, pH changes in the gel would also alter reactant concentrations. The formation of stable reaction–diffusion precipitation patterns in gels has been shown to depend on electrolyte flux, relative electrolyte concentration, and pH conditions throughout the diffusion medium [19–21], and in our experiments the formation of reproducible bilaterally symmetric morphologies requires that these parameters be held constant. In Figure 1D, instead of distributing chromate or dichromate evenly throughout the gel at a relatively low concentration as in Figure 1A, we placed two drops at a much higher concentration
on the midline, alternately spaced with two drops of iodide at the same concentration. The even more concentrated silver nitrate was added later, in two symmetrically placed drops after gradients of iodide and chromate (or dichromate) had formed by diffusion over a period of several days. Our results demonstrate how sensitive the self-organized morphologies produced in reactiondiffusion precipitation systems are to initial conditions, and also that a variety of complex morphologies can be produced from a small number of reacting components. 4.4. Relevance to patterning in biology controlled by diffusible molecules In biology, developmental pattern formation begins on a much smaller scale, the distances involved in embryonic development being orders of magnitude smaller than those in our experiments. The molecules controlling development are likely to be much larger and diffuse much more slowly to form significant diffusion gradients in such small distances. Biology is capable of producing many types of hydrophilic protein or polysaccharide chains that form gels or highly viscous solutions in water. In fact a gel environment can be formed with any randomly oriented polymer that is capable of binding water so as to restrain the bulk movement of water while allowing chemical diffusion to occur in a uniform manner. In biological development, polymers such as polysaccharides or polypeptides can increase the viscosity of the medium, either inside the cell or outside in the extracellular matrix. Gels create an environment in which rather complex reproducible structures can be made simply by specifying the initial conditions. Biological gels may initially be simple, but over time may become elaborated into more complex structures, after patterns have been established under diffusion control in the early simpler environments. A gel-like medium, preferably with uniform diffusion constants in all directions, might be sufficient to maintain the diffusion gradients of morphogens that control pattern formation, in a manner similar to our diffusion-controlled chemical precipitation experiments. In biological systems ‘What’ may be considered to represent the genes that are the source of DNA information required to make proteins, some of which synthesize the morphogens that control gene expression through signaling pathways. We may think of DNA transcription, translation, protein targeting and associated signaling pathways as the biological way of determining ‘How much’, ‘Where’, and ‘When’. The diffusion of morphogens determines their gradients, which in turn control the signaling pathways that regulate gene expression as a function of position and time in the growth of an organism. In this way, many forms of biological morphology can be made using the same genes, but altering the signaling pathways that control these genes, thus altering the time and place of gene activation. As we have shown here, arranging the chemical sources symmetrically about a midline is sufficient, in a diffusion-controlled (i.e. gel) environment, to create a bilaterally symmetric pattern of insoluble products. Once the sources and their positions relative to a midline are specified, the bilaterally symmetric pattern is self-assembling and highly reproducible. Thus the morphology obtained by diffusion-controlled precipitation resembles certain biological morphologies because both are regulated, at least in part, by diffusible molecules moving in accordance with the laws of diffusion. 5. Conclusions Our simple reaction-diffusion experiments in neutral agarose gel demonstrate how complex morphologies can arise from simple
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initial conditions in a uniform diffusion-controlled medium. In such a medium precipitation patterns are highly reproducible as long as the initial conditions in space and time are accurately reproduced. We obtained complex bilaterally symmetric patterns with only two competing precipitation reactions occurring in the gel. With such simple chemical systems, involving only chemical precipitation in diffusion gradients, we have mimicked the formation of facial structures, showing how readily a complex morphology with bilateral symmetry can arise from basic physical and chemical processes. Acknowledgement Part of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. Ó 2012. References [1] A.D. Lander, Cell 144 (2011) 955. [2] A.D. Lander, Cell 128 (2007) 245. [3] L. Wolpert, In Principles of Development, Oxford University Press, Oxford, England, 2007.
