One of the most important functions of immune T cells is to recognize the presence of the pathoge... more One of the most important functions of immune T cells is to recognize the presence of the pathogen-derived ligands and to quickly respond to them while at the same time not to respond to its own ligands. This is known as an absolute discrimination, and it is one of the most challenging phenomena to explain. The effectiveness of pathogen detection by T cell receptor (TCR) is limited by the chemical similarity of foreign and self-peptides and very low concentrations of foreign ligands. We propose a new mechanism of the absolute discrimination by T cells. It is suggested that the decision to activate or not to activate the immune response is controlled by the time to reach the stationary concentration of the TCR-ligand activated complex, which transfers the signal to downstream cellular biochemical networks. Our theoretical method models T-cell receptor phosphorylation events as a sequence of stochastic transitions between discrete biochemical states, and this allows us to explicitly d...
Cancer is a genetic disease that results from accumulation of unfavorable mutations. As soon as g... more Cancer is a genetic disease that results from accumulation of unfavorable mutations. As soon as genetic and epigenetic modifications associated with these mutations become strong enough, the uncontrolled tumor cell growth is initiated, eventually spreading through healthy tissues. Clarifying the dynamics of cancer initiation is thus critically important for understanding the molecular mechanisms of tumorigenesis. Here we present a new theoretical method to evaluate the dynamic processes associated with the cancer initiation. It is based on a discrete-state stochastic description of the formation of tumors as a fixation of cancerous mutations in tissues. Using a first-passage analysis the probabilities for the cancer to appear and the times before it happens, which are viewed as fixation probabilities and fixation times, respectively, are explicitly calculated. It is predicted that the slowest cancer initiation dynamics is observed for neutral mutations, while it is fast for both advantageous and, surprisingly, disadvantageous mutations. The method is applied for estimating the cancer initiation times from experimentally available lifetime cancer risks for different types of cancer. It is found that the higher probability of the cancer to occur does not necessary lead to the faster times of starting the cancer. Our theoretical analysis helps to clarify microscopic aspects of cancer initiation processes. It is well known that tumor cells are characterized by abnormal cell division rates, which is a result of mutations in cancer-susceptible genes (known as oncogenes) 1-4. Specifically, these mutations affect the regulation of cell proliferation and differentiation via activation of oncogenes or inactivation of tumor suppressor genes (TSGs) 2-5. Mutations are taking place randomly, and after several cellular replications some of them might occasionally lead to significant genetic and epigenetic alterations such that the normal cells behavior changes to the uncontrolled proliferation, eventually starting a cancer 3,6,7. After these cancer initiation events, rapid changes are taking place with a newly formed tumor being able to escape cellular control mechanisms, and the cancer progresses into more invasive forms 3,4,6,8,9. But this happens only after the initial stage of cancer succeeds, and thus it is critically important to understand the dynamics of cancer initiation 6. Human tissues and organs are composed of heterogeneous mixtures of cells: not all cells are equal in their potential to proliferate. An important role in tissue maintenance and repair is played by a population of so-called stem cells 10. These cells are characterized by their ability to self-renew and make more stem cells or ability to produce differentiated progenitor cells 11. Epithelial tissues are also known for subdivision into compartments where homeostatic mechanism, a balance between self-renewal and differentiation, maintains the constant cell number. Cancer appears in such compartments, breaking the homeostatic tissue equilibrium. However, having only a single mutated cell in the compartment does not lead to cancer. The cancer initiation event generally is associated with a fixation of one or several mutations, i.e., when all cells in the compartment become mutated, or when a significant fraction of them is mutated, producing noticeable genetic and epigenetic changes 6,9. One of the most important quantities that determines if the person gets a cancer is a cancer lifetime risk. It refers to a probability of being diagnosed with or dying from cancer during the person's lifespan. Lifetime risks strongly depend on the type of cancer. For example, a person's risk of getting a lung cancer is more than 11 times higher than of developing of a brain cancer, and 8 times greater than that of a stomach cancer 12,13. Various studies have attributed the differences in cancer rates to environmental risk factors, such as smoking, bad dietary habits
Understanding mechanisms of bacterial eradication is critically important for overcoming failures... more Understanding mechanisms of bacterial eradication is critically important for overcoming failures of antibiotic treatments. Current studies suggest that the clearance of large bacterial populations proceeds deterministically, while for smaller populations, the stochastic effects become more relevant. Here, we develop a theoretical approach to investigate the bacterial population dynamics under the effect of antibiotic drugs using a method of first-passage processes. It allows us to explicitly evaluate the most important characteristics of bacterial clearance dynamics such as extinction probabilities and extinction times. The new meaning of minimal inhibitory concentrations for stochastic clearance of bacterial populations is also discussed. In addition, we investigate the effect of fluctuations in population growth rates on the dynamics of bacterial eradication. It is found that extinction probabilities and extinction times generally do not correlate with each other when random fluctuations in the growth rates are taking place. Unexpectedly, for a significant range of parameters, the extinction times increase due to these fluctuations, indicating a slowing in the bacterial clearance dynamics. It is argued that this might be one of the initial steps in the pathway for the development of antibiotic resistance. Furthermore, it is suggested that extinction times is a convenient measure of bacterial tolerance.
