David Hayden

Strabismus has been known to have a significant genetic component, but the mode of inheritance and the identity of the relevant genes have been enigmatic. This paper reports linkage analysis of nonsyndromic strabismus. The principal results of this study are: (i) the demonstrated feasibility of identifying and recruiting large families in which multiple members have (or had) strabismus; (ii) the linkage in one large family of a presumptive strabismus susceptibility locus to 7p22.1 with a multipoint logarithm of odds score of 4.51 under a model of recessive inheritance; and (iii) the failure to observe significant linkage to 7p in six other multiplex families, consistent with genetic heterogeneity among families. These findings suggest that it will be possible to localize and ultimately identify strabismus susceptibility genes by linkage analysis and mutation screening of candidate genes.

This paper considers the problem of inferring an unknown network of dynamical systems driven by unknown, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> intrinsic</i> , noise inputs. Equivalently we seek to identify direct causal dependencies among manifest variables only from observations of these variables. For linear, time-invariant systems of minimal order, we characterise under what conditions this problem is well posed. We first show that if the transfer matrix from the inputs to manifest states is minimum phase, this problem has a unique solution irrespective of the network topology. This is equivalent to there being only one valid spectral factor (up to a choice of signs of the inputs) of the output spectral density. If the assumption of phase-minimality is relaxed, we show that the problem is characterised by a single Algebraic Riccati Equation (ARE), of dimension determined by the number of latent states. The number of solutions to this ARE is an upper bound on the number of solutions for the network. We give necessary and sufficient conditions for any two dynamical networks to have equal output spectral density, which can be used to construct all equivalent networks. Extensive simulations quantify the number of solutions for a range of problem sizes. For a slightly simpler case, we also provide an algorithm to construct all equivalent networks from the output spectral density.

The circadian oscillator, an internal time-keeping device found in most organisms, enables timely regulation of daily biological activities by maintaining synchrony with the external environment. The mechanistic basis underlying the adjustment of circadian rhythms to changing external conditions, however, has yet to be clearly elucidated. We explored the mechanism of action of nicotinamide in Arabidopsis thaliana, a metabolite that lengthens the period of circadian rhythms, to understand the regulation of circadian period. To identify the key mechanisms involved in the circadian response to nicotinamide, we developed a systematic and practical modeling framework based on the identification and comparison of gene regulatory dynamics. Our mathematical predictions, confirmed by experimentation, identified key transcriptional regulatory mechanisms of circadian period and uncovered the role of blue light in the response of the circadian oscillator to nicotinamide. We suggest that our methodology could be adapted to predict mechanisms of drug action in complex biological systems.