Natural frequencies and mode shapes in zero-force members of a truss

Trusses are everywhere; they are used in bridges, antenna towers, cranes, even in parts of the International Space Station. And for good reason, they allow us to create strong structures while using materials in very efficient and cost-effective way. Trusses it is essentially a rigid structure made up of a collection of straight members. The type of truss depends on how the horizontal and diagonal beams are arranged.

Protein-ligand dissociation rate constant from all-atom simulation

Dissociation of a ligand isoniazid from a protein catalase was investigated using all-atom Molecular Dynamics (MD) simulations. Random Acceleration MD (τ-RAMD) was used where a random artificial force applied to the ligand facilitates its dissociation. We have suggested an approach to extrapolate such obtained dissociation times to the zero-force limit that was never attempted before, thus allowing direct comparison with experimentally measured values. We have found that our calculated dissociation time was equal to 36.1 seconds with statistically significant values distributed in the interval 0.2-72.0 s, that quantitatively matches the experimental value of 50 ± 8 seconds despite the extrapolation over nine orders of magnitude in time.

Empirical lognormality of biological variation: implications for the ‘zero-force evolutionary law’

ABSTRACTThe zero-force evolutionary law (ZFEL) of McShea et al. states that independently evolving entities, with no forces or constraints acting on them, will tend to accumulate differences and therefore diverge from each other. McShea et al. quantified the law by assuming normality on an additive arithmetic scale and reflecting negative differences as absolute values, systematically augmenting perceived divergence. The appropriate analytical framework is not additive but proportional, where logarithmic transformation is required to achieve normality. Logarithms and logarithmic differences can be negative but the proportions they represent cannot be negative. Reformulation of ZFEL in a proportional or geometric reference frame indicates that when entities evolve randomly and independently, differences smaller than any initial difference are balanced by differences larger than the initial difference. Total variance increases with each step of a random walk, but there is no statistical expectation of divergence between random-walk lineages.

El estatus metateórico de ZFEL

In a recent book, McShea and Brandon argue that the observed diversity and complexity of life are explainable by a principle they call the “zero-force evolutionary law” or “ZFEL”. Although this principle would be implicit in many explanations given by biologists, it would have never been made explicit. Assuming that this idea is interesting, and that the authors are right, we will discuss the metatheoretical way in which they present said principle, as being a part of probability theory. This allows the authors to claim that probability theory provides the reductive basis for all evolutionary biology (given that they consider other principles, such as the principle of natural selection, as part of probability theory as well). We will defend, in accordance with them, that ZFEL is not a solely biological principle, but not because it is a part of probability theory, but rather because it is a specific version of the principle of common cause.

Role of Charge Regulation and Fluctuations in the Conformational and Mechanical Properties of Weak Flexible Polyelectrolytes

This work addresses the role of charge regulation (CR) and the associated fluctuations in the conformational and mechanical properties of weak polyelectrolytes. Due to CR, changes in the pH-value modifies the average macromolecular charge and conformational equilibria. A second effect is that, for a given average charge per site, fluctuations can alter the intensity of the interactions by means of correlation between binding sites. We investigate both effects by means of Monte Carlo simulations at constant pH-value, so that the charge is a fluctuating quantity. Once the average charge per site is available, we turn off the fluctuations by assigning the same average charge to every site. A constant charge MC simulation is then performed. We make use of a model which accounts for the main fundamental aspects of a linear flexible polyelectrolyte that is, proton binding, angle internal rotation, bond stretching and bending. Steric excluded volume and differentiated treatment for short-range and long-range interactions are also included. This model can be regarded as a kind of “minimal” in the sense that it contains a minimum number of parameters but still preserving the atomistic detail. It is shown that, if fluctuations are activated, gauche state bond probabilities increase and the persistence length decreases, so that the polymer becomes more folded. Macromolecular stretching is also analyzed in presence of CR (the charge depends on the applied force) and without CR (the charge is fixed to the value at zero force). The analysis of the low force scaling behavior concludes that Pincus exponent becomes pH-dependent. Both, with and without CR, a transition from 1/2 at high pH-values (phantom chain) to 3/5 at low pH-values (Pincus regime) is observed. Finally, the intermediate force stretching regime is investigated. It is found that CR induces a moderate influence in the force-extension curves and persistence length (which in this force regime becomes force-dependent). It is thus concluded that the effect of CR on the stretching curves is mainly due to the changes in the average charge at zero force. It is also found that, for the cases studied, the effect of steric excluded volume is almost irrelevant compared to electrostatic interactions.

