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Invited Special Paper |
Department of Plant Biology, Cornell University, Ithaca, New York 14853-5908 USA
Received for publication July 11, 2002. Accepted for publication October 25, 2002.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONTHE CIRCUIT/SUBSYSTEM PARADIGMPLANT MORPHOGENETIC...WHERE DO WE GO...APPENDIXLITERATURE CITED |
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Key Words: auxin • control systems • gene networks • logic circuits • morphogenesis • plant hormones • signal transduction • signal-activated subsystems
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONTHE CIRCUIT/SUBSYSTEM PARADIGMPLANT MORPHOGENETIC...WHERE DO WE GO...APPENDIXLITERATURE CITED |
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Nevertheless, uncovering the many synergistic layers of morphogenesis and learning how they are integrated in time and space remain daunting challenges even in the thrilling age of molecular biology. It is almost tautological to say that the metabolic and genomic "machinery" of development is exquisitely complex, especially in light of the concurrent molecular signaling required to keep this machinery operating in a coordinated manner across the many levels of plant organization. For example, we have long known that hormone signaling elicits rapid cellular responses predicated on preexisting metabolic and physical conditions and that it can also evoke delayed differential gene transcription, which can dramatically alter preexisting conditions. Recently, however, developmental signaling has been shown to involve the symplastic translocation of messenger RNAs to targeted sites of action (Aaziz et al., 2001
; Lucus et al., 2001
) as well as numerous interactions among a plethora of very small and thus difficult to detect molecular species, e.g., polyamines and FK506-binding proteins. Indeed, as biologists continue to explore the multifarious lines of plant molecular communication, the emerging picture is becoming more and more complicated.
Various attempts have been made to cope with this complexity in ways that are both conceptually robust and easily communicated without loss of information. In this respect, many biologists are converging on the pictorial and analytical conventions used by engineers and computer scientists who regularly deal with large networked systems. Specifically, signal pathways are being rendered in ways that are strikingly similar to logic circuits "hot-wiring" signal-activated metabolic or genomic subsystems (e.g., Klipp and Heinrich, 1999
; Cabanac and Russek, 2000
; Bhalla and Iyengar, 2001
; Fox and Hill, 2001
; Aoki et al., 2002
; Mortveit and Reidys, 2002
; Suzuki, 2002
).
The circuit/subsystem paradigm has merit. Seemingly insuperably complex phenomena can be diagrammed or predicted. As yet undetected components in these diagrams can be identified, often by visual inspection. Missing elements can be sought either experimentally or analytically. Complete diagrams can be modeled mathematically and manipulated to predict the consequences of changing one or more circuit or subsystem components, and the predicted responses can be evaluated by experimental manipulation of the biological prototypes. Finally, once verified, models for subcellular and cellular developmental phenomena can be grouped by progressive combination into larger models treating the behavior of higher levels of organization (see Davidson, 1986
; Kauffman, 1993
; Green, 1999
).
This paradigm is also attractive when viewed from the perspective of evolutionary biology. In theory, ancestral patterns of development can be "switched off" by suppressing a signal just as they can be evolutionarily transformed by establishing new signals or redirecting old ones (see Raff, 1996
). Genomic changes are required in either case, but the machinery of development can remain intact and lie dormant for generations only to be resurrected from the ‘dead’ unless corroded by random mutation. Indeed, when development is viewed in terms of its "logic" and "machinery," Dollo's Law (i.e., complex morphological features are unlikely to be evolutionarily regained in a clade once they are lost) appears terribly misleading, because it ignores the propinquity of repairing ancient developmental signaling pathways.
Nonetheless, the use of the circuit/subsystem paradigm in biology is not well established nor is it without potential pitfalls. Therefore, as auditors of morphogenesis, we must understand how logic circuits and signal-activated subsystems work. It is also necessary to evaluate their utility when confronted with real developmental phenomena. This paper is outlined around these two desiderata. The first section provides a skeletal review of logic circuits and signal-activated subsystems. The second illustrates how both can be used to render and examine a few selected developmental phenomena.
