Analysis of a circular code model

A circular code has been identified in the protein (coding) genes of both eukaryotes and prokaryotes by using a statistical method called trinucleotide frequency (TF) method [Arquès & Michel (1996). J. theor. Biol. 182, 45-58]. Recently, a probabilistic model based on the nucleotide frequencies with a hypothesis of absence of correlation between successive bases on a DNA strand, has been proposed by Koch & Lehmann [(1997). J. theor. Biol. 189, 171-174] for constructing some particular circular codes. Their interesting method which we call here nucleotide frequency (NF) method, reveals several limits for constructing the circular code observed with protein genes.     

Chemotaxis and chemokinesis in eukaryotic cells: The Keller-Segel equations as an approximation to a detailed model

More than 20 years after its proposal, Keller and Segel's model (1971,J. theor. Biol.,30, 235–248) remains by far the most popular model for chemical control of cell movement. However, before the Keller-Segel equations can be applied to a particular system, appropriate functional forms must be specified for the dependence on chemical concentration of the cell transport coefficients and the chemical degradation rate. In the vast majority of applications, these functional forms have been chosen using simple intuitive criteria. We focus on the particular case of eukaryotic cell movement, and derive an approximation to the detailed model of Sherrattet al. (1993,J. theor. Biol.,162, 23–40). The approximation consists of the Keller-Segel equations, with specific forms predicted for the cell transport coefficients and chemical degradation rate. Moreover, the parameter values in these functional forms can be directly measured experimentally. In the case of the much studied neutrophil-peptide system, we test our approximation using both the Boyden chamber and under-agarose assays. Finally, we show that for other cell-chemical interactions, a simple comparison of time scales provides a rapid check on the validity of our Keller-Segel approximation.     

Four strand recombination models

A main point of this paper is to develop the idea that synapsis of DNA duplexes might take place by Watson-Crick base pairing between essentially intact duplex structure to form a four stranded intermediate. This intermediate is the same regular and compact four strand structure already discussed (e.g., McGavin, 1971a, J. molec. Biol., 55, 293-298; 1979, J. theor. Biol., 77, 83-99) and which has been used in several related recombination models (see, for example, McGavin, 1977, Heredity, 39, 15-25; 1984, J. theor. Biol., 107, 37-56; Wilson, 1979, Proc. natn. Acad. Sci. U.S.A., 76, 3641-3645; Nash et al., 1980, Cold Spring Harbor Symposium of Quantitative Biology, 45, 417-428; Nash, 1981, A. Rev. Genetics, 15, 143-167). These models can also be related to one recently suggested by Hopkins (1986, J. theor. Biol. 120, 215-222). An immediate stimulus to the development of the idea was the recent work of Griffith & Nash (1985, Proc. natn. Acad. Sci. U.S.A., 82, 3124-3128), on the site specific recombination system of the lambda bacteriophage. They observed trefoil knots with exclusively positive nodes among the products of the interaction of two relatively inverted attachment sites within circular molecules. The model discussed here may though be of interest in itself. The paper also compares several closely related models for recombination which involve formation of either identical or closely related four strand secondary structures.     

Effects of calcium input/output on the stability of a system for calcium-regulated viscoelastic strain fields

The Goodwin and Trainor model of pattern generation in calcium-regulated strain fields is studied in the case where calcium input and calcium output processes are involved. It is shown that the properties of the original model may still remain provided that the input-output processes are not unstable. In this last case, despite the eventual stabilizing effect of the calcium exchange term, perturbations of the generalized system can grow and lead to inhomogeneous solutions. Applications to cell differentiation and cell growth are discussed.     

Can mixed strategies be stable in asymmetric games?