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[4] A. Roselló-Díez, M.A. Ros, M. Torres, Science 332 (2011) 1086. [5] C.-M. Lin, T.X. Jiang, R.E. Baker, P.K. Maini, R.B. Widelitz, C.-M. Chuong, Dev. Biol. 334 (2009) 369. [6] D.J. Headon, K.J. Painter, Math. Models Nat. Phenom. 4 (2009) 83. [7] G. Duester, Cell 134 (2008) 921. [8] J. Vermot, J.G. Llamas, V. Fraulob, K. Kiederreither, P. Chambon, P. Dollé, Science 308 (2005) 563. [9] G.C. Vilhais-Neto, M. Maruhashi, K.T. Smith, M. Vasseur-Cognet, A.S. Peterson, J.L. Workman, O. Pourquié, Nature 463 (2010) 953. [10] R.E. Liesegang, Naturwiss. Wochenschr. 11 (1896) 353. [11] S. Leduc, The Mechanism of Life 1914 Eng. Trans. by W. Deane Butcher, William Heinemann, London, 1911. 197p.. [12] H.K. Henisch, Crystals in Gels and Liesegang Rings, Cambridge University Press, Cambridge, 1988. [13] L.M. Barge, K. Nealson, J. Petruska, Chem. Phys. Lett. 493 (4–6) (2010) 340. [14] I.T. Bensemann, M. Fialkowski, B.A.J. Grzybowski, Phys. Chem. B 109 (2005) 2774. [15] S.K. Smoukov, I. Lagzi, B.A.J. Grzybowski, Phys. Chem. Lett. 2 (2011) 345. [16] R. Klajn et al., Nat. Mater. 3 (2004) 729. [17] B.A. Gryzbowski, K.J.M. Bishop, C.J. Campbell, M. Fialkowski, S.K. Smoukov, Soft Matter 1 (2005) 114. [18] C.-S. Kuo, E. López-Cabarcos, R. Bansil, Physica A 239 (1997) 120. [19] E. López-Cabarcos, C.-S. Kuo, A. Scala, R. Bansil, Phys. Rev. Lett. 77 (13) (1996) 2834. [20] A. Volford, F. Izsák, M. Ripszám, I.J. Lagzi, Phys. Chem. B 110 (2006) 4535. [21] F. Molnár Jr., L. Roszol, A. Volford, I. Lagzi, Chem. Phys. Lett. 503 (2011) 231.
Contents lists available at SciVerse ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Bilaterally symmetric facial morphology simulated by diffusion-controlled chemical precipitation in gel John Petruska a, Laura M. Barge b,⇑ a b
Molecular and Computational Biology, Department of Biological Sciences, University of Southern California, 1050 Child’s Way, Los Angeles, CA 90089, USA Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
a r t i c l e
i n f o
Article history: Received 9 October 2012 In final form 19 December 2012 Available online 27 December 2012
a b s t r a c t Reactions controlled by diffusion create self-organizing periodic patterns in chemical systems and play a key role in biological pattern formation through diffusion-generated morphogen gradients. To better understand the organizing ability of diffusion-controlled assembly, we investigated the formation of bilaterally symmetric morphologies by simple inorganic precipitation reactions in neutral agarose gel. Our results reveal that bilaterally symmetric ‘face-like’ deposits of insoluble products reproducibly form in gel, by reactions governed by the properties and concentrations of soluble reactants placed symmetrically relative to a midline and by the temporal and spatial distributions arising by diffusion from initial times and positions of reactant placement. Ó 2013 Published by Elsevier B.V.
