What is the minimal set of cell-biological ingredients needed to generate a Golgi apparatus? The ... more What is the minimal set of cell-biological ingredients needed to generate a Golgi apparatus? The compositions of eukaryotic organelles arise through a process of molecular exchange via vesicle traffic. Here we statistically sample tens of thousands of homeostatic vesicle traffic networks generated by realistic molecular rules governing vesicle budding and fusion. Remarkably, the plurality of these networks contain chains of compartments that undergo creation, compositional maturation, and dissipation, coupled by molecular recycling along retrograde vesicles. This motif precisely matches the cisternal maturation model of the Golgi, which was developed to explain many observed aspects of the eukaryotic secretory pathway. In our analysis cisternal maturation is a robust consequence of vesicle traffic homeostasis, independent of the underlying details of molecular interactions or spatial stacking. This architecture may have been exapted rather than selected for its role in the secretion of large cargo.
Vesicle traffic systems (VTSs) transport cargo among the intracellular compartments of eukaryotic... more Vesicle traffic systems (VTSs) transport cargo among the intracellular compartments of eukaryotic cells. The compartments are viewed as nodes that are labeled by their chemical identity and the transport vesicles are similarly viewed as labeled edges between the nodes. Several interesting questions about VTSs translate to combinatorial search and synthesis problems. We present novel encodings for the problems based on Boolean satisfiability (SAT), satisfiability modulo theories and quantified Boolean formula of the properties over vesicle traffic systems. We have implemented the presented encodings in a tool that searches for the networks that satisfy properties related to transport consistency conditions using these solvers. In our numerical experiments, we show that our tool can search for networks of sizes that are relevant to real cellular systems. Our work illustrates the potential of novel biological applications of SAT solving technology.
What is the minimal set of cell-biological ingredients needed to generate a Golgi apparatus? The ... more What is the minimal set of cell-biological ingredients needed to generate a Golgi apparatus? The compositions of eukaryotic organelles arise through a process of molecular exchange via vesicle traffic. Here we statistically sample tens of thousands of homeostatic vesicle traffic networks generated by realistic molecular rules governing vesicle budding and fusion. Remarkably, the plurality of these networks contain chains of compartments that undergo creation, compositional maturation, and dissipation, coupled by molecular recycling along retrograde vesicles. This motif precisely matches the cisternal maturation model of the Golgi, which was developed to explain many observed aspects of the eukaryotic secretory pathway. In our analysis cisternal maturation is a robust consequence of vesicle traffic homeostasis, independent of the underlying details of molecular interactions or spatial stacking. This architecture may have been exapted rather than selected for its role in the secretion of large cargo.
Eukaryotic cells use small membrane-enclosed vesicles to transport molecular cargo between intrac... more Eukaryotic cells use small membrane-enclosed vesicles to transport molecular cargo between intracellular compartments. Interactions between molecules on vesicles and compartments determine the source and target compartment of each vesicle type. The set of compartment and vesicle types in a cell define the nodes and edges of a transport graph known as the vesicle traffic network. The transmembrane SNARE proteins that regulate vesicle fusion to target compartments travel in cycles through the transport graph, but the paths they follow must be tightly regulated to avoid aberrant vesicle fusion. Here we use graph-theoretic ideas to understand how such molecular constraints place constraints on the structure of the transport graph. We identify edge connectivity (the minimum number of edges that must be removed to disconnect a graph) as a key determinant that separates allowed and disallowed types of transport graphs. As we increase the flexibility of molecular regulation, the required edge connectivity decreases, so more types of vesicle transport graphs are allowed. These results can be used to aid the discovery of new modes of molecular regulation and new vesicle traffic pathways.