Gastrulation is a fundamental phase during the biological development of most animals when a sing... more Gastrulation is a fundamental phase during the biological development of most animals when a single layer of identical embryo cells is transformed into a three-layer structure, from which the organs start to develop. Despite a remarkable progress in quantifying the gastrulation processes, molecular mechanisms of these processes remain not well understood. Here we theoretically investigate early spatial patterning in a geometrically confined colony of embryonic stem cells. Using a reaction-diffusion model, a role of Bone-Morphogenetic Protein 4 (BMP4) signaling pathway in gastrulation is specifically analyzed. Our results show that for slow diffusion rates of BMP4 molecules, a new length scale appears, which is independent of the size of the system. This length scale separates the central region of the colony with uniform low concentrations of BMP molecules from the region near the colony edge where the concentration of signaling molecules is elevated. The roles of different components of the signaling pathway are also explained. Theoretical results are consistent with recent in vitro experiments, providing microscopic explanations for some features of early embryonic spatial patterning. Physical-chemical mechanisms of these processes are discussed.
Mechanisms of the formation of biological signaling profiles
The formation and growth of multi-cellular organisms and tissues from several genetically identic... more The formation and growth of multi-cellular organisms and tissues from several genetically identical embryo cells is one of the most fundamental natural phenomena. These processes are stimulated and governed by multiple biological signaling molecules, which are also called morphogens. Embryo cells are able to read and pass genetic information by measuring the non-uniform concentration profiles of signaling molecules. It is widely believed that the establishment of concentration profiles of morphogens, commonly referred as morphogen gradients, is a result of complex biophysical and biochemical processes that might involve diffusion and degradation of locally produced signaling molecules. In this review, we discuss various theoretical aspects of the mechanisms for morphogen gradient formation, including stationary and transient dynamics, the effect of source delocalization, diffusion, different degradation mechanisms, and the role of spatial dimensions. Theoretical predictions are compared with experimental observations. In addition, we analyze the potential alternative mechanisms of the delivery of biological signals in embryo cells and tissues. Current challenges in understanding the mechanisms of morphogen gradients and future directions are also discussed.
Unlike most macromolecules that are homogeneously distributed in the bacterial cell, mRNAs that e... more Unlike most macromolecules that are homogeneously distributed in the bacterial cell, mRNAs that encode inner-membrane proteins can be concentrated near the inner membrane. Cotranslational insertion of the nascent peptide into the membrane brings the translating ribosome and the mRNA close to the membrane. This suggests that kinetic properties of translation can determine the spatial organization of these mRNAs and proteins, which can be modulated through posttranscriptional regulation. Here we use a simple stochastic model of translation to characterize the effect of mRNA properties on the dynamics and statistics of its spatial distribution. We show that a combination of the rate of translation initiation , the availability of secretory apparatuses, and the composition of the coding region determines the abundance of mRNAs near the membrane, as well as their residence time. We propose that the spatiotemporal dynamics of mRNAs can give rise to protein clusters on the membrane and determine their size distribution. translation | spatial organization | membrane proteins | protein clusters R ecent imaging techniques reveal the subcelllular locations of macromolecules in bacteria (1, 2). In contrast with the prevailing view of the bacterial cell as a spatially homogeneous reactor, these studies reveal an unexpected degree of subcellu-lar organization. In particular, some mRNAs have been shown to exhibit distinct localization patterns (3, 4). Large-scale assays demonstrate that mRNAs that code for inner-membrane binding proteins are highly enriched near the membrane (5). This is believed to be the result of cotranslational insertion, whereby a nascent peptide is inserted into the membrane as soon as a membrane-targeting signal or domain has been translated, bringing the translating ribosome and the entire polysome to the vicinity of the membrane (6, 7). Mechanisms of cotranslational insertion are under intense research due to their importance and universality (8, 9). Membrane association of mRNAs has also been suggested to affect the organization of the bacterial chromosome through " transertion, " the mechanism by which cotranslational insertion and transcription occur simultaneously (7, 10, 11). In bacteria, messenger RNAs are translated in the cytoplasm by diffusible ribosomes. Ribosomes bind the mRNA at a dedicated ribosomal binding site (RBS) at the upstream (5') end and translate the coding region until they reach a stop codon, where they release the newly synthesized protein and the mRNA. This suggests that translation can be localized near the membrane as long as one of the translating ribosomes is attached to a membrane-bound nascent protein. The rate of translation initiation varies widely among different genes and is influenced by physiological and environmental cues. Elongation rate is less sensitive, but rare codons may stall the elongating ribosome and slow down translation. Here we use a simple model, based on the totally asym-metric exclusion process (TASEP) (12, 13), to investigate how the dynamics of translation determines the spatial pattern of membrane-bound proteins and their mRNAs. We find that within the range of parameters typical to model bacteria, the spatial organization of mRNAs can range from a homogeneous distribution to a strong bias toward the membrane. We show how these patterns are determined by the organization of the coding sequence, the