The conclusion drawn from this brief foray is that the diagrammatic conventions of the circuit/subsystem paradigm are heuristically useful. However, the use of this paradigm will remain intellectually superficial until the mathematical tools that have been developed to analyze and model the intrinsic behavior of logic circuits and signal-activated subsystems are employed to full advantage.
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THE CIRCUIT/SUBSYSTEM PARADIGM |
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TOPABSTRACTINTRODUCTIONTHE CIRCUIT/SUBSYSTEM PARADIGMPLANT MORPHOGENETIC...WHERE DO WE GO...APPENDIXLITERATURE CITED |
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and Sikorski (1964)
; for an application to plant development, see Stein (1998)
; and for applications to chemical and genetic systems see Kauffman (1993)
. However, at a very basic level, there are only two kinds: combinatorial circuits, in which the output signal depends exclusively on the instantaneous value of the input signal, and sequential circuits, in which the output signal also depends on the history of prior inputs (for an example, see Fig. 3). Both types conceptualize a signaling pathway as an electrical circuit containing one or more switches. The "logic" of a circuit is the formal algorithm that describes the conditions (logical propositions) that dictate whether a signal passes through a circuit. These conditions are depicted as "switches" (denoted by letters A, B, ..., Z) each of which is either "on" if its condition holds true or "off" if its condition is not true (e.g., A and 
A, respectively).
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B, A · B, or A · B, respectively), the pathway is dormant (i.e., the cell is not physiologically competent to perceive or transduce the signal). Nevertheless, even a "dormant" (suppressed) pathway can convey a morphogenetic "signal," since the absence of a response is a response. Parallel and serial circuits exist. The former provides manifold responses to the same signal depending on current conditions, since parallel circuits allow an initial input signal to flow through two or more pathways, permitting two or more output signals at each terminus and thus, theoretically, four or more combinatorial responses from the machinery the circuits operate. Consider a parallel circuit constructed with three switches, A, B, and C. This trifurcate signal pathway (symbolized as A v B v C, where v denotes "or") has eight possible combinatorial responses, i.e., 2N=3 = 8, where N is the number of switches.
Responses coordinated by parallel logic circuits can manifest continuous variation in response to the passage of a single input signal if they contain even a modest number of switches (i.e., 2N=10 = 1024), if some switches activate or suppress other switches in a logic circuit, if a logic circuit has two or more input signals, or if the output signals interact combinatorially. Also, if switches respond to more than one signal then the number of possible output signals is F = 22N, where F is the number of input signals to which switches can respond. In contrast, machines operated by simple serial circuits generally have simple binary on/off responses.
Provided that the algorithms describing two or more logic circuits are logically equivalent, a signal will pass through them, evoke the same output signal, and thus produce the same response. Therefore, large and complex circuits can be redacted and simplified to obtain smaller (algorithms) circuits, which are functionally (logically) equivalent. For example, the logic circuit (A · C) v (A v B) is logically equivalent to [(A · C) v A] v B, which is equivalent to C v A v B (Fig. 1A–B). Similarly, the algorithm (A · B · C) v (C · A) is logically equivalent to C · [(A · B) v A] and thus identical to C · (B v A) (Fig. 1C–D).
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This last point is important because most morphogenetic phenomena are perceived as a series of continuous transformational events, whereas the logic circuit paradigm appears as an "either/or" proposition. This apparent paradox results from the different time-scales over which morphogenesis and its molecular signaling operate. Provided that a complex binary system operates combinatorially over short timescales, it can evoke seemingly seamless transformations, much as the plucking of harpsichord strings engenders a melody (and, whereas the number of strings is finite, the number of possible melodies is effectively boundless; see Kauffman, 1993
; Niklas, 1994
; Rand, 1994
).
Signal-activated subsystems
To be useful, logic circuits must be wedded to the subsystems they supervise. There are a variety of signal-activated subsystem configurations. However, the simplest is error-activated, i.e., the output signal is used to modulate the input signal.
