Biological Systems from an Engineer’s Point of View

Mathematical modeling of the processes that pattern embryonic development (often called biological pattern formation) has a long and rich history [1,2]. These models proposed sets of hypothetical interactions, which, upon analysis, were shown to be capable of generating patterns reminiscent of those seen in the biological world, such as stripes, spots, or graded properties. Pattern formation models typically demonstrated the sufficiency of given classes of mechanisms to create patterns that mimicked a particular biological pattern or interaction. In the best cases, the models were able to make testable predictions [3], permitting them to be experimentally challenged, to be revised, and to stimulate yet more experimental tests (see review in [4]). In many other cases, however, the impact of the modeling efforts was mitigated by limitations in computer power and biochemical data. In addition, perhaps the most limiting factor was the mindset of many modelers, using Occam’s razor arguments to make the proposed models as simple as possible, which often generated intriguing patterns, but those patterns lacked the robustness exhibited by the biological system. In hindsight, one could argue that a greater attention to engineering principles would have focused attention on these shortcomings, including potential failure modes, and would have led to more complex, but more robust, models. Thus, despite a few successful cases in which modeling and experimentation worked in concert, modeling fell out of vogue as a means to motivate decisive test experiments. The recent explosion of molecular genetic, genomic, and proteomic data—as well as of quantitative imaging studies of biological tissues—has changed matters dramatically, replacing a previous dearth of molecular details with a wealth of data that are difficult to fully comprehend. This flood of new data has been accompanied by a new influx of physical scientists into biology, including engineers, physicists, and applied mathematicians [5–7]. These individuals bring with them the mindset, methodologies, and mathematical toolboxes common to their own fields, which are proving to be appropriate for analysis of biological systems. However, due to inherent complexity, biological systems seem to be like nothing previously encountered in the physical sciences. Thus, biological systems offer cutting edge problems for most scientific and engineering-related disciplines. It is therefore no wonder that there might seem to be a “bandwagon” of new biology-related research programs in departments that have traditionally focused on nonliving systems. Modeling biological interactions as dynamical systems (i.e., systems of variables changing in time) allows investigation of systems-level topics such as the robustness of patterning mechanisms, the role of feedback, and the self-regulation of size. The use of tools from engineering and applied mathematics, such as sensitivity analysis and control theory, is becoming more commonplace in biology. In addition to giving biologists some new terminology for describing their systems, such analyses are extremely useful in pointing to missing data and in testing the validity of a proposed mechanism. A paper in this issue of PLoS Biology clearly and honestly applies analytical tools to the authors’ research and obtains insights that would have been difficult if not impossible by other means [8]

Online identification and nonlinear control of the electrically stimulated quadriceps muscle

A new approach for estimating nonlinear models of the electrically stimulated quadriceps muscle group under nonisometric conditions is investigated. The model can be used for designing controlled neuro-prostheses. In order to identify the muscle dynamics (stimulation pulsewidth-active knee moment relation) from discrete-time angle measurements only, a hybrid model structure is postulated for the shank-quadriceps dynamics. The model consists of a relatively well known time-invariant passive component and an uncertain time-variant active component. Rigid body dynamics, described by the Equation of Motion (EoM), and passive joint properties form the time-invariant part. The actuator, i.e. the electrically stimulated muscle group, represents the uncertain time-varying section. A recursive algorithm is outlined for identifying online the stimulated quadriceps muscle group. The algorithm requires EoM and passive joint characteristics to be known a priori. The muscle dynamics represent the product of a continuous-time nonlinear activation dynamics and a nonlinear static contraction function described by a Normalised Radial Basis Function (NRBF) network which has knee-joint angle and angular velocity as input arguments. An Extended Kalman Filter (EKF) approach is chosen to estimate muscle dynamics parameters and to obtain full state estimates of the shank-quadriceps dynamics simultaneously. The latter is important for implementing state feedback controllers. A nonlinear state feedback controller using the backstepping method is explicitly designed whereas the model was identified a priori using the developed identification procedure

