Models for stochastic climate prediction

There has been a recent burst of activity in the atmosphere/ocean sciences community in utilizing stable linear Langevin stochastic models for the unresolved degree of freedom in stochastic climate prediction. Here several idealized models for stochastic climate modeling are introduced and analyzed through unambiguous mathematical theory. This analysis demonstrates the potential need for more sophisticated models beyond stable linear Langevin equations. The new phenomena include the emergence of both unstable linear Langevin stochastic models for the climate mean and the need to incorporate both suitable nonlinear effects and multiplicative noise in stochastic models under appropriate circumstances. The strategy for stochastic climate modeling that emerges from this analysis is illustrated on an idealized example involving truncated barotropic flow on a beta-plane with topography and a mean flow. In this example, the effect of the original 57 degrees of freedom is well represented by a theoretically predicted stochastic model with only 3 degrees of freedom.

GeneSplicer: a new computational method for splice site prediction

GeneSplicer is a new, flexible system for detecting splice sites in the genomic DNA of various eukaryotes. The system has been tested successfully using DNA from two reference organisms: the model plant Arabidopsis thaliana and human. It was compared to six programs representing the leading splice site detectors for each of these species: NetPlantGene, NetGene2, HSPL, NNSplice, GENIO and SpliceView. In each case GeneSplicer performed comparably to the best alternative, in terms of both accuracy and computational efficiency.

Recent improvements in prediction of protein structure by global optimization of a potential energy function

Recent improvements of a hierarchical ab initio or de novo approach for predicting both α and β structures of proteins are described. The united-residue energy function used in this procedure includes multibody interactions from a cumulant expansion of the free energy of polypeptide chains, with their relative weights determined by Z-score optimization. The critical initial stage of the hierarchical procedure involves a search of conformational space by the conformational space annealing (CSA) method, followed by optimization of an all-atom model. The procedure was assessed in a recent blind test of protein structure prediction (CASP4). The resulting lowest-energy structures of the target proteins (ranging in size from 70 to 244 residues) agreed with the experimental structures in many respects. The entire experimental structure of a cyclic α-helical protein of 70 residues was predicted to within 4.3 Å α-carbon (Cα) rms deviation (rmsd) whereas, for other α-helical proteins, fragments of roughly 60 residues were predicted to within 6.0 Å Cα rmsd. Whereas β structures can now be predicted with the new procedure, the success rate for α/β- and β-proteins is lower than that for α-proteins at present. For the β portions of α/β structures, the Cα rmsd's are less than 6.0 Å for contiguous fragments of 30–40 residues; for one target, three fragments (of length 10, 23, and 28 residues, respectively) formed a compact part of the tertiary structure with a Cα rmsd less than 6.0 Å. Overall, these results constitute an important step toward the ab initio prediction of protein structure solely from the amino acid sequence.

Implications of fault constitutive properties for earthquake prediction.

The rate- and state-dependent constitutive formulation for fault slip characterizes an exceptional variety of materials over a wide range of sliding conditions. This formulation provides a unified representation of diverse sliding phenomena including slip weakening over a characteristic sliding distance Dc, apparent fracture energy at a rupture front, time-dependent healing after rapid slip, and various other transient and slip rate effects. Laboratory observations and theoretical models both indicate that earthquake nucleation is accompanied by long intervals of accelerating slip. Strains from the nucleation process on buried faults generally could not be detected if laboratory values of Dc apply to faults in nature. However, scaling of Dc is presently an open question and the possibility exists that measurable premonitory creep may precede some earthquakes. Earthquake activity is modeled as a sequence of earthquake nucleation events. In this model, earthquake clustering arises from sensitivity of nucleation times to the stress changes induced by prior earthquakes. The model gives the characteristic Omori aftershock decay law and assigns physical interpretation to aftershock parameters. The seismicity formulation predicts large changes of earthquake probabilities result from stress changes. Two mechanisms for foreshocks are proposed that describe observed frequency of occurrence of foreshock-mainshock pairs by time and magnitude. With the first mechanism, foreshocks represent a manifestation of earthquake clustering in which the stress change at the time of the foreshock increases the probability of earthquakes at all magnitudes including the eventual mainshock. With the second model, accelerating fault slip on the mainshock nucleation zone triggers foreshocks.

Nonuniformity of the constitutive law parameters for shear rupture and quasistatic nucleation to dynamic rupture: a physical model of earthquake generation processes.

