Physical Model of the Genotype-to-Phenotype Map of Proteins

Tlusty, Tsvi; Libchaber, Albert; Eckmann, Jean‐Pierre

doi:10.1103/physrevx.7.021037

Cited by 47 publications

(41 citation statements)

References 57 publications

(85 reference statements)

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“…Dimension reduction from high-dimensional phenotypic states has gathered much attention recently in the studying biological systems and in protein dynamics [11,[18][19][20][21][22][23][24]. Changes in the concentrations of most mRNA and protein species in response to environmental stress are suggested to be mainly restricted to a one-dimensional subspace.…”

Section: Discussionmentioning

confidence: 99%

Evolutionary dimension reduction in phenotypic space

Sato

Kaneko

2020

Phys. Rev. Research

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In general, cellular phenotypes, as measured by concentrations of cellular components, involve large degrees of freedom. However, recent measurement has demonstrated that phenotypic changes resulting from adaptation and evolution in response to environmental changes are effectively restricted to a low-dimensional subspace. Thus, uncovering the origin and nature of such a drastic dimension reduction is crucial to understanding the general characteristics of biological adaptation and evolution. Herein, we first formulated the dimension reduction in terms of dynamical systems theory: considering the steady growth state of cells, the reduction is represented by the separation of a few large singular values of the inverse Jacobian matrix around a fixed point. We then examined this dimension reduction by numerical evolution of cells consisting of thousands of chemicals whose concentrations determine phenotype. The model cells grow with catalytic reactions governed by genetically determined networks, which evolve to increase cellular fitness, i.e., growth speed. As a result of the evolution, phenotypic changes due to mutations and external perturbations were found to be mainly restricted to a one-dimensional subspace. One singular value of the inverse Jacobian matrix at a fixed point of concentrations was significantly larger than the others. The major phenotypic changes due to mutations and external perturbations occur along the corresponding leftsingular vector, which leads to phenotypic constraint, and fitness dominantly changes in the same direction. Once such phenotypic constraint is acquired, phenotypic evolution to a novel environment takes advantage of this restricted phenotypic direction. This results in the convergence of phenotypic pathways across genetically different strains, as is experimentally observed, while accelerating further evolution. We also confirmed that this one-dimensional constraint on phenotypic changes is imposed even by evolution under fluctuating conditions with environmental changes occurring every few generations, where the fitness for each condition is embedded into the evolving one-dimensional direction for major phenotypic changes. Thus, while genetic evolution can be random, phenotypic evolution appears to be constrained.

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Section: Discussionmentioning

confidence: 99%

Evolutionary dimension reduction in phenotypic space

Sato

Kaneko

2020

Phys. Rev. Research

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“…Scalar models, where the response of a node is described by a scalar instead of a vector, have been introduced to study coevolution and allostery [19,20]. Although these models can capture the rigid motion of a part of the system, they cannot address the propagation of more complex mechanical information, such as that illustrated in Fig.…”

Section: Description Of the Evolution Modelmentioning

confidence: 99%

Architecture and Co-Evolution of Allosteric Materials

Yan

Ravasio

Brito

et al. 2016

Preprint

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We introduce a numerical scheme to evolve functional materials that can accomplish a specified mechanical task. In this scheme, the number of solutions, their spatial architectures and the correlations among them can be computed. As an example, we consider an "al-losteric" task, which requires the material to respond specifically to a stimulus at a distant active site. We find that functioning materials evolve a less-constrained trumpet-shaped region connecting the stimulus and active sites, and that the amplitude of the elastic response varies non-monotonically along the trumpet. As previously shown for some proteins, we find that correlations appearing during evolution alone are sufficient to identify key aspects of this design. Finally, we show that the success of this architecture stems from the emergence of soft edge modes recently found to appear near the surface of marginally connected materials. Overall, our in silico evolution experiment offers a new window to study the relationship between structure, function and correlations emerging during evolution. Evolution | Disordered materials | Proteins Proteins are long polymers that can fold in a reproducible way and achieve a specific function. Often, the activity of the main functional site depends on the binding of an effector on a distant site [1]. Such an allosteric behavior can occur over large distances, such as 20 residues or more [2], and often involves only a sparse subset of residues in the protein [2, 3]. Allosteric regulation offers an appealing target for drug design [4], and there is a considerable interest in predicting allosteric pathways [5, 6]. One central difficulty is that the physical mechanisms allowing such an action-at-a-distance remain elusive. In some cases, allostery can be understood as the modulation of a hinge connecting two extended rigid parts of the protein [7, 8], but often the displacement field induced by the binding of the effector cannot be described in these terms [9, 10, 3]. Another route, statistical coupling analysis [11], considers correlations within sequences of proteins of the same family to infer allosteric pathways [3, 6]. The generality of this elegant approach is however debated [12]. From a physical viewpoint, specific response at a distance is surprising. The structure of proteins is similar to randomly packed spheres [13]. Generically, the response of such systems is non-specific and decays rapidly in space (in a manner similar to a continuum medium) at distances larger than the particle size. This is true except close to a critical point where the number of constraints coming from strongly interacting particles is just sufficient to match the number of degrees of freedom of the particles [14]. There, the elastic response becomes heterogeneous on all scales [15, 16]. This point is illustrated in Fig. 1.A showing the rapidly-decaying response of a random spring network to a stimulus. However, as shown in Fig. 1.B (and independently found in [17] using a different algorithm), springs can be moved so that th...

