Dynamic mutation-selection balance as an evolutionary attractor

The vast majority of mutations are deleterious and are eliminated by purifying selection. Yet in finite asexual populations, purifying selection cannot completely prevent the accumulation of deleterious mutations due to Muller's ratchet: once lost by stochastic drift, the most-fit class of genotypes is lost forever. If deleterious mutations are weakly selected, Muller's ratchet can lead to a rapid degradation of population fitness. Evidently, the long-term stability of an asexual population requires an influx of beneficial mutations that continuously compensate for the accumulation of the weakly deleterious ones. Hence any stable evolutionary state of a population in a static environment must involve a dynamic mutation-selection balance, where accumulation of deleterious mutations is on average offset by the influx of beneficial mutations. We argue that such a state can exist for any population size N and mutation rate U and calculate the fraction of beneficial mutations, ε, that maintains the balanced state. We find that a surprisingly low ε suffices to achieve stability, even in small populations in the face of high mutation rates and weak selection, maintaining a well-adapted population in spite of Muller's ratchet. This may explain the maintenance of mitochondria and other asexual genomes.     

Dynamic modifications of biomacromolecules: mechanism and chemical interventions

Biological macromolecules(proteins, nucleic acids, polysaccharides, etc.) are the building blocks of life, which constantly undergo chemical modifications that are often reversible and spatial-temporally regulated. These dynamic properties of chemical modifications play fundamental roles in physiological processes as well as pathological changes of living systems. The Major Research Project(MRP) funded by the National Natural Science Foundation of China(NSFC)—"Dynamic modifications of biomacromolecules: mechanism and chemical interventions" aims to integrate cross-disciplinary approaches at the interface of chemistry, life sciences, medicine, mathematics, material science and information science with the following goals:(i) developing specific labeling techniques and detection methods for dynamic chemical modifications of biomacromolecules,(ii)analyzing the molecular mechanisms and functional relationships of dynamic chemical modifications of biomacromolecules, and(iii) exploring biomacromolecules and small molecule probes as potential drug targets and lead compounds.     

Effective visual working memory capacity: an emergent effect from the neural dynamics in an attractor network

The study of working memory capacity is of outmost importance in cognitive psychology as working memory is at the basis of general cognitive function. Although the working memory capacity limit has been thoroughly studied, its origin still remains a matter of strong debate. Only recently has the role of visual saliency in modulating working memory storage capacity been assessed experimentally and proved to provide valuable insights into working memory function. In the computational arena, attractor networks have successfully accounted for psychophysical and neurophysiological data in numerous working memory tasks given their ability to produce a sustained elevated firing rate during a delay period. Here we investigate the mechanisms underlying working memory capacity by means of a biophysically-realistic attractor network with spiking neurons while accounting for two recent experimental observations: 1) the presence of a visually salient item reduces the number of items that can be held in working memory, and 2) visually salient items are commonly kept in memory at the cost of not keeping as many non-salient items.OUR MODEL SUGGESTS THAT WORKING MEMORY CAPACITY IS DETERMINED BY TWO FUNDAMENTAL PROCESSES: encoding of visual items into working memory and maintenance of the encoded items upon their removal from the visual display. While maintenance critically depends on the constraints that lateral inhibition imposes to the mnemonic activity, encoding is limited by the ability of the stimulated neural assemblies to reach a sufficiently high level of excitation, a process governed by the dynamics of competition and cooperation among neuronal pools. Encoding is therefore contingent upon the visual working memory task and has led us to introduce the concept of effective working memory capacity (eWMC) in contrast to the maximal upper capacity limit only reached under ideal conditions.     