Background: Multicellular organisms are characterized by a wide diversity of forms and complexity... more Background: Multicellular organisms are characterized by a wide diversity of forms and complexity despite a restricted set of key molecules and mechanisms at the base of organismal development. Development combines three basic processes-asymmetric cell division, signaling and gene regulation-in a multitude of ways to create this overwhelming diversity of multicellular life-forms. Here, we use a generative model to test the limits to which such processes can be combined to generate multiple differentiation paths during development, and attempt to chart the diversity of multicellular organisms generated. Results: We sample millions of biologically feasible developmental schemes, allowing us to comment on the statistical properties of cell-differentiation trajectories they produce. We characterize model-generated 'organisms' using the graph topology of their cell-type lineage maps. Remarkably, tree-type lineage differentiation maps are the rarest in our data. Additionally, a majority of the 'organisms' generated by our model appear to be endowed with the ability to regenerate using pluripotent cells. Conclusions: Our results indicate that, in contrast to common views, cell-type lineage graphs are unlikely to be tree-like. Instead, they are more likely to be directed acyclic graphs, with multiple lineages converging on the same terminal cell-type. Furthermore, the high incidence of pluripotent cells in model-generated organisms stands in line with the long-standing hypothesis that whole body regeneration is an epiphenomenon of development. We discuss experimentally testable predictions of our model, and some ways to adapt the generative framework to test additional hypotheses about general features of development.
Rapid advance of experimental techniques provides an unprecedented in-depth view into complex dev... more Rapid advance of experimental techniques provides an unprecedented in-depth view into complex developmental processes. Still, little is known on how the complexity of multicellular organisms evolved by elaborating developmental programs and inventing new cell types. A hurdle to understanding developmental evolution is the difficulty of even describing the intertwined network of spatiotemporal processes underlying the development of complex multicellular organisms. Nonetheless, an overview of developmental trajectories can be obtained from cell type lineage maps. Here, we propose that these lineage maps can also reveal how developmental programs evolve: the modes of evolving new cell types in an organism should be visible in its developmental trajectories, and therefore in the geometry of its cell type lineage map. This idea is demonstrated using a parsimonious generative model of developmental programs, which allows us to reliably survey the universe of all possible programs and examine their topological features. We find that, contrary to belief, tree-like lineage maps are rare and lineage maps of complex multicellular organisms are likely to be directed acyclic graphs where multiple developmental routes can converge on the same cell type. While cell type evolution prescribes what developmental programs come into existence, natural selection prunes those programs which produce low-functioning organisms. Our model indicates that additionally, lineage map topologies are correlated with such a functional property: the ability of organisms to regenerate. SIGNIFICANCE Cell type invention is a chief process in the evolution of developmental programs. Traditionally, developmental trajectories are represented as cell type lineage maps. Here we propose that systematic analysis of these maps, in particular their topology, should reveal traces of the manner in which cell types were invented. This is illustrated using a generative model of developmental programs, which allows one to robustly survey the geometry of cell lineage maps and link them to modes of cell type invention. We suggest that predictions made by such mathematical models, in conjunction with surveys of real cell-lineage maps of different multicellular lineages could uncover mechanisms underlying evolution of developmental programs. STATISTICS OF LINEAGE MAPS REFLECT DEVELOPMENTAL EVOLUTION How can one understand the astounding richness of life forms?-While molecules and mechanisms of biological development are conserved within each multicellular lineage (1), these lineages are extraordinarily diverse; land plants and animals include many thousands to millions of species (2). This diversity is in part due to the distinct cell types present in different organisms. And in this sense, developmental programs evolve by inventing new cell types (3). While ancestral lineages likely resembled the simplest multicellular organisms alive today, such as Volvox carterii that has two cell types (4), the extant diversity of today's organisms ranges from those with a few cell types to those with hundreds. What molecular mechanisms and logic could produce such diversity remains a persistent question in development. One way to tackle this question is by comparing developmental programs across species of various levels of complexity. Analyzing developmental genes in order to see how gene families have expanded is fairly easy. But we now realize that this is far from sufficient, because genes interact combinatorially to express cell types. For example, looking at genomes of sponges, one might be tempted to conclude that they posses neurons since they have all the necessary components to make synapses. In reality, however, it was only in the bilaterian/cnidarian ancestor that these components were arranged in a manner that expresses the synapse (3). This example is a reminder that developmental programs are functions or algorithms for the assembly of organisms. Long ago it was recognized by Cantor that there are always many more conceivable functions than combinations of variables (5). Perhaps the simplest example-which is used as a
Vesicle Traffic Systems (VTSs) are the material transport mechanisms among the compartments insid... more Vesicle Traffic Systems (VTSs) are the material transport mechanisms among the compartments inside the biological cells. The compartments are viewed as nodes that are labeled with the containing chemicals and the transport channels are similarly viewed as labeled edges between the nodes. Understanding VTSs is an ongoing area of research and for many cells they are partially known. For example, there may be undiscovered edges, nodes, or their labels in a VTS of a cell. It has been speculated that there are properties that the VTSs must satisfy. For example, stability, i.e., every chemical that is leaving a compartment comes back. Many synthesis questions may arise in this scenario, where we want to complete a partially known VTS under a given property. In the paper, we present novel encodings of the above questions into the QBF (quantified Boolean formula) satisfiability problems. We have implemented the encodings in a highly configurable tool and applied to a couple of found-in-nature VTSs and several synthetic graphs. Our results demonstrate that our method can scale up to the graphs of interest.