1. Introduction In developmental biology, gradients of diffusible biochemicals called morphogens control cell growth and differentiation by binding to cell-membrane receptors in complex biochemical signaling pathways that regulate cellular gene expression and resultant products [1,2]. Diffusion-controlled biochemical reactions are thought to play a key role in the development of many biological patterns [3], e.g., periodic segmentation in Drosophilia embryos, limb segmentation in vertebrates [4], and striped or spotted patterns in feather or hair growth [5,6]. In the case of vertebrate skeletal growth and facial features, bilateral symmetry seems to require retinoic acid, a vitamin A-derived amphipathic molecule able to diffuse through cell membranes [7–9]. Perhaps such a morphogen can stimulate the combination of intracellular and extracellular activities needed for fibroblasts to abundantly produce and secrete the triple-helical protein, collagen, which aggregates (i.e. precipitates) in extracellular space to form the connective tissue fibers of skeleton and skin. How collagen fiber production is regulated to achieve bilateral symmetry in the whole body plan has yet to be determined. Symmetric patterns can arise in simple chemical precipitation systems when soluble reactants, such as inorganic anions and cations, move only by diffusion while forming insoluble ionic combinations (precipitates) in an aqueous gel. The formation of an insoluble precipitate occurs when the combination of interacting anion and cation concentrations exceeds a certain threshold (the solubility product), whereupon precipitation may spontaneously ⇑ Corresponding author. E-mail address: [email protected] (L.M. Barge). 0009-2614/$ - see front matter Ó 2013 Published by Elsevier B.V. http://dx.doi.org/10.1016/j.cplett.2012.12.041
yield crystals or organized particulate deposits, such as periodic (Liesegang) bands or rings, held by the gel fibrous network [10–12]. Previously we have shown that periodic banding in agarose gel, observed for inorganic precipitates such as silver chromate or dichromate, is caused by soluble ionic impurities that can be removed by extracting agarose powder with pure water [13]. In the resultant neutral agarose gel, we can study the precipitation properties of inorganic ions in the absence of ionic impurities that induce the periodic banding observed in commercial agarose [13] and animal gelatin [13–16]. By using water-extracted agarose to avoid the effects of ionic impurities, we have begun to examine how diffusion-controlled patterns of ionic precipitation in neutral agarose gel depend on (i) the choice of ionic reactants and their concentrations, and (ii) where and when each reactant is introduced in the system. In this Letter we illustrate some examples of bilaterally symmetric ‘facial’ patterns formed by diffusion-controlled precipitation of inorganic ions in a thin layer of neutral agarose gel formed in a standard Petri dish. Such a gel allows anionic (a) and cationic (c) reactants to diffuse freely in two dimensions, while holding in place the insoluble (ac) products formed. Bilateral symmetry of insoluble product deposition is achieved in a reproducible fashion simply by using diffusion to regulate the ionic reactant concentrations as a function of distance and time from initial sites of highest concentration symmetrically placed with respect to a midline. 2. Experimental Gels of neutral agarose (0.5% by weight) were prepared by using electrophoresis grade agarose powder (Bio Rad), which was extracted with ultrapure water to remove ionic impurities [13],
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before being dissolved with stirring in hot water or aqueous solution at 99–100 °C. In each case, a 10-ml aliquot of hot agarose solution was transferred to a Petri dish (100 10 mm) on a level plate warmer (70 °C) and kept there for 10–15 min before slowly cooling to room temperature, in order to eliminate any pouringinduced effects in the gel. After cooling, gels were stored in a cold room at 4 °C in the dark to avoid light-induced conversion of Ag+ ion to Ag metal (photographic effect). To obtain the bilaterally symmetric diffusion-controlled morphologies shown here (Fig. 1), we used localized and extended competition on the midline, between two anionic reactants, a and b, competing to form an insoluble precipitate with symmetrically placed cationic reactant c (Fig. 1A and D, respectively). It should be noted that each Petri dish of gel was placed on top of a graph paper template showing the positions of drops to be added, to ensure accurate geometry for bilateral symmetry.
