Comparing in vitro, in situ, and in vivo experimental data in a three-dimensional model of mammalian cochlear mechanics

Normal mammalian hearing is refined by amplification of the motion of the cochlear partition. This partition, comprising the organ of Corti sandwiched between the basilar and tectorial membranes, contains the outer hair cells that are thought to drive this amplification process. Force generation by outer hair cells has been studied extensively in vitro and in situ, but, to understand cochlear amplification fully, it is necessary to characterize the role played by each of the components of the cochlear partition in vivo. Observations of cochlear partition motion in vivo are severely restricted by its inaccessibility and sensitivity to surgical trauma, so, for the present study, a computer model has been used to simulate the operation of the cochlea under different experimental conditions. In this model, which uniquely retains much of the three-dimensional complexity of the real cochlea, the motions of the basilar and tectorial membranes are fundamentally different during in situ- and in vivo-like conditions. Furthermore, enhanced outer hair cell force generation in vitro leads paradoxically to a decrease in the gain of the cochlear amplifier during sound stimulation to the model in vivo. These results suggest that it is not possible to extrapolate directly from experimental observations made in vitro and in situ to the normal operation of the intact organ in vivo.

Immunity to retroviral infection: The Friend virus model

Friend virus infection of adult immunocompetent mice is a well established model for studying genetic resistance to infection by an immunosuppressive retrovirus. This paper reviews both the genetics of immune resistance and the types of immune responses required for recovery from infection. Specific major histocompatibility complex (MHC) class I and II alleles are necessary for recovery, as is a non-MHC gene, Rfv-3, which controls virus-specific antibody responses. In concordance with these genetic requirements are immunological requirements for cytotoxic T lymphocyte, T helper, and antibody responses, each of which provides essential nonoverlapping functions. The complexity of responses necessary for recovery from Friend virus infection has implications for both immunotherapies and vaccines. For example, it is shown that successful passive antibody therapy is dependent on MHC type because of the requirement for T cell responses. For vaccines, successful immunization requires priming of both T cell and B cell responses. In vivo depletion experiments demonstrate different requirements for CD8+ T cells depending on the vaccine used. The implications of these studies for human retroviral diseases are discussed.

Flower color variation: A model for the experimental study of evolution

We review the study of flower color polymorphisms in the morning glory as a model for the analysis of adaptation. The pathway involved in the determination of flower color phenotype is traced from the molecular and genetic levels to the phenotypic level. Many of the genes that determine the enzymatic components of flavonoid biosynthesis are redundant, but, despite this complexity, it is possible to associate discrete floral phenotypes with individual genes. An important finding is that almost all of the mutations that determine phenotypic differences are the result of transposon insertions. Thus, the flower color diversity seized on by early human domesticators of this plant is a consequence of the rich variety of mobile elements that reside in the morning glory genome. We then consider a long history of research aimed at uncovering the ecological fate of these various flower phenotypes in the southeastern U.S. A large body of work has shown that insect pollinators discriminate against white phenotypes when white flowers are rare in populations. Because the plant is self-compatible, pollinator bias causes an increase in self-fertilization in white maternal plants, which should lead to an increase in the frequency of white genes, according to modifier gene theory. Studies of geographical distributions indicate other, as yet undiscovered, disadvantages associated with the white phenotype. The ultimate goal of connecting ecology to molecular genetics through the medium of phenotype is yet to be attained, but this approach may represent a model for analyzing the translation between these two levels of biological organization.

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.