Molecular and Biochemical Parasitology, Sep 1, 2016
Microbial eukaryotes present a stunning diversity of endomembrane organization. From specialized ... more Microbial eukaryotes present a stunning diversity of endomembrane organization. From specialized secretory organelles such as the rhoptries and micronemes of apicomplexans, to peroxisome-derived metabolic compartments such as the glycosomes of kinetoplastids, different microbial taxa have explored different solutions to the compartmentalization and processing of cargo. The basic secretory and endocytic system, comprising the ER, Golgi, endosomes, and plasma membrane, as well as diverse taxonspecific specialized endomembrane organelles, are coupled by a complex network of cargo transport via vesicle traffic. It is tempting to connect form to function, ascribing biochemical roles to each compartment and vesicle of such a system. Here we argue that traffic systems of high complexity could arise through non-adaptive mechanisms via purely physical constraints, and subsequently be exapted for various taxon-specific functions. Our argument is based on a Boolean mathematical model of vesicle traffic: we specify rules of how compartments exchange vesicles; these rules then generate hypothetical cells with different types of endomembrane organization. Though one could imagine a large number of hypothetical vesicle traffic systems, very few of these are consistent with molecular interactions. Such molecular constraints are the bottleneck of a metaphorical hourglass, and the rules that make it through the bottleneck are expected to generate cells with many special properties. Sampling at random from among such rules represents an evolutionary null hypothesis: any properties of the resulting cells must be non-adaptive. We show by example that vesicle traffic systems generated in this random manner are reminiscent of the complex trafficking apparatus of real cells.
Eukaryotic cells use small membrane-enclosed vesicles to transport molecular cargo between intrac... more Eukaryotic cells use small membrane-enclosed vesicles to transport molecular cargo between intracellular compartments. Interactions between molecules on vesicles and compartments determine the source and target compartment of each vesicle type. The set of compartment and vesicle types in a cell define the nodes and edges of a transport graph known as the vesicle traffic network. The transmembrane SNARE proteins that regulate vesicle fusion to target compartments travel in cycles through the transport graph, but the paths they follow must be tightly regulated to avoid aberrant vesicle fusion. Here we use graph-theoretic ideas to understand how such molecular constraints place constraints on the structure of the transport graph. We identify edge connectivity (the minimum number of edges that must be removed to disconnect a graph) as a key determinant that separates allowed and disallowed types of transport graphs. As we increase the flexibility of molecular regulation, the required edge connectivity decreases, so more types of vesicle transport graphs are allowed. These results can be used to aid the discovery of new modes of molecular regulation and new vesicle traffic pathways.
Vesicle Traffic Systems (VTSs) are the material transport mechanisms among the compartments insid... more Vesicle Traffic Systems (VTSs) are the material transport mechanisms among the compartments inside the biological cells. The compartments are viewed as nodes that are labeled with the containing chemicals and the transport channels are similarly viewed as labeled edges between the nodes. Understanding VTSs is an ongoing area of research and for many cells they are partially known. For example, there may be undiscovered edges, nodes, or their labels in a VTS of a cell. It has been speculated that there are properties that the VTSs must satisfy. For example, stability, i.e., every chemical that is leaving a compartment comes back. Many synthesis questions may arise in this scenario, where we want to complete a partially known VTS under a given property. In the paper, we present novel encodings of the above questions into the QBF (quantified Boolean formula) satisfiability problems. We have implemented the encodings in a highly configurable tool and applied to a couple of found-in-nature VTSs and several synthetic graphs. Our results demonstrate that our method can scale up to the graphs of interest.
