Optimal control approach to gradient-index design for beam reshaping.

We address the problem of reshaping light in the Schrödinger optics regime from the perspective of the optimal control theory. In technological applications, Schrödinger optics is often used to model a slowly varying amplitude of a para-axially propagating electric field where the square of the waveguide's index of refraction is treated as the potential. The objective of the optimal control problem is to find the controlling potential which, together with the constraining Schrödinger dynamics, optimally reshapes the intensity distribution of Schrödinger eigenfunctions from one end of the waveguide to the other. This work considers reshaping problems found in work by Kunkel and Leger, and addresses computational needs by adopting tools from the quantum control literature. The success of the optimal control approach is demonstrated numerically.

Reduction-based strategy for optimal control of Bose-Einstein condensates.

Applications of Bose-Einstein condensates (BEC) often require that the condensate be prepared in a specific complex state. Optimal control is a reliable framework to prepare such a state while avoiding undesirable excitations, and, when applied to the time-dependent Gross-Pitaevskii equation (GPE) model of BEC in multiple space dimensions, results in a large computational problem. We propose a control method based on first reducing the problem, using a Galerkin expansion, from a partial differential equation to a low-dimensional Hamiltonian ordinary differential equation system. We then apply a two-stage hybrid control strategy. At the first stage, we approximate the control using a second Galerkin-like method known as the chopped random basis to derive a finite-dimensional nonlinear programing problem, which we solve with a differential evolution algorithm. This search method then yields a candidate local minimum which we further refine using a variant of gradient descent. This hybrid strategy allows us to greatly reduce excitations both in the reduced model and the full GPE system.

Effect of wetting and drying and dilution on moisture migration through oil contaminated hydrophobic soils.

Hydrophobic soils display resistance to wetting and frequently do not hold water to support good plant growth. A laboratory investigation was conducted to study moisture movement through hydrophobic soils. Test results indicated that hydrophobic soils have a critical moisture content beyond which they behave as wettable or hydrophilic soils. Soil hydrophobicity decreased and water infiltration increased when the soil was subjected to an increasing number of wetting and drying cycles. The effect of diluting hydrophobic soil with hydrophilic soil on water infiltration was also studied. The results indicated that water infiltration into soil becomes more rapid and uniform as the mass fraction of hydrophilic soil is increased in the mix. Water infiltration was observed even in hydrophobic-hydrophilic soil mixtures classified as severely water-repellent by commonly used arbitrary ordinal scales.

CREB signaling--timing is everything.

Depolarization of neurons can lead to changes in gene expression that are important for such processes as synaptic plasticity, neuronal differentiation, and apoptosis. Impey and Goodman discuss some of the opposing models for how gene transcription in response to neuronal activity and elevations in intracellular calcium concentration is regulated. The pathways appear to converge on cyclic AMP response element-binding (CREB) protein, with the mitogen-activated protein kinase pathways playing an important role. The continuing debate about the involvement of calmodulin kinase IV is also described.

Acetylation of nuclear hormone receptor-interacting protein RIP140 regulates binding of the transcriptional corepressor CtBP.

CtBP (carboxyl-terminal binding protein) participates in regulating cellular development and differentiation by associating with a diverse array of transcriptional repressors. Most of these interactions occur through a consensus CtBP-binding motif, PXDLS, in the repressor proteins. We previously showed that the CtBP-binding motif in E1A is flanked by a Lys residue and suggested that acetylation of this residue by the p300/CBP-associated factor P/CAF disrupts the CtBP interaction. In this study, we show that the interaction between CtBP and the nuclear hormone receptor corepressor RIP140 is regulated similarly, in this case by p300/CBP itself. CtBP was shown to interact with RIP140 in vitro and in vivo through a sequence, PIDLSCK, in the amino-terminal third of the RIP140 protein. Acetylation of the Lys residue in this motif, demonstrated in vivo by using an acetylated RIP140-specific antibody, dramatically reduced CtBP binding. Mutation of the Lys residue to Gln resulted in a decrease in CtBP binding in vivo and a loss of transcriptional repression. We suggest that p300/CBP-mediated acetylation disrupts the RIP140-CtBP complex and derepresses nuclear hormone receptor-regulated genes. Disruption of repressor-CtBP interactions by acetylation may be a general mode of gene activation.