NMR detection of slow conformational dynamics in an endonuclease toxin

The cytotoxic activity of the secreted bacterial toxin colicin E9 is due to a non-specific DNase housed in the C-terminus of the protein. Double-resonance and triple-resonance NMR studies of the 134-amino acid¹⁵ N- and ¹³C/¹⁵N-labelled DNase domain are presented. Extensive conformational heterogeneity was evident from the presence of far more resonances than expected based on the amino acid sequence of the DNase, and from the appearance of chemical exchange cross-peaks in TOCSY and NOESY spectra. EXSY spectra were recorded to confirm that slow chemical exchange was occurring. Unambiguous sequence-specific resonance assignments are presented for one region of the protein, Pro⁶⁵-Asn⁷², which exists in two slowly exchanging conformers based on the identification of chemical exchange cross-peaks in 3D ¹H-¹H-¹⁵N EXSY-HSQC, NOESY-HSQC and TOCSY-HSQC spectra, together with C and C chemical shifts measured in triple-resonance spectra and sequential NH NOEs. The rates of conformational exchange for backbone amide resonances in this stretch of amino acids, and for the indole NH of either Trp²² or Trp⁵⁸, were determined from the intensity variation of the appropriate diagonal and chemical exchange cross-peaks recorded in 3D¹ H-¹H-¹⁵N NOESY-HSQC spectra. The data fitted a model in which this region of the DNase has two conformers, N_A and N_B, which interchange at 15 °C with a forward rate constant of 1.61 ± 0.5 s^-1 and a backward rate constant of 1.05 ± 0.5 s^-1. Demonstration of this conformational equilibrium has led to a reappraisal of a previously proposed kinetic scheme describing the interaction of E9 DNase with immunity proteins [Wallis et al. (1995) Biochemistry, 34, 13743–13750 and 13751–13759]. The revised scheme is consistent with the specific inhibitor protein for the E9 DNase, Im9, associating with both the N_A and N_B conformers of the DNase and with binding only to the N_B conformer detected because the rate of dissociation of the complex of Im9 and the N_A conformer, N_AI, is extremely rapid. In this model stoichiometric amounts of Im9 convert, the E9 DNase is converted wholly into the N_BI form. The possibility that cis–trans isomerisation of peptide bonds preceding proline residues is the cause of the conformational heterogeneity is discussed. E9 DNase contains 10 prolines, with two bracketing the stretch of amino acids that have allowed the N_A N_B interconversion to be identified, Pro⁶⁵ and Pro⁷³. The model assumes that one or both of these can exist in either the cis or trans form with strong Im9 binding possible to only one form.     

Structural basis for the slow dynamics of the actin filament pointed end

The actin filament has clear polarity where one end, the pointed end, has a much slower polymerization and depolymerization rate than the other end, the barbed end. This intrinsic difference of the ends significantly affects all actin dynamics in the cell, which has central roles in a wide spectrum of cellular functions. The detailed mechanism underlying this difference has remained elusive, because high-resolution structures of the filament ends have not been available. Here, we present the structure of the actin filament pointed end obtained using a single particle analysis of cryo-electron micrographs. We determined that the terminal pointed end subunit is tilted towards the penultimate subunit, allowing specific and extra loop-to-loop inter-strand contacts between the two end subunits, which is not possible in other parts of the filament. These specific contacts prevent the end subunit from dissociating. For elongation, the loop-to-loop contacts also inhibit the incorporation of another actin monomer at the pointed end. These observations are likely to account for the less dynamic pointed end.     

Solvent effects in the slow dynamics of proteins

The influence of solvent on the slow internal dynamics of proteins is studied by comparing molecular dynamics simulations of solvated and unsolvated lysozyme. The dynamical trajectories are projected onto the protein's normal modes in order to obtain a separate analysis for each of the associated time scales. The results show that solvent effects are important for the slowest motions (below approximately 1 ps(-1)) but negligible for faster motions. The damping effects seen in the latter show that the principal source of friction in protein dynamics is not the solvent, but the protein itself.     