For localized competition (Fig. 1A), the agarose was dissolved in a hot solution of anionic reactant a (3 mM potassium chromate or potassium dichromate). After this gel containing uniformly distributed a had cooled to 4 °C, competing anionic reactant b was added as a 50 ll drop of 0.3 M potassium iodide, placed on spot marked b on the midline (Fig. 1A). Then a 50 ll drop of 4.0 M silver nitrate solution was placed at each of the two spots marked c, equidistant from the midline. For extended competition (Fig. 1D), the agarose gel was prepared without any added chemical and cooled to 4 °C, before placing a 50 ll drop of 0.3 M potassium chromate or dichromate at each of the two positions marked a on the midline and a 50 ll drop of 0.3 M potassium iodide at each of the two b positions on the same midline. These drops were allowed to diffuse into the gel for 5 days in the dark at 4 °C, to create bilaterally symmetric concentration gradients of chromate (or dichromate) and iodide within the gel. Then a 50 ll drop of 4 M silver nitrate was carefully placed at each of the two spots marked c, equidistant from the midline (Fig. 1D). In each experimental setup, after the silver nitrate drops were added, the gel was kept for at least three more days at 4 °C in the dark, before being photographed. As silver ions diffused into the gels, the following reactions occurred to produce insoluble precipitates (;) with the chromate, or dichromate, and iodide anions: þ 2 2Agþ þ CrO2 4 ! Ag2 CrO4 #, or 2Ag þ Cr2 O7 ! Ag2 Cr2 O7 #, and Agþ þ I ! AgI #. 3. Results 3.1. Facial morphologies formed by bilaterally symmetric diffusioncontrolled precipitation The two ‘eyes’ in our simulated facial morphologies (Fig. 1) are defined by the equidistant placement, relative to the midline, of two small (50 ll) drops of concentrated reactant c, in the form of colorless silver cation (Ag+) at 4 M concentration, as its highly soluble silver nitrate salt (AgNO3). These drops are added only after all the anionic reactants (a and b) have been placed to define ‘face with nose’ centered on the midline, as indicated in Figure 1A and D. As reactant a for ‘face’ formation, we chose the colored anion 2 of chromate (CrO2 4 ) or dichromate (Cr2 O7 ), which might be viewed as a colored mimic of the dominant but colorless phosphate or pyrophosphate anion in biology. As reactant b that competes with a for ‘nose’ formation, we chose the colorless iodide anion (I), also as potassium salt, after finding that chloride (Cl) and bromide (Br) gave less satisfactory results (data not shown). The results shown here (Fig. 1B, C, E and F) clearly reveal that even simple chemical precipitation reactions between inorganic ions, when controlled by diffusion from symmetric reactant arrangements, can produce insoluble product morphologies resembling those made by complex biological organisms.
Figure 1. Experimental setups and resulting diffusion-controlled precipitation patterns obtained with one cationic reactant and two competing anionic reactants. (A) First experimental setup, where colored anionic reactant a (potassium chromate or dichromate) was uniformly distributed in the agarose gel at low concentration, before a drop of competing colorless anionic reactant b (potassium iodide) at higher concentration was placed at one spot marked by a dot on the gel, along with two symmetrically placed drops of colorless cationic reactant c (silver nitrate) at even higher concentration. (B and C) are the resultant diffusion-controlled precipitation patterns for colored silver chromate and dichromate, respectively. (D) The second experimental setup, starting with plain agarose gel with alternating drops of reactants a and b at equal concentration placed as indicated by dots and allowed to diffuse for 5 days to create diffusion gradients of a and b before drops of reactant c were added in the same two symmetric locations. These produced the very different precipitation patterns (E) and (F) for colored silver chromate and dichromate, respectively. (The concentrations and volumes of the a–c drops are detailed in the Section 2).
3.2. Morphologies formed with localized competition on the midline In our first experimental setup (Fig. 1A), used to obtain the results in Figure 1B and C, anionic reactant a was uniformly distributed at low concentration (3 mM) in the hot agarose gel solution before a 10 ml aliquot was pipetted into a Petri dish and then covered on a plate warmer. After the gel had been cooled slowly to 4 °C, anionic reactant b and cationic reactant c were carefully placed as 50 ll drops on top of the solidified gel, as indicated by the dots in Figure 1A. The covered gel was then kept in the dark at 4 °C for at least two days to obtain complete diffusion-controlled precipitation of both silver iodide and silver chromate or dichromate.
