VTechWorks Repository :: Browsing by Author "Kulkarni, Rahul V."

Browsing by Author "Kulkarni, Rahul V."

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Applications of Field Theory to Reaction Diffusion Models and Driven Diffusive Systems
Mukherjee, Sayak (Virginia Tech, 2009-08-25)
In this thesis, we focus on the steady state properties of two systems which are genuinely out of equilibrium. The first project is an application of dynamic field theory to a specific non equilibrium critical phenomenon, while the second project involves both simulations and analytical calculations. The methods of field theory are used on both these projects. In the first part of this thesis, we investigate a generalization of the well-known field theory for directed percolation (DP). The DP theory is known to describe an evolving population, near extinction. We have coupled this evolving population to an environment with its own nontrivial spatio-temporal dynamics. Here, we consider the special case where the environment follows a simple relaxational (model A) dynamics. We find two marginal couplings with upper critical dimension of four, which couple the two theories in a nontrivial way. While the Wilson-Fisher fixed point remains completely unaffected, a mismatch of time scales destabilizes the usual DP fixed point. Some open questions and future work remain. In the second project, we focus on a simple particle transport model far from equilibrium, namely, the totally asymmetric simple exclusion process (TASEP). While its stationary properties are well studied, many of its dynamic features remain unexplored. Here, we focus on the power spectrum of the total particle occupancy in the system. This quantity exhibits unexpected oscillations in the low density phase. Using standard Monte Carlo simulations and analytic calculations, we probe the dependence of these oscillations on boundary effects, the system size, and the overall particle density. Our simulations are fitted to the predictions of a linearized theory for the fluctuation of the particle density. Two of the fit parameters, namely the diffusion constant and the noise strength, deviate from their naive bare values [6]. In particular, the former increases significantly with the system size. Since this behavior can only be caused by nonlinear effects, we calculate the lowest order corrections in perturbation theory. Several open questions and future work are discussed.
Driven Magnetic Flux Lines in Type-II Superconductors: Nonequilibrium Steady States and Relaxation Properties
Klongcheongsan, Thananart (Virginia Tech, 2009-03-31)
We investigate the nonequilibrium steady state of driven magnetic flux lines in type-II superconductors subject to strong point or columnar pinning centers and the aging dynamics of nonequilibrium relaxation process in the presence of weak point pinning centers. We employ a three-dimensional elastic line model and Metropolis Monte Carlo simulations. For the first part, we characterize the system by means of the force-velocity / current-voltage curve, static structure factor, mean vortex radius of gyration, number of double-kink and half-loop excitations, and velocity / voltage noise features. We compare the results for the above quantities for randomly distributed point and columnar defects. Most of both numerical works have been done in two-dimensional systems such as thin film in which the structure of flux lines is treated as a point-like particle. Our main point of investigation in this paper is to demonstrate that the vortex structure and its other transport properties may exhibit a remarkable variety of complex phenomena in three-dimensional or bulk superconductors. The second part devotes to the study of aging phenomena in the absence of a driving force in disordered superconductors with much weaker point disorder. By investigating the density autocorrelation function, we observe all three crucial properties of the aging phenomena; slow power-law relaxation, breaking of time-translation invariance, and the presence of the dynamical scaling. We measure the dynamical exponents b and lambda_c/z and compare to other work. We find exponent values increase for increasing pinning strength, smaller interaction range, lower temperature, and denser defect density while the exponents measured in other approach tend to decrease.
Exact protein distributions for stochastic models of gene expression using partitioning of Poisson processes
Pendar, Hodjat; Platini, Thierry; Kulkarni, Rahul V. (American Physical Society, 2013-04-26)
Stochasticity in gene expression gives rise to fluctuations in protein levels across a population of genetically identical cells. Such fluctuations can lead to phenotypic variation in clonal populations; hence, there is considerable interest in quantifying noise in gene expression using stochastic models. However, obtaining exact analytical results for protein distributions has been an intractable task for all but the simplest models. Here, we invoke the partitioning property of Poisson processes to develop a mapping that significantly simplifies the analysis of stochastic models of gene expression. The mapping leads to exact protein distributions using results for mRNA distributions in models with promoter-based regulation. Using this approach, we derive exact analytical results for steady-state and time-dependent distributions for the basic two-stage model of gene expression. Furthermore, we show how the mapping leads to exact protein distributions for extensions of the basic model that include the effects of posttranscriptional and posttranslational regulation. The approach developed in this work is widely applicable and can contribute to a quantitative understanding of stochasticity in gene expression and its regulation.
