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.

The 5' coding region of Paramecium surface antigen genes controls mutually exclusive transcription.

Paramecium tetraurelia stock 51 can express at least 11 different types of surface antigens, yet only a single type is expressed on the surface of an individual cell at any one time. The differential expression of stock 51 type A and B surface antigen genes (51A and 51B) is regulated at the level of transcription. Previously, we reported that nucleotide sequences upstream of position -26 (relative to the start of translation) in the 51A and 51B surface antigen genes are necessary for transcriptional activity but are not sufficient to direct differential transcriptional control. In this report we demonstrate that at least some of the critical elements necessary for differential transcription of the 51A and 51B genes lie within the 5' coding region. A hybrid gene that contains 51B upstream sequences (-475 to +1) attached to the ATG start codon of 51A is not cotranscribed with the 51B gene. In contrast, further substitution with 51B sequences (-1647 to +885) allows the chimeric gene to be coexpressed with 51B. A different hybrid gene containing a substitution of 51B sequence from -26 to +885 in the 51A gene is also coexpressed with 51B, revealing that the critical elements within the coding region of 51B do not require 51B upstream sequences for their effect. Coinjection of the 51A gene with the chimeric gene that contains 51B up to +885 showed that the same sequences that allow coexpression with 51B prevent cotranscription with 51A. Together, these results demonstrate that a region downstream of the transcriptional start site between nucleotide positions +1 and +885 (relative to translational start) is necessary to control differential transcriptional activity.

Circuitry for color coding in the primate retina.

Human color vision starts with the signals from three cone photoreceptor types, maximally sensitive to long (L-cone), middle (M-cone), and short (S-cone) wavelengths. Within the retina these signals combine in an antagonistic way to form red-green and blue-yellow spectral opponent pathways. In the classical model this antagonism is thought to arise from the convergence of cone type-specific excitatory and inhibitory inputs to retinal ganglion cells. The circuitry for spectral opponency is now being investigated using an in vitro preparation of the macaque monkey retina. Intracellular recording and staining has shown that blue-ON/yellow-OFF opponent responses arise from a distinctive bistratified ganglion cell type. Surprisingly, this cone opponency appears to arise by dual excitatory cone bipolar cell inputs: an ON bipolar cell that contacts only S-cones and an OFF bipolar cell that contacts L- and M-cones. Red-green spectral opponency has long been linked to the midget ganglion cells, but an underlying mechanism remains unclear. For example, receptive field mapping argues for segregation of L-and M-cone signals to the midget cell center and surround, but horizontal cell interneurons, believed to generate the inhibitory surround, lack opponency and cannot contribute selective L- or M-cone input to the midget cell surround. The solution to this color puzzle no doubt lies in the great diversity of cell types in the primate retina that still await discovery and analysis.

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.

A transgene coding for a human insulin analog has a mitogenic effect on murine embryonic beta cells.

We have investigated the mitogenic effect of three mutant forms of human insulin on insulin-producing beta cells of the developing pancreas. We examined transgenic embryonic and adult mice expressing (i) human [AspB10]-proinsulin/insulin ([AspB10]ProIN/IN), produced by replacement of histidine by aspartic acid at position 10 of the B chain and characterized by an increased affinity for the insulin receptor; (ii) human [LeuA3]insulin, produced by the substitution of leucine for valine in position 3 of the A chain, which exhibits decreased receptor binding affinity; and (iii) human [LeuA3, AspB10]insulin "double" mutation. During development, beta cells of AspB10 embryos were twice as abundant and had a 3 times higher rate of proliferation compared with beta cells of littermate controls. The mitogenic effect of [AspB10]ProIN/IN was specific for embryonic beta cells because the rate of proliferation of beta cells of adults and of glucagon (alpha) cells and adrenal chromaffin cells of embryos was similar in AspB10 mice and controls. In contrast to AspB10 embryos, the number of beta cells in the LeuA3 and "double" mutant lines was similar to the number in controls. These findings indicate that the [AspB10]ProIN/IN analog increased the rate of fetal beta-cell proliferation. The mechanism or mechanisms that mediate this mitogenic effect remain to be determined.

Accelerated evolution in the protein-coding regions is universal in crotalinae snake venom gland phospholipase A2 isozyme genes.

The nucleotide sequences of four genes encoding Trimeresurus gramineus (green habu snake, crotalinae) venom gland phospholipase A2 (PLA2; phosphatidylcholine 2-acylhydrolase, EC 3.1.1.4) isozymes were compared internally and externally with those of six genes encoding Trimeresurus flavoviridis (habu snake, crotalinae) venom gland PLA2 isozymes. The numbers of nucleotide substitutions per site (KN) for the noncoding regions including introns were one-third to one-eighth of the numbers of nucleotide substitutions per synonymous site (KS) for the protein-coding regions of exons, indicating that the noncoding regions are much more conserved than the protein-coding regions. The KN values for the introns were found to be nearly equivalent to those of introns of T. gramineus and T. flavoviridis TATA box-binding protein genes, which are assumed to be a general (nonvenomous) gene. Thus, it is evident that the introns of venom gland PLA2 isozyme genes have evolved at a similar rate to those of nonvenomous genes. The numbers of nucleotide substitutions per nonsynonymous site (KA) were close to or larger than the KS values for the protein-coding regions in venom gland PLA2 isozyme genes. All of the data combined reveal that Darwinian-type accelerated evolution has universally occurred only in the protein-coding regions of crotalinae snake venom PLA2 isozyme genes.

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