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Figure 1B shows the results obtained when the uniformly distributed reactant a was 3 mM chromate (K2CrO4) and Figure 1C, when a was 3 mM dichromate (K2Cr2O7) instead. In each case, the competing anionic reactant b was applied as a 50 ll drop of 0.3 M iodide (KI) to define the ‘nose’ position. Also, in each case, the two symmetrically placed drops of cationic reactant c, defining the two ‘eye’ positions, were each 50 ll of 4 M AgNO3. Therefore in each experiment the diffusing Ag+ ions were at sufficiently high concentration to act as morphogens in precipitating silver chromate or dichromate (2Agþ þ CrO2 or 2Agþ þ 4 ! Ag2 CrO4 #, Cr2 O2 ! Ag Cr O #), not only in the ‘eye’ region, but also every2 7 2 7 where else in the gel, including the ‘nose’ region where silver iodide precipitation (Ag+ + I ? AgI;) competed with silver chromate or dichromate precipitation to shape the nose morphology. As we see in Figure 1B and C, a sharply defined zone of precipitation roughly triangular in shape is formed in this region and a ‘nose-like’ morphology appears in this region over a period of time (about 48 h). In the case of Figure 1B, the silver chromate is precipitated in very fine particles outside the nose region, while in Figure 1C the crystals of silver dichromate are much more conspicuous. In both cases, crystals are no longer apparent in the nose region where iodide is competing with chromate for the silver, and the triangular shape of this region is defined by the diffusion of silver ions from two bilaterally symmetric locations. 3.3. Morphologies formed with extended competition in chemical gradients In our second experimental setup, shown in Figure 1D, we started with a 0.5% agarose gel devoid of any added chemicals. Instead of using a uniform distribution of chromate or dichromate, we created gradients of chromate or dichromate alternating with iodide, prior to addition of the silver nitrate. Gradients were created by placing alternating drops of competing anionic reactants, a and b, evenly spaced on the midline (Fig. 1D). In this case the gradient was allowed to form over a period of several days before cationic reactant c (silver nitrate) was added as two symmetrically placed drops in the same positions and same concentration as before. Figure 1E and F show the results for the two cases: a as chromate and dichromate, respectively. Comparing Figure 1B and E, we see the strong effect on morphology of having a gradient of chromate and iodide anions competing for silver cations instead of having a uniform distribution of chromate with competing iodide restricted to a ‘nose-like’ domain. The same is true for the comparison of Figure 1C and F, for dichromate instead of chromate. By creating concentration gradients of the competing a and b reactants, we not only observe (Fig. 1E and F) a dramatic change in both eye and nose morphology, but also no longer see any evidence of the crystalline structures observed in Figure 1B and C. The experimental setup in Figure 1A gives similar nose morphologies with a as chromate (Fig. 1B) or dichromate (Fig. 1C), but the setup in Figure 1D gives very different nose as well as eye morphologies, as seen in Figure 1E and F. In the case of chromate (Fig. 1E) there is a sharp boundary around the ‘eyes’ and ‘nose’ regions, and the ‘forehead’ above the eyes is very different from the ‘mouth’ region below the nose. In contrast, the dichromate case (Fig. 1F) yields more diffuse boundaries and less difference between the ‘forehead’ and ‘mouth’ regions. 4. Discussion In this Letter we present experimental examples of reproducible bilaterally symmetric morphologies resulting from competing precipitation reactions in a diffusion-controlled system, starting
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with very simple initial conditions. Rather than introducing a complex template of localized sources for the outer reactant, as Grzybowski and colleagues have done in a wet stamping technique [14–17], we chose to focus on systems where there are only two sources of the outer reactant located symmetrically about a midline to simulate bilaterally symmetric pattern formation – a hallmark of biology. As a diffusion medium we used neutral agarose gel (electrophoresis-grade agarose purified by successive extractions with deionized-and-distilled water). Such a gel contains little or no soluble ionic components, in contrast to the gelatin used by the majority of previous workers. Gelatin is often being used without taking into account that its soluble organic ions can induce periodic banding in inorganic precipitates, especially silver chromate and dichromate [13]. Since gelatin is primarily used in the wet stamping technique [14–16], it is likely that the soluble organic components of gelatin are responsible for the periodic banding patterns observed, rather than the precipitation reactions themselves [13].