Experimental Observation of Geometric Phases in Narrow-Gap Semiconductor Heterostructures
Lillianfeld, Robert Brian (Virginia Tech, 2011-04-01)
We have studied the electron quantum phase by fabricating low dimensional (d ≤ 2) mesoscopic interferometers in high-quality narrow-gap semiconductor (NGS) heterostructures. The low effective-mass electrons in NGS heterostructures enable observation of delicate quantum phases; and the strong spin-orbit interaction (SOI) in the systems gives us means by which we can manipulate the quantum-mechanical spin of these electrons through the orbital properties of the electrons. This enables the observation of spin-dependent phenomena otherwise inaccessible in non-magnetic systems. We have performed low temperature (0.4 K ≤ T ≤ 8 K), low noise (â V ~ 1μV ) transport measurements, and observed evidence of Aharonov-Bohm (AB) and Alâ tshuler-Aronov-Spivak (AAS) quantum oscillations in meso- scopic devices that we fabricated on these NGSs. Our measurements are unique in that we observe both AB and AAS in comparable magnitude in ballistic networks with strong SOI. We show that, with appropriate considerations, diffusive formalisms can be used to describe ballistic transport through rings, even in the presence of SOI. This work also contains an introduction to the physics of geometric phases in mesoscopic systems, and the experimental and analytic processes through which these phases are probed. A discussion of the results of our measurements presents the case that quantum interferometric measurements of geometric phases can be understood quite thoroughly, and that these measurements may have deeper utility in discovery than has yet been recognized.
Inhomogeneous Totally Asymmetric Simple Exclusion Processes: Simulations, Theory and Application to Protein Synthesis
Dong, Jiajia (Virginia Tech, 2008-03-26)
In the process of translation, ribosomes, a type of macromolecules, read the genetic code on a messenger RNA template (mRNA) and assemble amino acids into a polypeptide chain which folds into a functioning protein product. The ribosomes perform discrete directed motion that is well modeled by a totally asymmetric simple exclusion process (TASEP) with open boundaries. We incorporate the essential components of the translation process: Ribosomes, cognate tRNA concentrations, and mRNA templates correspond to particles (covering ell > 1 sites), hopping rates, and the underlying lattice, respectively. As the hopping rates in an mRNA are given by its sequence (in the unit of codons), we are especially interested in the effects of a finite number of slow codons to the overall stationary current. To study this matter systematically, we first explore the effects of local inhomogeneities, i.e., one or two slow sites of hopping rate q<1 in TASEP for particles of size ell > 1(in the unit of lattice site) using Monte Carlo simulation. We compare the results of ell =1 and ell >1 and notice that the existence of local defects has qualitatively similar effects to 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 ell =1 and ell >1 cases. In particular, we notice a novel "edge" effect, i.e., the interaction of a single slow codon with the system boundary. When two slow sites are introduced, more intriguing phenomena such as dramatic decreases in the current when the two are close together emerge. We analyze the simulation results using several different levels of mean-field theory. A finite-segment mean-field approximation is especially successful in understanding the "edge effect." If we consider the systems with finite defects as "contrived mRNA's", the real mRNA's are of more biological significance. Inspired by the previous results, we study several mRNA sequences from Escherichia coli. We argue that an effective translation rate including the context of each codon needs to be taken into consideration when seeking an efficient strategy to optimize the protein production.
Modeling of nucleation-based stochastic processes in cellular systems
Xu, Xiaohua (Virginia Tech, 2010-08-11)
Molecular cell biology has been an intensively studied interdisciplinary field with the rapid development of experimental techniques and fast upgrade of computational hardware and numerical tools. Recent technological developments have led to single-cell experiments which allow us to probe the role of stochasticity in cellular processes. Stochastic modeling of the corresponding processes is thus an essential ingredient for the understanding and interpretation of cellular systems of interest. In this thesis, we explore several nucleation-based stochastic cellular processes, i.e. Min protein oscillation in Escherichia coli, pausing phenomena in DNA transcription, and single-molecule enzyme kinetics. We focus on the key experimental results and build up stochastic models accordingly to provide quantitative insights to the underlying physical mechanisms for the corresponding biological processes. We utilize specific mathematical methods and computational algorithms to gain a better understanding and make predictions for further experimental explorations in the relevant fields.