Effect of the thermostat in the molecular dynamics simulation on the folding of the model protein chignolin

Molecular dynamics simulations of the model protein chignolin with explicit solvent were carried out, in order to analyze the influence of the Berendsen thermostat on the evolution and folding of the peptide. The dependence of the peptide behavior on temperature was tested with the commonly employed thermostat scheme consisting of one thermostat for the protein and another for the solvent. The thermostat coupling time of the protein was increased to infinity, when the protein is not in direct contact with the thermal bath, a situation known as minimally invasive thermostat. In agreement with other works, it was observed that only in the last situation the instantaneous temperature of the model protein obeys a canonical distribution. As for the folding studies, it was shown that, in the applications of the commonly utilized thermostat schemes, the systems are trapped in local minima regions from which it has difficulty escaping. With the minimally invasive thermostat the time that the protein needs to fold was reduced by two to three times. These results show that the obstacles to the evolution of the extended peptide to the folded structure can be overcome when the temperature of the peptide is not directly controlled.     

Numerical modeling of the dynamics of a slow Z-pinch

A study is made of the method for numerical modeling of pulsed plasma systems by simultaneously solving two-temperature MHD equations and the equations of ionization kinetics. As an example, the method is applied to simulate a relatively slow moderate-density Z-pinch, whose dynamics is well studied experimentally. A specially devised two-dimensional computer code makes use of a promising technique of parallel modeling.     

Large-scale cortical dynamics of sleep slow waves

Slow waves constitute the main signature of sleep in the electroencephalogram (EEG). They reflect alternating periods of neuronal hyperpolarization and depolarization in cortical networks. While recent findings have demonstrated their functional role in shaping and strengthening neuronal networks, a large-scale characterization of these two processes remains elusive in the human brain. In this study, by using simultaneous scalp EEG and intracranial recordings in 10 epileptic subjects, we examined the dynamics of hyperpolarization and depolarization waves over a large extent of the human cortex. We report that both hyperpolarization and depolarization processes can occur with two different characteristic time durations which are consistent across all subjects. For both hyperpolarization and depolarization waves, their average speed over the cortex was estimated to be approximately 1 m/s. Finally, we characterized their propagation pathways by studying the preferential trajectories between most involved intracranial contacts. For both waves, although single events could begin in almost all investigated sites across the entire cortex, we found that the majority of the preferential starting locations were located in frontal regions of the brain while they had a tendency to end in posterior and temporal regions.     

Protein dynamics in supercooled water: the search for slow motional modes

The impact of studying protein dynamics in supercooled water for identifying slow motional modes on the s time scale is demonstrated. Backbone ¹⁵N spin relaxation parameters were measured at –13°C for ubiquitin, which plays a central role for signaling proteolysis, cellular trafficking and kinase activation in eukaryotic organisms. A hitherto undetected motional mode involving Val 70 was found, which may well play an important role for ubiquitin recognition. The measurement of rotating frame ¹⁵N relaxation times as a function of the spin-lock field allowed determination of the correlation time of this motional mode, which would not have been feasible above 0°C.     

Cell assembly dynamics in detailed and abstract attractor models of cortical associative memory

Summary During the last few decades we have seen a convergence among ideas and hypotheses regarding functional principles underlying human memory. Hebb’s now more than fifty years old conjecture concerning synaptic plasticity and cell assemblies, formalized mathematically as attractor neural networks, has remained among the most viable and productive theoretical frameworks. It suggests plausible explanations for Gestalt aspects of active memory like perceptual completion, reconstruction and rivalry. We review the biological plausibility of these theories and discuss some critical issues concerning their associative memory functionality in the light of simulation studies of models with palimpsest memory properties. The focus is on memory properties and dynamics of networks modularized in terms of cortical minicolumns and hypercolumns. Biophysical compartmental models demonstrate attractor dynamics that support cell assembly operations with fast convergence and low firing rates. Using a scaling model we obtain reasonable relative connection densities and amplitudes. An abstract attractor network model reproduces systems level psychological phenomena seen in human memory experiments as the Sternberg and von Restorff effects. We conclude that there is today considerable substance in Hebb’s theory of cell assemblies and its attractor network formulations, and that they have contributed to increasing our understanding of cortical associative memory function. The criticism raised with regard to biological and psychological plausibility as well as low storage capacity, slow retrieval etc has largely been disproved. Rather, this paradigm has gained further support from new experimental data as well as computational modeling.     