presence of slow codons, the rate of translation initiation, and the availability of auxiliary proteins required for membrane targeting (referred to as the secretory machinery). By calculating the distribution of the number of proteins placed together in the membrane, we suggest implications of mRNA localization on the organization of proteins on the membrane. We thus propose a mechanism for the formation of protein clusters in the membrane and investigate its implications on the regulation of their size distribution. Model We model an mRNA molecule as a one-dimensional lattice with L sites and open boundaries (Fig. 1A). Each site can be occupied by at most one ribosome. A ribosome enters the first site of the lattice at a rate α if that site is empty. Once in the lattice, they move unidirectionally, hopping from one lattice site to the next at a rate γ when it is empty. Ribosomes at the very last site exit the lattice at a rate β. This model, known as the TASEP, is a canonical model of nonequilibrium statistical mechanics and has been used—among many other things—to study aspects of translation (14–17). In the cell, the translation initiation rate α depends on the concentration of free ribosomes, which varies with the growth rate and stress level of the bacteria. The initiation rate of individual mRNAs depends on the affinity of ribosomes to their RBS, as well as their folding structure, which may interfere with ribo-some binding (18). In addition, the rate of translation initiation Significance Unlike their eukaryotic counterparts, bacterial cells are composed of a single compartment. This allows many rapidly diffusing macromolecules, such as proteins and mRNAs, to be evenly distributed in the cell. Important exceptions are proteins embedded in the cell membrane, which transport material and information across the membrane. Often these proteins attach to the membrane before their translation is complete, anchoring their mRNAs to the vicinity of the membrane. This coupling between translation and localization suggests that the dynamics of translation may shape the spatial organization. In this paper, we use a canonical model of nonequilibrium statistical physics to characterize this connection and show how tunable kinetic properties allow the cell to regulate the spatial organization of both mRNAs and proteins.
The journal of physical chemistry letters, Jan 7, 2016
Biological signaling is a crucial natural process that governs the formation of all multicellular... more Biological signaling is a crucial natural process that governs the formation of all multicellular organisms. It relies on efficient and fast transfer of information between different cells and tissues. It has been presumed for a long time that these long-distance communications in most systems can take place only indirectly via the diffusion of signaling molecules, also known as morphogens, through the extracellular fluid; however, recent experiments indicate that there is also an alternative direct delivery mechanism. It utilizes dynamic tubular cellular extensions, called cytonemes, that directly connect cells, supporting the flux of morphogens to specific locations. We present a first quantitative analysis of the cytoneme-mediated mechanism of biological signaling. Dynamics of the formation of signaling molecule profiles, which are also known as morphogen gradients, is discussed. It is found that the direct-delivery mechanism is more robust with respect to fluctuations in compari...
The journal of physical chemistry. B, Jan 17, 2016
Successful biological development via spatial and temporal regulations of cell differentiation re... more Successful biological development via spatial and temporal regulations of cell differentiation relies on the action of multiple signaling molecules that are known as morphogens. It is now well established that biological signaling molecules create nonuniform concentration profiles, called morphogen gradients, that activate different genes, leading to patterning in the developing organisms. The current view of the formation of morphogen gradients is that it is a result of complex reaction-diffusion processes that include production, diffusion, and degradation of signaling molecules. Recent studies also suggest that the degradation of morphogens is a critically important step in the whole process. We develop a theoretical model that allows us to investigate the role of a spatially varying degradation in the formation of morphogen gradients. Our analysis shows that the spatial inhomogeneities in degradation might strongly influence the dynamics of formation of signaling profiles. Physi...
Fundamental biological processes of development of tissues and organs in multicellular organisms ... more Fundamental biological processes of development of tissues and organs in multicellular organisms are governed by various signaling molecules, which are called morphogens. It is known that spatial and temporal variations in the concentration profiles of signaling molecules, which are frequently referred as morphogen gradients, lead to a cell differentiation via activating specific genes in a concentration-dependent manner. It is widely accepted that the establishment of the morphogen gradients involves multiple biochemical reactions and diffusion processes. One of the critical elements in the formation of morphogen gradients is a degradation of signaling molecules. We develop a new theoretical approach that provides a comprehensive description of the degradation mechanisms. It is based on the idea that the degradation works as an effective potential that drives the signaling molecules away from the source region. Utilizing the method of first-passage processes, the dynamics of the formation of morphogen gradients for various degradation mechanisms is explicitly evaluated. It is found that linear degradation processes lead to a dynamic behavior specified by times to form the morphogen gradients that depend linearly on the distance from the source. This is because the effective potential due to the degradation is quite strong. At the same time, nonlinear degradation mechanisms yield a quadratic scaling in the morphogen gradients formation times since the effective potentials are much weaker. Physical-chemical explanations of these phenomena are presented.