Modeling Protein Regulatory Networks that Control Mammalian Cell Cycle Progression and that Exhibit Near-Perfect Adaptive Responses
Singhania, Rajat (Virginia Tech, 2011-04-22)
Protein regulatory networks are the hallmark of many important biological functionalities. Two of these functionalities are mammalian cell cycle progression and near-perfect adaptive responses. Modeling and simulating these functionalities are crucial stages to understanding and predicting them as systems-level properties of cells. In the context of the mammalian cell cycle, the timing of DNA synthesis, mitosis and cell division is regulated by a complex network of biochemical reactions that control the activities of a family of cyclin-dependent kinases. The temporal dynamics of this reaction network is typically modeled by nonlinear differential equations describing the rates of the component reactions. This approach provides exquisite details about molecular regulatory processes but is hampered by the need to estimate realistic values for the many kinetic constants that determine the reaction rates. To avoid this problem, modelers often resort to "qualitative" modeling strategies, such as Boolean switching networks, but these models describe only the coarsest features of cell cycle regulation. In this work, we describe a hybrid approach that combines features of continuous and discrete networks. The model is evaluated in terms of flow cytometry measurements of cyclin proteins in asynchronous populations of human cell lines. Using our hybrid approach, modelers can quickly create quantitatively accurate, computational models of protein regulatory networks found in various contexts within cells. Large-scale protein regulatory networks, such as the one that controls the progression of the mammalian cell cycle, also contain small-scale motifs or modules that carry out specific dynamical functions. Systematic characterization of smaller, interacting, network motifs whose individual behavior is well known under certain conditions is therefore of great interest to systems biologists. We model and simulate various 3-node network motifs to find near-perfect adaptation behavior. This behavior entails that a system responds to a change in its environmental cues, or signals, by coming back nearly to its pre-signal state even in the continued presence of the signal. We let various topologies evolve in their parameter space such that they eventually stumble upon a region where they score well under a pre-defined scoring metric. We find many such parameter sample sets across various classes of topologies.
Multi-tiered Regulation of luxR Provides Precise Timing and Maintenance of the Quorum Sensing Response of Vibrio fischeri
Williams, Joshua W. (Virginia Tech, 2009-06-04)
The quorum-sensing response of Vibrio fischeri involves a complex network of genes (encoding regulatory proteins as well as sRNAs), that govern host-association and production of bioluminescence. A key regulator of this system is LuxR, which is the transcriptional activator of the lux operon as well as several other genes in. LuxR also autoregulates its own transcription, which we have shown causes bistability and hysteresis in the quorum-sensing response. This behavior allows the system to maintain a stable and robust response in the face of environmental fluctuation or decreases in external autoinducer concentration caused by other sources. There are many factors that are known to regulate luxR expression, including the ArcA redox-responsive regulator, the cAMP-CRP secondary metabolism regulator, and components of the quorum-sensing pathway like LitR. Because of this, LuxR levels are critical in both the timing of quorum-sensing induction, as well as the maintenance of the response over time. This makes it a potential target for multiple levels of regulation in response to factors such as environmental and metabolic conditions, as well as other components of the quorum-sensing network. Another important global regulatory protein in V. fischeri (and most other species of Gram-negative proteobacteria) is the post-transcriptional regulator CsrA. CsrA controls processes involved in carbon storage and utilization, as well as the transition from exponential to stationary phase growth. We have demonstrated that CsrA is regulated by two sRNAs (CsrB1 and CsrB2) in V. fischeri. Because CsrA regulates changes in cell behavior and is an important metabolic regulator, there is a good possibility that it has some interactions with the quorum-sensing regulon, whose endproduct, bioluminescence, creates a large metabolic demand from the cell. In an effort to determine at which point in the quorum-sensing regulatory network CsrA regulation is important, epistasis experiments were designed using factorial design, which is a subset of statistical analysis of variance (ANOVA). This method was used to generate a high degree of confidence in the data, so that even minor interactions in the regulatory networks could be established. By altering the levels of CsrA expression in various mutant strains of V. fischeri, we have demonstrated that CsrA acts by an unknown mechanism to increase the transcription of luxR when the quorum-sensing regulator LitR is absent. Our results also demonstrated that CsrA mediates this effect through repression of ArcA activity, which is known to act directly on the luxR and luxI intergenic region as a repressor. This indicates that CsrA may bypass the upstream parts of the quorum-sensing regulatory cascade that lead to litR activation, so that LitR and LuxR may be regulated differently in response to certain conditions. This work has shown that the interactions between global regulons can coordinately control the amount of quorum-sensing induction by affecting the level of LuxR in the cell. The balance of these regulatory networks allows the cell to tightly regulate the quorum-sensing response. Thus, LuxR serves as a critical regulatory hub in the cell, at which multiple signals can be integrated in order to generate the appropriate cellular response.