Vesicle traffic systems (VTSs) transport cargo among the intracellular compartments of eukaryotic... more Vesicle traffic systems (VTSs) transport cargo among the intracellular compartments of eukaryotic cells. The compartments are viewed as nodes that are labeled by their chemical identity and the transport vesicles are similarly viewed as labeled edges between the nodes. Several interesting questions about VTSs translate to combinatorial search and synthesis problems. We present novel encodings for the problems based on Boolean satisfiability (SAT), satisfiability modulo theories and quantified Boolean formula of the properties over vesicle traffic systems. We have implemented the presented encodings in a tool that searches for the networks that satisfy properties related to transport consistency conditions using these solvers. In our numerical experiments, we show that our tool can search for networks of sizes that are relevant to real cellular systems. Our work illustrates the potential of novel biological applications of SAT solving technology.
What is the minimal set of cell-biological ingredients needed to generate a Golgi apparatus? The ... more What is the minimal set of cell-biological ingredients needed to generate a Golgi apparatus? The compositions of eukaryotic organelles arise through a process of molecular exchange via vesicle traffic. Here we statistically sample tens of thousands of homeostatic vesicle traffic networks generated by realistic molecular rules governing vesicle budding and fusion. Remarkably, the plurality of these networks contain chains of compartments that undergo creation, compositional maturation, and dissipation, coupled by molecular recycling along retrograde vesicles. This motif precisely matches the cisternal maturation model of the Golgi, which was developed to explain many observed aspects of the eukaryotic secretory pathway. In our analysis cisternal maturation is a robust consequence of vesicle traffic homeostasis, independent of the underlying details of molecular interactions or spatial stacking. This architecture may have been exapted rather than selected for its role in the secretion of large cargo.
Microbial eukaryotes present a stunning diversity of endomembrane organization. From specialized ... more Microbial eukaryotes present a stunning diversity of endomembrane organization. From specialized secretory organelles such as the rhoptries and micronemes of apicomplexans, to peroxisome-derived metabolic compartments such as the glycosomes of kinetoplastids, different microbial taxa have explored different solutions to the compartmentalization and processing of cargo. The basic secretory and endocytic system, comprising the ER, Golgi, endosomes, and plasma membrane, as well as diverse taxonspecific specialized endomembrane organelles, are coupled by a complex network of cargo transport via vesicle traffic. It is tempting to connect form to function, ascribing biochemical roles to each compartment and vesicle of such a system. Here we argue that traffic systems of high complexity could arise through non-adaptive mechanisms via purely physical constraints, and subsequently be exapted for various taxon-specific functions. Our argument is based on a Boolean mathematical model of vesicle traffic: we specify rules of how compartments exchange vesicles; these rules then generate hypothetical cells with different types of endomembrane organization. Though one could imagine a large number of hypothetical vesicle traffic systems, very few of these are consistent with molecular interactions. Such molecular constraints are the bottleneck of a metaphorical hourglass, and the rules that make it through the bottleneck are expected to generate cells with many special properties. Sampling at random from among such rules represents an evolutionary null hypothesis: any properties of the resulting cells must be non-adaptive. We show by example that vesicle traffic systems generated in this random manner are reminiscent of the complex trafficking apparatus of real cells.
What is the minimal set of cell-biological ingredients needed to generate a Golgi apparatus? The ... more What is the minimal set of cell-biological ingredients needed to generate a Golgi apparatus? The compositions of eukaryotic organelles arise through a process of molecular exchange via vesicle traffic. Here we statistically sample tens of thousands of homeostatic vesicle traffic networks generated by realistic molecular rules governing vesicle budding and fusion. Remarkably, the plurality of these networks contain chains of compartments that undergo creation, compositional maturation, and dissipation, coupled by molecular recycling along retrograde vesicles. This motif precisely matches the cisternal maturation model of the Golgi, which was developed to explain many observed aspects of the eukaryotic secretory pathway. In our analysis cisternal maturation is a robust consequence of vesicle traffic homeostasis, independent of the underlying details of molecular interactions or spatial stacking. This architecture may have been exapted rather than selected for its role in the secretion...
