Jiajia Dong

Modeling Translation in Protein Synthesis with TASEP: A Tutorial and Recent Developments

The phenomenon of protein synthesis has been modeled in terms of totally asymmetric simple exclusion processes (TASEP) since 1968. In this article, we provide a tutorial of the biological and mathematical aspects of this approach. We also summarize several new results, concerned with limited resources in the cell and simple estimates for the current (protein production rate) of a TASEP with inhomogeneous hopping rates, reflecting the characteristics of real genes.

Towards a model for protein production rates

In the process of translation, ribosomes read the genetic code on an mRNA and assemble the corresponding polypeptide chain. The ribosomes perform discrete directed motion which is well modeled by a totally asymmetric simple exclusion process (TASEP) with open boundaries. Using Monte Carlo simulations and a simple mean-field theory, we discuss the effect of one or two “bottlenecks” (i.e., slow codons) on the production rate of the final protein. Confirming and extending previous work by Chou and Lakatos, we find that the location and spacing of the slow codons can affect the production rate quite dramatically. In particular, we observe a novel “edge” effect, i.e., an interaction of a single slow codon with the system boundary. We focus in detail on ribosome density profiles and provide a simple explanation for the length scale which controls the range of these interactions.

Inhomogeneous exclusion processes with extended objects: the effect of defect locations.

We study the effects of local inhomogeneities, i.e., slow sites of hopping rate q<1, in a totally asymmetric simple exclusion process for particles of size l>or=1 (in units of the lattice spacing). We compare the simulation results of l=1 and l>1 and notice that the existence of local defects has qualitatively similar effects on the steady state. We focus on the stationary current as well as the density profiles. If there is only a single slow site in the system, we observe a significant dependence of the current on the location of the slow site for both l=1 and l>1 cases. When two slow sites are introduced, more intriguing phenomena emerge, e.g., dramatic decreases in the current when the two are close together. In addition, we study the asymptotic behavior when q-->0. We also explore the associated density profiles and compare our findings to an earlier study using a simple mean-field theory. We then outline the biological significance of these effects.

On ribosome load, codon bias and protein abundance.

Different codons encoding the same amino acid are not used equally in protein-coding sequences. In bacteria, there is a bias towards codons with high translation rates. This bias is most pronounced in highly expressed proteins, but a recent study of synthetic GFP-coding sequences did not find a correlation between codon usage and GFP expression, suggesting that such correlation in natural sequences is not a simple property of translational mechanisms. Here, we investigate the effect of evolutionary forces on codon usage. The relation between codon bias and protein abundance is quantitatively analyzed based on the hypothesis that codon bias evolved to ensure the efficient usage of ribosomes, a precious commodity for fast growing cells. An explicit fitness landscape is formulated based on bacterial growth laws to relate protein abundance and ribosomal load. The model leads to a quantitative relation between codon bias and protein abundance, which accounts for a substantial part of the observed bias for E. coli. Moreover, by providing an evolutionary link, the ribosome load model resolves the apparent conflict between the observed relation of protein abundance and codon bias in natural sequences and the lack of such dependence in a synthetic gfp library. Finally, we show that the relation between codon usage and protein abundance can be used to predict protein abundance from genomic sequence data alone without adjustable parameters.

Probing the Mechanical Properties of Magnetosome Chains in Living Magnetotactic Bacteria

The mechanical properties of cytoskeletal networks are intimately involved in determining how forces and cellular processes are generated, directed, and transmitted in living cells. However, determining the mechanical properties of subcellular molecular complexes in vivo has proven to be difficult. Here, we combine in vivo measurements by optical microscopy, X-ray diffraction, and transmission electron microscopy with theoretical modeling to decipher the mechanical properties of the magnetosome chain system encountered in magnetotactic bacteria. We exploit the magnetic properties of the endogenous intracellular nanoparticles to apply a force on the filament-connector pair involved in the backbone formation and stabilization. We show that the magnetosome chain can be broken by the application of external field strength higher than 30 mT and suggest that this originates from the rupture of the magnetosome connector MamJ. In addition, we calculate that the biological determinants can withstand in vivo a force of 25 pN. This quantitative understanding provides insights for the design of functional materials such as actuators and sensors using cellular components.