Based on the recent high-resolution laboratory experiments on propagating shear rupture, the constitutive law that governs shear rupture processes is discussed in view of the physical principles and constraints, and a specific constitutive law is proposed for shear rupture. It is demonstrated that nonuniform distributions of the constitutive law parameters on the fault are necessary for creating the nucleation process, which consists of two phases: (i) a stable, quasistatic phase, and (ii) the subsequent accelerating phase. Physical models of the breakdown zone and the nucleation zone are presented for shear rupture in the brittle regime. The constitutive law for shear rupture explicitly includes a scaling parameter Dc that enables one to give a common interpretation to both small scale rupture in the laboratory and large scale rupture as earthquake source in the Earth. Both the breakdown zone size Xc and the nucleation zone size L are prescribed and scaled by Dc, which in turn is prescribed by a characteristic length lambda c representing geometrical irregularities of the fault. The models presented here make it possible to understand the earthquake generation process from nucleation to unstable, dynamic rupture propagation in terms of physics. Since the nucleation process itself is an immediate earthquake precursor, deep understanding of the nucleation process in terms of physics is crucial for the short-term (or immediate) earthquake prediction.

Rock friction and its implications for earthquake prediction examined via models of Parkfield earthquakes.

The friction of rocks in the laboratory is a function of time, velocity of sliding, and displacement. Although the processes responsible for these dependencies are unknown, constitutive equations have been developed that do a reasonable job of describing the laboratory behavior. These constitutive laws have been used to create a model of earthquakes at Parkfield, CA, by using boundary conditions appropriate for the section of the fault that slips in magnitude 6 earthquakes every 20-30 years. The behavior of this model prior to the earthquakes is investigated to determine whether or not the model earthquakes could be predicted in the real world by using realistic instruments and instrument locations. Premonitory slip does occur in the model, but it is relatively restricted in time and space and detecting it from the surface may be difficult. The magnitude of the strain rate at the earth's surface due to this accelerating slip seems lower than the detectability limit of instruments in the presence of earth noise. Although not specifically modeled, microseismicity related to the accelerating creep and to creep events in the model should be detectable. In fact the logarithm of the moment rate on the hypocentral cell of the fault due to slip increases linearly with minus the logarithm of the time to the earthquake. This could conceivably be used to determine when the earthquake was going to occur. An unresolved question is whether this pattern of accelerating slip could be recognized from the microseismicity, given the discrete nature of seismic events. Nevertheless, the model results suggest that the most likely solution to earthquake prediction is to look for a pattern of acceleration in microseismicity and thereby identify the microearthquakes as foreshocks.

Prediction of the stability of DNA triplexes.

We present rules that allow one to predict the stability of DNA pyrimidine.purine.pyrimidine (Y.R.Y) triple helices on the basis of the sequence. The rules were derived from van't Hoff analysis of 23 oligonucleotide triplexes tested at a variety of pH values. To predict the enthalpy of triplex formation (delta H degrees), a simple nearest-neighbor model was found to be sufficient. However, to accurately predict the free energy of the triplex (delta G degrees), a combination model consisting of five parameters was needed. These parameters were (i) the delta G degrees for helix initiation, (ii) the delta G degrees for adding a T-A.T triple, (iii) the delta G degrees for adding a C(+)-G.C triple, (iv) the penalty for adjacent C bases, and (v) the pH dependence of the C(+)-G.C triple's stability. The fitted parameters are highly consistent with thermodynamic data from the basis set, generally predicting both delta H degrees and delta G degrees to within the experimental error. Examination of the parameters points out several interesting features. The combination model predicts that C(+) -G.C. triples are much more stabilizing than T-A.T triples below pH 7.0 and that the stability of the former increases approximately equal to 1 kcal/mol per pH unit as the pH is decreased. Surprisingly though, the most stable sequence is predicted to be a CT repeat, as adjacent C bases partially cancel the stability of one another. The parameters successfully predict tm values from other laboratories, with some interesting exceptions.

Repacking protein cores with backbone freedom: structure prediction for coiled coils.

Progress in homology modeling and protein design has generated considerable interest in methods for predicting side-chain packing in the hydrophobic cores of proteins. Present techniques are not practically useful, however, because they are unable to model protein main-chain flexibility. Parameterization of backbone motions may represent a general and efficient method to incorporate backbone relaxation into such fixed main-chain models. To test this notion, we introduce a method for treating explicitly the backbone motions of alpha-helical bundles based on an algebraic parameterization proposed by Francis Crick in 1953 [Crick, F. H. C. (1953) Acta Crystallogr. 6, 685-689]. Given only the core amino acid sequence, a simple calculation can rapidly reproduce the crystallographic main-chain and core side-chain structures of three coiled coils (one dimer, one trimer, and one tetramer) to within 0.6-A root-mean-square deviations. The speed of the predictive method [approximately 3 min per rotamer choice on a Silicon Graphics (Mountain View, CA) 4D/35 computer] permits it to be used as a design tool.