Selten (1980, J. theor. Biol. 84, 93(N)/01) has shown that mixed strategies cannot be evolutionarily stable in asymmetric games. Because every interaction features some asymmetry, this result apparently precludes mixed strategies in an evolutionary setting. In Maynard Smith's Hawk-Dove game (1982, Evolution and the theory of games (UP-Cambridge), for example, Selten's result restricts attention to pure-strategy evolutionarily stable outcomes in which the animals use the ability to condition their actions on asymmetries to coordinate, with one playing Hawk and one playing Dove, and with conflicts in which both animals play Hawk never arising. This result contrasts with the intuition that the mixed equilibrium of the Hawk-Dove game captures important aspects of many animal interactions, including the possibility of conflict. In this paper, we follow Eshel and Sansone (1995, J. theor. Biol. 177, 341-356) in enriching Selten's model to incorporate an important aspect of animal interactions, namely that payoffs and asymmetries may both be imperfectly observed. In the richer model, we find conditions under which effectively mixed strategies are stable in asymmetric games, as well as conditions under which they are not stable. Behavior will be conditioned on asymmetries, leading to pure-strategy equilibria in which conflict is avoided, when there are relatively large, observable asymmetries and small observable variations in payoffs. Under opposite conditions, evolutionarily stable equilibria will appear that are effectively mixed, including the potential for conflict.     

The diffusive vesicle supply center model for tip growth in fungal hyphae

We propose the diffusive vesicle supply center model for tip growth in fungal hyphae. The model is based on the three-dimensional vesicle supply center (VSC) model [Gierz, G., Bartnicki-García, S., 2001. A three-dimensional model of fungal morphogenesis based on the vesicle supply center concept: J. Theor. Biol. 208, 151-164], but incorporates two aspects of a more realistic vesicle delivery mechanism: vesicle diffusion from the VSC and a finite rate constant for vesicle fusion with the cell membrane. We develop a framework to describe tip growth for a general class of models based on the vesicle supply center concept. Combining this with a method for calculating the steady state distribution of diffusive vesicles we iteratively solve for stationary cell shapes. These show a blunter tip than predicted by the original VSC model, which we attribute to increased forward-directed vesicle delivery via diffusion. The predicted distance between the VSC and the utmost tip of the cell is set by the ratio between the diffusion constant and the rate constant for vesicle exocytosis. Combined with the cell radius, these define the only dimensionless parameter for our model.     

A unique zinc-binding site revealed by a high-resolution X-ray structure of homotrimeric Apo2L/TRAIL

Apoptosis-inducing ligand 2 (Apo2L, also called TRAIL), a member of the tumor necrosis factor (TNF) family, induces apoptosis in a variety of human tumor cell lines but not in normal cells [Wiley, S. R., Schooley, K., Smolak, P. J., Din, W. S., Huang, C.-P., Nicholl, J. K., Sutherland, G. R., Smith, T. D., Rauch, C., Smith, C. A., and Goodwin, R. G. (1995) Immunity 3, 673-682; Pitti, R. M., Marsters, S. A., Ruppert, S., Donahue, C. J., Moore, A., and Ashkenazi, A. (1996) J. Biol. Chem. 271, 12687-12690]. Here we describe the structure of Apo2L at 1.3 A resolution and use alanine-scanning mutagenesis to map the receptor contact regions. The structure reveals a homotrimeric protein that resembles TNF with receptor-binding epitopes at the interface between monomers. A zinc ion is buried at the trimer interface, coordinated by the single cysteine residue of each monomer. The zinc ion is required for maintaining the native structure and stability and, hence, the biological activity of Apo2L. This is the first example of metal-dependent oligomerization and function of a cytokine.     

