70% efficiency of bistate molecular machines explained by information theory, high dimensional geometry and evolutionary convergence

Solvent constraints for biopolymer folding and evolution in extraterrestrial environments

We propose that spontaneous folding and molecular evolution of biopolymers are two universal aspects that must concur for life to happen. These aspects are fundamentally related to the chemical composition of biopolymers and crucially depend on the solvent in which they are embedded. We show that molecular information theory and energy landscape theory allow us to explore the limits that solvents impose on biopolymer existence. We consider 54 solvents, including water, alcohols, hydrocarbons, halogenated solvents, aromatic solvents, and low molecular weight substances made up of elements abundant in the universe, which may potentially take part in alternative biochemistries. We find that along with water, there are many solvents for which the liquid regime is compatible with biopolymer folding and evolution. We present a ranking of the solvents in terms of biopolymer compatibility. Many of these solvents have been found in molecular clouds or may be expected to occur in extrasolar planets.

Generalizing the isothermal efficiency by using Gaussian distributions

Unlike the Carnot heat engine efficiency published in 1824, an isothermal efficiency derived from thermodynamics and information theory can be applied to biological systems. The original approach by Pierce and Cutler in 1959 to derive the isothermal efficiency equation came from Shannon's channel capacity of 1949 and from Felker's 1952 determination of the minimum energy dissipation needed to gain a bit. In 1991 and 2010 Schneider showed how the isothermal efficiency equation can be applied to molecular machines and that this can be used to explain why several molecular machines are 70% efficient. Surprisingly, some macroscopic biological systems, such as whole ecosystems, are also 70% efficient but it is hard to see how this could be explained by a thermodynamic and molecular theory. The thesis of this paper is that the isothermal efficiency can be derived without using thermodynamics by starting from a set of independent Gaussian distributions. This novel derivation generalizes the isothermal efficiency equation for use at all levels of biology, from molecules to ecosystems.

Molecular Information Theory Meets Protein Folding

We propose an application of molecular information theory to analyze the folding of single domain proteins. We analyze results from various areas of protein science, such as sequence-based potentials, reduced amino acid alphabets, backbone configurational entropy, secondary structure content, residue burial layers, and mutational studies of protein stability changes. We found that the average information contained in the sequences of evolved proteins is very close to the average information needed to specify a fold ∼2.2 ± 0.3 bits/(site·operation). The effective alphabet size in evolved proteins equals the effective number of conformations of a residue in the compact unfolded state at around 5. We calculated an energy-to-information conversion efficiency upon folding of around 50%, lower than the theoretical limit of 70%, but much higher than human-built macroscopic machines. We propose a simple mapping between molecular information theory and energy landscape theory and explore the connections between sequence evolution, configurational entropy, and the energetics of protein folding.

Rethinking Causation for Data-intensive Biology: Constraints, Cancellations, and Quantized Organisms: Causality in complex organisms is sculpted by constraints rather than instigators, with outcomes perhaps better described by quantized patterns than rectilinear pathways

Complex organisms thwart the simple rectilinear causality paradigm of "necessary and sufficient," with its experimental strategy of "knock down and overexpress." This Essay organizes the eccentricities of biology into four categories that call for new mathematical approaches; recaps for the biologist the philosopher's recent refinements to the causation concept and the mathematician's computational tools that handle some but not all of the biological eccentricities; and describes overlooked insights that make causal properties of physical hierarchies such as emergence and downward causation straightforward. Reviewing and extrapolating from similar situations in physics, it is suggested that new mathematical tools for causation analysis incorporating feedback, signal cancellation, nonlinear dependencies, physical hierarchies, and fixed constraints rather than instigative changes will reveal unconventional biological behaviors. These include "eigenisms," organisms that are limited to quantized states; trajectories that steer a system such as an evolving species toward optimal states; and medical control via distributed "sheets" rather than single control points.

Effective CRISPRa-mediated control of gene expression in bacteria must overcome strict target site requirements

In bacterial systems, CRISPR-Cas transcriptional activation (CRISPRa) has the potential to dramatically expand our ability to regulate gene expression, but we lack predictive rules for designing effective gRNA target sites. Here, we identify multiple features of bacterial promoters that impose stringent requirements on CRISPRa target sites. Notably, we observe narrow, 2-4 base windows of effective sites with a periodicity corresponding to one helical turn of DNA, spanning ~40 bases and centered ~80 bases upstream of the TSS. However, we also identify two features suggesting the potential for broad scope: CRISPRa is effective at a broad range of σ70-family promoters, and an expanded PAM dCas9 allows the activation of promoters that cannot be activated by S. pyogenes dCas9. These results provide a roadmap for future engineering efforts to further expand and generalize the scope of bacterial CRISPRa.