MLL and CREB bind cooperatively to the nuclear coactivator CREB-binding protein.

A fragment of the mixed-lineage leukemia (MLL) gene (Mll, HRX, ALL-1) was identified in a yeast genetic screen designed to isolate proteins that interact with the CREB-CREB-binding protein (CBP) complex. When tested for binding to CREB or CBP individually, this MLL fragment interacted directly with CBP, but not with CREB. In vitro binding experiments refined the minimal region of interaction to amino acids 2829 to 2883 of MLL, a potent transcriptional activation domain, and amino acids 581 to 687 of CBP (the CREB-binding or KIX domain). The transactivation activity of MLL was dependent on CBP, as either adenovirus E1A expression, which inhibits CBP activity, or alteration of MLL residues important for CBP interaction proved effective at inhibiting MLL-mediated transactivation. Single amino acid substitutions within the MLL activation domain revealed that five hydrophobic residues, potentially forming a hydrophobic face of an amphipathic helix, were critical for the interaction of MLL with CBP. Using purified components, we found that the MLL activation domain facilitated the binding of CBP to phosphorylated CREB. In contrast with paradigms in which factors compete for limiting quantities of CBP, these results reveal that two distinct transcription factor activation domains can cooperatively target the same motif on CBP.

Consensus and variant cAMP-regulated enhancers have distinct CREB-binding properties.

Recent determination of the cAMP response element-binding protein (CREB) basic leucine zipper (bZIP) consensus CRE crystal structure revealed key dimerization and DNA binding features that are conserved among members of the CREB/CREM/ATF-1 family of transcription factors. Dimerization appeared to be mediated by a Tyr(307)-Glu(312) interhelical hydrogen bond and a Glu(319)-Arg(314) electrostatic interaction. An unexpected hexahydrated Mg(2+) ion was centered above the CRE in the dimer cavity. In the present study, we related these features to CREB dimerization and DNA binding. A Y307F substitution reduced dimer stability and DNA binding affinity, whereas a Y307R mutation produced a stabilizing effect. Mutation of Glu(319) to Ala or Lys attenuated dimerization and DNA binding. Mg(2+) ions enhanced the binding affinity of wild-type CREB to the palindromic CRE by approximately 20-fold but did not do so for divergent CREs. Similarly, mutation of Lys(304), which mediates the CREB interaction with the hydrated Mg(2+), blocked CREB binding to the palindromic but not the variant CRE sequences. The distinct binding characteristics of the K304A mutants to the consensus and variant CRE sequences indicate that CREB binding to these elements is differentially regulated by Mg(2+) ions. We suggest that CREB binds the consensus and variant CRE sequences through fundamentally distinct mechanisms.

Cooperative mechanism of transcriptional activation by a cyclic AMP-response element modulator alpha mutant containing a motif for constitutive binding to CREB-binding protein.

Cyclic AMP-response element modulator alpha (CREMalpha) is a transcription factor that is highly related to cAMP-response element-binding protein (CREB) but represses cAMP-induced gene expression from simple artificial promoters containing a cAMP-response element (CRE). CREMalpha lacks two glutamine-rich Q regions that, in CREB, are thought to be necessary for transcriptional activation. Nevertheless, protein kinase A stimulation induces CREMalpha to activate the complex native promoter in the phosphoenolpyruvate carboxykinase (PEPCK) gene. To study this phenomenon in the absence of protein kinase A stimulation, we introduced a mutation into CREMalpha to allow constitutive binding to the coactivator CREB-binding protein. This mutant, CREMalpha(DIEDML), constitutively activated the PEPCK promoter. By engineering the leucine zipper regions of CREMalpha(DIEDML) and CREB(DIEDML) to direct their patterns of dimerization, we found that only CREMalpha(DIEDML) homodimers fully activated the PEPCK promoter. By using a series of deletion and block mutants of the PEPCK promoter, we found that activation by CREMalpha(DIEDML) depended on the CRE and two CCAAT/enhancer-binding protein (C/EBP) sites. A dominant negative inhibitor of C/EBP, A-C/EBP, suppressed activation by CREMalpha(DIEDML). Furthermore, a GAL4-C/EBPalpha fusion protein and CREMalpha(DIEDML) cooperatively activated a promoter containing three GAL4 sites and the PEPCK CRE. Thus, we propose that the C/EBP sites in the PEPCK promoter allow CREMalpha to activate transcription despite its lack of Q regions.