Network Modeling Stochastic and Deterministic Approaches
Sansavini, Giovanni (Virginia Tech, 2010-09-01)
Stochastic and deterministic approaches for modeling complex networks are presented. The methodology combines analysis of the structure formed by the interconnections among the elements of a network with an assessment of the vulnerability towards the propagation of cascading failures. The goal is to understand the mutual interplay between the structure of the network connections and the propagation of cascading failures. Two fundamental issues related to the optimal design and operation of complex networks are addressed. The first concerns the impact that cascading failures have on networks due to the connectivity pattern linking their components. If the state of load on the network components is high, the risk of cascade spreadings becomes significant. In this case, the needed reduction of the connectivity efficiency to prevent the propagation of failures affecting the entire system is quantified. The second issue concerns the realization of the most efficient connectivity in a network that minimizes the propagations of cascading failures. It is found that a system that routinely approaches the critical load for the onset of cascading failures during its operation should have a larger efficiency value. This allows for a smoother transition to the cascade region and for a reasonable reaction time to counteract the onset of significant cascading failures. The interplay between the structure of the network connections and the propagation of cascading failures is assessed also in interdependent networks. In these systems, the linking among several network infrastructures is necessary for their optimal and economical operation. Yet, the interdependencies introduce weaknesses due to the fact that failures may cascade from one system to other interdependent systems, possibly affecting their overall functioning. Inspired by the global efficiency, a measure of the communication capabilities among interdependent systems, i.e. the interdependency efficiency, is defined. The relations between the structural parameters, i.e. the system links and the interdependency links, and the interdependency efficiency, are also quantified, as well as the relations between the structural parameters and the vulnerability towards the propagation of cascading failures. Resorting to this knowledge, the optimal interdependency connectivity is identified. Similar to the spreading of failures, the formation of a giant component is a critical phenomenon emerging as a result of the connectivity pattern in a network. This structural transition is exploited to identify the formation of macrometastases in the developed model for metastatic colonization in tumor growth. The methods of network theory proves particularly suitable to reproduce the local interactions among tumor cells that lead to the emergent global behavior of the metastasis as a community. This model for intercellular sensing reproduces the stepwise behavior characteristic of metastatic colonization. Moreover, it prompts the consideration of a curative intervention that hinders intercellular communication, even in the presence of a significant tumor cell population.
Nonequilibrium Relaxation and Aging Scaling Properties of the Coulomb Glass and Bose Glass
Shimer, Matthew Timothy (Virginia Tech, 2011-08-26)
We use Monte Carlo simulations in order to investigate the density of states and the two-time density autocorrelation function for the two- and three-dimensional Coulomb glass as well as the Bose glass phase of flux lines in type-II superconductors. We find a very fast forming gap in the density of states and explore the dependence of temperature and filling fraction. By studying two scaling methods, we find that the nonequilibrium relaxation properties can be described sufficiently by a full-aging scaling analysis. The scaling exponents depend on both temperature and filling fraction, and are thus non-universal. We look at the trends of these exponents and found that as either the temperature decreases or the filling fraction deviates more from half-filling, the exponents reflect slower relaxation kinetics. With two separate interaction potentials, a comparison of relaxation rates and the gap in the density of states is made.
Prediction of CsrA-regulating small RNAs in bacteria and their experimental verification in Vibrio fischeri
Kulkarni, Prajna R.; Cui, Xiaohui; Williams, Joshua W.; Stevens, Ann M.; Kulkarni, Rahul V. (2006-01-01)
The role of small RNAs as critical components of global regulatory networks has been highlighted by several recent studies. An important class of such small RNAs is represented by CsrB and CsrC of Escherichia coli, which control the activity of the global regulator CsrA. Given the critical role played by CsrA in several bacterial species, an important problem is the identification of CsrA-regulating small RNAs. In this paper, we develop a computer program (CSRNA_FIND) designed to locate potential CsrA-regulating small RNAs in bacteria. Using CSRNA_FIND to search the genomes of bacteria having homologs of CsrA, we identify all the experimentally known CsrA-regulating small RNAs and also make predictions for several novel small RNAs. We have verified experimentally our predictions for two CsrA-regulating small RNAs in Vibrio fischeri. As more genomes are sequenced, CSRNA_FIND can be used to locate the corresponding small RNAs that regulate CsrA homologs. This work thus opens up several avenues of research in understanding the mode of CsrA regulation through small RNAs in bacteria.