This configuration has four essential components (for classic references, see Harrison, 1965
; Hill and Peterson, 1968
): (1) a comparator to measure the difference (error) between the actual and the desired output of the subsystem, (2) an actuator/suppressor to convert the error-signal into an internal signal, (3) the actual machinery or assemblage that is controlled (the subsystem assembly), and (4) a feedback element to direct the immediate output signal of the assemblage back to the comparator (Fig. 1E). In some respects, the feedback element is the most important of these four components, because its influence (and thus presence) can be rapidly diagnosed, thereby permitting an experimentalist to determine whether a particular biological phenomenon is appropriately treated as an error-activated subsystem.
Technically, feedback is defined as that property of a closed-loop system that permits the comparison of the output signal (or some other variable controlled by the subsystem) to the input of the subsystem (or an input to some other internal component) so that the control action is some function of the input-to-output ratio. An investigator need not know the details of the feedback element to ascertain its presence, because a feedback element confers four characteristics: an increased range of input signals over which the subsystem responds satisfactorily, reduced sensitivity to variations in the output to input signal ratio, reduced effects of nonlinear distortions, and a tendency toward initial oscillatory behavior. Negative and positive feedback loops exist and a single loop can serve in both capacities, especially in the case of a subsystem hot-wired by a sequential (history-dependent) logic circuit (for an interesting example, see Bhalla et al., 2002
).
To illustrate a signal-activated subsystem, consider the lactose (lac) operon of Escherichia coli (Fig. 2). The I structural gene encodes for the lac repressor protein that binds with the O operon sequence to block the transcription of the polycistronic mRNA encoded by the Z–Y–A structural gene sequence. In the presence of lactose or lactose analogs, the repressor protein configuration changes, the O operon is de-repressed, and ß-galactosidase, permease, and transacetylase are transcribed. Here, the comparator is the lac repressor protein, the feedback element is lactose cell concentration, the assemblage is the molecular machinery required for polycistronic mRNA transcription and translation, and the actuator/suppressor is the I structural gene.
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The linkage of two or more subsystems confers two emergent properties, viz. the ability to achieve global stability and recursive combinatorial regulation. The importance of global behavior cannot be overemphasized, because it confers homeostasis. Much like an open chemical system, any network composed of two or more error-actuated subsystems rapidly achieves a steady state regardless of its initial conditions (e.g., reactant-product concentrations). Likewise, recursive combinatorial regulation is important. This property refers to the synergistic feedback signaling of numerous components that can permit a network to repeatedly cycle through a programmed series of transformations.
These features are illustrated by returning to the logic circuit paradigm and a simple circuit consisting of three switches (1, 2, and 3), one of which is governed by an "and" function (switch 1) and two of which are governed by "or" functions (Fig. 3A). In this example, each switch receives signals from the other two, examines their combined input signals, checks its logic "rules," and assumes its designated state in synchrony with the other two switches to achieve an instantaneous configuration. This process is repeated; each configuration updates all the switches such that recursive cycles reconfigure the responses of the system driven by the circuit. In this way, the circuit-driven system achieves a predictable series of transformations (Fig. 3B). This system is deterministic in the sense that the series of transformations it achieves is finite and repetitive, i.e., at some point the input signals return to their initial conditions and the entire series of transformations is repeated. An obvious analogy is the cell cycle.
Although no single "master" actuator or suppressor switch exists in isolation once this system is set into operation, the network governed by the aforementioned three-switch logic circuit as a whole requires "initiation," that is, one subsystem must receive a signal and temporarily function as an epistatic actuator. When switched on or off, this subsystem sparks the operation of the entire network, suppressing or activating one or more of the networked subsystems.
This feature is illustrated by considering a hypothetical "master" gene Gcr that encodes for a regulatory protein Gcr, which activates or suppresses four other genes, G1–G4 (Fig. 3C). In this model, Gcr "initiates" the G1-4 network and obtains two different P1-4 protein expression patterns depending on whether Gcr is activated or suppressed in a particular cell. Some of these gene products serve as recursive elements by suppressing or maintaining the activity of Gcr. However, the "initiation" of the master gene requires an external signal or stimulus (just as in all of the previous examples of signal-activated systems).