Acetylation of adenovirus E1A regulates binding of the transcriptional corepressor CtBP.

Adenovirus E1A mediates its effects on cellular transformation and transcription by interacting with critical cellular proteins involved in cell growth and differentiation. The amino terminus of E1A binds to CBP/p300 and associated histone acetyltransferases such as P/CAF. The carboxyl terminus binds to the carboxyl-terminal binding protein (CtBP), which associates with histone deacetylases. We show that 12S E1A can be acetylated by p300 and P/CAF and map one of the acetylation sites to Lys-239. This Lys residue is adjacent to the consensus CtBP binding motif, PXDLS. Mutation of Lys-239 to Gln or Ala blocks CtBP binding in vitro and disrupts the E1A-CtBP interaction in vivo. Peptide competition assays demonstrated that the interaction of E1A with CtBP is also blocked by Lys-239 acetylation. Supporting a functional role for Lys-239 in CtBP binding, mutation of this residue to Ala decreases the ability of E1A to block cAMP-regulated enhancer (CRE)-binding protein (CREB)-stimulated gene expression. Finally, we demonstrate that Lys-239 is acetylated in cells by using an antibody directed against an acetyl-Lys-239 E1A peptide. CtBP interacts with a wide variety of other transcriptional repressors through the PXDLS motif, and, in many instances, this motif is followed by a Lys residue. We suggest that acetylation of this residue by histone acetyltransferases, and the consequent disruption of repressor complexes, might be a general mechanism for gene activation.

Functional interaction between the coactivator Drosophila CREB-binding protein and ASH1, a member of the trithorax group of chromatin modifiers.

CREB-binding protein (CBP) is a coactivator for multiple transcription factors that transduce a variety of signaling pathways. Current models propose that CBP enhances gene expression by bridging the signal-responsive transcription factors with components of the basal transcriptional machinery and by augmenting the access of transcription factors to DNA through the acetylation of histones. To define the pathways and proteins that require CBP function in a living organism, we have begun a genetic analysis of CBP in flies. We have overproduced Drosophila melanogaster CBP (dCBP) in a variety of cell types and obtained distinct adult phenotypes. We used an uninflated-wing phenotype, caused by the overexpression of dCBP in specific central nervous system cells, to screen for suppressors of dCBP overactivity. Two genes with mutant versions that act as dominant suppressors of the wing phenotype were identified: the PKA-C1/DCO gene, encoding the catalytic subunit of cyclic AMP protein kinase, and ash1, a member of the trithorax group (trxG) of chromatin modifiers. Using immunocolocalization, we showed that the ASH1 protein is specifically expressed in the majority of the dCBP-overexpressing cells, suggesting that these proteins have the potential to interact biochemically. This model was confirmed by the findings that the proteins interact strongly in vitro and colocalize at specific sites on polytene chromosomes. The trxG proteins are thought to maintain gene expression during development by creating domains of open chromatin structure. Our results thus implicate a second class of chromatin-associated proteins in mediating dCBP function and imply that dCBP might be involved in the regulation of higher-order chromatin structure.

The structure of a CREB bZIP.somatostatin CRE complex reveals the basis for selective dimerization and divalent cation-enhanced DNA binding.