What is the minimal set of cell-biological ingredients needed to generate a Golgi apparatus? The ... more What is the minimal set of cell-biological ingredients needed to generate a Golgi apparatus? The compositions of eukaryotic organelles arise through a process of molecular exchange via vesicle traffic. Here we statistically sample tens of thousands of homeostatic vesicle traffic networks generated by realistic molecular rules governing vesicle budding and fusion. Remarkably, the plurality of these networks contain chains of compartments that undergo creation, compositional maturation, and dissipation, coupled by molecular recycling along retrograde vesicles. This motif precisely matches the cisternal maturation model of the Golgi, which was developed to explain many observed aspects of the eukaryotic secretory pathway. In our analysis cisternal maturation is a robust consequence of vesicle traffic homeostasis, independent of the underlying details of molecular interactions or spatial stacking. This architecture may have been exapted rather than selected for its role in the secretion of large cargo.
Vesicle traffic systems (VTSs) transport cargo among the intracellular compartments of eukaryotic... more Vesicle traffic systems (VTSs) transport cargo among the intracellular compartments of eukaryotic cells. The compartments are viewed as nodes that are labeled by their chemical identity and the transport vesicles are similarly viewed as labeled edges between the nodes. Several interesting questions about VTSs translate to combinatorial search and synthesis problems. We present novel encodings for the problems based on Boolean satisfiability (SAT), satisfiability modulo theories and quantified Boolean formula of the properties over vesicle traffic systems. We have implemented the presented encodings in a tool that searches for the networks that satisfy properties related to transport consistency conditions using these solvers. In our numerical experiments, we show that our tool can search for networks of sizes that are relevant to real cellular systems. Our work illustrates the potential of novel biological applications of SAT solving technology.
What is the minimal set of cell-biological ingredients needed to generate a Golgi apparatus? The ... more What is the minimal set of cell-biological ingredients needed to generate a Golgi apparatus? The compositions of eukaryotic organelles arise through a process of molecular exchange via vesicle traffic. Here we statistically sample tens of thousands of homeostatic vesicle traffic networks generated by realistic molecular rules governing vesicle budding and fusion. Remarkably, the plurality of these networks contain chains of compartments that undergo creation, compositional maturation, and dissipation, coupled by molecular recycling along retrograde vesicles. This motif precisely matches the cisternal maturation model of the Golgi, which was developed to explain many observed aspects of the eukaryotic secretory pathway. In our analysis cisternal maturation is a robust consequence of vesicle traffic homeostasis, independent of the underlying details of molecular interactions or spatial stacking. This architecture may have been exapted rather than selected for its role in the secretion of large cargo.
Eukaryotic cells use small membrane-enclosed vesicles to transport molecular cargo between intrac... more Eukaryotic cells use small membrane-enclosed vesicles to transport molecular cargo between intracellular compartments. Interactions between molecules on vesicles and compartments determine the source and target compartment of each vesicle type. The set of compartment and vesicle types in a cell define the nodes and edges of a transport graph known as the vesicle traffic network. The transmembrane SNARE proteins that regulate vesicle fusion to target compartments travel in cycles through the transport graph, but the paths they follow must be tightly regulated to avoid aberrant vesicle fusion. Here we use graph-theoretic ideas to understand how such molecular constraints place constraints on the structure of the transport graph. We identify edge connectivity (the minimum number of edges that must be removed to disconnect a graph) as a key determinant that separates allowed and disallowed types of transport graphs. As we increase the flexibility of molecular regulation, the required edge connectivity decreases, so more types of vesicle transport graphs are allowed. These results can be used to aid the discovery of new modes of molecular regulation and new vesicle traffic pathways.