Journal of Statistical Mechanics: Theory and Experiment, 2015
Enzymatic molecules that actively support many cellular processes, including transport, cell divi... more Enzymatic molecules that actively support many cellular processes, including transport, cell division and cell motility, are known as motor proteins or molecular motors. Experimental studies indicate that they interact with each other and they frequently work together in large groups. To understand the mechanisms of collective behavior of motor proteins we study the effect of interactions in the transport of molecular motors along linear filaments. It is done by analyzing a recently introduced class of totally asymmetric exclusion processes that takes into account the intermolecular interactions via thermodynamically consistent approach. We develop a new theoretical method that allows us to compute analytically all dynamic properties of the system. Our analysis shows that correlations play important role in dynamics of interacting molecular motors. Surprisingly, we find that the correlations for repulsive interactions are weaker and more short-range than the correlations for the attractive interactions. In addition, it is shown that symmetry of interactions affect dynamic properties of molecular motors. The implications of these findings for motor proteins transport are discussed. Our theoretical predictions are tested by extensive Monte Carlo computer simulations.
Successful biological development via spatial regulation of cell differentiation relies on the ac... more Successful biological development via spatial regulation of cell differentiation relies on the action of multiple signaling molecules that are known as morphogens. It is now well-established that signaling molecules create non-uniform concentration profiles, morphogen gradients, that activate different genes, leading to patterning in the developing embryos. The current view of the formation of morphogen gradients is that it is a result of complex reaction-diffusion processes that include the strongly localized production, diffusion and uniform degradation of signaling molecules. However, multiple experimental studies also suggest that the production of morphogen in many cases is delocalized. We develop a theoretical method that allows us to investigate the role of the delocalization in the formation of morphogen gradients. The approach is based on discrete-state stochastic models that can be solved exactly for arbitrary production lengths and production rates of morphogen molecules....
Journal of physics. A, Mathematical and theoretical, Jan 13, 2015
Biological transport is supported by collective dynamics of enzymatic molecules that are called m... more Biological transport is supported by collective dynamics of enzymatic molecules that are called motor proteins or molecular motors. Experiments suggest that motor proteins interact locally via short-range potentials. We investigate the fundamental role of these interactions by analyzing a new class of totally asymmetric exclusion processes where interactions are accounted for in a thermodynamically consistent fashion. It allows us to connect explicitly microscopic features of motor proteins with their collective dynamic properties. Theoretical analysis that combines various mean-field calculations and computer simulations suggests that dynamic properties of molecular motors strongly depend on interactions, and correlations are stronger for interacting motor proteins. Surprisingly, it is found that there is an optimal strength of interactions (weak repulsion) that leads to a maximal particle flux. It is also argued that molecular motors transport is more sensitive to attractive inter...
The fundamental processes of biological development are governed by multiple signaling molecules ... more The fundamental processes of biological development are governed by multiple signaling molecules that create non-uniform concentration profiles known as morphogen gradients. It is widely believed that the establishment of morphogen gradients is a result of complex processes that involve diffusion and degradation of locally produced signaling molecules. We developed a multi-dimensional discrete-state stochastic approach for investigating the corresponding reaction-diffusion models. It provided a full analytical description for stationary profiles and for important dynamic properties such as local accumulation times, variances and mean first-passage times. The role of discreteness in developing of morphogen gradients is analyzed by comparing with available continuum descriptions. It is found that the continuum models prediction about multiple time scales near the source region in two-dimensional and three-dimensional systems is not supported in our analysis. Using ideas that view the degradation process as an effective potential, the effect of dimensionality on establishment of morphogen gradients is also discussed. In addition, we investigated how these reaction-diffusion processes are modified with changing the size of the source region.
The concept of continuous-time random walks (CTRW) is a generalization of ordinary random walk mo... more The concept of continuous-time random walks (CTRW) is a generalization of ordinary random walk models, and it is a powerful tool for investigating a broad spectrum of phenomena in natural, engineering, social and economic sciences. Recently, several theoretical approaches have been developed that allowed to analyze explicitly dynamics of CTRW at all times, which is critically important for understanding mechanisms of underlying phenomena. However, theoretical analysis has been done mostly for systems with a simple geometry. Here we extend the original method based on generalized master equations to analyze all-time dynamics of CTRW models on complex networks. Specific calculations are performed for models on lattices with branches and for models on coupled parallel-chain lattices. Exact expressions for velocities and dispersions are obtained. Generalized fluctuations theorems for CTRW models on complex networks are discussed.