The cAMP responsive element-binding protein (CREB) is central to second messenger regulated transcription. To elucidate the structural mechanisms of DNA binding and selective dimerization of CREB, we determined to 3.0 A resolution, the structure of the CREB bZIP (residues 283-341) bound to a 21-base pair deoxynucleotide that encompasses the canonical 8-base pair somatostatin cAMP response element (SSCRE). The CREB dimer is stabilized in part by ionic interactions from Arg(314) to Glu(319') and Glu(328) to Lys(333') as well as a hydrogen bond network that links the carboxamide side chains of Gln(322')-Asn(321)-Asn(321')-Gln(322). Critical to family selective dimerization are intersubunit hydrogen bonds between basic region residue Tyr(307) and leucine zipper residue Glu(312), which are conserved in all CREB/CREM/ATF-1 family members. Strikingly, the structure reveals a hexahydrated Mg(2+) ion bound in the cavity between the basic region and SSCRE that makes a water-mediated DNA contact. DNA binding studies demonstrate that Mg(2+) ions enhance CREB bZIP:SSCRE binding by more than 25-fold and suggest a possible physiological role for this ion in somatostatin cAMP response element and potentially other CRE-mediated gene expression.

Calcium and cAMP signals differentially regulate cAMP-responsive element-binding protein function via a Rap1-extracellular signal-regulated kinase pathway.

Two major intracellular signals that regulate neuronal function are calcium and cAMP. In many cases, the actions of these two second messengers involve long term changes in gene expression. One well studied target of both calcium and cAMP signaling is the transcription factor cAMP-responsive element-binding protein (CREB). Multiple signaling pathways have been shown to contribute to the regulation of CREB-dependent transcription, including both protein kinase A (PKA)- and mitogen-activated protein (MAP) kinase/extracellular signal-regulated kinase (ERK)-dependent kinase cascades. We have previously described a mechanism by which cAMP and calcium influx may stimulate ERKs in neuronal cells. This pathway involves the PKA-dependent activation of the Ras-related small G-protein, Rap1, and subsequent stimulation of the neuronal Raf isoform, B-Raf. In this study, we examined the contribution of the Rap1-ERK pathway to the control of gene transcription by calcium influx and cAMP. Using the PC12 cell model system, we found that both calcium influx and cAMP stimulated CREB-dependent transcription via a Rap1-ERK pathway, but this regulation occurred through distinct mechanisms. Calcium-mediated phosphorylation of CREB through the PKA-Rap1-ERK pathway. In contrast, cAMP phosphorylated CREB via PKA directly but required a Rap1-ERK pathway to activate a component downstream of CREB phosphorylation and CREB-binding protein recruitment. These data suggest that the Rap1/B-Raf signaling pathway may have an important role in the regulation of CREB-dependent gene expression.

Histone binding protein RbAp48 interacts with a complex of CREB binding protein and phosphorylated CREB.

A CREB-CREB binding protein (CBP) complex was used as bait to screen a mouse embryo cDNA library in yeast. One of the strongest interactions identified the histone binding protein RbAp48. RbAp48 also interacted weakly with CBP alone but did not interact with phosphorylated or nonphosphorylated CREB. CBP (or its homologue p300) from HeLa cell nuclear extracts coimmunoprecipitated with RbAp48 and its homologue RbAp46 and bound to a glutathione S-transferase-RbAp48 fusion protein. This interaction was stimulated by the addition of phosphorylated CREB and allowed the association of core histones and mononucleosomes in an acetylation-dependent manner. RbAp48 lowered the K(m) of CBP histone acetylase activity and facilitated p300-mediated in vitro transcription of a chromatinized template in the presence of acetylcoenzyme A. These data indicate that the association of phosphorylated CREB with CBP promotes the binding of RbAp48 and its homologue RbAp46, allowing the formation of a complex that facilitates histone acetylation during transcriptional activation.

Recruitment of CREB binding protein is sufficient for CREB-mediated gene activation.