Background: Multicellular organisms are characterized by a wide diversity of forms and complexity... more Background: Multicellular organisms are characterized by a wide diversity of forms and complexity despite a restricted set of key molecules and mechanisms at the base of organismal development. Development combines three basic processes-asymmetric cell division, signaling and gene regulation-in a multitude of ways to create this overwhelming diversity of multicellular life-forms. Here, we use a generative model to test the limits to which such processes can be combined to generate multiple differentiation paths during development, and attempt to chart the diversity of multicellular organisms generated. Results: We sample millions of biologically feasible developmental schemes, allowing us to comment on the statistical properties of cell-differentiation trajectories they produce. We characterize model-generated 'organisms' using the graph topology of their cell-type lineage maps. Remarkably, tree-type lineage differentiation maps are the rarest in our data. Additionally, a majority of the 'organisms' generated by our model appear to be endowed with the ability to regenerate using pluripotent cells. Conclusions: Our results indicate that, in contrast to common views, cell-type lineage graphs are unlikely to be tree-like. Instead, they are more likely to be directed acyclic graphs, with multiple lineages converging on the same terminal cell-type. Furthermore, the high incidence of pluripotent cells in model-generated organisms stands in line with the long-standing hypothesis that whole body regeneration is an epiphenomenon of development. We discuss experimentally testable predictions of our model, and some ways to adapt the generative framework to test additional hypotheses about general features of development.
Rapid advance of experimental techniques provides an unprecedented in-depth view into complex dev... more Rapid advance of experimental techniques provides an unprecedented in-depth view into complex developmental processes. Still, little is known on how the complexity of multicellular organisms evolved by elaborating developmental programs and inventing new cell types. A hurdle to understanding developmental evolution is the difficulty of even describing the intertwined network of spatiotemporal processes underlying the development of complex multicellular organisms. Nonetheless, an overview of developmental trajectories can be obtained from cell type lineage maps. Here, we propose that these lineage maps can also reveal how developmental programs evolve: the modes of evolving new cell types in an organism should be visible in its developmental trajectories, and therefore in the geometry of its cell type lineage map. This idea is demonstrated using a parsimonious generative model of developmental programs, which allows us to reliably survey the universe of all possible programs and examine their topological features. We find that, contrary to belief, tree-like lineage maps are rare and lineage maps of complex multicellular organisms are likely to be directed acyclic graphs where multiple developmental routes can converge on the same cell type. While cell type evolution prescribes what developmental programs come into existence, natural selection prunes those programs which produce low-functioning organisms. Our model indicates that additionally, lineage map topologies are correlated with such a functional property: the ability of organisms to regenerate. SIGNIFICANCE Cell type invention is a chief process in the evolution of developmental programs. Traditionally, developmental trajectories are represented as cell type lineage maps. Here we propose that systematic analysis of these maps, in particular their topology, should reveal traces of the manner in which cell types were invented. This is illustrated using a generative model of developmental programs, which allows one to robustly survey the geometry of cell lineage maps and link them to modes of cell type invention. We suggest that predictions made by such mathematical models, in conjunction with surveys of real cell-lineage maps of different multicellular lineages could uncover mechanisms underlying evolution of developmental programs. STATISTICS OF LINEAGE MAPS REFLECT DEVELOPMENTAL EVOLUTION How can one understand the astounding richness of life forms?-While molecules and mechanisms of biological development are conserved within each multicellular lineage (1), these lineages are extraordinarily diverse; land plants and animals include many thousands to millions of species (2). This diversity is in part due to the distinct cell types present in different organisms. And in this sense, developmental programs evolve by inventing new cell types (3). While ancestral lineages likely resembled the simplest multicellular organisms alive today, such as Volvox carterii that has two cell types (4), the extant diversity of today's organisms ranges from those with a few cell types to those with hundreds. What molecular mechanisms and logic could produce such diversity remains a persistent question in development. One way to tackle this question is by comparing developmental programs across species of various levels of complexity. Analyzing developmental genes in order to see how gene families have expanded is fairly easy. But we now realize that this is far from sufficient, because genes interact combinatorially to express cell types. For example, looking at genomes of sponges, one might be tempted to conclude that they posses neurons since they have all the necessary components to make synapses. In reality, however, it was only in the bilaterian/cnidarian ancestor that these components were arranged in a manner that expresses the synapse (3). This example is a reminder that developmental programs are functions or algorithms for the assembly of organisms. Long ago it was recognized by Cantor that there are always many more conceivable functions than combinations of variables (5). Perhaps the simplest example-which is used as a
Vesicle Traffic Systems (VTSs) are the material transport mechanisms among the compartments insid... more Vesicle Traffic Systems (VTSs) are the material transport mechanisms among the compartments inside the biological cells. The compartments are viewed as nodes that are labeled with the containing chemicals and the transport channels are similarly viewed as labeled edges between the nodes. Understanding VTSs is an ongoing area of research and for many cells they are partially known. For example, there may be undiscovered edges, nodes, or their labels in a VTS of a cell. It has been speculated that there are properties that the VTSs must satisfy. For example, stability, i.e., every chemical that is leaving a compartment comes back. Many synthesis questions may arise in this scenario, where we want to complete a partially known VTS under a given property. In the paper, we present novel encodings of the above questions into the QBF (quantified Boolean formula) satisfiability problems. We have implemented the encodings in a highly configurable tool and applied to a couple of found-in-nature VTSs and several synthetic graphs. Our results demonstrate that our method can scale up to the graphs of interest.