Probe of Coherent and Quantum States in Narrow-Gap Based Semiconductors in the Presence of Strong Spin-Orbit Coupling
Frazier, Matthew Allen (Virginia Tech, 2010-09-03)
The goal of this project was to study some unexplored optical and magneto-optical properties of the newest member of III-V ferromagnetic structures, InMnSb, as well as InSb films and InSb/AlInSb quantum wells. The emphasis was on dynamical aspects such as charge and spin dynamics in order to address several important issues of the spin-related phenomena. The objectives in this project were to: 1) understand charge/spin dynamics in NGS with different confinement potentials, 2) study phenomena such as interband photo-galvanic effects, in order to generate spin polarized current, 3) probe the effect of magnetic impurities on the spin/charge dynamics. This thesis describes three experiments: detection and measurement of spin polarized photocurrents in InSb films and quantum wells arising from the circular photogalvanic effect, and measurements of the carrier and spin relaxation in InSb and InMnSb structures by magneto-optical Kerr effect and differential transmission. The samples for our studies have been provided by Prof. Heremans at Virginia Tech, Prof. Santos at the University of Oklahoma, and Prof. Furdyna at the University of Notre Dame.
Regulatory targets of quorum sensing in Vibrio cholerae: evidence for two distinct HapR-binding motifs
Tsou, Amy M.; Cai, Tao; Liu, Zhi; Zhu, Jun; Kulkarni, Rahul V. (2009-05)
The quorum-sensing pathway in Vibrio cholerae controls the expression of the master regulator HapR, which in turn regulates several important processes such as virulence factor production and biofilm formation. While HapR is known to control several important phenotypes, there are only a few target genes known to be transcriptionally regulated by HapR. In this work, we combine bioinformatic analysis with experimental validation to discover a set of novel direct targets of HapR. Our results provide evidence for two distinct binding motifs for HapR-regulated genes in V. cholerae. The first binding motif is similar to the motifs recently discovered for orthologs of HapR in V. harveyi and V. vulnificus. However, our results demonstrate that this binding motif can be of variable length in V. cholerae. The second binding motif shares common elements with the first motif, but is of fixed length and lacks dyad symmetry at the ends. The contributions of different bases to HapR binding for this second motif were demonstrated using systematic mutagenesis experiments. The current analysis presents an approach for systematically expanding our knowledge of the quorum-sensing regulon in V. cholerae and other related bacteria.
Relaxation phenomena during non-equilibrium growth
Chou, Yen-Liang (Virginia Tech, 2011-08-01)
The surface width, a global quantity that depends on time, is used to characterize the temporal evolution of growing surfaces. One of the most successful concepts for describing the property of the surface width is the famous Family-Vicsek scaling relation. We discuss an extended scaling relation that yields a complete description for various growth models. For two linear Langevin equations, namely the Edwards-Wilkinson equation and the Mullins-Herring equation, we furthermore study analytically the behavior of global quantities related to the surface width or to a quantity which is conjugated to the diffusion constant. The global quantities depend in a non-trivial way on two different times. We discuss the dynamical scaling forms of global correlation and response functions. For global functions related to the surface width, we show that the scaling behavior of the response can depend on how the system is perturbed. Different dynamic regimes, characterized by a power-law or by an exponential relaxation, are identified, and a dynamic phase diagram is constructed. We discuss global fluctuation-dissipation ratios and how to use them for the characterization of non-equilibrium growth processes. We also numerically study the same two-time quantities for the non-linear Kardar-Parisi-Zhang equation. For global functions related to the quantity which is conjugated to the diffusion constant of the linear Langevin equations, we show that the integrated response is proportional to the correlation in the linear response regime. In the aging regime, the autocorrelation and autoresponse exponents are identical and the aging exponent for the response is equal to the aging exponent for the correlation. We investigate the non-equilibrium fluctuation-dissipation theorem for non-equilibrium states based on this quantity. In the non-linear response regime a certain dissipation-fluctuation ratio approximates unity for small waiting times but approaches the ratio of perturbed and unperturbed diffusion constants for larger waiting times.