One of the most important functions of immune T cells is to recognize the presence of the pathoge... more One of the most important functions of immune T cells is to recognize the presence of the pathogen-derived ligands and to quickly respond to them while at the same time not to respond to its own ligands. This is known as an absolute discrimination, and it is one of the most challenging phenomena to explain. The effectiveness of pathogen detection by T cell receptor (TCR) is limited by the chemical similarity of foreign and self-peptides and very low concentrations of foreign ligands. We propose a new mechanism of the absolute discrimination by T cells. It is suggested that the decision to activate or not to activate the immune response is controlled by the time to reach the stationary concentration of the TCR-ligand activated complex, which transfers the signal to downstream cellular biochemical networks. Our theoretical method models T-cell receptor phosphorylation events as a sequence of stochastic transitions between discrete biochemical states, and this allows us to explicitly d...
Cancer is a genetic disease that results from accumulation of unfavorable mutations. As soon as g... more Cancer is a genetic disease that results from accumulation of unfavorable mutations. As soon as genetic and epigenetic modifications associated with these mutations become strong enough, the uncontrolled tumor cell growth is initiated, eventually spreading through healthy tissues. Clarifying the dynamics of cancer initiation is thus critically important for understanding the molecular mechanisms of tumorigenesis. Here we present a new theoretical method to evaluate the dynamic processes associated with the cancer initiation. It is based on a discrete-state stochastic description of the formation of tumors as a fixation of cancerous mutations in tissues. Using a first-passage analysis the probabilities for the cancer to appear and the times before it happens, which are viewed as fixation probabilities and fixation times, respectively, are explicitly calculated. It is predicted that the slowest cancer initiation dynamics is observed for neutral mutations, while it is fast for both advantageous and, surprisingly, disadvantageous mutations. The method is applied for estimating the cancer initiation times from experimentally available lifetime cancer risks for different types of cancer. It is found that the higher probability of the cancer to occur does not necessary lead to the faster times of starting the cancer. Our theoretical analysis helps to clarify microscopic aspects of cancer initiation processes. It is well known that tumor cells are characterized by abnormal cell division rates, which is a result of mutations in cancer-susceptible genes (known as oncogenes) 1-4. Specifically, these mutations affect the regulation of cell proliferation and differentiation via activation of oncogenes or inactivation of tumor suppressor genes (TSGs) 2-5. Mutations are taking place randomly, and after several cellular replications some of them might occasionally lead to significant genetic and epigenetic alterations such that the normal cells behavior changes to the uncontrolled proliferation, eventually starting a cancer 3,6,7. After these cancer initiation events, rapid changes are taking place with a newly formed tumor being able to escape cellular control mechanisms, and the cancer progresses into more invasive forms 3,4,6,8,9. But this happens only after the initial stage of cancer succeeds, and thus it is critically important to understand the dynamics of cancer initiation 6. Human tissues and organs are composed of heterogeneous mixtures of cells: not all cells are equal in their potential to proliferate. An important role in tissue maintenance and repair is played by a population of so-called stem cells 10. These cells are characterized by their ability to self-renew and make more stem cells or ability to produce differentiated progenitor cells 11. Epithelial tissues are also known for subdivision into compartments where homeostatic mechanism, a balance between self-renewal and differentiation, maintains the constant cell number. Cancer appears in such compartments, breaking the homeostatic tissue equilibrium. However, having only a single mutated cell in the compartment does not lead to cancer. The cancer initiation event generally is associated with a fixation of one or several mutations, i.e., when all cells in the compartment become mutated, or when a significant fraction of them is mutated, producing noticeable genetic and epigenetic changes 6,9. One of the most important quantities that determines if the person gets a cancer is a cancer lifetime risk. It refers to a probability of being diagnosed with or dying from cancer during the person's lifespan. Lifetime risks strongly depend on the type of cancer. For example, a person's risk of getting a lung cancer is more than 11 times higher than of developing of a brain cancer, and 8 times greater than that of a stomach cancer 12,13. Various studies have attributed the differences in cancer rates to environmental risk factors, such as smoking, bad dietary habits
Understanding mechanisms of bacterial eradication is critically important for overcoming failures... more Understanding mechanisms of bacterial eradication is critically important for overcoming failures of antibiotic treatments. Current studies suggest that the clearance of large bacterial populations proceeds deterministically, while for smaller populations, the stochastic effects become more relevant. Here, we develop a theoretical approach to investigate the bacterial population dynamics under the effect of antibiotic drugs using a method of first-passage processes. It allows us to explicitly evaluate the most important characteristics of bacterial clearance dynamics such as extinction probabilities and extinction times. The new meaning of minimal inhibitory concentrations for stochastic clearance of bacterial populations is also discussed. In addition, we investigate the effect of fluctuations in population growth rates on the dynamics of bacterial eradication. It is found that extinction probabilities and extinction times generally do not correlate with each other when random fluctuations in the growth rates are taking place. Unexpectedly, for a significant range of parameters, the extinction times increase due to these fluctuations, indicating a slowing in the bacterial clearance dynamics. It is argued that this might be one of the initial steps in the pathway for the development of antibiotic resistance. Furthermore, it is suggested that extinction times is a convenient measure of bacterial tolerance.