Molecular and Biochemical Parasitology, Sep 1, 2016
Microbial eukaryotes present a stunning diversity of endomembrane organization. From specialized ... more Microbial eukaryotes present a stunning diversity of endomembrane organization. From specialized secretory organelles such as the rhoptries and micronemes of apicomplexans, to peroxisome-derived metabolic compartments such as the glycosomes of kinetoplastids, different microbial taxa have explored different solutions to the compartmentalization and processing of cargo. The basic secretory and endocytic system, comprising the ER, Golgi, endosomes, and plasma membrane, as well as diverse taxonspecific specialized endomembrane organelles, are coupled by a complex network of cargo transport via vesicle traffic. It is tempting to connect form to function, ascribing biochemical roles to each compartment and vesicle of such a system. Here we argue that traffic systems of high complexity could arise through non-adaptive mechanisms via purely physical constraints, and subsequently be exapted for various taxon-specific functions. Our argument is based on a Boolean mathematical model of vesicle traffic: we specify rules of how compartments exchange vesicles; these rules then generate hypothetical cells with different types of endomembrane organization. Though one could imagine a large number of hypothetical vesicle traffic systems, very few of these are consistent with molecular interactions. Such molecular constraints are the bottleneck of a metaphorical hourglass, and the rules that make it through the bottleneck are expected to generate cells with many special properties. Sampling at random from among such rules represents an evolutionary null hypothesis: any properties of the resulting cells must be non-adaptive. We show by example that vesicle traffic systems generated in this random manner are reminiscent of the complex trafficking apparatus of real cells.
Eukaryotic cells use small membrane-enclosed vesicles to transport molecular cargo between intrac... more Eukaryotic cells use small membrane-enclosed vesicles to transport molecular cargo between intracellular compartments. Interactions between molecules on vesicles and compartments determine the source and target compartment of each vesicle type. The set of compartment and vesicle types in a cell define the nodes and edges of a transport graph known as the vesicle traffic network. The transmembrane SNARE proteins that regulate vesicle fusion to target compartments travel in cycles through the transport graph, but the paths they follow must be tightly regulated to avoid aberrant vesicle fusion. Here we use graph-theoretic ideas to understand how such molecular constraints place constraints on the structure of the transport graph. We identify edge connectivity (the minimum number of edges that must be removed to disconnect a graph) as a key determinant that separates allowed and disallowed types of transport graphs. As we increase the flexibility of molecular regulation, the required edge connectivity decreases, so more types of vesicle transport graphs are allowed. These results can be used to aid the discovery of new modes of molecular regulation and new vesicle traffic pathways.
Vesicle Traffic Systems (VTSs) are the material transport mechanisms among the compartments insid... more Vesicle Traffic Systems (VTSs) are the material transport mechanisms among the compartments inside the biological cells. The compartments are viewed as nodes that are labeled with the containing chemicals and the transport channels are similarly viewed as labeled edges between the nodes. Understanding VTSs is an ongoing area of research and for many cells they are partially known. For example, there may be undiscovered edges, nodes, or their labels in a VTS of a cell. It has been speculated that there are properties that the VTSs must satisfy. For example, stability, i.e., every chemical that is leaving a compartment comes back. Many synthesis questions may arise in this scenario, where we want to complete a partially known VTS under a given property. In the paper, we present novel encodings of the above questions into the QBF (quantified Boolean formula) satisfiability problems. We have implemented the encodings in a highly configurable tool and applied to a couple of found-in-nature VTSs and several synthetic graphs. Our results demonstrate that our method can scale up to the graphs of interest.