Actin's propensity for dynamic filament patterning

Actin, through its various forms of assembly, provides the basic framework for cell motility, cell shape and intracellular organization in all eukaryotic cells. Many other cellular processes, for example endocytosis and cytokinesis, are also associated with dynamic changes of the actin cytoskeleton. Important prerequisites for actin's functional diversity are its intrinsic ability to rapidly assemble and disassemble filaments and its spatially and temporally well-controlled supramolecular organization. A large number of proteins that interact with actin, collectively referred to as actin-binding proteins (ABPs), carefully orchestrate different scenarios. Since its isolation in 1994 [Machesky, L.M. et al. (1994) J. Cell Biol. 127, 107-115], the Arp2/3 complex containing the actin-related proteins Arp2 and Arp3 has evolved to be one of the main players in the assembly and maintenance of many actin-based structures in the cell (for review see [Borths, E.L. and Welch, M.D. (2002) Structure 10, 131-135; May, R.C. (2001) Cell Mol. Life Sci. 58, 1607-1626; Pollard, T.D. et al. (2000) Rev. Biophys. Biomol. Struct. 29, 545-576; Welch, M.D. (1999) Trends Cell Biol. 11, 423-427]). In particular, when it comes to the assembly of the intricate branched actin network at the leading edge of lamellipodia, the Arp2/3 complex seems to have received all the attention in recent years. In parallel, but not so much in the spotlight, several reports showed that actin on its own can assume different conformations [Bubb, M.R. et al. (2002) J. Biol. Chem. 277, 20999-21006; Schoenenberger, C.-A. et al. (1999) Microsc. Res. Tech. 47, 38-50; Steinmetz, M.O. et al. (1998) J. Mol. Biol. 278, 793-811; Steinmetz, M.O. et al. (1997) J. Cell Biol. 138, 559-574; Millonig, R., Salvo, H. and Aebi, U. (1988) J. Cell Biol. 106, 785-796] through which it drives its supramolecular patterning, and which ultimately generate its functional diversity.     

Integrin-associated protein: a 50-kD plasma membrane antigen physically and functionally associated with integrins

Phagocytosis by monocytes or neutrophils can be enhanced by interaction with several proteins or synthetic peptides containing the Arg-Gly-Asp sequence. Recently we showed that an mAb, B6H12, specifically inhibited this enhancement of neutrophil phagocytosis by inhibiting Arg-Gly-Asp binding to the leukocyte response integrin (Gresham, H. D., J. L. Goodwin, P. M. Allen, D. C. Anderson, and E. J. Brown. 1989. J. Cell Biol. 108:1935-1943). Now, we have purified the antigen recognized by B6H12 to homogeneity. Surprisingly, it is a 50-kD molecule that is expressed on the plasma membranes of all hematopoietic cells, including erythrocytes, which express no known integrins. On platelets and placenta, but not on erythrocytes, this protein is associated with an integrin that can be recognized by an anti-beta 3 antibody. In addition, both the anti-beta 3 and several mAbs recognizing the 50-kD protein inhibit Arg-Gly-Asp stimulation of phagocytosis. These data demonstrate an association between integrins and the 50-kD protein on several cell types. For this reason, we call it Integrin-associated Protein (IAP). We hypothesize that IAP may play a role in signal transduction for enhanced phagocytosis by Arg-Gly-Asp ligands.     

Mathematical modeling and validation of the ergosterol pathway in Saccharomyces cerevisiae

The de novo biosynthetic machinery for both sphingolipid and ergosterol production in yeast is localized in the endoplasmic reticulum (ER) and Golgi. The interconnections between the two pathways are still poorly understood, but they may be connected in specialized membrane domains, and specific knockouts strongly suggest that both routes have different layers of mutual control and are co-affected by drugs. With the goal of shedding light on the functional integration of the yeast sphingolipid-ergosterol (SL-E) pathway, we constructed a dynamic model of the ergosterol pathway using the guidelines of Biochemical Systems Theory (BST) (Savageau., J. theor. Biol., 25, 365-9, 1969). The resulting model was merged with a previous mathematical model of sphingolipid metabolism in yeast (Alvarez-Vasquez et al., J. theor. Biol., 226, 265-91, 2004; Alvarez-Vasquez et al., Nature433, 425-30, 2005). The S-system format within BST was used for analyses of consistency, stability, and sensitivity of the SL-E model, while the GMA format was used for dynamic simulations and predictions. Model validation was accomplished by comparing predictions from the model with published results on sterol and sterol-ester dynamics in yeast. The validated model was used to predict the metabolomic dynamics of the SL-E pathway after drug treatment. Specifically, we simulated the action of drugs affecting sphingolipids in the endoplasmic reticulum and studied changes in ergosterol associated with microdomains of the plasma membrane (PM).     

Intracytoplasmic membrane synthesis in synchronous cell populations of Rhodopseudomonas sphaeroides. Fate of "old" and "new" membrane.