Xwnt-5A: a maternal Wnt that affects morphogenetic movements after overexpression in embryos of Xenopus laevis

To contribute to an understanding of the roles and mechanisms of action of Wnts in early vertebrate development, we have characterized the normal expression of Xenopus laevis Wnt-5A, and investigated the consequences of misexpression of this putative signalling factor. Xwnt-5A transcripts are expressed throughout development, and are enriched in both the anterior and posterior regions of embryos at late stages of development, where they are found primarily in ectoderm, with lower levels of expression in mesoderm. Overexpression of Xwnt-5A in Xenopus embryos leads to complex malformations distinct from those achieved by ectopic expression of Xwnts −1, −3A, or −8. This phenotype is unlikely to result from Xwnt-5A acting as an inducing agent, as overexpression of Xwnt-5A does not rescue dorsal structures in UV-irradiated embryos, does not induce mesoderm in blastula caps, and Xwnt-5A does not alter the endogenous patterns of expression of goosecoid, Xbra, or Xwnt-8. To pursue whether Xwnt-5A has the capacity to affect morphogenetic movements, we investigated whether overexpression of Xwnt-5A alters the normal elongation of blastula cap explants induced by activin. Intriguingly, Xwnt-5A blocks the elongation of blastula caps in response to activin, without blocking the differentiation of either dorsal or ventral mesoderm within these explants. The data are consistent with Xwnt-5A having the potential activity of modifying the morphogenetic movements of tissues

TRIPPy: Trailed Image Photometry in Python

Photometry of moving sources typically suffers from reduced signal-to-noise (SNR) or flux measurements biased to incorrect low values through the use of circular apertures. To address this issue we present the software package, TRIPPy: TRailed Image Photometry in Python. TRIPPy introduces the pill aperture, which is the natural extension of the circular aperture appropriate for linearly trailed sources. The pill shape is a rectangle with two semicircular end-caps, and is described by three parameters, the trail length and angle, and the radius. The TRIPPy software package also includes a new technique to generate accurate model point-spread functions (PSF) and trailed point-spread functions (TSF) from stationary background sources in sidereally tracked images. The TSF is merely the convolution of the model PSF, which consists of a moffat profile, and super sampled lookup table. From the TSF, accurate pill aperture corrections can be estimated as a function of pill radius with a accuracy of 10 millimags for highly trailed sources. Analogous to the use of small circular apertures and associated aperture corrections, small radius pill apertures can be used to preserve signal-to-noise of low flux sources, with appropriate aperture correction applied to provide an accurate, unbiased flux measurement at all SNR.Comment: 8 Figures, 11 Pages, Accepted to the Astronomical Journa

A model for MRI contrast enhancement using T_1 agents

Contrast in MRI relies on differences in the local environment of water and is often enhanced by using contrast agents. We present a simple model for evaluating the minimal contrast agent concentration required to produce “satisfactory” contrast enhancement in magnetic resonance images. Previous strategies have been based largely on empirical results for specific systems. The present tissue contrast model (TCM) can be applied to “conventional,” targeted, or biochemically responsive agents. The model results are formulated so that only a small number of parameters are required to analyze a given scenario. The TCM is a particularly useful tool in the development of new classes of magnetic resonance contrast media. These agents will have the ability to target specific cells or tissue, and perhaps be able to report on their physiological status. As an example of the applicability of the TCM, we test it against in vivo magnetic resonance microscopy results in frog embryos that have focal cell populations labeled with contrast agent by using calibrated single-cell microinjection techniques