Vesicle traffic systems (VTSs) transport cargo among the intracellular compartments of eukaryotic... more Vesicle traffic systems (VTSs) transport cargo among the intracellular compartments of eukaryotic cells. The compartments are viewed as nodes that are labeled by their chemical identity and the transport vesicles are similarly viewed as labeled edges between the nodes. Several interesting questions about VTSs translate to combinatorial search and synthesis problems. We present novel encodings for the problems based on Boolean satisfiability (SAT), satisfiability modulo theories and quantified Boolean formula of the properties over vesicle traffic systems. We have implemented the presented encodings in a tool that searches for the networks that satisfy properties related to transport consistency conditions using these solvers. In our numerical experiments, we show that our tool can search for networks of sizes that are relevant to real cellular systems. Our work illustrates the potential of novel biological applications of SAT solving technology.
What is the minimal set of cell-biological ingredients needed to generate a Golgi apparatus? The ... more What is the minimal set of cell-biological ingredients needed to generate a Golgi apparatus? The compositions of eukaryotic organelles arise through a process of molecular exchange via vesicle traffic. Here we statistically sample tens of thousands of homeostatic vesicle traffic networks generated by realistic molecular rules governing vesicle budding and fusion. Remarkably, the plurality of these networks contain chains of compartments that undergo creation, compositional maturation, and dissipation, coupled by molecular recycling along retrograde vesicles. This motif precisely matches the cisternal maturation model of the Golgi, which was developed to explain many observed aspects of the eukaryotic secretory pathway. In our analysis cisternal maturation is a robust consequence of vesicle traffic homeostasis, independent of the underlying details of molecular interactions or spatial stacking. This architecture may have been exapted rather than selected for its role in the secretion of large cargo.
Microbial eukaryotes present a stunning diversity of endomembrane organization. From specialized ... more Microbial eukaryotes present a stunning diversity of endomembrane organization. From specialized secretory organelles such as the rhoptries and micronemes of apicomplexans, to peroxisome-derived metabolic compartments such as the glycosomes of kinetoplastids, different microbial taxa have explored different solutions to the compartmentalization and processing of cargo. The basic secretory and endocytic system, comprising the ER, Golgi, endosomes, and plasma membrane, as well as diverse taxonspecific specialized endomembrane organelles, are coupled by a complex network of cargo transport via vesicle traffic. It is tempting to connect form to function, ascribing biochemical roles to each compartment and vesicle of such a system. Here we argue that traffic systems of high complexity could arise through non-adaptive mechanisms via purely physical constraints, and subsequently be exapted for various taxon-specific functions. Our argument is based on a Boolean mathematical model of vesicle traffic: we specify rules of how compartments exchange vesicles; these rules then generate hypothetical cells with different types of endomembrane organization. Though one could imagine a large number of hypothetical vesicle traffic systems, very few of these are consistent with molecular interactions. Such molecular constraints are the bottleneck of a metaphorical hourglass, and the rules that make it through the bottleneck are expected to generate cells with many special properties. Sampling at random from among such rules represents an evolutionary null hypothesis: any properties of the resulting cells must be non-adaptive. We show by example that vesicle traffic systems generated in this random manner are reminiscent of the complex trafficking apparatus of real cells.
What is the minimal set of cell-biological ingredients needed to generate a Golgi apparatus? The ... more What is the minimal set of cell-biological ingredients needed to generate a Golgi apparatus? The compositions of eukaryotic organelles arise through a process of molecular exchange via vesicle traffic. Here we statistically sample tens of thousands of homeostatic vesicle traffic networks generated by realistic molecular rules governing vesicle budding and fusion. Remarkably, the plurality of these networks contain chains of compartments that undergo creation, compositional maturation, and dissipation, coupled by molecular recycling along retrograde vesicles. This motif precisely matches the cisternal maturation model of the Golgi, which was developed to explain many observed aspects of the eukaryotic secretory pathway. In our analysis cisternal maturation is a robust consequence of vesicle traffic homeostasis, independent of the underlying details of molecular interactions or spatial stacking. This architecture may have been exapted rather than selected for its role in the secretion...
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