Restriction enzymes use a 24 dimensional coding space to recognize 6 base long DNA sequences

Restriction enzymes recognize and bind to specific sequences on invading bacteriophage DNA. Like a key in a lock, these proteins require many contacts to specify the correct DNA sequence. Using information theory we develop an equation that defines the number of independent contacts, which is the dimensionality of the binding. We show that EcoRI, which binds to the sequence GAATTC, functions in 24 dimensions. Information theory represents messages as spheres in high dimensional spaces. Better sphere packing leads to better communications systems. The densest known packing of hyperspheres occurs on the Leech lattice in 24 dimensions. We suggest that the single protein EcoRI molecule employs a Leech lattice in its operation. Optimizing density of sphere packing explains why 6 base restriction enzymes are so common.

Energy Transfer as A Driving Force in Nucleic Acid⁻Protein Interactions

Many nucleic acid–protein structures have been resolved, though quantitative structure-activity relationship remains unclear in many cases. Thrombin complexes with G-quadruplex aptamers are striking examples of a lack of any correlation between affinity, interface organization, and other common parameters. Here, we tested the hypothesis that affinity of the aptamer–protein complex is determined with the capacity of the interface to dissipate energy of binding. Description and detailed analysis of 63 nucleic acid–protein structures discriminated peculiarities of high-affinity nucleic acid–protein complexes. The size of the amino acid sidechain in the interface was demonstrated to be the most significant parameter that correlates with affinity of aptamers. This observation could be explained in terms of need of efficient energy transfer from interacting residues. Application of energy dissipation theory provided an illustrative tool for estimation of efficiency of aptamer–protein complexes. These results are of great importance for a design of efficient aptamers.

Core promoter information content correlates with optimal growth temperature

The subtle mechanisms by which protein-DNA interactions remain functional across a wide range of temperatures are largely unknown. In this work, we manually curated available information relating fully sequenced archaeal genomes with organism growth temperatures. We built a motif that represents the core promoter of each species and calculated its information content. We then studied the relation between optimal growth temperature (OGT) and information content (IC) in the promoter region.We found a positive correlation between G + C content and OGT in tRNA regions and not in overall genome. Furthermore, we found that there is a positive correlation between information content and optimal growth temperatures in Archaea. This can't be explained by an increased C+G composition nor by other obvious mechanisms. These findings suggest that increased information content could produce a positive fitness in organisms living at high temperatures. We suggest that molecular information theory may need to be adapted for hyperthermophiles.

Sorting Carbon Nanotubes

Sorting of single-wall carbon nanotubes by their electronic and atomic structures in liquid phases is reviewed in this chapter. We first introduce the sorting problem, and then provide an overview of several sorting methodologies, following roughly the chronological order of their development over the past 15 years or so. Major methods discussed include ion-exchange chromatography, density-gradient ultracentrifugation, selective extraction in organic solvents, gel chromatography, and aqueous two-phase extraction. A main focus of the review is on the common mechanisms underlining all sorting processes. We propose that differences in solvation among different nanotube species are the ultimate driving force of sorting, and we corroborate this proposal by presenting analysis on how the differences are realized in electronic-structure-based sorting and atomic-structure-based sorting. In the end, we offer some suggestions on future directions that may grow out of carbon nanotube sorting. In particular, the prospect of expanding the function of DNA/carbon nanotube hybrid to control inter-particle interactions both inside and outside the nanotube is discussed.

Heterogeneous dynamics in DNA site discrimination by the structurally homologous DNA-binding domains of ETS-family transcription factors

The ETS family of transcription factors exemplifies current uncertainty in how eukaryotic genetic regulators with overlapping DNA sequence preferences achieve target site specificity. PU.1 and Ets-1 represent archetypes for studying site discrimination by ETS proteins because their DNA-binding domains are the most divergent in sequence, yet they share remarkably superimposable DNA-bound structures. To gain insight into the contrasting thermodynamics and kinetics of DNA recognition by these two proteins, we investigated the structure and dynamics of site discrimination by their DNA-binding domains. Electrophoretic mobilities of complexes formed by the two homologs with circularly permuted binding sites showed significant dynamic differences only for DNA complexes of PU.1. Free solution measurements by dynamic light scattering showed PU.1 to be more dynamic than Ets-1; moreover, dynamic changes are strongly coupled to site discrimination by PU.1, but not Ets-1. Interrogation of the protein/DNA interface by DNA footprinting showed similar accessibility to dimethyl sulfate for PU.1/DNA and Ets-1/DNA complexes, indicating that the dynamics of PU.1/DNA complexes reside primarily outside that interface. An information-based analysis of the two homologs’ binding motifs suggests a role for dynamic coupling in PU.1's ability to enforce a more stringent sequence preference than Ets-1 and its proximal sequence homologs.