Phosphorylation of the transcription factor CREB leads to the recruitment of the coactivator, CREB binding protein (CBP). Recent studies have suggested that CBP recruitment is not sufficient for CREB function, however. We have identified a conserved protein-protein interaction motif within the CBP-binding domains of CREB and another transcription factor, SREBP (sterol-responsive element binding protein). In contrast to CREB, SREBP interacts with CBP in the absence of phosphorylation. We have exploited the conservation of this interaction motif to test whether CBP recruitment to CREB is sufficient for transcriptional activation. Substitution of six nonconserved amino acids from SREBP into the activation domain of CREB confers high-affinity, phosphorylation-independent CBP binding. The mutated CREB molecule, CREB(DIEDML), activates transcription in F9 teratocarcinoma and PC12 cells even in the absence of protein kinase A (PKA). Addition of exogenous CBP augments the level of transcription mediated by CREB(DIEDML), and adenovirus 12S E1A blocks transcription, implicating CBP in the activation process. Thus, recruitment of CBP to CREB is sufficient for transcriptional activation. Addition of PKA stimulates transcription induced by CREB(DIEDML) further, suggesting that a phosphorylation event downstream from CBP recruitment augments CREB signaling.

Cubitus interruptus requires Drosophila CREB-binding protein to activate wingless expression in the Drosophila embryo.

CREB-binding protein (CBP) serves as a transcriptional coactivator in multiple signal transduction pathways. The Drosophila homologue of CBP, dCBP, interacts with the transcription factors Cubitus interruptus (CI), MAD, and Dorsal (DL) and functions as a coactivator in several signaling pathways during Drosophila development, including the hedgehog (hh), decapentaplegic (dpp), and Toll pathways. Although dCBP is required for the expression of the hh target genes, wingless (wg) and patched (ptc) in vivo, and potentiates ci-mediated transcriptional activation in vitro, it is not known that ci absolutely requires dCBP for its activity. We used a yeast genetic screen to identify several ci point mutations that disrupt CI-dCBP interactions. These mutant proteins are unable to transactivate a reporter gene regulated by ci binding sites and have a lower dCBP-stimulated activity than wild-type CI. When expressed exogenously in embryos, the CI point mutants cannot activate endogenous wg expression. Furthermore, a CI mutant protein that lacks the entire dCBP interaction domain functions as a negative competitor for wild-type CI activity, and the expression of dCBP antisense RNAs can suppress CI transactivation in Kc cells. Taken together, our data suggest that dCBP function is necessary for ci-mediated transactivation of wg during Drosophila embryogenesis.

Mutants of cubitus interruptus that are independent of PKA regulation are independent of hedgehog signaling.

Hedgehog (HH) is an important morphogen involved in pattern formation during Drosophila embryogenesis and disc development. cubitus interruptus (ci) encodes a transcription factor responsible for transducing the hh signal in the nucleus and activating hh target gene expression. Previous studies have shown that CI exists in two forms: a 75 kDa proteolytic repressor form and a 155 kDa activator form. The ratio of these forms, which is regulated positively by hh signaling and negatively by PKA activity, determines the on/off status of hh target gene expression. In this paper, we demonstrate that the exogenous expression of CI that is mutant for four consensus PKA sites [CI(m1-4)], causes ectopic expression of wingless (wg) in vivo and a phenotype consistent with wg overexpression. Expression of CI(m1-4), but not CI(wt), can rescue the hh mutant phenotype and restore wg expression in hh mutant embryos. When PKA activity is suppressed by expressing a dominant negative PKA mutant, the exogenous expression of CI(wt) results in overexpression of wg and lethality in embryogenesis, defects that are similar to those caused by the exogenous expression of CI(m1-4). In addition, we demonstrate that, in cell culture, the mutation of any one of the three serine-containing PKA sites abolishes the proteolytic processing of CI. We also show that PKA directly phosphorylates the four consensus phosphorylation sites in vitro. Taken together, our results suggest that positive hh and negative PKA regulation of wg gene expression converge on the regulation of CI phosphorylation.