Indeed, an "incompleteness theorem" governs the working of networked systems. The operation of a subsystem cannot be fully diagnosed in isolation of the operations of the other subsystems to which it is networked. This theorem can be proved mathematically, but is illustrated by means of another hypothetical example. Consider two nuclear genes (G1, G2), their enhancer-promoters (EP1, EP2), a plasmalemma docking protein (DP) activated or suppressed by a hormone (H), and two regulatory proteins (P1, P2). For convenience, all the elements in this network may be diagrammed as suppression or activation switches (Fig. 4). At the structural level, this network is a self-contained system regardless of the presence of H. However, in terms of its operation, this network is suppressed or activated by H, which is delivered from an external source.
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PLANT MORPHOGENETIC CIRCUIT/SUBSYSTEM DIAGRAMS |
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TOPABSTRACTINTRODUCTIONTHE CIRCUIT/SUBSYSTEM PARADIGMPLANT MORPHOGENETIC...WHERE DO WE GO...APPENDIXLITERATURE CITED |
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; Taiz and Zeiger, 1998
; Cooke et al., 2002
).
Auxin signal perception/transduction
The mechanisms for IAA perception and response are poorly understood in part because more than one response pathway may be activated or repressed by a single signal-receptor mechanism. However, IAA-induced rapid responses, such as cell membrane hyperpolarization, help to identify the mechanism of IAA perception, whereas delayed IAA-mediated responses, such as gene transcription or cell expansion, can be used to evaluate long-term responses (see Barbier-Brygoo, 1995
).
Studies of rapid IAA-mediated responses have identified a single IAA-binding protein (ABP1), which is the first plant protein identified to contain a C-terminal KDEL sequence, i.e., an endoplasmic reticulum lumen-retention sequence (Pelham, 1988
; Jones et al., 1998
). Although this sequence suggests that IAA perception and signal transduction reside in the ER lumen and not on the cell membrane, studies indicate that ABP1 has low affinity for IAA at typical pH levels in the ER.
This paradox is partially resolved by the observation that ABP1 is present on the surface of the plasmalemma in amounts estimated at 1000 molecules per cell (see Timpte, 2001
). Because a small number of receptors is required to achieve half-maximum hormone occupancy and response, cell membrane-bound ABP1 may provide high IAA-sensitivity. Nevertheless, the presence of higher concentrations of ABP1 in the ER (and to a lesser extent in the golgi) in tandem with delayed IAA-mediated responses favors a "dual signal transduction site" hypothesis (Timpte, 2001
), wherein cell membrane ABP1 binding of IAA evokes rapid responses and intracellular ABP1-IAA binding sites may evoke delayed responses.
Technologically divergent studies provide convincing evidence that ABP1 mediates cell perception of IAA and subsequent signal transduction. Cell membrane hyperpolarization assays in tandem with antibodies directed against ABP1 indicate that the native protein rapidly transduces the IAA-mediated signal to effect membrane electrical potential but fails to do so when antibodies are present (Leblanc et al., 1999
). Likewise, KDEL-deleted ABP1 gives the same response as in control plants. These lines of evidence suggest that IAA binds to and changes the plasmalemma-bound ABP1 configuration, which then interacts with docking proteins or ion channels to transmit a signal rapidly. This hypothesis is compatible with the phenomenology predicted by the acid-growth theory. The ABP1-IAA conjugate could rapidly upgrade the activity of electrogenic plasmalemma-bound ATPases that acidify the apoplast and subsequently activate one or more apoplastic polysaccharidases (PSases) to cleave load-bearing cell wall bonds allowing for plastic and thus permanent cell wall expansion (Fig. 5).
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). Some of these gene products may be involved in the synthesis of cell wall components, whereas others may mediate the vesicular transport and delivery of these components to the apoplast.