Understanding the edge effect in TASEP with mean-field theoretic approaches

We study a totally asymmetric simple exclusion process (TASEP) with one defect site, hopping rate q < 1, near the system boundary. Regarding our system as a pair of uniform TASEPs coupled through the defect, we study various methods to match a finite TASEP and an infinite one across a common boundary. Several approximation schemes are investigated. Utilizing the finite segment mean-field (FSMF) method, we set up a framework for computing the steady state current J as a function of the entry rate α and q. For the case where the defect is located at the entry site, we obtain an analytical expression for J(α, q) which is in good agreement with Monte Carlo simulation results. When the defect is located deeper in the bulk, we refined the scheme of MacDonald et al (1968 Biopolymers 6 1) and find reasonably good fits to the density profiles before the defect site. We discuss the strengths and limitations of each method, as well as possible avenues for further studies.

Dynamic blockage in an exclusion process

We study an asymmetric exclusion model with one dynamic roadblock particle. The roadblock particle is allowed to move diffusively as well as by long-range jumps mimicking an unbinding/rebinding process. Using Monte Carlo simulations and analytical arguments, the two types of roadblock moves are considered both separately and in combination. Several interesting dynamic phenomena are observed. The long-range jumps of the roadblock lead to a current that depends on the number of particles in the system rather than on the particle density, and thus scales linearly with the system size (up to a critical size). This behavior can be explained by a collective motion of all particles following the roadblock. The diffusive roadblock movements on the other hand lead to a ratcheting motion with the active (driven) particles pushing the roadblock forward.

Shorter Exposures to Harder X-Rays Trigger Early Apoptotic Events in Xenopus laevis Embryos

Background A long-standing conventional view of radiation-induced apoptosis is that increased exposure results in augmented apoptosis in a biological system, with a threshold below which radiation doses do not cause any significant increase in cell death. The consequences of this belief impact the extent to which malignant diseases and non-malignant conditions are therapeutically treated and how radiation is used in combination with other therapies. Our research challenges the current dogma of dose-dependent induction of apoptosis and establishes a new parallel paradigm to the photoelectric effect in biological systems. Methodology/Principal Findings We explored how the energy of individual X-ray photons and exposure time, both factors that determine the total dose, influence the occurrence of cell death in early Xenopus embryo. Three different experimental scenarios were analyzed and morphological and biochemical hallmarks of apoptosis were evaluated. Initially, we examined cell death events in embryos exposed to increasing incident energies when the exposure time was preset. Then, we evaluated the embryos response when the exposure time was augmented while the energy value remained constant. Lastly, we studied the incidence of apoptosis in embryos exposed to an equal total dose of radiation that resulted from increasing the incoming energy while lowering the exposure time. Conclusions/Significance Overall, our data establish that the energy of the incident photon is a major contributor to the outcome of the biological system. In particular, for embryos exposed under identical conditions and delivered the same absorbed dose of radiation, the response is significantly increased when shorter bursts of more energetic photons are used. These results suggest that biological organisms display properties similar to the photoelectric effect in physical systems and provide new insights into how radiation-mediated apoptosis should be understood and utilized for therapeutic purposes.

Power spectra of TASEPs with a localized slow site

The totally asymmetric simple exclusion process (TASEP) with a localized defect is revisited in this paper with attention paid to the power spectra of the particle occupancy N(t). Intrigued by the oscillatory behaviors in the power spectra of an ordinary TASEP in high/low density (HD/LD) phases observed previously, we introduce a single slow site with hopping rate q < 1 to the system. As the power spectrum contains time-correlation information on the particle occupancy of the system, we are particularly interested in how the defect affects fluctuation in particle number of the left and right subsystems as well as that of the entire system. Exploiting Monte Carlo simulations, we observe the disappearance of oscillations when the defect is located at the center of the system. When the defect is off-center, oscillations are restored. To explore the origin of such a phenomenon, we use a linearized Langevin equation to calculate the power spectrum for the sublattices and the whole lattice. We provide insights into the interactions between the sublattices coupled through the defect site for both simulation and analytical results.

Simulation of colony pattern formation under differential adhesion and cell proliferation

Proliferation of individual cells is one of the hallmarks of living systems, and collectively the cells within a colony or tissue form highly structured patterns, influencing the properties at the population level. We investigate the joint effect of proliferation in the form of cell division and cell sorting due to differential adhesion using a cellular automaton model. Through simulations and theoretical analysis akin to interface growth, we show that this model gives rise to slower than exponential growth in the case of a single cell type as well as novel colony patterns in the case of two cell types. In particular, engulfment of one cell type by the other is strongly enhanced compared to the prediction from the differential adhesion hypothesis in the absence of proliferation. These observations provide new insights in predicting and characterizing colony morphology using experimentally accessible information such as single cell growth rate and cell adhesion strength.