4.1. Diffusion-controlled pattern formation in neutral agarose The patterns formed by inorganic precipitates in neutral agarose are highly reproducible given the same set of initial conditions, as revealed by the striking maintenance of bilateral symmetry in our simple diffusion-controlled chemical precipitation experiments. Chemical diffusion obeys Fick’s laws for describing the concentration at any point as a function of distance and time, in terms of a diffusion constant. In our work we ensured that the gel was uniform by keeping the Petri dish of gel on a plate warmer for at least 10–15 min before it was allowed to cool slowly, in order to minimize any asymmetry or distortions caused by pouring. We also made sure the plates were horizontal so the thickness of the gel would be the same at every point. By specifying the initial conditions accurately, the concentration of reactants and insoluble products at every position can then be reproduced accurately. This enables resultant (insoluble) product structures to be defined in two (and possibly 3) dimensions by defining initial reactant conditions in small areas, e.g., placing a small drop of reactant at a specific site. In reaction-diffusion systems, the geometry of reactant placement [18] along with the chemical conditions such as electrolyte concentration and pH [19–21] can affect the resulting precipitation pattern. Precipitation in the form of crystals or small colloidal particles can be considered as an assembly process of soluble reactive units (e.g. inorganic ions) that form insoluble products held in place by the gel fibers. In our simple system, we chose silver cation (Ag+) at high enough concentration to precipitate all the anions placed in or on the gel. The silver cation therefore behaves like a morphogen, since it is at sufficiently high concentration to diffuse throughout the entire gel and precipitate all of the anionic components, which may be viewed as behaving like morphogen receptors. The fact that the patterns we obtained are bilaterally symmetric is a good indication of the reproducibility of patterns formed by diffusioncontrolled product formation. As seen in Figure 1B and C, at each of the two points where we added the silver cation in a concentrated drop, we obtained a dense precipitate of silver chromate (Fig. 1B) or silver dichromate (Fig. 1C). This silver precipitate formed in a circular shape of limited size in the place where the drop made direct contact with the gel. Where silver came in contact with chromate or dichromate alone, the precipitate was densely packed at the point of highest silver concentration, but beyond that point we observed crystalline growth with clear spaces between the crystals.
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4.2. Inhibition of silver chromate/silver dichromate crystal growth by iodide When the silver reached the area where iodide was present along with chromate or dichromate as a consequence of diffusion, there was no visual evidence of typical silver chromate or dichromate crystal growth, suggesting that iodide was inhibiting crystal growth. There was a sharp boundary that marked the leading edge of the iodide diffusion front, separating the ‘nose’ region from the region which contained chromate or dichromate alone without iodide. Within this bounded region we could see changes in deposition that gave rise to structures resembling the shape of a nose (Fig. 1B and C). When we alternated drops of chromate (or dichromate) and iodide on the midline and allowed them to mix together by diffusion to create a gradient ranging from chromate at the top to iodide at the bottom, before adding the silver ion (Fig. 1D), no crystal growth was seen at any point within the various structures that were formed (Fig. 1E and F), indicating that iodide ion inhibits crystal growth of both silver chromate and dichromate. (It should be noted that silver iodide on its own produces very fine colloidal particles of precipitate.) The resultant patterns in Figure 1E and F reveal the complex changes in morphology obtained simply by changing the initial arrangement of the reactants in space and time. 4.3. Specification of initial conditions In this simple chemical experiment, there are four independent variables that need to be specified in order to reproduce the results. We can simply term these as ‘What?’, ‘How much?’, ‘Where?’, and ‘When?’