An approximate line attractor in the hypothalamus encodes an aggressive state

1. Download : Download high-res image (203KB)
2. Download : Download full-size image

     

Singular behavior of slow dynamics of single excitable cells

In various kinds of cultured cells, it has been reported that the membrane potential exhibits fluctuations with long-term correlations, although the underlying mechanism remains to be elucidated. A cardiac muscle cell culture serves as an excellent experimental system to investigate this phenomenon because timings of excitations can be determined over an extended time period in a noninvasive manner through visualization of contractions, although the properties of beat-timing fluctuations of cardiac muscle cells at the single-cell level remains to be fully clarified. In this article, we report on our investigation of spontaneous contractions of cultured rat cardiac muscle cells at the single-cell level. It was found that single cells exhibit several typical temporal patterns of contractions and spontaneous transitions among them. Detrended fluctuation analysis on the time series of interbeat intervals revealed the presence of 1/f^β noise at sufficiently large timescales. Furthermore, multifractality was also found in the time series of interbeat intervals. These experimental trends were successfully explained using a simple mathematical model, incorporating correlated noise into ionic currents. From these findings, it was established that singular fluctuations accompanying 1/f^β noise and multifractality are intrinsic properties of single cardiac muscle cells.     

The nature of the charge carriers in solvated biomacromolecules

Solid state electrolysis experiments were performed on the biomolecules, hemoglobin, cytochromec, collagen, lecithin and melanin at various hydration states; and for hemoglobin at various solvation states with methanol adsorbate. The evolved hydrogen was measured and compared with theoretical (Faraday's Law) expectations for the known amount of charge passed through the adsorbents. The difference between the theoretical and actual is a measure of the contributions of electronic charge carriers to the total current. Thus the protonic/electronic conduction ratios are determined.All biomolecules tested appear to be mixed semiconductors. That is, both electronic and protonic charge carriers make significant contributions to the currents over hydration ranges from 6% to above 50%. The constant temperature conductivity increases exponentially with hydration (solvation) but the ratio of protonic to electronic conduction increases linearly with hydration for the globular proteins, hemoglobin and cytochromec. The fibrous protein, collagen, may be a protonic semiconductor in the dry state, with an electronic component that increases linearly with hydration. The hemoglobin-methanol system shows only electronic conductivity below 2 BET monolayers, with a sharp onset to 70% protonic conductivity above this value. This result is similar to the DNA-water system previously reported. The protonic/electronic ratio in hydrated hemoglobin may be a function of the applied voltage; being predominantly electronic below 30 volts (300 volts/cm), and a constant mixed value above 100 volts (1000 volts/cm). Our results suggest that both electronic and protonic conduction are intrinsic processes in these substances and subject to control by a number of techniques.     

Characterization of slow conformational dynamics in solids: dipolar CODEX

A solid state NMR experiment is introduced for probing relatively slow conformational exchange, based on dephasing and refocusing dipolar couplings. The method is closely related to the previously described Centerband-Only Detection of Exchange or CODEX experiment. The use of dipolar couplings for this application is advantageous because their values are known a priori from molecular structures, and their orientations and reorientations relate in a simple way to molecular geometry and motion. Furthermore the use of dipolar couplings in conjunction with selective isotopic enrichment schemes is consistent with selection for unique sites in complex biopolymers. We used this experiment to probe the correlation time for the motion of ¹³C, ¹⁵N enriched urea molecules within their crystalline lattice.     

Analysis of metabolic systems with complex slow and fast dynamics

We briefly review the results of other authors concerning the analysis of systems with time hierarchy, especially the Tikhonov theorem. A theorem, recently proved by the authors, making possible rigorous analysis of systems with complex fast dynamics is stated and discussed. A model example of a simple enzymatic reaction with product activation and slow (genetically driven) enzyme turnover is rigorously studied. It is shown that even in such a simple model there exist certain regions of parameters for which fast variables oscillate. Thus the classical Tikhonov theorem is not applicable here and we are forced to use another method-for example the author's presented theorem—or a purely numerical solution. These two methods are compared.