Mathematical modelling of dynamics and control in metabolic networks. II. Simple dimeric enzymes

The dynamics of enzyme cooperativity are examined by studying a homotropic dimeric enzyme with identical reaction sites, both of which follow irreversible Michaelis-Menten kinetics. The problem is approached via scaling and linearization of the governing mass action kinetic equations. Homotropic interaction between the two sites are found to depend on three dimensionless groups, two for the substrate binding step and one for the chemical transformation. The interaction between the two reaction sites is shown capable of producing dynamic behavior qualitatively different from that of a simple Michaelis-Menten system; when the two sites interact to increase enzymatic activity over that of two independent monomeric enzymes (positive cooperativity) damped oscillatory behavior is possible, and for negative cooperativity in the chemical transformation step a multiplicity of steady states can occur, with one state unstable and leading to runaway behavior. Linear analysis gives significant insight into system dynamics, and their parametric sensitivity, and a way to identify regions of the parameter space where the approximate quasi-stationary and quasi-equilibrium analyses are appropriate.     

Interstrand duplexes in Friend erythroleukemia nuclear RNA. The interaction of non-polyadenylated nuclear RNA with polyadenylated nuclear RNA and with small nuclear RNAs

Intermolecular duplexes among large nuclear RNAs, and between small nuclear RNA and heterogeneous nuclear RNA, were studied after isolation by a procedure that yielded protein-free RNA without the use of phenol or high salt. The bulk of the pulse-labeled RNA had a sedimentation coefficient greater than 45 S. After heating in 50% (v/v) formamide, it sedimented between the 18 S and 28 S regions of the sucrose gradient. Proof of the existence of interstrand duplexes prior to deproteinization was obtained by the introduction of interstrand cross-links using 4'-aminomethyl-4,5',8-trimethylpsoralen and u.v. irradiation. Thermal denaturation did not reduce the sedimentation coefficient of pulse-labeled RNA obtained from nuclei treated with this reagent and u.v. irradiated. Interstrand duplexes were observed among the non-polyadenylated RNA species as well as between polyadenylated and non-polyadenylated RNAs. beta-Globin mRNA but not beta-globin pre-mRNA also contained interstrand duplex regions. In this study, we were able to identify two distinct classes of polyadenylated nuclear RNA, which were differentiated with respect to whether or not they were associated with other RNA molecules. The first class was composed of poly(A)+ molecules that were free of interactions with other RNAs. beta-Globin pre-mRNA belongs to this class. The second class included poly(A)+ molecules that contained interstrand duplexes. beta-Globin mRNA is involved in this kind of interaction. In addition, hybrids between small nuclear RNAs and heterogeneous nuclear RNA were isolated. These hybrids were formed with all the U-rich species, 4.5 S, 4.5 SI and a novel species designated W. Approximately equal numbers of hybrids were formed by species U1a, U1b, U2, U6 and W; however, species U4 and U5 were significantly under-represented. Most of these hybrids were found to be associated stably with non-polyadenylated RNA. These observations demonstrated for the first time that small nuclear RNA-heterogeneous nuclear RNA hybrids can be isolated without crosslinking, and that proteins are not necessary to stabilize the complexes. However, not all molecules of a given small nuclear RNA species are involved in the formation of these hybrids. The distribution of a given small nuclear RNA species between the free and bound state does not reflect the stability of the complex in vitro but rather the abundance of complementary sequences in the heterogeneous nuclear RNA.(ABSTRACT TRUNCATED AT 400 WORDS)     

Interaction of coupled nonlinear oscillators having different intrinsic resting levels

The interaction among coupled oscillators is governed by oscillator properties (intrinsic frequency and amplitude) and coupling mechanisms. This study considers another oscillator property, the intrinsic resting level, and evaluates its role in governing oscillator interactions. The results of computer experiments on a chain of either three or five bidirectionally coupled nonlinear oscillators, suggest that an intrinsic resting level gradient, if present, is one of the factors governing the interaction between coupled oscillators. If there is no intrinsic frequency gradient, then an intrinsic resting level gradient is sufficient to produce many features of interaction among coupled oscillators. If both intrinsic frequency and intrinsic resting level gradients are present, then both of them determine the manner in which the coupled oscillators interact with each other.     