Gastrulation is a fundamental phase during the biological development of most animals when a sing... more Gastrulation is a fundamental phase during the biological development of most animals when a single layer of identical embryo cells is transformed into a three-layer structure, from which the organs start to develop. Despite a remarkable progress in quantifying the gastrulation processes, molecular mechanisms of these processes remain not well understood. Here we theoretically investigate early spatial patterning in a geometrically confined colony of embryonic stem cells. Using a reaction-diffusion model, a role of Bone-Morphogenetic Protein 4 (BMP4) signaling pathway in gastrulation is specifically analyzed. Our results show that for slow diffusion rates of BMP4 molecules, a new length scale appears, which is independent of the size of the system. This length scale separates the central region of the colony with uniform low concentrations of BMP molecules from the region near the colony edge where the concentration of signaling molecules is elevated. The roles of different components of the signaling pathway are also explained. Theoretical results are consistent with recent in vitro experiments, providing microscopic explanations for some features of early embryonic spatial patterning. Physical-chemical mechanisms of these processes are discussed.
Mechanisms of the formation of biological signaling profiles
The formation and growth of multi-cellular organisms and tissues from several genetically identic... more The formation and growth of multi-cellular organisms and tissues from several genetically identical embryo cells is one of the most fundamental natural phenomena. These processes are stimulated and governed by multiple biological signaling molecules, which are also called morphogens. Embryo cells are able to read and pass genetic information by measuring the non-uniform concentration profiles of signaling molecules. It is widely believed that the establishment of concentration profiles of morphogens, commonly referred as morphogen gradients, is a result of complex biophysical and biochemical processes that might involve diffusion and degradation of locally produced signaling molecules. In this review, we discuss various theoretical aspects of the mechanisms for morphogen gradient formation, including stationary and transient dynamics, the effect of source delocalization, diffusion, different degradation mechanisms, and the role of spatial dimensions. Theoretical predictions are compared with experimental observations. In addition, we analyze the potential alternative mechanisms of the delivery of biological signals in embryo cells and tissues. Current challenges in understanding the mechanisms of morphogen gradients and future directions are also discussed.
Unlike most macromolecules that are homogeneously distributed in the bacterial cell, mRNAs that e... more Unlike most macromolecules that are homogeneously distributed in the bacterial cell, mRNAs that encode inner-membrane proteins can be concentrated near the inner membrane. Cotranslational insertion of the nascent peptide into the membrane brings the translating ribosome and the mRNA close to the membrane. This suggests that kinetic properties of translation can determine the spatial organization of these mRNAs and proteins, which can be modulated through posttranscriptional regulation. Here we use a simple stochastic model of translation to characterize the effect of mRNA properties on the dynamics and statistics of its spatial distribution. We show that a combination of the rate of translation initiation , the availability of secretory apparatuses, and the composition of the coding region determines the abundance of mRNAs near the membrane, as well as their residence time. We propose that the spatiotemporal dynamics of mRNAs can give rise to protein clusters on the membrane and determine their size distribution. translation | spatial organization | membrane proteins | protein clusters R ecent imaging techniques reveal the subcelllular locations of macromolecules in bacteria (1, 2). In contrast with the prevailing view of the bacterial cell as a spatially homogeneous reactor, these studies reveal an unexpected degree of subcellu-lar organization. In particular, some mRNAs have been shown to exhibit distinct localization patterns (3, 4). Large-scale assays demonstrate that mRNAs that code for inner-membrane binding proteins are highly enriched near the membrane (5). This is believed to be the result of cotranslational insertion, whereby a nascent peptide is inserted into the membrane as soon as a membrane-targeting signal or domain has been translated, bringing the translating ribosome and the entire polysome to the vicinity of the membrane (6, 7). Mechanisms of cotranslational insertion are under intense research due to their importance and universality (8, 9). Membrane association of mRNAs has also been suggested to affect the organization of the bacterial chromosome through " transertion, " the mechanism by which cotranslational insertion and transcription occur simultaneously (7, 10, 11). In bacteria, messenger RNAs are translated in the cytoplasm by diffusible ribosomes. Ribosomes bind the mRNA at a dedicated ribosomal binding site (RBS) at the upstream (5') end and translate the coding region until they reach a stop codon, where they release the newly synthesized protein and the mRNA. This suggests that translation can be localized near the membrane as long as one of the translating ribosomes is attached to a membrane-bound nascent protein. The rate of translation initiation varies widely among different genes and is influenced by physiological and environmental cues. Elongation rate is less sensitive, but rare codons may stall the elongating ribosome and slow down translation. Here we use a simple model, based on the totally asym-metric exclusion process (TASEP) (12, 13), to investigate how the dynamics of translation determines the spatial pattern of membrane-bound proteins and their mRNAs. We find that within the range of parameters typical to model bacteria, the spatial organization of mRNAs can range from a homogeneous distribution to a strong bias toward the membrane. We show how these patterns are determined by the organization of the coding sequence, the