Southern hemispheric halon trends and global halon emissions, 1978–2011

The atmospheric records of four halons, H-1211 (CBrClF2), H-1301 (CBrF3), H-2402 (CBrF2CBrF2) and H-1202 (CBr2F2), measured from air collected at Cape Grim, Tasmania, between 1978 and 2011, are reported. Mixing ratios of H-1211, H-2402 and H-1202 began to decline in the early to mid-2000s, but those of H-1301 continue to increase up to mid-2011. These trends are compared to those reported by NOAA (National Oceanic and Atmospheric Administration) and AGAGE (Advanced Global Atmospheric Experiment). The observations suggest that the contribution of the halons to total tropospheric bromine at Cape Grim has begun to decline from a peak in 2008 of about 8.1 ppt. An extrapolation of halon mixing ratios to 2060, based on reported banks and predicted release factors, shows this decline becoming more rapid in the coming decades, with a contribution to total tropospheric bromine of about 3 ppt in 2060. Top-down global annual emissions of the halons were derived using a two-dimensional atmospheric model. The emissions of all four have decreased since peaking in the late 1980s–mid-1990s, but this decline has slowed recently, particularly for H-1301 and H-2402 which have shown no decrease in emissions over the past five years. The UEA (University of East Anglia) top-down model-derived emissions are compared to those reported using a top-down approach by NOAA and AGAGE and the bottom-up estimates of HTOC (Halons Technical Options Committee). The implications of an alternative set of steady-state atmospheric lifetimes are discussed. Using a lifetime of 14 yr or less for H-1211 to calculate top-down emissions estimates would lead to small, or even negative, estimated banks given reported production data. Finally emissions of H-1202, a product of over-bromination during the production process of H-1211, have continued despite reported production of H-1211 ceasing in 2010. This raises questions as to the source of these H-1202 emissions

Chlorine isotope composition in chlorofluorocarbons CFC-11, CFC-12 and CFC-113 in firn, stratospheric and tropospheric air

The stratospheric degradation of chlorofluorocarbons (CFCs) releases chlorine, which is a major contributor to the destruction of stratospheric ozone (O3). A recent study reported strong chlorine isotope fractionation during the breakdown of the most abundant CFC (CFC-12, CCl2F2, Laube et al., 2010a), similar to effects seen in nitrous oxide (N2O). Using air archives to obtain a long-term record of chlorine isotope ratios in CFCs could help to identify and quantify their sources and sinks. We analyse the three most abundant CFCs and show that CFC-11 (CCl3F) and CFC-113 (CClF2CCl2F) exhibit significant stratospheric chlorine isotope fractionation, in common with CFC-12. The apparent isotope fractionation (εapp) for mid- and high-latitude stratospheric samples are (-2.4±0.5) ‰ and (-2.3±0.4) ‰ for CFC-11, (-12.2±1.6) ‰ and (-6.8±0.8) ‰ for CFC-12 and (-3.5±1.5) ‰ and (-3.3±1.2) ‰ for CFC-113, respectively. Assuming a constant isotope composition of emissions, we calculate the expected trends in the tropospheric isotope signature of these gases based on their stratospheric 37Cl enrichment and stratosphere-troposphere exchange. We compare these projections to the long-term δ(37Cl) trends of all three CFCs, measured on background tropospheric samples from the Cape Grim air archive (Tasmania, 1978 – 2010) and tropospheric firn air samples from Greenland (NEEM site) and Antarctica (Fletcher Promontory site). From 1970 to the present-day, projected trends agree with tropospheric measurements, suggesting that within analytical uncertainties a constant average emission isotope delta is a compatible scenario. The measurement uncertainty is too high to determine whether the average emission isotope delta has been affected by changes in CFC manufacturing processes, or not. Our study increases the suite of trace gases amenable to direct isotope ratio measurements in small air volumes (approximately 200 ml), using a single-detector gas chromatography-mass spectrometry system

The diagnostic accuracy and cost-effectiveness of magnetic resonance spectroscopy and enhanced magnetic resonance imaging techniques in aiding the localisation of prostate abnormalities for biopsy : a systematic review and economic evaluation

Peer reviewedPublisher PD