This dual signal transduction site hypothesis is rendered in Fig. 5 as a logic circuit governing the machinery of cell expansion. The plasmalemma-bound ABP1-IAA conjugate is diagrammed as the actuator/suppressor switch for ATPases. Once activated, the apoplast is acidified, cell wall bonds are broken (expansins have been implicated in this process; Cosgrove, 2000
), and turgor pressure drives cell expansion (not shown). The ABP1-IAA switch is also diagrammed to trigger delayed cytoplasmic and genomic responses involving the synthesis and delivery of cell wall components. The posited logic circuit diagram shows that sustained osmoregulation and cell wall loosening are required for continued cell expansion. The diagram also shows that the feedback loop and comparator for the output signal of the cell expansion machinery are unknown and must be sought experimentally (Fig. 5). The IAA degradation, the down-regulation of solute concentrations, the synthesis of new cell-wall-binding polymers, the reorientation of cellulose microfibrils, the deposition of secondary wall layers, and the degradation of wall-loosening enzymes are among the many viable candidates for these missing network components.
This ABP1-IAA circuit/subsystem diagram indirectly addresses the role of IAA in early embryogenesis. In Arabidopsis, ABP1 is encoded by a single gene (At-ERabp1). Knockout plants harboring a T-DNA insertion in the first At-ERabp1 exon fail to produce viable homozygous plants (Palme et al., 1992
). Knockout embryos abort at the globular stage of development, whereas transgenic addition of a functional copy of ABP1 rescues embryos. Disruption of At-ERabp1 is thus lethal and normal development requires at least one functional At-ERabp1 copy.
Examination of aborted embryos reveals anomalous cell wall patterns and the absence of normal cell elongation (Chen et al., 2001b
), whereas analyses of tobacco cell line ABP1 loss-of-function mutants indicate that ABP1 gene disruption abolishes the ability to achieve cell volumes beyond those of parent cells. Thus, the failure to mediate sustained IAA-induced cell expansion may be the cause of embryo lethality in Arabidopsis knockout plants. Because cell expansion occurs in the absence of normal cell elongation, the ABP1-IAA logic circuit diagram for Arabidopsis suggests that the At-ERabp1 transcript interacts with an unidentified networked subsystem that governs anisometric cell expansion.
The cell cycle
Various lines of evidence indicate that the ABP1-IAA circuit/subsystem cross-talks at some level with the mitotic cell cycle network (Fig. 6). Cell expansion normally precedes the G2 advance in the cell cycle and IAA-mediated events activate S phase genes (see Stals and Inzé, 2001
). Likewise, ABP1 over-expression in tobacco leaves prematurely advances cells to the G2 phase relative to control plants (Chen et al., 2001a
), whereas antisense suppression of ABP1 eliminates IAA-induced elongation and reduces cell division (Chen et al., 2001b
).
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), the key elements of the RB pathway are highly conserved. The non-phosphorylated form of RB (tumor suppressor) protein binds to and suppresses a family of E2F-DP transcription factors for multiple genes regulating the procession of the cell-cycle phases. Phosphorylation of RB requires the active forms of a cyclin-dependent kinase A (CDKA) and the D-type cyclins (CycD) complex, both of which are suppressed by the CDK inhibitory kinase protein (ICK) (Harbour and Dean, 2000
; Stals and Inzé, 2001
).
The cross-talking in this network is very complex and incompletely understood. However, a variety of plant regulators are known to either activate or suppress the transcription of CDKA, CycD, or ICK (Fig. 6). Specifically, during G1, the transcription of the CDKA catalytic subunit is activated by IAA and suppressed by abscisic acid (ABA); the transcription of CycD is activated by sugars, cytokinin (CK), and brassinosteroids (BR); and the transcription of ICK is activated by ABA and gibberellin (GA). The G1 to S phase transition involves GA, which upgrades the transcription of the CDK-activating kinase CDKD1, which phosphorylates CDKA, thereby activating the CDKA-CycD complex (see Stals and Inzé, 2001
). In turn, this complex phosphorylates RB in late G1, which de-suppresses the E2F-DP complex, thereby activating the transcription of genes required for entry into the S phase (Fig. 6).