Analysis of DevR regulated genes in Mycobacterium tuberculosis

The DevRS two component system of Mycobacterium tuberculosis is responsible for its dormancy in host and becomes operative under hypoxic condition. It is experimentally known that phosphorylated DevR controls the expression of several downstream genes in a complex manner. In the present work we propose a theoretical model to show role of binding sites in DevR mediated gene expression. Individual and collective role of binding sites in regulating DevR mediated gene expression has been shown via modeling. Objective of the present work is twofold. First, to describe qualitatively the temporal dynamics of wild type genes and their known mutants. Based on these results we propose that DevR controlled gene expression follows a specific pattern which is efficient in describing other DevR mediated gene expression. Second, to analyze behavior of the system from information theoretical point of view. Using the tools of information theory we have calculated molecular efficiency of the system and have shown that it is close to the maximum limit of isothermal efficiency.

NeuroPID: a predictor for identifying neuropeptide precursors from metazoan proteomes

MOTIVATION

The evolution of multicellular organisms is associated with increasing variability of molecules governing behavioral and physiological states. This is often achieved by neuropeptides (NPs) that are produced in neurons from a longer protein, named neuropeptide precursor (NPP). The maturation of NPs occurs through a sequence of proteolytic cleavages. The difficulty in identifying NPPs is a consequence of their diversity and the lack of applicable sequence similarity among the short functionally related NPs.

RESULTS

Herein, we describe Neuropeptide Precursor Identifier (NeuroPID), a machine learning scheme that predicts metazoan NPPs. NeuroPID was trained on hundreds of identified NPPs from the UniProtKB database. Some 600 features were extracted from the primary sequences and processed using support vector machines (SVM) and ensemble decision tree classifiers. These features combined biophysical, chemical and informational-statistical properties of NPs and NPPs. Other features were guided by the defining characteristics of the dibasic cleavage sites motif. NeuroPID reached 89-94% accuracy and 90-93% precision in cross-validation blind tests against known NPPs (with an emphasis on Chordata and Arthropoda). NeuroPID also identified NPP-like proteins from extensively studied model organisms as well as from poorly annotated proteomes. We then focused on the most significant sets of features that contribute to the success of the classifiers. We propose that NPPs are attractive targets for investigating and modulating behavior, metabolism and homeostasis and that a rich repertoire of NPs remains to be identified.

AVAILABILITY

NeuroPID source code is freely available at http://www.protonet.cs.huji.ac.il/neuropid

Optimization of isopolar microtubule arrays

Isopolar arrays of aligned cytoskeletal filaments are components in a number of designs of hybrid nanodevices incorporating biomolecular motors. For example, a combination of filament arrays and motor arrays can form an actuator or a molecular engine resembling an artificial muscle. Here, isopolar arrays of microtubules are fabricated by flow alignment, and their quality is characterized by their degree of alignment. We find, in agreement with our analytical models, that the degree of alignment is ultimately limited by thermal forces, while the kinetics of the alignment process are influenced by the flow strength, the microtubule stiffness, the gliding velocity, and the tip length. Strong flows remove microtubules from the surface and reduce the filament density, suggesting that there is an optimal flow strength for the fabrication of ordered arrays.

