Technical Briefs

On the Role of Autonomous Control in Organ Development

[+] Author and Article Information
Ashok Ramasubramanian

Assistant Professor
Department of Mechanical Engineering,
Union College,
Schenectady, NY 12309
e-mail: ramasuba@union.edu

In the next phase, the primitive atrium (part marked “A” in Fig. 1) moves to its definitive position above the primitive ventricle (part marked “V” in Fig. 1). This phase is called “s-looping,” Please see Ref. [4] for details.

Since λgx is the ratio of new length to the old length, it can never actually be zero. It can, however, get arbitrarily close to zero when the new length is a small fraction of the old one.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received August 11, 2012; final manuscript received July 5, 2013; published online August 23, 2013. Assoc. Editor: Sergey Nersesov.

J. Dyn. Sys., Meas., Control 135(6), 064503 (Aug 23, 2013) (6 pages) Paper No: DS-12-1260; doi: 10.1115/1.4024996 History: Received August 11, 2012; Revised July 05, 2013

Developmental biology (“development” for short) deals with how the mature animal or plant results from a single fertilized cell. This paper is concerned with one aspect of development, morphogenesis—the formation of complex shapes from simpler ones. In particular, this paper focuses on organ development and illustrates the central role that mechanical feedback plays in effecting the final shape of various organs. The first aim of this paper is to illustrate how self-governing autonomous control systems can lead to the development of organs such as the heart. Although feedback plays a key role in these processes, the field is largely unexplored by controls engineers; hence, the second aim of this paper is to introduce mechanical feedback during development to controls engineers and suggest avenues for future research.

Copyright © 2013 by ASME
Topics: Stress , Feedback , Shapes
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Grahic Jump Location
Fig. 1

Cardiac c-looping in the chick embryo with hearts shown enclosed in the dotted rectangle. At 36 h of incubation (a), the chick heart is simply a straight tube flanked by the primitive atria. At 48 h of incubation (b), the straight tube is transformed into a c-shaped tube. Note the dramatic increase in curvature of the heart tube (indicated by arrows), which results in the first major break of left-right symmetry in the developing embryo. C = conotruncus (outflow tube), V = primitive ventricle, A = primitive atrium. Scale bar = 300 μm.

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Fig. 2

Morphogenesis effected using stress feedback. Morphogenesis (shape change) continues till the shape corresponding to the target stress field is attained. The “stress error,” i.e., the difference between the actual stress (σ) and the target stress (σ*) drives morphogenesis via various cell-level processes such as growth, cytoskeletal contraction, cell shape changes, etc. σ, σ*, and a, the proportional gain are field variables whose values change with position. Once a certain shape is reached, genes can then modify σ* to initiate the next phase of morphogenesis. Please note that a pure proportional control topology is used. The system reacts to the instantaneous error and there is no integral or derivative action. Please see text for a mathematical description. Please also see Appendix for details on how biological processes such as growth and cytoskeletal contraction are modeled mathematically. (Modified from Ref. [9]; used with kind permission from Springer.)

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Fig. 3

Morphogenetic regulation in a cantilever beam. A target stress (σ* = 1.0) is specified in the bottom half of the beam while the top half remains passive. This arrangement leads to a curved beam (a). What is remarkable is that the beam curvature (κ) increases only until a specific shape is reached (b). At this point, the target stress distribution specified in (a) is reached and the beam ceases to bend. A plot of stress in a representative element at the bottom (indicated by the solid square in (a)) also shows a steady rise until steady-state reached (c). Stress across the beam section (indicated by the solid line in (a), going from bottom to top) shows that the stress in the passive portion (top of the beam) self-equilibrates in order to satisfy the constant stress requirement in the bottom of the beam (d). (Modified from Ref. [9]; used with kind permission from Springer.)

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Fig. 4

Phase plane portrait for the morphogenetic feedback mechanism discussed in this paper. A cantilever beam is used in all simulations (Sec. 3.2). Note that the system converges to a stable node (marked “SN”) irrespective of initial conditions. Actually, there is an entire region of convergence in the phase plane (indicated by the dotted box) where the responses are indistinguishable. This sort of convergent response is often found during development (please see text for details).

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Fig. 5

Growth in a constrained column. The cartoon on top illustrates the process. Growth here can be thought of as a two-step process. In the first step, the boundary conditions are released and the column of original length L0 is allowed to grow freely. This stress-free process produces a column of greater length, L. In the next step, compressive forces due to the boundary conditions are imposed to bring the length back to L0. The growth stretch ratio is defined as λgx = L/L0. Please note that for negative growth (atrophy), L < L0 and hence λgx < 1. In this case, the column shrinks first and then is expanded by the end forces due to the boundary condition. Buckling is ignored and boundary constraints apply only in the x-direction; the beam is free to move in the y- and z-directions (z-direction is out of the page). Graph (a) shows a plot of λ·gx versus λgx (Eq. (4)) with C = a = 1.0 and σx*=2.0. Graph (b) shows the time trace of λgx according to Eq. (4) for various initial conditions. The system convergences to a stable equilibrium point, λgxE≈0.8.




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