The G2 to M phase transition is associated with a Thr160 phosphorylation of CDK by a CDK-activating kinase (CAK) and by dephosphorylation of the inhibitory Tyr phosphorylation induced by CK. In conjunction, IAA, GA, and CK also regulate the kinase activity of A- and B-type CDKs by activating their transcription and that of A- and B-type cyclins. A ubiquitin-dependent degradation pathway targeting B-type cyclins for proteolysis by the anaphase-promoting complex (APC) at the metaphase-anaphase transition activates the exit from mitosis. The ubiquitin proteolysis system may also play a central role by activating the degradation of one or more gene product suppressors of the mitotic cell cycle. In contrast, a number of stress-induced plant hormones are known to suppress cell division. For example, ABA inhibits cell division, suggesting that ABA may mediate the induction of ICK and thus down-regulate CDK activity. An additional level of complexity is added by the roles played by cytochrome P450 monooxygenases (P450s), a large group of heme-containing enzymes, most of which catalyze hydroxylation reactions and thus play a critical role in the biosynthesis of IAA, GA, and BR (Kim and Tsukaya, 2002
). Because the concentrations of these enzymes influence the activation or suppression of CDKA, CycD, or ICK transcription, P450s may serve as the comparators in some cell-cycle phases (Fig. 6).
Intercellular auxin transport
The preceding circuit/subsystem diagrams do not address intercellular IAA transport, which is largely basipetal in shoots and both acropetal and basipetal in roots. Nor do they cope with lateral IAA transport, which is important to photo- and gravitropic responses. Nonetheless, these diagrams must network at some level to the intercellular IAA polar and lateral transport diagram provided in Fig. 7.
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). One of these is a transmembrane transport protein, which is encoded by members of the PIN gene family. The second is an IAA-inhibitor-binding protein, which performs a regulatory function in response to endogenous inhibitors, e.g., flavonoids. The mechanism by which IAA-transport inhibitors affect IAA-efflux carrier proteins is unknown. However, the activity of many regulatory proteins is controlled by post-translational modifications mediated by protein kinases and phosphatases that produce rapid and reversible changes in protein conformation, which can adapt to changing intra- or intercellular physiological conditions. Phosphorylation and dephosphorylation can increase or decrease the activity of an enzyme or even alter the reaction catalyzed. These features are tentatively incorporated in the circuit/subsystem diagram shown in Fig. 7.
Evidence that dephosphorylation and phosphorylation regulate the activity of the IAA-efflux carrier protein comes from a variety of sources. For example, the Arabidopsis roots curl in NPA1 gene (RCN1) encodes a regulatory subunit of protein phosphatase 2A (PP2A). This gene is expressed in seedling root tips, lateral root primordia, the pericycle, and the stele. The rcn1 mutant exhibits reduced PP2A activity and defects in IAA-mediated responses involving anisotropic cell expansion (see Muday and DeLong, 2001
). The rcn1 mutant also exhibits a near twofold increase in IAA basipetal transport. Treatment of control plants with phosphatase inhibitors, such as cantharidin, produces the rcn1 phenotype. These lines of evidence indicate that PP2A regulates the IAA-polar-efflux carrier protein complex but that the regulatory effects of PP2A on basipetal and acropetal IAA transport are different. The activities of 1 or more protein kinases may counterbalance the effects of PP2A. Indeed, the results of inhibitor studies suggest that genes encoding several kinases may play a key role in regulating polar IAA transport, e.g., the treatment of tobacco cells with staurosporine or K252a, which are both broad-spectrum kinase inhibitors, rapidly reduces IAA efflux without affecting IAA influx. It must be noted, however, that the non-enzymatic, pH-driven influx of neutral IAA may account for the latter.
Based on this limited information, the suppressor/activator in the IAA polar transport circuit/subsystem diagram consists de minimis of IAA-efflux protein inhibitors (e.g., flavonoids) and the RCN1 gene encoding for the regulatory subunit of PP2A. Once again, the feedback loop and comparator in this diagram are unknown. Viable candidates for these missing components include intracellular IAA concentrations, which may indirectly or directly regulate RCN1 gene transcription. Nevertheless, the incompleteness of the logic circuit diagram emphasizes our incomplete knowledge of this important morphogenetic system.