Application of reaction-diffusion models to cell patterning in Xenopus retina. Initiation of patterns and their biological stability

We have examined the behavior of two reaction-diffusion models, originally proposed by Gierer & Meinhardt (1972) and by Kauffman, Shymko & Trabert (1978), for biological pattern formation. Calculations are presented for pattern formation on a disc (approximating the geometry of a number of embryonic anlagen including the frog eye rudiment), emphasizing the sensitivity of patterns to changes in initial conditions and to perturbations in the geometry of the morphogen-producing space. Analysis of the linearized equations from the models enabled us to select appropriate parameters and disc size for pattern growth. A computer-implemented finite element method was used to solve the non-linear model equations reiteratively. For the Gierer-Meinhardt model, initial activation (varying in size over two orders of magnitude) of one point on the disc's edge was sufficient to generate the primary gradient. Various parts of the disc were removed (remaining only as diffusible space) from the morphogen-producing cycle to investigate the effects of cells dropping out of the cycle due to cell death or malfunction (single point removed) or differentiation (center removed), as occur in the Xenopus eye rudiment. The resulting patterns had the same general shape and amplitude as normal gradients. Nor did a two-fold increase in disc size affect the pattern-generating ability of the model. Disc fragments bearing their primary gradient patterns were fused (with gradients in opposite directions, but each parallel to the fusion line). The resulting patterns generated by the model showed many similarities to results of "compound eye" experiments in Xenopus. Similar patterns were obtained with the model of Kauffman's group (1978), but we found less stability of the pattern subject to simulations of central differentiation. However, removal of a single point from the morphogen cycle (cell death) did not result in any change. The sensitivity of the Kauffman et al. model to shape perturbations is not surprising since the model was originally designed to use shape and increasing size during growth to generate a sequence of transient patterns. However, the Gierer-Meinhardt model is remarkably stable even when subjected to a wide range of perturbations in the diffusible space, thus allowing it to cope with normal biological variability, and offering an exciting range of possibilities for reaction-diffusion models as mechanisms underlying the spatial patterns of tissue structures.     

腺苷酸激酶在我国九个民族中的多态分布

用淀粉胶电泳及特异染色的方法,对我国9个民族的腺苷酸激酶(AK)多态分布进行了测定。9个民族中维吾尔族AK表型分布具有多态性。维吾尔族中AK_1~1基因频率为0.965,AK_1~2基因频率为0.035,而侗、回、白、土家、苗、彝、藏、满等8个民族的AK_1~2均未达到多态水平。在9个民族中AK_1表型分布均符合Hardy-Weinberg平衡,并且未发现其它罕见表型。     

Growth in vitro of arrested embryos from lethal mutants ofArabidopsis thaliana

Summary Seventeen embryo-lethal mutants ofArabidopsis thaliana with lethal phases ranging from the globular to mature cotyledon stages of development were analyzed by culturing arrested embryos on nutrient media designed to promote either callus formation or the completion of embryo development and the recovery of homozygous mutant plants. Enriched media supplemented with vitamins, amino acids, and nucleosides were used to identify potential auxotrophic mutants. Wild-type embryos produced extensive callus on basal and enriched media supplemented with 2,4-D and kinetin. Numerous roots developed when wildtype callus was grown in the presence of NAA and kinetin. Mutant embryos arrested prior to the heart stage of development formed only a slight amount of callus on basal and enriched media. Arrested embryos from mutants 122G-E and 112A-2A reached a later stage of development and gave the most interesting responses in culture. 122G-E mutant embryos failed to grow on basal media but produced extensive callus and homozygous mutant plants on enriched media. The specific nutrient required for growth of this mutant remains to be determined. Arrested embryos from mutant 112A-2A developed into abnormal plants without roots when placed in culture. Mutant callus also failed to form roots on a variety of root-inducing media. Expression of this mutant gene therefore disrupts development of the root apical meristem during both embryogenesis in vivo and organogenesis in vitro.     

Assembly of microfibrils in vivo and in vitro from (1»3)-β-d-glucan synthesized by protoplasts of Saccharomyces cerevisiae