presence of slow codons, the rate of translation initiation, and the availability of auxiliary proteins required for membrane targeting (referred to as the secretory machinery). By calculating the distribution of the number of proteins placed together in the membrane, we suggest implications of mRNA localization on the organization of proteins on the membrane. We thus propose a mechanism for the formation of protein clusters in the membrane and investigate its implications on the regulation of their size distribution. Model We model an mRNA molecule as a one-dimensional lattice with L sites and open boundaries (Fig. 1A). Each site can be occupied by at most one ribosome. A ribosome enters the first site of the lattice at a rate α if that site is empty. Once in the lattice, they move unidirectionally, hopping from one lattice site to the next at a rate γ when it is empty. Ribosomes at the very last site exit the lattice at a rate β. This model, known as the TASEP, is a canonical model of nonequilibrium statistical mechanics and has been used—among many other things—to study aspects of translation (14–17). In the cell, the translation initiation rate α depends on the concentration of free ribosomes, which varies with the growth rate and stress level of the bacteria. The initiation rate of individual mRNAs depends on the affinity of ribosomes to their RBS, as well as their folding structure, which may interfere with ribo-some binding (18). In addition, the rate of translation initiation Significance Unlike their eukaryotic counterparts, bacterial cells are composed of a single compartment. This allows many rapidly diffusing macromolecules, such as proteins and mRNAs, to be evenly distributed in the cell. Important exceptions are proteins embedded in the cell membrane, which transport material and information across the membrane. Often these proteins attach to the membrane before their translation is complete, anchoring their mRNAs to the vicinity of the membrane. This coupling between translation and localization suggests that the dynamics of translation may shape the spatial organization. In this paper, we use a canonical model of nonequilibrium statistical physics to characterize this connection and show how tunable kinetic properties allow the cell to regulate the spatial organization of both mRNAs and proteins.
The journal of physical chemistry letters, Jan 7, 2016
Biological signaling is a crucial natural process that governs the formation of all multicellular... more Biological signaling is a crucial natural process that governs the formation of all multicellular organisms. It relies on efficient and fast transfer of information between different cells and tissues. It has been presumed for a long time that these long-distance communications in most systems can take place only indirectly via the diffusion of signaling molecules, also known as morphogens, through the extracellular fluid; however, recent experiments indicate that there is also an alternative direct delivery mechanism. It utilizes dynamic tubular cellular extensions, called cytonemes, that directly connect cells, supporting the flux of morphogens to specific locations. We present a first quantitative analysis of the cytoneme-mediated mechanism of biological signaling. Dynamics of the formation of signaling molecule profiles, which are also known as morphogen gradients, is discussed. It is found that the direct-delivery mechanism is more robust with respect to fluctuations in compari...
The journal of physical chemistry. B, Jan 17, 2016
Successful biological development via spatial and temporal regulations of cell differentiation re... more Successful biological development via spatial and temporal regulations of cell differentiation relies on the action of multiple signaling molecules that are known as morphogens. It is now well established that biological signaling molecules create nonuniform concentration profiles, called morphogen gradients, that activate different genes, leading to patterning in the developing organisms. The current view of the formation of morphogen gradients is that it is a result of complex reaction-diffusion processes that include production, diffusion, and degradation of signaling molecules. Recent studies also suggest that the degradation of morphogens is a critically important step in the whole process. We develop a theoretical model that allows us to investigate the role of a spatially varying degradation in the formation of morphogen gradients. Our analysis shows that the spatial inhomogeneities in degradation might strongly influence the dynamics of formation of signaling profiles. Physi...
Fundamental biological processes of development of tissues and organs in multicellular organisms ... more Fundamental biological processes of development of tissues and organs in multicellular organisms are governed by various signaling molecules, which are called morphogens. It is known that spatial and temporal variations in the concentration profiles of signaling molecules, which are frequently referred as morphogen gradients, lead to a cell differentiation via activating specific genes in a concentration-dependent manner. It is widely accepted that the establishment of the morphogen gradients involves multiple biochemical reactions and diffusion processes. One of the critical elements in the formation of morphogen gradients is a degradation of signaling molecules. We develop a new theoretical approach that provides a comprehensive description of the degradation mechanisms. It is based on the idea that the degradation works as an effective potential that drives the signaling molecules away from the source region. Utilizing the method of first-passage processes, the dynamics of the formation of morphogen gradients for various degradation mechanisms is explicitly evaluated. It is found that linear degradation processes lead to a dynamic behavior specified by times to form the morphogen gradients that depend linearly on the distance from the source. This is because the effective potential due to the degradation is quite strong. At the same time, nonlinear degradation mechanisms yield a quadratic scaling in the morphogen gradients formation times since the effective potentials are much weaker. Physical-chemical explanations of these phenomena are presented.
