Slip complexity in earthquake fault models.

We summarize studies of earthquake fault models that give rise to slip complexities like those in natural earthquakes. For models of smooth faults between elastically deformable continua, it is critical that the friction laws involve a characteristic distance for slip weakening or evolution of surface state. That results in a finite nucleation size, or coherent slip patch size, h*. Models of smooth faults, using numerical cell size properly small compared to h*, show periodic response or complex and apparently chaotic histories of large events but have not been found to show small event complexity like the self-similar (power law) Gutenberg-Richter frequency-size statistics. This conclusion is supported in the present paper by fully inertial elastodynamic modeling of earthquake sequences. In contrast, some models of locally heterogeneous faults with quasi-independent fault segments, represented approximately by simulations with cell size larger than h* so that the model becomes "inherently discrete," do show small event complexity of the Gutenberg-Richter type. Models based on classical friction laws without a weakening length scale or for which the numerical procedure imposes an abrupt strength drop at the onset of slip have h* = 0 and hence always fall into the inherently discrete class. We suggest that the small-event complexity that some such models show will not survive regularization of the constitutive description, by inclusion of an appropriate length scale leading to a finite h*, and a corresponding reduction of numerical grid size.

Dynamic friction and the origin of the complexity of earthquake sources.

We study a simple antiplane fault of finite length embedded in a homogeneous isotropic elastic solid to understand the origin of seismic source heterogeneity in the presence of nonlinear rate- and state-dependent friction. All the mechanical properties of the medium and friction are assumed homogeneous. Friction includes a characteristic length that is longer than the grid size so that our models have a well-defined continuum limit. Starting from a heterogeneous initial stress distribution, we apply a slowly increasing uniform stress load far from the fault and we simulate the seismicity for a few 1000 events. The style of seismicity produced by this model is determined by a control parameter associated with the degree of rate dependence of friction. For classical friction models with rate-independent friction, no complexity appears and seismicity is perfectly periodic. For weakly rate-dependent friction, large ruptures are still periodic, but small seismicity becomes increasingly nonstationary. When friction is highly rate-dependent, seismicity becomes nonperiodic and ruptures of all sizes occur inside the fault. Highly rate-dependent friction destabilizes the healing process producing premature healing of slip and partial stress drop. Partial stress drop produces large variations in the state of stress that in turn produce earthquakes of different sizes. Similar results have been found by other authors using the Burridge and Knopoff model. We conjecture that all models in which static stress drop is only a fraction of the dynamic stress drop produce stress heterogeneity.

Slip complexity in dynamic models of earthquake faults.

We summarize recent evidence that models of earthquake faults with dynamically unstable friction laws but no externally imposed heterogeneities can exhibit slip complexity. Two models are described here. The first is a one-dimensional model with velocity-weakening stick-slip friction; the second is a two-dimensional elastodynamic model with slip-weakening friction. Both exhibit small-event complexity and chaotic sequences of large characteristic events. The large events in both models are composed of Heaton pulses. We argue that the key ingredients of these models are reasonably accurate representations of the properties of real faults.

A complexity measure for selective matching of signals by the brain.

We have previously derived a theoretical measure of neural complexity (CN) in an attempt to characterize functional connectivity in the brain. CN measures the amount and heterogeneity of statistical correlations within a neural system in terms of the mutual information between subsets of its units. CN was initially used to characterize the functional connectivity of a neural system isolated from the environment. In the present paper, we introduce a related statistical measure, matching complexity (CM), which reflects the change in CN that occurs after a neural system receives signals from the environment. CM measures how well the ensemble of intrinsic correlations within a neural system fits the statistical structure of the sensory input. We show that CM is low when the intrinsic connectivity of a simulated cortical area is randomly organized. Conversely, CM is high when the intrinsic connectivity is modified so as to differentially amplify those intrinsic correlations that happen to be enhanced by sensory input. When the input is represented by an individual stimulus, a positive value of CM indicates that the limited mutual information between sensory sheets sampling the stimulus and the rest of the brain triggers a large increase in the mutual information between many functionally specialized subsets within the brain. In this way, a complex brain can deal with context and go "beyond the information given."

Complexity of the erythroid transcription factor NF-E2 as revealed by gene targeting of the mouse p18 NF-E2 locus.