Polymer chains of (13)--d-glucan were dissolved with 1 M NaOH at 4° C from native microfibrillar protoplast nets. The chains associated into microfibrils during NaOH neutralization or dialysis. In contrast to the native microfibrils which are of uniform width individually (10 to 20 nm) and arranged in flat bundles, the microfibrils formed in vitro showed no band formation and consisted of fibrous spindle-shaped subunits of variable width or loose elementary fibrils about 1.7 nm wide. X-ray diagrams of native nets indicated a fairly high crystallinity and were different for wet and dry specimens. They corresponded to those of paramylon. Precipitated glucans produced diagrams different from the former and revealing a lower crystallinity especially with the dry samples.The X-ray pattern, combined with other data, allowed the precipitated microfibrils to be identified as aggregates of molecular strands composed each of three intertwined helical glucan chains. Since these triple helical chains are about 1.7 nm wide the elementary fibrils of this width can represent only single triple-helical strands. These helices have 7 glucose residues per turn and therefore a low symmetry which explains the poor crystallizing properties. The 7 membered helix represents a basic difference with the well crystallized native glucan which is built of highly symmetrical triple helices with 6 glucose residues per turn. Since 6₁ helical conformation is not formed in vitro at normal temperatures its generation in vivo must be due to the action of synthesizing enzymes at the protoplast membrane. The intertwining of these helices and crystallization of the strands are determined by their symmetry and physical properties of the chains. This characterizes the native microfibrils as products of self-assembly of enzymegenerated 6₁ helices.     

Molecular basis for the special properties of proteins and enzymes from Halobacterium marismortui

Abstract Three proteins from Halobacterium marismortui , malate dehydrogenase (hMDH), glutamate dehydrogenase (hGDH) and ferredoxin (hFD) were purified and characterized with respect to their molecular masses, amino acid composition and, for hFD only, primary structure. Striking features of halophilic proteins are: the high excess of acidic over basic residues; acidic clusters in the sequence. Low-salt concentration causes inactivation and changes in structural parameters of hMDH and hGDH. Reactivation of hMDH involves long-lived stable intermediates. The salt concentration optimum of enzymic activity is independent of salt nature. The high capacity of halophilic proteins to retain water and salt is due to unique molecular properties, studied by physico-chemical techniques.     

Factors affecting the oligomeric structure of yeast external invertase

It has been assumed that yeast external invertase is a dimer, with each subunit composed of a 60-kDa polypeptide chain. We now present evidence that at its optimal pH of 5.0, the predominant form of external invertase is an octamer with an average size of 8 X 10(5) Da. During ultracentrifugation the octamer dissociated to lower molecular weight forms, including a hexamer, tetramer, and dimer. All forms of the enzyme were shown to possess identical specific activities and to contain a similar carbohydrate to protein ratio. Although the monomer subunits (1 X 10(5) Da) were heterogenous in carbohydrate content, each subunit possessed nine oligosaccharide chains. When stained for protein and enzyme activity following sodium dodecyl sulfate-polyacrylamide gel electrophoresis, only the oligomeric form of the enzyme appeared to be active. Thus, on partially inactivating invertase with 4 M guanidine hydrochloride both octamer and monomer were evident on the gels but only the former was active. Similarly, incubating at pH 2.5 in the presence of sodium dodecyl sulfate yielded only inactive monomer. The monomer, unlike the active oligomeric aggregate, was unable to hydrolyze sucrose after sodium dodecyl sulfate-polyacrylamide gel electrophoresis. Consistent with the in vitro studies, freshly prepared yeast lysate was shown to contain the octameric species of external invertase as the major active form of this enzyme. From these studies and others which employed deglycosylated invertase, it is concluded that the carbohydrate component of external invertase contributes not only to stabilizing enzyme activity, but also to maintaining its oligomeric structure.     

Comparative kinetic studies of the dealkylation reaction and steroid hydroxylations in various oxygen and carbon monoxide:oxygen atmospheres

The time-course kinetics of the cytochrome P-450-catalyzed dealkylations of the exogenous compounds benzphetamine, ethylmorphine, codeine, and 7-ethoxycoumarin were compared to the hydroxylation of the endogenous compound testosterone. Using liver microsomes from phenobarbital-induced rats, the time course of the demethylations of ethylmorphine, codeine, and especially benzphetamine was characterized by a fast initial phase of enzymatic activity and then a steady decline in the rate throughout the remainder of the reaction. In contrast, under the same experimental conditions, both the dealkylation of 7-ethoxycoumarin and the hydroxylation of testosterone showed no initial fast phase of activity and a constant rate of product formation for most of the remainder of the time course. The difference also held for the carbon monoxide inhibition studies in which the degree of inhibition of the demethylation reactions by a variety of CO:O₂ mixtures was time dependent, in contrast to the constant, time-independent degree of CO inhibition of the other two reactions. The kinetics of the demethylation reactions could not be explained by enzyme destruction, back reaction, or product adduct formation and were further confirmed by measurements of the rate of O₂ utilization and NADPH oxidation. The complexity of the demethylation reaction should be taken into consideration in any detailed studies of the monooxygenation reaction system.