The diagram shown in Fig. 7 indirectly addresses the manner in which carrier protein-membrane asymmetries for IAA efflux are established and maintained. Among asymmetric animal cell types (e.g., nerve cells), proteins characterizing different membrane domains are sorted by means of targeting golgi-vesicle delivery. Attachment to the actin cytoskeleton, either directly or by means of protein complexes, maintains membrane asymmetry once achieved. This model may hold true for plants. PIN gene family proteins typically show asymmetric plasmalemma localization, whereas inhibitors of golgi-vesicle secretion impede IAA transport. There is also some evidence that IAA-influx and -efflux carrier proteins are attached to the actin cytoskeleton (Cox and Muday, 1994
).
Lateral membrane asymmetries are suggested by recent genetic studies and implied by the Cholodny-Went hypothesis, i.e., lateral IAA transport across light- or gravity-stimulated tissues drives differential cell growth in volume. For example, mutations in genes encoding for IAA transport proteins (e.g., aux 1 and pin 2) obtain agravitropic phenotypes. Changes in the gravity vector produce asymmetric patterns of IAA-induced gene expression in the shoots and roots of transgenic plants expressing the GUS reporter under the control of IAA-response promoters. Also, some IAA transport inhibitors block gravitropic bending, have no evident affect on polar IAA transport, and evoke differential IAA-regulated gene expression. The existence of numerous PIN genes with distinct patterns of expression and PIN proteins with different patterns of membrane location indicate that polar and lateral IAA efflux involves different efflux carriers (Fig. 7).
Symplastic trafficking
The concept for plant signal molecules now embraces messenger RNAs, which can be symplastically translocated over long distances and targeted to specific sites. This signal trafficking, which is regulated in part by plasmodesmata (Aaziz et al., 2001
; Lucus et al., 2001
), is rendered very incompletely as a crude circuit/subsystem diagram in Fig. 8.
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). Evidence for the role of phloem plasmodesmatal networks comes from the presence of unique companion cell mRNAs in sieve cells (e.g., sucrose transporter 1 RNA) and post-transcriptional gene silencing propagation patterns in transgenic plants that conform to phloem nutrient-translocation patterns (Kühn et al., 1997
).
Importantly, transcript delivery can be targeted to specific sites in the plant body (Jansen, 2001
). For example, in mutant (stock) and wild-type (scion) tomato grafts, mutant mRNAs differentially accumulate in shoot meristems and leaf primordia (Min et al., 2001
). The mechanisms controlling the delivery system are unknown. However, in the tentative circuit/subsystem diagram shown in Fig. 8, plant nucleotide-specific cis-acting elements (i.e., zip codes) are postulated to interact with cell-specific conjugate proteins to potentiatate transcript delivery to targeted sites (see Lucus et al., 2001
). Size-exclusion-limit (SEL) recognition proteins on cell membranes bordering plasmodesmata (in conjunction with ER plasmodesmatal docking proteins and receptors) are also postulated to regulate the properties of plasmodesmatal cytoplasmic annuli to differentially transport mRNA complexes among adjoining cells.
Plasmodesmatal transport and molecular surveillance of mRNAs can provide a mechanism to activate or suppress regional or more global (whole-plant) gene expression patterns. The structure of this delivery and surveillance system may be developmentally dynamic (Fig. 8). Plants have the capacity not only to regulate the size of information molecules passing through symplastic domains established by plasmodesmata early in ontogeny, but they also have the ability to shift or disconnect subdomains during subsequent development by establishing new plasmodesmatal connections or closing old plasmodesmata (Biao et al., 1988
; Ding et al., 1999
). Thus, changeable channeling networks are available for the signal trafficking and cross-talking required for the coordination of primary meristems, xylogenesis, the formation of a vascular cambium, and a variety of other developmental phenomena.
