Biomedical subjects

R. Edwards

Publications and source records attributed to R. Edwards.

4 recordsLinked to original sources

PubMed2001

Symbolic dynamics and computation in model gene networks.

We analyze a class of ordinary differential equations representing a simplified model of a genetic network. In this network, the model genes control the production rates of other genes by a logical function. The dynamics in these equations are represented by a directed graph on an n-dimensional hypercube (n-cube) in which each edge is directed in a unique orientation. The vertices of the n-cube correspond to orthants of state space, and the edges correspond to boundaries between adjacent orthants. The dynamics in these equations can be represented symbolically. Starting from a point on the boundary between neighboring orthants, the equation is integrated until the boundary is crossed for a second time. Each different cycle, corresponding to a different sequence of orthants that are traversed during the integration of the equation always starting on a boundary and ending the first time that same boundary is reached, generates a different letter of the alphabet. A word consists of a sequence of letters corresponding to a possible sequence of orthants that arise from integration of the equation starting and ending on the same boundary. The union of the words defines the language. Letters and words correspond to analytically computable Poincare maps of the equation. This formalism allows us to define bifurcations of chaotic dynamics of the differential equation that correspond to changes in the associated language. Qualitative knowledge about the dynamics found by integrating the equation can be used to help solve the inverse problem of determining the underlying network generating the dynamics. This work places the study of dynamics in genetic networks in a context comprising both nonlinear dynamics and the theory of computation. (c) 2001 American Institute of Physics.

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PubMed2000

Combinatorial explosion in model gene networks.

The explosive growth in knowledge of the genome of humans and other organisms leaves open the question of how the functioning of genes in interacting networks is coordinated for orderly activity. One approach to this problem is to study mathematical properties of abstract network models that capture the logical structures of gene networks. The principal issue is to understand how particular patterns of activity can result from particular network structures, and what types of behavior are possible. We study idealized models in which the logical structure of the network is explicitly represented by Boolean functions that can be represented by directed graphs on n-cubes, but which are continuous in time and described by differential equations, rather than being updated synchronously via a discrete clock. The equations are piecewise linear, which allows significant analysis and facilitates rapid integration along trajectories. We first give a combinatorial solution to the question of how many distinct logical structures exist for n-dimensional networks, showing that the number increases very rapidly with n. We then outline analytic methods that can be used to establish the existence, stability and periods of periodic orbits corresponding to particular cycles on the n-cube. We use these methods to confirm the existence of limit cycles discovered in a sample of a million randomly generated structures of networks of 4 genes. Even with only 4 genes, at least several hundred different patterns of stable periodic behavior are possible, many of them surprisingly complex. We discuss ways of further classifying these periodic behaviors, showing that small mutations (reversal of one or a few edges on the n-cube) need not destroy the stability of a limit cycle. Although these networks are very simple as models of gene networks, their mathematical transparency reveals relationships between structure and behavior, they suggest that the possibilities for orderly dynamics in such networks are extremely rich and they offer novel ways to think about how mutations can alter dynamics. (c) 2000 American Institute of Physics.

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PubMed1994

The Effects of Heavy Metals and Root Immersion on Isoflavonoid Metabolism in Alfalfa (Medicago sativa L.).

Modest increases in the concentration of medicarpin, 6-fold in leaves and 4-fold in roots, were observed in alfalfa (Medicago sativa L.) seedlings treated with 1 mM metal salts for 72 h. However, medicarpin-3-O-glucoside-6"-O-malonate (MGM) and formononetin-7-O-glucoside-6"-O-malonate (FGM) levels were up to 50-fold lower in metal-treated compared to control roots. Approximately 10% of the "missing" conjugates could be accounted for in the root treatment solution, where FGM and MGM transiently accumulated prior to their hydrolysis. Time-course studies revealed that total isoflavonoid content (roots plus solution) increased slightly after CuCl2 treatment, whereas the levels of FGM and MGM increased rapidly in alfalfa roots immersed in water. This increase was reduced by aeration. The phenylalanine ammonia-lyase inhibitor L-[alpha]-aminooxy-[beta]-phenylpropionic acid was used to show that immersion of the roots reduced conjugate rates of degradation, which explains their accumulation. In contrast, conjugate rates of degradation were elevated in CuCl2-treated roots, with 50% of the increase being due to hydrolysis. Up to 90% of formononetin and medicarpin produced in response to CuCl2 treatment arose via conjugate hydrolysis. Our results demonstrate that both immersion/anaerobiosis and abiotic elicitation modify isoflavonoid metabolism in alfalfa, and that metal-stimulated accumulation of phytoalexins may arise through the release from preformed stores rather than de novo synthesis.

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PubMed1993

Stress Responses in Alfalfa (Medicago sativa L.) (XIV. Changes in the Levels of Phenylpropanoid Pathway Intermediates in Relation to Regulation of L-Phenylalanine Ammonia-Lyase in Elicitor-Treated Cell-Suspension Cultures).

We have used high-resolution gas chromatography to determine the levels of trans-cinnamic acid (CA) and trans-4-coumaric acid (4CA) in alfalfa (Medicago sativa L.) cell-suspension cultures to address the role of these phenylpropanoid pathway intermediates as potential negative regulators of phenylalanine ammonia-lyase (PAL) in vivo. Exogenous addition of CA to elicitor-treated cultures resulted in rapid increases in endogenous CA, 4CA, and CA-conjugate levels associated with inhibition of the appearance of PAL transcripts. Treatment of elicited cultures with [alpha]-aminooxy-[beta]-phenylpropionic acid (AOPP), a potent and specific inhibitor of PAL activity in vivo, resulted in reductions of CA and 4CA, with concomitant increases in PAL transcripts and extractable enzyme activity. In contrast, treatment with tetcyclacis, an inhibitor of CA 4-hydroxylase, resulted in increased CA and CA-conjugate levels, decreased 4CA levels, and decreased PAL transcript levels and enzyme activity. In tetcyclasis-treated cells, the inhibition of PAL transcript appearance preceded the increase in the levels of free CA and its conjugates. In elicited cells in which the phenylpropanoid pathway was not perturbed by metabolic inhibitors, PAL transcripts accumulated rapidly and transiently, beginning to decline by 2 h postelicitation. Changes in levels of total free or conjugated CA or 4CA did not consistently correlate with these changes in transcript levels. We propose that regulation of PAL transcript levels by endogenous phenylpropanoid pathway intermediates could involve compartmentalized pools that may exist because of the microsomal localization of cinnamic acid 4-hydroxylase.

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