High-level globin expression in erythroid precursor cells depends on the integrity of NF-E2 recognition sites, transcription factor AP-1-like protein-binding motifs, located in the upstream regulatory regions of the alpha- and beta-globin loci. The NF-E2 transcription factor, which recognizes these sites, is a heterodimer consisting of (i) p45 NF-E2 (the larger subunit), a hematopoietic-restricted basic leucine zipper protein, and (ii) a widely expressed basic leucine zipper factor, p18 NF-E2, the smaller subunit. p18 NF-E2 protein shares extensive homology with the maf protooncogene family. To determine an in vivo role for p18 NF-E2 protein we disrupted the p18 NF-E2-encoding gene by homologous recombination in murine embryonic stem cells and generated p18 NF-E2-/- mice. These mice are indistinguishable from littermates throughout all phases of development and remain healthy in adulthood. Despite the absence of expressed p18 NF-E2, DNA-binding activity with the properties of the NF-E2 heterodimer is present in fetal liver erythroid cells of p18 NF-E2-/- mice. We speculate that another member of the maf basic leucine zipper family substitutes for the p18 subunit in a complex with p45 NF-E2. Thus, p18 NF-E2 per se appears to be dispensable in vivo.

Identification of a minimal sequence of the mouse pro-alpha 1(I) collagen promoter that confers high-level osteoblast expression in transgenic mice and that binds a protein selectively present in osteoblasts.

Based on our previous transgenic mice results, which strongly suggested that separate cell-specific cis-acting elements of the mouse pro-alpha 1(I) collagen promoter control the activity of the gene in different type I collagen-producing cells, we attempted to delineate a short segment in this promoter that could direct high-level expression selectively in osteoblasts. By generating transgenic mice harboring various fragments of the promoter, we identified a 117-bp segment (-1656 to -1540) that is a minimal sequence able to confer high-level expression of a lacZ reporter gene selectively in osteoblasts when cloned upstream of the proximal 220-bp pro-alpha 1(I) promoter. This 220-bp promoter by itself was inactive in transgenic mice and unable to direct osteoblast-specific expression. The 117-bp enhancer segment contained two sequences that appeared to have different functions. The A sequence (-1656 to -1628) was required to obtain expression of the lacZ gene in osteoblasts, whereas the C sequence (-1575 to -1540) was essential to obtain consistent and high-level expression of the lacZ gene in osteoblasts. Gel shift assays showed that the A sequence bound a nuclear protein present only in osteoblastic cells. A mutation in the A segment that abolished the binding of this osteoblast-specific protein also abolished lacZ expression in osteoblasts of transgenic mice.

Fine specificity of the antibody response to myelin basic protein in the central nervous system in multiple sclerosis: the minimal B-cell epitope and a model of its features.

T cells, B cells, and antibody are found in the white matter of the central nervous system in multiple sclerosis. The epitope center for the antibody response to human myelin basic protein (MBP) fits precisely the minimal epitope Pro85-Val-Val-His-Phe-Phe-Lys-Asn-Ile-Val-Thr-Pro96 for that reported for HLA DR2b (DRB1*1501)-restricted T cells that recognize MBP [Wucherpfenning, K.W., Sette, A., Southwood, S., Oseroff, C., Matsui, M., Strominger, J. & Hafler, D. (1994) J. Exp. Med. 179, 279-290], and overlaps with the reported DR2a-restricted epitope for T cells reactive to MBP [Martin, R., Howell, M. D., Jaraquemada, D., Furlage, M., Richert, J., Brostoff, S., Long, E. O., McFarlin, D. E. & McFarland, H. F. (1991) J. Exp. Med. 173, 19-24]. We describe a molecular model of this epitope.

Growth hormone secretagogues: characterization, efficacy, and minimal bioactive conformation.

Another class of growth hormone (GH) secretagogues has been discovered by altering the backbone structure of a flexible linear GH-releasing peptide (GHRP). In vitro and in vivo characterization confirms these GH secretagogues as the most potent and smallest (M(r) < 500) reported. Anabolic efficacy is demonstrated in rodents with intermittent delivery. A convergent model of the bioactive conformation of GHRPs is developed and is supported by the NMR structure of a highly potent cyclic analog of GHRP-2. The model and functional data provide a logical framework for the further design of low-molecular weight secretagogues and illustrate the utility of an interdisciplinary approach to elucidating potential bound-state conformations of flexible peptide ligands.

Radiometal labeling of recombinant proteins by a genetically engineered minimal chelation site: technetium-99m coordination by single-chain Fv antibody fusion proteins through a C-terminal cysteinyl peptide.

