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Register a new userOptimal elasticity of biological networks
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Added by
Henrik Ronellenfitsch
Publication date
2020
fields
Physics
and research's language is
English
Authors
Henrik Ronellenfitsch
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Reinforced elastic sheets surround us in daily life, from concrete shell buildings to biological structures such as the arthropod exoskeleton or the venation network of dicotyledonous plant leaves. Natural structures are often highly optimized through evolution and natural selection, leading to the biologically and practically relevant problem of understanding and applying the principles of their design. Inspired by the hierarchically organized scaffolding networks found in plant leaves, here we model networks of bending beams that capture the discrete and non-uniform nature of natural materials. Using the principle of maximal rigidity under natural resource constraints, we show that optimal discrete beam networks reproduce the structural features of real leaf venation. Thus, in addition to its ability to efficiently transport water and nutrients, the venation network also optimizes leaf rigidity using the same hierarchical reticulated network topology. We study the phase space of optimal mechanical networks, providing concrete guidelines for the construction of elastic structures. We implement these natural design rules by fabricating efficient, biologically inspired metamaterials.
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We review the trade-offs between speed, fluctuations, and thermodynamic cost involved with biological processes in nonequilibrium states, and discuss how optimal these processes are in light of the universal bound set by the thermodynamic uncertainty relation (TUR). The values of the uncertainty product $mathcal{Q}$ of TUR, which can be used as a measure of the precision of enzymatic processes realized for a given thermodynamic cost, are suboptimal when the substrate concentration $[S]$ is at the Michaelis constant ($K_text{M}$), and some of the key biological processes are found to work around this condition. We illustrate the utility of $mathcal{Q}$ in assessing how close the molecular motors and biomass producing machineries are to the TUR bound, and for the cases of biomass production (or biological copying processes) we discuss how their optimality quantified in terms of $mathcal{Q}$ is balanced with the error rate in the information transfer process. We also touch upon the trade-offs in other error-minimizing processes in biology, such as gene regulation and chaperone-assisted protein folding. A spectrum of $mathcal{Q}$ recapitulating the biological processes surveyed here provides glimpses into how biological systems are evolved to optimize and balance the conflicting functional requirements.
Energy efficiency is closely related to the evolution of biological systems and is important to their information processing. In this paper, we calculated the excitation probability of a simple model of a bistable biological unit in response to pulsatile inputs, and its spontaneous excitation rate due to noise perturbation. Then we analytically calculated the mutual information, energy cost, and energy efficiency of an array of these bistable units. We found that the optimal number of units could maximize this arrays energy efficiency in encoding pulse inputs, which depends on the fixed energy cost. We conclude that demand for energy efficiency in biological systems may strongly influence the size of these systems under the pressure of natural selection.
The eye grows during childhood to position the retina at the correct distance behind the lens to enable focused vision, a process called emmetropization. Animal studies have demonstrated that this growth process is dependent upon visual stimuli, while genetic and environmental factors that affect the likelihood of developing myopia have also been identified. The coupling between growth, remodeling and elastic response in the eye is particularly challenging to understand. To analyse this coupling, we develop a simple model of an eye growing under intraocular pressure in response to visual stimuli. Distinct to existing three-dimensional finite-element models of the eye, we treat the sclera as a thin axisymmetric hyperelastic shell which undergoes local growth in response to external stimulus. This simplified analytic model provides a tractable framework in which to evaluate various emmetropization hypotheses and understand different types of growth feedback, which we exemplify by demonstrating that local growth laws are sufficient to tune the global size and shape of the eye for focused vision across a range of parameter values.
In physics of living systems, a search for relationships of a few macroscopic variables that emerge from many microscopic elements is a central issue. We evolved gene regulatory networks so that the expression of target genes (partial system) is insensitive to environmental changes. Then, we found the expression levels of the remaining genes autonomously increase as a plastic response. Negative proportionality was observed between the average changes in target and remnant genes, reflecting reciprocity between the macroscopic robustness of homeostatic genes and plasticity of regulator genes. This reciprocity follows the lever principle, which was satisfied throughout the evolutionary course, imposing an evolutionary constraint.
Disordered biopolymer gels have striking mechanical properties including strong nonlinearities. In the case of athermal gels (such as collagen-I) the nonlinearity has long been associated with a crossover from a bending dominated to a stretching dominated regime of elasticity. The physics of this crossover is related to the existence of a central-force isostatic point and to the fact that for most gels the bending modulus is small. This crossover induces scaling behavior for the elastic moduli. In particular, for linear elasticity such a scaling law has been demonstrated [Broedersz et al. Nature Physics, 2011 7, 983]. In this work we generalize the scaling to the nonlinear regime with a two-parameter scaling law involving three critical exponents. We test the scaling law numerically for two disordered lattice models, and find a good scaling collapse for the shear modulus in both the linear and nonlinear regimes. We compute all the critical exponents for the two lattice models and discuss the applicability of our results to real systems.
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