Quantitative Biology

In a recent paper, Michael J. Saxton proposes to interpret as anomalous diffusion the occurrence of apparent transient sub-diffusive regimes in mean-squared displacements (MSD) plots, calculated from experimental trajectories of molecules diffusing in living cells, acquired by Single Particle (or Molecule) Tracking techniques (SPT or SMT). In this Comment, without questioning the existence of sub-diffusive behaviors, which certainly play a key role in numbers of mechanisms in living systems, we point out that the data used by J.M. Saxton can as well be fitted by a simple law, resulting from confined diffusion at short times, with a slower free diffusion superimposed at larger times. When visualizing MSD plots, the transition from short-term diffusion confined in domains of size L, to slower, longer-term free diffusion, can be confused with anomalous diffusion over several orders of magnitude of time.

Motility is characteristic of life, but a common basis for movement has remained to be identified. Diverse systems in motion shift between two states depending on interactions that turnover at the rate of an applied cycle of force. Although one phase of the force cycle terminates the decay of the most recent state, continuation of the cycle of force regenerates the original decay process in a recursive cycle. By completing a cycle, kinetic energy is transformed into probability of sustaining the most recent state and the system gains a frame of reference for discrete transitions having static rather than time-dependent probability. The probability of completing a recursive cycle is computed with a Markov chain comprised of two equilibrium states and a kinetic intermediate. Given rate constants for the reactions, a random walk reproduces bias and recurrence times of walking motor molecules and bacterial flagellar switching with unrivaled fidelity.

Deprivation of essential nutrients can have stark consequences for many processes in a cell. We consider amino acid starvation, which can result in bottlenecks in mRNA translation when ribosomes stall due to lack of resources, i.e. tRNAs charged with the missing amino acid. Recent experiments also show less obvious effects such as increased charging of other (non-starved) tRNA species and selective charging of isoaccepting tRNAs. We present a mechanism which accounts for these observations, and shows that production of some proteins can actually increase under starvation. One might assume that such responses could only be a result of sophisticated control pathways, but here we show that these effects can occur naturally due to changes in the supply and demand for different resources, and that control can be accomplished through selective use of rare codons. We develop a model for translation which includes the dynamics of the charging and use of aa-tRNAs, explicitly taking into account the effect of specific codon sequences. This constitutes a new control mechanism in gene regulation which emerges at the community level, i.e., via resources used by all ribosomes.

Thyroid hormone (TH) signalling, an evolutionary conserved pathway, is crucial for brain function and cognition throughout life, from early development to ageing. In humans, TH deficiency during pregnancy alters offspring brain development, increasing the risk of cognitive disorders. How TH regulates neurogenesis and subsequent behaviour and cognitive functions remains a major research challenge. Cellular and molecular mechanisms underlying TH signalling on proliferation, survival, determination, migration, differentiation and maturation have been studied in mammalian animal models for over a century. However, recent data show that THs also influence embryonic and adult neurogenesis throughout vertebrates (from mammals to teleosts). These latest observations raise the question of how TH availability is controlled during neurogenesis and particularly in specific neural stem cell populations. This review deals with the role of TH in regulating neurogenesis in the developing and the adult brain across different vertebrate species. Such evo-devo approaches can shed new light on (i) the evolution of the nervous system and (ii) the evolutionary control of neurogenesis by TH across animal phyla. We also discuss the role of thyroid disruptors on brain development in an evolutionary context.

Local Ca Releases (LCRs) are crucial events involved in cardiac pacemaker cell function. However, specific algorithms for automatic LCR detection and analysis have not been developed in live, spontaneously beating pacemaker cells. Here we measured LCRs using a high-speed 2D-camera in spontaneously contracting sinoatrial (SA) node cells isolated from rabbit and guinea pig and developed a new algorithm capable of detecting and analyzing the LCRs spatially in two-dimensions, and in time. Our algorithm tracks points along the midline of the contracting cell. It uses these points as a coordinate system for affine transform, producing a transformed image series where the cell does not contract. Action potential-induced Ca transients and LCRs were thereafter isolated from recording noise by applying a series of spatial filters. The LCR birth and death events were detected by a differential (frame-to-frame) sensitivity algorithm. An LCR was detected when its signal changes sufficiently quickly within a sufficiently large area. The LCR is considered to have died when its amplitude decays substantially, or when it merges into the rising whole cell Ca transient. Our algorithm provides major LCR parameters such as period, signal mass, duration, and path area. As LCRs propagate within cells, the algorithm identifies splitting and merging behaviors, indicating the importance of Ca-induced-Ca-release for the fate of LCRs and for generating a powerful ensemble Ca signal. Thus, our new computer algorithms eliminate motion artifacts and detect 2D local spatiotemporal Ca release events from recording noise and global signals. While the algorithms detect LCRs in sinoatrial nodal cells, they have the potential to be used in other applications in biophysics and cell physiology, for example, to detect Ca wavelets (abortive waves), sparks and embers in muscle cells and Ca puffs and syntillas in neurons.