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“…This result supports that in at least some proteins elasticity -possibly non-linear -is an appropriate language to describe allostery (in contrast to intrinsically disordered proteins that may be considered more as liquids than solids, for which the analysis proposed here would not hold). Very recently, there has been a considerable effort to use insilico evolution [16,17] to study how linear elastic materials can evolve to accomplish an allosteric task [18][19][20][21][22][23][24][25][26]. In general, binding a ligand locally distorts the protein, which is modelled by imposing local displacements at some site, generating an extended elastic response that in turn determines fitness (chosen specifically to accomplish a given task).…”

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confidence: 99%

Mechanics of allostery: contrasting the induced fit and population shift scenarios

Ravasio

Flatt

Yan

et al. 2019

Preprint

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In allosteric proteins, binding a ligand can affect function at a distant location, for example by changing the binding affinity of a substrate at the active site. The induced fit and population shift models, which differ by the assumed number of stable configurations, explain such cooperative binding from a thermodynamic viewpoint. Yet, understanding what mechanical principles constrain these models remains a challenge. Here we provide an empirical study on 34 proteins supporting the idea that allosteric conformational change generally occurs along a soft elastic mode presenting extended regions of high shear. We argue, based on a detailed analysis of how the energy profile along such a mode depends on binding, that in the induced fit scenario there is an optimal stiffness k * a ∼ 1/N for cooperative binding, where N is the number of residues involved in the allosteric response. We find that the population shift scenario is more robust to mutation affecting stiffness, as binding becomes more and more cooperative with stiffness up to the same characteristic value k * a , beyond which cooperativity saturates instead of decaying. We confirm numerically these findings in a non-linear mechanical model. Dynamical considerations suggest that a stiffness of order k * a is favorable in that scenario as well, supporting that for proper function proteins must evolve a functional elastic mode that is softer as their size increases. In consistency with this view, we find a significant anticorrelation between the stiffness of the allosteric response and protein size in our data set.Many proteins are allosteric: binding a ligand at one or several allosteric sites can regulate function at a distant site, a long-range communication often accompanied by large conformational changes [1,2]. There is a considerable interest in predicting the amino acids involved in this communication, or "allosteric pathway", from structure or sequence data [3,4], since they can be used as targets for drug design [5]. Yet, understanding the physical principles underlying such action at a distance in proteins remains a challenge [6,7]. From a thermodynamic standpoint, two distinct views have been proposed. In the induced fit scenario, exemplified by the Koshland-Némethy-Filmer (KNF) model [8], the protein essentially lies in one single state. The latter changes as binding occurs, leading to a conformational change. In an energy landscape picture such as that of Fig.1B, it corresponds to a displacement of the energy minimum upon binding. By contrast, in the population shift model, exemplified by the Monod-Wyman-Changeux (MWC) model [9], two states are always present. Their relative stability can change sign upon binding, leading to an average conformational change. Although each of these models presumably applies to various proteins, they do not specify which designs allow for efficient action at a distance, and how robust these designs are to mutations [10].In several proteins -see below for a systematic study -it has been observed that the allosteri...

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Physical Model of the Genotype-to-Phenotype Map of Proteins

Cited by 47 publications

References 57 publications

Evolutionary dimension reduction in phenotypic space

Evolutionary dimension reduction in phenotypic space

Architecture and Co-Evolution of Allosteric Materials

Mechanics of allostery: contrasting the induced fit and population shift scenarios

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