Pursuit of food versus pursuit of information in a Markovian perception-action loop model of foraging

Efficient coding, redundancy reduction, and other information theoretic optimization principles have successfully explained the organization of many biological phenomena, from the physiology of sensory receptive fields to the variability of certain DNA sequence ensembles. Here we examine the hypothesis that behavioral strategies that are optimal for survival must necessarily involve efficient information processing, and ask whether there can be circumstances in which deliberately sacrificing some information can lead to higher utility? To this end, we present an analytically tractable model for a particular instance of a perception-action loop: a creature searching for a randomly moving food source confined to a 1D ring world. The model incorporates the statistical structure of the creature's world, the effects of the creature's actions on that structure, and the creature's strategic decision process. The underlying model takes the form of a Markov process on an infinite dimensional state space. To analyze it we construct an exact coarse graining that reduces the model to a Markov process on a finite number of "information states". This mathematical technique allows us to make quantitative comparisons between the performance of an information-theoretically optimal strategy with other candidate search strategies on a food gathering task. We find that 1. Information optimal search does not necessarily optimize utility (expected food gain). 2. The rank ordering of search strategies by information performance does not predict their ordering by expected food obtained. 3. The relative advantage of different strategies depends on the statistical structure of the environment, in particular the variability of motion of the source. We conclude that there is no simple relationship between information and utility. Even in the absence of information processing costs or bandwidth constraints, behavioral optimality does not imply information efficiency, nor is there a simple tradeoff between the two objectives of gaining information about a food source versus obtaining the food itself. For a wide range of values of the food source's movement parameter, the strategy of collecting the most information possible about the unknown source location carries an ineliminable structural cost, leading to a situation in which a foraging creature could actually choose to be less well-informed while simultaneously being, on average, better fed.

Molecular thermodynamics for cell biology as taught with boxes

Thermodynamic principles are basic to an understanding of the complex fluxes of energy and information required to keep cells alive. These microscopic machines are nonequilibrium systems at the micron scale that are maintained in pseudo-steady-state conditions by very sophisticated processes. Therefore, several nonstandard concepts need to be taught to rationalize why these very ordered systems proliferate actively all over our planet in seeming contradiction to the second law of thermodynamics. We propose a model consisting of boxes with different shapes that contain small balls that are in constant motion due to a stream of air blowing from below. This is a simple macroscopic system that can be easily visualized by students and that can be understood as mimicking the behavior of a set of molecules exchanging energy. With such boxes, the basic concepts of entropy, enthalpy, and free energy can be taught while reinforcing a molecular understanding of the concepts and stressing the stochastic nature of the thermodynamic laws. In addition, time-related concepts, such as reaction rates and activation energy, can be readily visualized. Moreover, the boxes provide an intuitive way to introduce the role in cellular organization of "information" and Maxwell's demons operating under nonequilibrium conditions.

Communication theory and multicellular biology

In this Perspective, we propose that communication theory--a field of mathematics concerned with the problems of signal transmission, reception and processing--provides a new quantitative lens for investigating multicellular biology, ancient and modern. What underpins the cohesive organisation and collective behaviour of multicellular ecosystems such as microbial colonies and communities (microbiomes) and multicellular organisms such as plants and animals, whether built of simple tissue layers (sponges) or of complex differentiated cells arranged in tissues and organs (members of the 35 or so phyla of the subkingdom Metazoa)? How do mammalian tissues and organs develop, maintain their architecture, become subverted in disease, and decline with age? How did single-celled organisms coalesce to produce many-celled forms that evolved and diversified into the varied multicellular organisms in existence today? Some answers can be found in the blueprints or recipes encoded in (epi)genomes, yet others lie in the generic physical properties of biological matter such as the ability of cell aggregates to attain a certain complexity in size, shape, and pattern. We suggest that Lasswell's maxim "Who says what to whom in what channel with what effect" provides a foundation for understanding not only the emergence and evolution of multicellularity, but also the assembly and sculpting of multicellular ecosystems and many-celled structures, whether of natural or human-engineered origin. We explore how the abstraction of communication theory as an organising principle for multicellular biology could be realised. We highlight the inherent ability of communication theory to be blind to molecular and/or genetic mechanisms. We describe selected applications that analyse the physics of communication and use energy efficiency as a central tenet. Whilst communication theory has and could contribute to understanding a myriad of problems in biology, investigations of multicellular biology could, in turn, lead to advances in communication theory, especially in the still immature field of network information theory.

A brief review of molecular information theory

The idea that we could build molecular communications systems can be advanced by investigating how actual molecules from living organisms function. Information theory provides tools for such an investigation. This review describes how we can compute the average information in the DNA binding sites of any genetic control protein and how this can be extended to analyze its individual sites. A formula equivalent to Claude Shannon's channel capacity can be applied to molecular systems and used to compute the efficiency of protein binding. This efficiency is often 70% and a brief explanation for that is given. The results imply that biological systems have evolved to function at channel capacity, which means that we should be able to build molecular communications that are just as robust as our macroscopic ones.