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WHERE DO WE GO FROM HERE? |
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TOPABSTRACTINTRODUCTIONTHE CIRCUIT/SUBSYSTEM PARADIGMPLANT MORPHOGENETIC...WHERE DO WE GO...APPENDIXLITERATURE CITED |
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To visualize and conceptualize what is currently known about the logic and machinery of development, biologists are increasingly adopting the pictorial conventions of the logic circuit/signal-activated subsystem paradigm. The objective of this paper was to explore how this paradigm works and to illustrate its merits and detractions in terms of a few morphogenetic phenomena mediated by the "classic" plant hormones. No attempt was made to interconnect the diagrams posited for these phenomena, because each diagram draws sharp attention to unidentified, missing components, which increased in number as the subcellular to supracellular levels of organization were ascended. Indeed, the ease with which missing circuit or subsystem components can be identified by means of these diagrams is one of the merits of this approach.
However, the real power of the circuit/subsystem paradigm lies not in its pictorial appeal, which is superficial, but in the mathematical tools that have been developed to identify the emergent and potentially unique properties of specific networked systems. Every network, regardless of its complexity, can be described and characterized mathematically to represent its behavior. In some cases, simplifying assumptions must be made. But, in most cases, this description can be cast in terms of linear, ordinary differential equations. Techniques for solving these equations and modeling them are well documented in the mathematical, engineering, and ecological literature. These tools were not developed or used here, because they are extremely sophisticated and demand extensive explanation. A very simple illustration is provided in the Appendix. This example illustrates that even a very simple system requires familiarity with mathematics. It also shows the naïve notion of "one signal, one response."
If morphogenesis and thus evolution are to be understood at their deeper mechanistic levels, collaborative efforts among biologists, computer scientists, modelers, and mathematicians are required as never before. Signal-trafficking and cross-talking and the synergistic metabolic/genomic responses they engender must be empirically dissected and identified at their deepest levels. This work requires the expertise of biologists. However, as the details of development are excavated from the molecular level of plant organization, they must be archived, transformed into robust algorithms, analyzed mathematically, and modeled rigorously. These tasks require the aptitudes of those fluent in the language of mathematics, network modeling, and computer programming.
By juxtaposing and sharing different tools and perspectives, the cross-talk among seemingly disparate disciplines will enrich all participants. Biologists will undoubtedly learn more about the logic that drives the machinery of development, and engineers will learn more about the bio-logic of the oldest and most fascinating networks on the planet.
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APPENDIX |
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TOPABSTRACTINTRODUCTIONTHE CIRCUIT/SUBSYSTEM PARADIGMPLANT MORPHOGENETIC...WHERE DO WE GO...APPENDIXLITERATURE CITED |
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In terms of formal system analysis, the known components are lj for j = 1 to 7. The unknown components are hi for i = 2 to 5 and vj for j = 1 to 7. The task is to determine the magnitudes of the unknown components. From Fig. A1, the system components are logically restricted such that lj – vj = hk – hi. Because vj is the time measurement error, it must be subtracted from lj to correct for the temporal difference between any two morphogenetic events. This procedure gives the matrix:
For foregoing axiomatically shows that three relationships specify the temporal properties of the system shown in Fig. A1:
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FOOTNOTES |
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LITERATURE CITED |
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TOPABSTRACTINTRODUCTIONTHE CIRCUIT/SUBSYSTEM PARADIGMPLANT MORPHOGENETIC...WHERE DO WE GO...APPENDIXLITERATURE CITED |
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Aoki T. H. Kintano N. Kameya I. Nakamura 2002 Accelerated shoot overgrowth of rice mutant ao-1 is epistatic to gibberellin-sensitive and -insensitive dwarf mutants. Journal of Plant Research 115: 195-202[CrossRef][Web of Science][Medline]
Barbier-Brygoo H. 1995 Tracking auxin receptors using functional approaches. Critical Reviews in Plant Science 14: 1-25
Bhalla U. S. R. Iyengar 2001 Robustness of the bistable behavior of a biological signaling feedback loop. Chaos 11: 221-226[CrossRef][Web of Science][Medline]
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