Simple Physical Approaches to Complex Biological Systems
Fenley, Andrew Townsend (Virginia Tech, 2010-07-02)
Properly representing the principle physical interactions of complex biological systems is paramount for building powerful, yet simple models. As an in depth look into different biological systems at different scales, multiple models are presented. At the molecular scale, an analytical solution to the (linearized) Poisson-Boltzmann equation for the electrostatic potential of any size biomolecule is derived using spherical geometry. The solution is tested both on an ideal sphere relative to an exact solution and on a multitude of biomolecules relative to a numerical solution. In all cases, the bulk of the error is within thermal noise. The computational power of the solution is demonstrated by finding the electrostatic potential at the surface of a viral capsid that is nearly half a million atoms in size. Next, a model of the nucleosome using simplified geometry is presented. This system is a complex of protein and DNA and acts as the first level of DNA compaction inside the nucleus of eukaryotes. The analytical model reveals a mechanism for controlling the stability of the nucleosome via changes to the total charge of the protein globular core. The analytical model is verified by a computational study on the stability change when the charge of individual residues is altered. Finally, a multiple model approach is taken to study bacteria that are capable of different responses depending on the size of their surrounding colony. The first model is capable of determining how the system propagates the information about the colony size to those specific genes that control the concentration of a master regulatory protein. A second model is used to analyze the direct RNA interference mechanism the cell employs to tune the available gene transcripts of the master regulatory protein, i.e. small RNA - messenger RNA regulation. This model provides a possible explanation for puzzling experimentally measured phenotypic responses.
Stochastic Modeling of Gene Expression and Post-transcriptional Regulation
Jia, Tao (Virginia Tech, 2011-07-21)
Stochasticity is a ubiquitous feature of cellular processes such as gene expression that can give rise to phenotypic differences for genetically identical cells. Understanding how the underlying biochemical reactions give rise to variations in mRNA/protein levels is thus of fundamental importance to diverse cellular processes. Recent technological developments have enabled single-cell measurements of cellular macromolecules which can shed new light on processes underlying gene expression. Correspondingly, there is a need for the development of theoretical tools to quantitatively model stochastic gene expression and its consequences for cellular processes. In this dissertation, we address this need by developing general stochastic models of gene expression. By mapping the system to models analyzed in queueing theory, we derive analytical expressions for the noise in steady-state protein distributions. Furthermore, given that the underlying processes are intrinsically stochastic, cellular regulation must be designed to control the`noise' in order to adapt and respond to changing environments. Another focus of this dissertation is to develop and analyze stochastic models of post-transcription regulation. The analytical solutions of the models proposed provide insight into the effects of different mechanisms of regulation and the role of small RNAs in fine-tunning the noise in gene expression. The results derived can serve as building blocks for future studies focusing on regulation of stochastic gene expression.
Totally Asymmetric Simple Exclusion Processes with Finite Resources
Cook, Larry Jonathan (Virginia Tech, 2009-12-04)
In many situations in the world, the amount of resources available for use is limited. This statement is especially true in the cells of living organisms. During the translation process in protein synthesis, ribosomes move along the mRNA strand constructing proteins based on the sequence of codons that form a gene. The totally asymmetric simple exclusion process (TASEP) models well the translation process. However, these genes are constantly competing for ribosomes and other resources in the cell. To see how finite resources and competition affects such a system, we must construct a simple model to account for the limited resources. We consider coupling multiple TASEPs to a finite reservoir of particles where the entry rate of particles into the TASEPs depends on the number of particles left in the reservoir. Starting with a single TASEP connected to the reservoir, we study the system using both Monte Carlo simulations and theoretical approaches. We explore how the average overall density, density profile, and current change as a function of the number of particles initially in the reservoir for various parameters. New features arise not seen in the ordinary TASEP model, even for a single TASEP connected to the pool of particles. These features include a localized shock in the density profile. To explain what is seen in the simulations, we use an appropriately generalized version of a domain wall theory. The dynamics of the TASEPs with finite resources are also studied through the power spectra associated with the total particle occupancy of each TASEP and the reservoir. Again, we find new phenomena not seen in the power spectrum of the ordinary TASEP. For a single constrained TASEP, we find a suppression at low frequencies when compared to the power spectrum of the ordinary TASEP. The severity of this suppression is found to depend on how the entry rate changes with respect to the number of particles in the pool. For two TASEPs of different lengths, we find an enhancement of the power spectrum of the smaller TASEP when compared to the ordinary TASEP's power spectrum. We explain these findings using a linearized Langevin equation. Finally, we model competition between ten genes found in Escherichia coli using a modified version of the TASEP. This modified version includes extended objects and inhomogeneous internal hopping rates. We use the insight gained from the previous studies of finite resources and competition as well as other studies to gain some insight into how competition affects protein production.

Browsing by Author "Kulkarni, Rahul V."

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