We describe a method to facilitate radioimaging with technetium-99m (99mTc) by genetic incorporation of a 99mTc chelation site in recombinant single-chain Fv (sFv) antibody proteins. This method relies on fusion of the sFv C terminus with a Gly4Cys peptide that specifically coordinates 99mTc. By using analogues of the 26-10 anti-digoxin sFv as our primary model, we find that addition of the chelate peptide, to form 26-10-1 sFv', does not alter the antigen-binding affinity of sFv. We have demonstrated nearly quantitative chelation of 0.5-50 mCi of 99mTc per mg of 26-10-1 sFv' (1 Ci = 37 GBq). These 99mTc-labeled sFv' complexes are highly stable to challenge with saline buffers, plasma, or diethylenetriaminepentaacetic acid. We find that the 99mTc-labeled 741F8-1 sFv', specific for the c-erbB-2 tumor-associated antigen, is effective in imaging human ovarian carcinoma in a scid mouse tumor xenograft model. This fusion chelate methodology should be applicable to diagnostic imaging with 99mTc and radioimmunotherapy with 186Re or 188Re, and its use could extend beyond the sFv' to other engineered antibodies, recombinant proteins, and synthetic peptides.

Physical mapping of the minimal region of loss in 5q- chromosome.

Acquired interstitial loss of all or part of the long arm of human chromosome 5 (5q-) is an anomaly that is seen frequently in patients with preleukemic myelodysplasia and acute myelogenous leukemia. Loss of a critical region of overlap at band 5q31.1 in all of these cases, with various cytogenetic breaks, signifies the existence of a key negative regulator of leukemogenesis. Previous studies have defined the proximal and distal ends of the critical region to reside between the genes for IL9 and EGR1, respectively. In this report, we describe a yeast artificial chromosome contig spanning this myeloid tumor suppressor locus. The combined order of the polymorphic loci is centromere-IL9-(D5S525-D5S558-D5S89-D5S526 -D5S393)-D5S399-D5S396-D5S414-EGR1 and telomere. The physical distance between the IL9 and EGR1 genes is estimated to be < 2.4 Mb. Here we report the utility of these polymorphic loci by detecting a submicroscopic deletion of 5q31; an acute myelogenous leukemia patient with a three-way translocation, t(5;18;17)(q31;p11;q11), as the sole anomaly revealed allele loss of the D5S399 and D5S396 loci.

Complexity, contingency, and criticality.

Complexity originates from the tendency of large dynamical systems to organize themselves into a critical state, with avalanches or "punctuations" of all sizes. In the critical state, events which would otherwise be uncoupled become correlated. The apparent, historical contingency in many sciences, including geology, biology, and economics, finds a natural interpretation as a self-organized critical phenomenon. These ideas are discussed in the context of simple mathematical models of sandpiles and biological evolution. Insights are gained not only from numerical simulations but also from rigorous mathematical analysis.

Minimal epitopes expressed in a recombinant polyepitope protein are processed and presented to CD8+ cytotoxic T cells: implications for vaccine design.

The epitopes recognized by CD8+ cytotoxic T lymphocytes (CTL) are generated from cytosolic proteins by proteolytic processing. The nature of the influences exerted by the sequences flanking CTL epitopes on these processing events remains controversial. Here we show that each epitope within an artificial polyepitope protein containing nine minimal CD8+ CTL epitopes in sequence was processed and presented to appropriate CTL clones. Natural flanking sequences were thus not required to direct class I proteolytic processing. In addition, unnatural flanking sequences containing other CTL epitopes did not interfere with processing. The ability of every CTL epitope to be effectively processed from a protein containing only CTL epitopes is likely to find application in the construction of recombinant polyepitope CTL vaccines.

Contrasting complexity of two rust resistance loci in flax.

DNA probes from the L6 rust resistance gene of flax (Linum usitatissimum) hybridize to resistance genes at the unlinked M locus, indicating sequence similarities between genes at the two loci. Genetic and molecular data indicate that the L locus is simple and contains a single gene with 13 alleles and that the M locus is complex and contains a tandem array of genes of similar sequence. Thus the evolution of these two related loci has been different. The consequence of the contrasting structures of the L and M loci on the evolution of different rust resistance specificities can now be investigated at the molecular level

Hayek and complexity: coordination, evolution and methodology in social adaptive systems

The affinity between the work of the Austrian economist Friedrich A. Hayek and the approach of Complexity Economics is widely recognized by the literature. In spite of this, there still is a lack of studies that seek to analyze in depth the relationship between Hayek and complexity. This dissertation is a contribution to the filling of this large gap in the literature. In the first part of the work, we analyze the various periods in the development of Hayek\'s vision of complexity, showing that this vision is strongly present in his works on knowledge, competition, methodology, evolution, and spontaneous order. In the second part, we explore how Hayek was influenced by two of the main precursors of modern complexity theory - cybernetics and general system theory - from the time he was working on his book on theoretical psychology, The Sensory Order (1952), until the end of his intellectual career.