A nonspecific density labeling technique has been employed to monitor the synthesis of intracytoplasmic membrane in synchronously dividing populations of Rhodopseudomonas sphaeroides. The intracytoplasmic membranes of cells synchronized in D2O-based medium were found to undergo discontinuous decreases in specific density during synchronous cell growth following transfer to H2O-based medium. These abrupt decreases in membrane specific density occurred immediately prior to cell division and were not observed with intracytoplasmic membranes prepared from asynchronously dividing cells (see also Kowakowski, H., and Kaplan, S. (1974) J. Bacteriol. 118, 1144-1157). Discontinuous increases in the net accumulation of cellular phospholipid were also observed during the synchronous growth of R. sphaeroides. This is to be contrasted to the continuous insertion of protein and the photopigment components of the photosynthetic apparatus into the intracytoplasmic membrane during the cell division cycle (Fraley, R.T., Lueking, D.R., and Kaplan, S. (1978) J. Biol. Chem. 253, 458-464; Wraight, C.A., Lueking, D.R., Fraley, R.T., and Kaplan, S. (1978) J. Biol. Chem. 253, 465-471). Further, examination of the protein/phospholipid ratios of purified intracytoplasmic membrane preparations revealed that this ratio undergoes cyclical changes of 35 to 40% during a normal cycle of cell division. In contrast to the results of Ferretti and Gray ((1968) J. Bacteriol, 95, 1400-1406), DNA synthesis was found to occur in a stepwise manner in synchronously dividing cell populations of R. sphaeroides.     

Micropropagation of Dendrobium nobile from shoot tip sections

Successful shoot regeneration of Dendrobium nobile was achieved using thin shoot tip sections and triacontanol (TRIA) for the first time. Protocorm-like bodies (PLBs) or proliferating shoot buds were observed when thin shoot tip sections were cultured on the basal medium of Mitra et at. (Indian J. Exp. Biol. 14 (1976) 350) supplemented with 4.0 microg L(-1) TRIA. The highest percentage of explants (93%) produced PLBs or proliferating shoot buds (21) at 4.0 microg L(-1) TRIA-supplemented basal medium. All the newly formed PLBs or proliferating shoot buds survived and ultimately produced healthy shoots with 2-3 leaves. Shoots produced roots when cultured on basal medium supplemented with 2.0 microg L(-1) TRIA. The well-rooted shoots were transferred to pots containing charcoal chips, coconut husk and broken tiles (2:2:1), and a 92% survival rate was achieved. This work reveals that TRIA can be used as an effective growth regulator in the micropropagation and conservation of D. nobile.     

Analysis of the CK2-dependent phosphorylation of serine 13 in Cdc37 using a phospho-specific antibody and phospho-affinity gel electrophoresis

The CK2-dependent phosphorylation of Ser13 in cell division cycle protein 37 (Cdc37), a kinase-specific heat shock protein 90 (Hsp90) cochaperone, has previously been reported to be essential for the association of Cdc37 with signaling protein kinases [Bandhakavi S, McCann RO, Hanna DE & Glover CVC (2003) J Biol Chem278, 2829-2836; Shao J, Prince T, Hartson SD & Matts RL (2003) J Biol Chem278, 38117-38220; Miyata Y & Nishida E (2004) Mol Cell Biol24, 4065-4074]. Here we describe a new phospho-specific antibody against Cdc37 that recognizes recombinant purified Cdc37 only when incubated with CK2 in the presence of Mg(2+) and ATP. The replacement of Ser13 in Cdc37 by nonphosphorylatable amino acids abolished binding to this antibody. The antibody was specific for phosphorylated Cdc37 and did not crossreact with other CK2 substrates such as Hsp90 and FK506-binding protein 52. Using this antibody, we showed that complexes of Hsp90 with its client signaling kinases, Cdk4, MOK, v-Src, and Raf1, contained the CK2-phosphorylated form of Cdc37 in vivo. Immunofluorescent staining showed that Hsp90 and the phosphorylated form of Cdc37 accumulated in epidermal growth factor-induced membrane ruffles. We further characterized the phosphorylation of Cdc37 using phospho-affinity gel electrophoresis. Our analyses demonstrated that the CK2-dependent phosphorylation of Cdc37 on Ser13 caused a specific gel mobility shift, and that Cdc37 in the complexes between Hsp90 and its client signaling protein kinases was in the phosphorylated form. Our results show the physiological importance of CK2-dependent Cdc37 phosphorylation and the usefulness of phospho-affinity gel electrophoresis in protein phosphorylation analysis.     