Role of Charge Regulation and Fluctuations in the Conformational and Mechanical Properties of Weak Flexible Polyelectrolytes

This work addresses the role of charge regulation (CR) and the associated fluctuations in the conformational and mechanical properties of weak polyelectrolytes. Due to CR, changes in the pH-value modifies the average macromolecular charge and conformational equilibria. A second effect is that, for a given average charge per site, fluctuations can alter the intensity of the interactions by means of correlation between binding sites. We investigate both effects by means of Monte Carlo simulations at constant pH-value, so that the charge is a fluctuating quantity. Once the average charge per site is available, we turn off the fluctuations by assigning the same average charge to every site. A constant charge MC simulation is then performed. We make use of a model which accounts for the main fundamental aspects of a linear flexible polyelectrolyte i.e. proton binding, angle internal rotation, bond stretching and bending. Steric excluded volume and differentiated treatment for short-range and long-range interactions are also included in the model. It can be regarded as a kind of "minimal'' model in the sense that contains a minimum number of parameters but still preserving the atomistic detail. It is shown that, if fluctuations are activated, gauche state bond probabilities increase, and the persistence length decreases, so that the polymer becomes more folded. Macromolecular stretching is also analyzed in presence of CR (the charge depends on the applied force) and without CR (the charge is fixed to the value at zero force). The analysis of the low force scaling behavior concludes that Pincus exponent becomes pH-dependent. Both with and without CR, a transition from 1/2 at high pH-values (phantom chain) to 3/5 to low pH-values (Pincus regime), is observed. Finally, the intermediate force stretching regime is investigated. It is found that CR induces a moderate influence in the force-extension curves and persistence length (which in this force regime becomes force-dependent). It is thus concluded that the effect of CR on the stretching curves is mainly due to changes in the average charge at zero force. It is also found that, for the cases studied, the effect of steric excluded volume is almost irrelevant compared to electrostatic interactions.

Thermal versus Mechanical Unfolding in a Model Protein

Force spectroscopy techniques are often used to learn about the free energy landscape of single biomolecules, typically by recovering free energy quantities that, extrapolated to zero force, are compared to those measured in bulk experiments. However, it is not always clear how the information obtained from a mechanically perturbed system can be related to that obtained using other denaturants, since tensioned molecules unfold and refold along a reaction coordinate imposed by the force, which is unlikely meaningful in its absence. Here, we explore this dichotomy by investigating the unfolding landscape of a model protein, which is first unfolded mechanically through typical force spectroscopy-like protocols, and next thermally. When unfolded by non-equilibrium force extension and constant force protocols, we recover a simple two-barrier landscape, as the protein reaches the extended conformation through a metastable intermediate. Interestingly, folding-unfolding equilibrium simulations at low forces suggested a totally different scenario, where this metastable state plays little role in the unfolding mechanism, and the protein unfolds through two competing pathways27. Finally, we use Markov state models to describe the configurational space of the unperturbed protein close to the critical temperature. The thermal dynamics is well understood by a one-dimensional landscape along an appropriate reaction coordinate, however very different from the mechanical picture. In this sense, in our protein model the mechanical and thermal descriptions provide incompatible views of the folding/unfolding landscape of the system, and the estimated quantities to zero force result hard to interpret.

Programmable Constant-Force Multistable Mechanisms

Programmable multistable mechanisms exhibit stability behavior whereby the stiffness and the number of stable states can be controlled via programming inputs. In this paper, we report the zero stiffness behavior of a 2-degree of programming (DOP) T-combined, axially loaded double parallelogram multistable mechanism. We demonstrate zero force monostability, constant force monostability, zero force bistability, constant force bistability and zero force tristability behaviors by tuning the programming input. We derive analytically the reaction force of the mechanism for each configuration and verify our analytical results using numerical simulations and experimental measurements, showing less than 10% discrepancy. The concept of constant-force programming can be extended to N-DOP T-combined, serial combined and parallel combined programmable multistable mechanisms. Finally, we present potential applications of stability programming.

Bow Actuator: Low Voltage Switching in Electrostatically Actuated Bistable Beams

Curved bistable beams subjected to transverse loading may exhibit latching, namely remain in their buckled state under zero force. Under such circumstances, an opposite force is required for snapping-back (release) of the beam to its initial configuration. For an electrostatically actuated beam, two electrodes located at either side of the beam may therefore be required for bidirectional actuation. In this study, a new snapping and release procedures, are considered. The approach involves the preloading of the beam using an electrostatic force in the direction opposite to the beam desired movement, followed by a sudden release of the voltage. We show, by means of a reduced order (RO) model, resulting from the Galerkin decomposition, that such an actuation paradigm can not only be used to release a beam from its latched position, but can also create a snap-through response at a significantly low voltage.