. ‘What’ refers to the choice of chemicals being used to create the gradients and precipitated products in the morphology. This condition is approximately the same in all of our experiments, since all contain colorless silver cation reacting with colorless iodide anion competing with colored chromate or dichromate anion. However, as can be seen by comparing the silver chromate results (Fig. 1B and E) with silver dichromate results (Fig. 1C and F), a change in only one reactant (chromate replaced by dichromate) can dramatically alter the diffusion-controlled precipitation pattern. In our two experimental setups (Fig. 1A and D), we used the same three chemical reactants and similar but not identical total amounts of each reactant, i.e., ‘What’ and ‘How much’ were only slightly changed. However, between Figure 1A and D, the ‘Where’ and ‘When’ components were changed significantly. The ‘Where’ and ‘When’ components of reaction-diffusion systems refer to the geometry and timing of initial reactant placement, and it has been shown in previous work that the geometry of reactants can affect precipitation patterns through interference of reaction fronts [18]. The ‘What’ and ‘How much’ components refer to the chemical conditions of the experiment: for example, the pH of the gel can affect the solubility of precipitating compounds (as shown in aluminum hydroxide reaction–diffusion experiments [20–21]), and in the case of chromate/dichromate where relative abundances of these precipitating ions are pH dependent, pH changes in the gel would also alter reactant concentrations. The formation of stable reaction–diffusion precipitation patterns in gels has been shown to depend on electrolyte flux, relative electrolyte concentration, and pH conditions throughout the diffusion medium [19–21], and in our experiments the formation of reproducible bilaterally symmetric morphologies requires that these parameters be held constant. In Figure 1D, instead of distributing chromate or dichromate evenly throughout the gel at a relatively low concentration as in Figure 1A, we placed two drops at a much higher concentration
on the midline, alternately spaced with two drops of iodide at the same concentration. The even more concentrated silver nitrate was added later, in two symmetrically placed drops after gradients of iodide and chromate (or dichromate) had formed by diffusion over a period of several days. Our results demonstrate how sensitive the self-organized morphologies produced in reactiondiffusion precipitation systems are to initial conditions, and also that a variety of complex morphologies can be produced from a small number of reacting components. 4.4. Relevance to patterning in biology controlled by diffusible molecules In biology, developmental pattern formation begins on a much smaller scale, the distances involved in embryonic development being orders of magnitude smaller than those in our experiments. The molecules controlling development are likely to be much larger and diffuse much more slowly to form significant diffusion gradients in such small distances. Biology is capable of producing many types of hydrophilic protein or polysaccharide chains that form gels or highly viscous solutions in water. In fact a gel environment can be formed with any randomly oriented polymer that is capable of binding water so as to restrain the bulk movement of water while allowing chemical diffusion to occur in a uniform manner. In biological development, polymers such as polysaccharides or polypeptides can increase the viscosity of the medium, either inside the cell or outside in the extracellular matrix. Gels create an environment in which rather complex reproducible structures can be made simply by specifying the initial conditions. Biological gels may initially be simple, but over time may become elaborated into more complex structures, after patterns have been established under diffusion control in the early simpler environments. A gel-like medium, preferably with uniform diffusion constants in all directions, might be sufficient to maintain the diffusion gradients of morphogens that control pattern formation, in a manner similar to our diffusion-controlled chemical precipitation experiments. In biological systems ‘What’ may be considered to represent the genes that are the source of DNA information required to make proteins, some of which synthesize the morphogens that control gene expression through signaling pathways. We may think of DNA transcription, translation, protein targeting and associated signaling pathways as the biological way of determining ‘How much’, ‘Where’, and ‘When’. The diffusion of morphogens determines their gradients, which in turn control the signaling pathways that regulate gene expression as a function of position and time in the growth of an organism. In this way, many forms of biological morphology can be made using the same genes, but altering the signaling pathways that control these genes, thus altering the time and place of gene activation. As we have shown here, arranging the chemical sources symmetrically about a midline is sufficient, in a diffusion-controlled (i.e. gel) environment, to create a bilaterally symmetric pattern of insoluble products. Once the sources and their positions relative to a midline are specified, the bilaterally symmetric pattern is self-assembling and highly reproducible. Thus the morphology obtained by diffusion-controlled precipitation resembles certain biological morphologies because both are regulated, at least in part, by diffusible molecules moving in accordance with the laws of diffusion. 5. Conclusions Our simple reaction-diffusion experiments in neutral agarose gel demonstrate how complex morphologies can arise from simple
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