Further analysis of the molecular jet hypothesis during muscle contraction

We analyse the Molecular Jet-hypothesis proposed by Morel & Bachouchi (1988, J. theor. Biol. 132, 83.). This hypothesis attempts to explain the movement of covaspheres that contain myosin heads attached to actin filaments. This movement occurs during muscle contraction. However, the hypothesis does not predict the velocity of covaspheres correctly. Therefore, we are studying additional aspects of the hypothesis.     

Evaluating CK2 activity with the antibody specific for the CK2-phosphorylated form of a kinase-targeting cochaperone Cdc37

CK2-dependent phosphorylation of a kinase-specific Hsp90 co-chaperone Cdc37 on a conserved serine residue (Ser13) is essential for the function of Cdc37 [Bandhakavi S. et al. J. Biol. Chem. 278:2829-2836, 2003; Shao J. et al. J. Biol. Chem. 278:38117-38220, 2003; Miyata Y., & Nishida E. Mol. Cell. Biol. 24:4065-4074, 2004]. We have recently produced an anti-[pSer13]-Cdc37 antibody which specifically recognizes Cdc37 that is phosphorylated on Ser 13 [Miyata Y. & Nishida E. FEBS J. 274:5690-5703, 2007]. Here we investigated CK2 activity both in vitro and in cultured cells by using anti-[pSer13]-Cdc37 antibody. Immunoblotting with this antibody showed that heparin and 4,5,6,7-tetrabromobenzotriazole (TBB), known CK2 inhibitors, inhibited in vitro phosphorylation of Cdc37 on Ser13 by CK2 holoenzyme or CK2alpha, confirming the specificity of the antibody to detect CK2 activity. Treatment of cells with TBB resulted in the decrease in the phosphorylation level of endogenous Cdc37 on Ser13, as revealed by anti-[pSer13]-Cdc37, and overexpression of either CK2alpha or CK2beta subunit enhanced the Cdc37 phosphorylation level. While CK2 is suggested to be involved in cell proliferation, mitogenic stimulation of starved cells by fresh serum or insulin-like growth factor-I did not enhance phosphorylation of Cdc37 on Ser13. CK2 inhibitors are known to induce cell apoptosis, suggesting a reverse correlation between cell apoptosis and CK2 activity. However, cellular apoptotic stresses, such as anisomycin treatment and UV irradiation, were found to rather modestly increase phosphorylation of Cdc37 on Ser13. These results show that the anti-[pSer13]-Cdc37 antibody can be a promising new tool to evaluate in vivo CK2 activity.     

Distinct antitumor properties of a type IV collagen domain derived from basement membrane

Vascular basement membrane is an important structural component of blood vessels. During angiogenesis this membrane undergoes many alterations and these changes are speculated to influence the formation of new capillaries. Type IV collagen is a major component of vascular basement membrane, and recently we identified a fragment of type IV collagen alpha2 chain with specific anti-angiogenic properties (Kamphaus, G. D., Colorado, P. C., Panka, D. J., Hopfer, H., Ramchandran, R., Torre, A., Maeshima, Y., Mier, J. W., Sukhatme, V. P., and Kalluri, R. (2000) J. Biol. Chem. 275, 1209-1215). In the present study we characterize two different antitumor activities associated with the noncollagenous 1 (NC1) domain of the alpha3 chain of type IV collagen. This domain was previously discovered to possess a C-terminal peptide sequence (amino acids 185-203) that inhibits melanoma cell proliferation (Han, J., Ohno, N., Pasco, S., Monboisse, J. C., Borel, J. P., and Kefalides, N. A. (1997) J. Biol. Chem. 272, 20395-20401). In the present study, we identify the anti-angiogenic capacity of this domain using several in vitro and in vivo assays. The alpha3(IV)NC1 inhibited in vivo neovascularization in matrigel plug assays and suppressed tumor growth of human renal cell carcinoma (786-O) and prostate carcinoma (PC-3) in mouse xenograft models associated with in vivo endothelial cell-specific apoptosis. The anti-angiogenic activity was localized to amino acids 54-132 using deletion mutagenesis. This anti-angiogenic region is separate from the 185-203 amino acid region responsible for the antitumor cell activity. Additionally, our experiments indicate that the antitumor cell activity is not realized until the peptide region is exposed by truncation of the alpha3(IV)NC1 domain, a requirement not essential for the anti-angiogenic activity of this domain. Collectively, these results effectively highlight the distinct and unique antitumor properties of the alpha3(IV)NC1 domain and the potential use of this molecule for inhibition of tumor growth.     