The cellular cytoskeleton is an active material, driven out of equilibrium by molecular motor proteins. It is not understood how the collective behaviors of cytoskeletal networks emerge from the properties of the network's constituent motor proteins and filaments. Here we present experimental results on networks of stabilized microtubules in Xenopus oocyte extracts, which undergo spontaneous bulk contraction driven by the motor protein dynein, and investigate the effects of varying the initial microtubule density and length distribution. We find that networks contract to a similar final density, irrespective of the length of microtubules or their initial density, but that the contraction timescale varies with the average microtubule length. To gain insight into why this microscopic property influences the macroscopic network contraction time, we developed simulations where microtubules and motors are explicitly represented. The simulations qualitatively recapitulate the variation of contraction timescale with microtubule length, and allowed stress contributions from different sources to be estimated and decoupled.

In this paper, we develop further the theory of thermostated systems along the lines of our earlier paper. Two results are highlighted: 1) in the Markov limit of the contracted description, a least dissipation of Helmholtz free energy principle is established; and 2) a detailed account of the appropriateness of this principle for nano-biology, including the evolution of life, is presented.

Messenger RNA encodes a sequence of amino acids by using codons. For most amino acids there are multiple synonymous codons that can encode the amino acid. The translation speed can vary from one codon to another, thus there is room for changing the ribosome speed while keeping the amino acid sequence and hence the resulting protein. Recently, it has been noticed that the choice of the synonymous codon, via the resulting distribution of slow- and fast-translated codons, affects not only on the average speed of one ribosome translating the messenger RNA (mRNA) but also might have an effect on nearby ribosomes by affecting the appearance of "traffic jams" where multiple ribosomes collide and form queues. To test this "context effect" further, we here investigate the effect of the sequence of synonymous codons on the ribosome traffic by using a ribosome traffic model with codon-dependent rates, estimated from experiments. We compare the ribosome traffic on wild type sequences and sequences where the synonymous codons were swapped randomly. By simulating translation of 87 genes, we demonstrate that the wild type sequences, especially those with a high bias in codon usage, tend to have the ability to reduce ribosome collisions, hence optimizing the cellular investment in the translation apparatus. The magnitude of such reduction of the translation time might have a significant impact on the cellular growth rate and thereby have importance for the survival of the species.

In this paper, three multiscale methods for coupling of mesoscopic (compartment-based) and microscopic (molecular-based) stochastic reaction-diffusion simulations are investigated. Two of the three methods that will be discussed in detail have been previously reported in the literature; the two-regime method (TRM) and the compartment-placement method (CPM). The third method that is introduced and analysed in this paper is the ghost cell method (GCM). Presented is a comparison of sources of error. The convergent properties of this error are studied as the time step Δt (for updating the molecular-based part of the model) approaches zero. It is found that the error behaviour depends on another fundamental computational parameter h , the compartment size in the mesoscopic part of the model. Two important limiting cases, which appear in applications, are considered: (i) \Delta t approaches 0 and h is fixed; and (ii) \Delta t approaches 0 and h approaches 0 such that \Delta t/h^2 is fixed. The error for previously developed approaches (the TRM and CPM) converges to zero only in the limiting case (ii), but not in case (i). It is shown that the error of the GCM converges in the limiting case (i). Thus the GCM is superior to previous coupling techniques if the mesoscopic description is much coarser than the microscopic part of the model.

We investigate the cooperative dynamics of an ensemble of N microtubules growing against an elastic barrier. Microtubules undergo so-called catastrophes, which are abrupt stochastic transitions from a growing to a shrinking state, and rescues, which are transitions back to the growing state. Microtubules can exert pushing or polymerization forces on an obstacle, such as an elastic barrier if the growing end is in contact with the obstacle. We use dynamical mean-field theory and stochastic simulations to analyze a model where each microtubule undergoes catastrophes and rescues and where microtubules interact by force sharing. For zero rescue rate, cooperative growth terminates in a collective catastrophe. The maximal polymerization force before catastrophes grows linearly with N for small N or a stiff elastic barrier, in agreement with available experimental results, whereas it crosses over to a logarithmic dependence for larger N or a soft elastic barrier. For a nonzero rescue rate and a soft elastic barrier, the dynamics becomes oscillatory with both collective catastrophe and rescue events, which are part of a robust limit cycle. Both the average and maximal polymerization forces then grow linearly with N, and we investigate their dependence on tubulin on-rates and rescue rates, which can be involved in cellular regulation mechanisms. We further investigate the robustness of the collective catastrophe and rescue oscillations with respect to different catastrophe models.