Journal of Statistical Mechanics: Theory and Experiment, 2015
Enzymatic molecules that actively support many cellular processes, including transport, cell divi... more Enzymatic molecules that actively support many cellular processes, including transport, cell division and cell motility, are known as motor proteins or molecular motors. Experimental studies indicate that they interact with each other and they frequently work together in large groups. To understand the mechanisms of collective behavior of motor proteins we study the effect of interactions in the transport of molecular motors along linear filaments. It is done by analyzing a recently introduced class of totally asymmetric exclusion processes that takes into account the intermolecular interactions via thermodynamically consistent approach. We develop a new theoretical method that allows us to compute analytically all dynamic properties of the system. Our analysis shows that correlations play important role in dynamics of interacting molecular motors. Surprisingly, we find that the correlations for repulsive interactions are weaker and more short-range than the correlations for the attractive interactions. In addition, it is shown that symmetry of interactions affect dynamic properties of molecular motors. The implications of these findings for motor proteins transport are discussed. Our theoretical predictions are tested by extensive Monte Carlo computer simulations.
Successful biological development via spatial regulation of cell differentiation relies on the ac... more Successful biological development via spatial regulation of cell differentiation relies on the action of multiple signaling molecules that are known as morphogens. It is now well-established that signaling molecules create non-uniform concentration profiles, morphogen gradients, that activate different genes, leading to patterning in the developing embryos. The current view of the formation of morphogen gradients is that it is a result of complex reaction-diffusion processes that include the strongly localized production, diffusion and uniform degradation of signaling molecules. However, multiple experimental studies also suggest that the production of morphogen in many cases is delocalized. We develop a theoretical method that allows us to investigate the role of the delocalization in the formation of morphogen gradients. The approach is based on discrete-state stochastic models that can be solved exactly for arbitrary production lengths and production rates of morphogen molecules....
Journal of physics. A, Mathematical and theoretical, Jan 13, 2015
Biological transport is supported by collective dynamics of enzymatic molecules that are called m... more Biological transport is supported by collective dynamics of enzymatic molecules that are called motor proteins or molecular motors. Experiments suggest that motor proteins interact locally via short-range potentials. We investigate the fundamental role of these interactions by analyzing a new class of totally asymmetric exclusion processes where interactions are accounted for in a thermodynamically consistent fashion. It allows us to connect explicitly microscopic features of motor proteins with their collective dynamic properties. Theoretical analysis that combines various mean-field calculations and computer simulations suggests that dynamic properties of molecular motors strongly depend on interactions, and correlations are stronger for interacting motor proteins. Surprisingly, it is found that there is an optimal strength of interactions (weak repulsion) that leads to a maximal particle flux. It is also argued that molecular motors transport is more sensitive to attractive inter...
The fundamental processes of biological development are governed by multiple signaling molecules ... more The fundamental processes of biological development are governed by multiple signaling molecules that create non-uniform concentration profiles known as morphogen gradients. It is widely believed that the establishment of morphogen gradients is a result of complex processes that involve diffusion and degradation of locally produced signaling molecules. We developed a multi-dimensional discrete-state stochastic approach for investigating the corresponding reaction-diffusion models. It provided a full analytical description for stationary profiles and for important dynamic properties such as local accumulation times, variances and mean first-passage times. The role of discreteness in developing of morphogen gradients is analyzed by comparing with available continuum descriptions. It is found that the continuum models prediction about multiple time scales near the source region in two-dimensional and three-dimensional systems is not supported in our analysis. Using ideas that view the degradation process as an effective potential, the effect of dimensionality on establishment of morphogen gradients is also discussed. In addition, we investigated how these reaction-diffusion processes are modified with changing the size of the source region.
The concept of continuous-time random walks (CTRW) is a generalization of ordinary random walk mo... more The concept of continuous-time random walks (CTRW) is a generalization of ordinary random walk models, and it is a powerful tool for investigating a broad spectrum of phenomena in natural, engineering, social and economic sciences. Recently, several theoretical approaches have been developed that allowed to analyze explicitly dynamics of CTRW at all times, which is critically important for understanding mechanisms of underlying phenomena. However, theoretical analysis has been done mostly for systems with a simple geometry. Here we extend the original method based on generalized master equations to analyze all-time dynamics of CTRW models on complex networks. Specific calculations are performed for models on lattices with branches and for models on coupled parallel-chain lattices. Exact expressions for velocities and dispersions are obtained. Generalized fluctuations theorems for CTRW models on complex networks are discussed.
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Papers by Hamid Teimouri