Transformation by the oncogenic latent membrane protein correlates with its rapid turnover, membrane localization, and cytoskeletal association.

The latent membrane protein (LMP) of Epstein-Barr virus (EBV) has a short half-life (V. R. Baichwal and B. Sugden, J. Virol, 61:866-875, 1987; K.P. Mann and D. Thorley-Lawson, J. Virol, 61:2100-2108, 1987), is localized in patches in the membrane (D. Liebowitz, D. Wang, and E, Kieff, J. Virol, 58:233-237, 1986), and associates with the cytoskeleton in EBV-immortalized B lymphocytes (D. Liebowitz, R. Kopan, E. Fuchs, J. Sample, and E. Kieff, Mol. Cell. Biol. 7:2299-2308, 1987; K. P. Mann and D. Thorley-Lawson, J. Virol. 61:2100-2108, 1987). Deletion mutants of LMP that are either positive or negative in the induction both of anchorage-independent growth of BALB/c 3T3 cells (V. R. Baichwal and B. Sugden, Oncogene 4:67-74, 1989) and of cytotoxicity in a variety of cells (W. Hammerschmidt, B. Sugden, and V. R. Baichwal, J. Virol. 63:2469-2475, 1989) have been studied to identify the biochemical properties of this protein that correlate with its effects on cell growth. Mutant LMP proteins that are metabolically stable, do not associate with the cytoskeleton, and exhibit a diffuse plasma membrane localization also do not induce anchorage-independent growth in rodent cells or cytotoxicity in B lymphoblastoid cells. In contrast, a mutant of LMP that is functionally identical to the wild-type protein has a half-life, membrane localization, and cytoskeletal association similar or identical to those of LMP. These results are consistent with the hypothesis that LMP's rapid turnover, association with the cytoskeleton, and patching in the membrane are required for it to affect cell growth.     

Survival of replicators with parabolic growth tendency and exponential decay

The claim that the competition of parabolically growing self-replicators leads to dynamically stable coexistence was challenged by Lifson & Lifson [(1999). J. theor. Biol.199, 425-433]. They have shown that, if single- and double-strands are treated separately, and only single-strands undergo spontaneous decay, then there is natural selection rather than survival of everybody. We use their models to show that if double-strand decay is not neglected, then dynamical coexistence is still possible under a wide range of parameter values, in agreement with the chromatographized replicator model of von Kiedrowski & Szathmáry [(2000). Selection 1-3, 173-179]. Coexistence is always ensured above a critical resource (monomer) inflow rate. Recycling of decayed replicators into monomers further favours dynamical coexistence. The claim that parabolic growth invariably results in coexistence remains valid for the model for which it was meant to apply, namely for parabolic growth without template decay. Exponential decay acting on single- and double-strands, combined with parabolic growth, may or may not result in a dynamical coexistence of self-replicators.     

A calcium model with random absorption: a stochastic approach.

Absorption of calcium, or any mineral, by the body is subject to the random fluctuations typical of diffusion through membranes. In this paper we consider the absorption of calcium from the gut as a white noise process added to the deterministic model of Sen & Mohr (1990, J. theor. Biol. 142, 179-188). The first two moments for the amount of calcium in the extracellular fluid (ECF) have been derived using the Ito Calculus. A confidence interval for the total amount of calcium in the ECF is constructed. The equations for the first two moments of the fraction of dose calcium in the ECF are also given. Suggestions are made for the collection of experimental data in a form which should be helpful in investigating the magnitude of the stochastic effect.