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Kirk Durston

University of Guelph, School of Computer Science, Post-Doc

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Ph.D. Biophysics, University of Guelph, 2010
M.A. Philosophy, University of Manitoba, 1997
B.Sc. Mechanical Engineering, University of Manitoba, 1979
B.Sc. Physics, University of Manitoba, 1976
Currently continuing Post Doc research with David Chiu

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Devlina Chakravarty

Bose Institute

Katarzyna Hanna Kaminska

International Institute of Molecular and Cell Biology

Subash Chandra Pakhrin

Birthe Kragelund

Stockholm University

Davi Nakajima An

CSIC (Consejo Superior de Investigaciones Científicas-Spanish National Research Council)

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Papers by Kirk Durston

PSICalc: a novel approach to identifying and ranking critical non-proximal interdependencies within the overall protein structure

Bioinformatics Advances

Motivation AlphaFold has been a major advance in predicting protein structure, but still leaves t... more Motivation AlphaFold has been a major advance in predicting protein structure, but still leaves the problem of determining which sub-molecular components of a protein are essential for it to carry out its function within the cell. Direct coupling analysis predicts two- and three-amino acid contacts, but there may be essential interdependencies that are not proximal within the 3D structure. The problem to be addressed is to design a computational method that locates and ranks essential non-proximal interdependencies within a protein involving five or more amino acids, using large, multiple sequence alignments (MSAs) for both globular and intrinsically unstructured proteins. Results We developed PSICalc (Protein Subdomain Interdependency Calculator), a laptop-friendly, pattern-discovery, bioinformatics software tool that analyzes large MSAs for both structured and unstructured proteins, locates both proximal and non-proximal inter-dependent sites, and clusters them into pairwise (seco...

Apparently unjustified evil and the existence of God

Trevors: Measuring the functional sequence complexity of proteins. Theor Biol Med Model

This is an Open Access article distributed under the terms of the Creative Commons Attribution Li... more

Functional Sequence Complexity in Biopolymers

It is generally recognized that biopolymers such as DNA, RNA and proteins demonstrate a form of s... more It is generally recognized that biopolymers such as DNA, RNA and proteins demonstrate a form of sequence complexity. Recent work has provided a more detailed insight into biopolymeric complexity by introducing three types of sequence complexity, Random Sequence Complexity (RSC), Ordered Sequence Complexity (OSC) and Functional Sequence Complexity (FSC). The primary feature of FSC that distinguishes it from RSC and OSC, is the imposition of functional controls upon the sequence. In this paper, we propose that it can be measured using an extended form of Shannon uncertainty that includes a variable of functionality. Clearly, FSC can be found in human languages and carefully designed computer code, but the measure we propose in this paper reveals that it is also found in biopolymers. In the case of proteins, the measure of FSC provides an estimate for the target size of a protein family in the amino acid sequence space, revealing that functional sequences occupy an extremely small frac...

The incompatibility of God and gratuitous evil: implications for the termination of civilizations

Religious Studies, 2015

Setting aside the discussion of whether the biblical destruction of the Canaanites actually occur... more Setting aside the discussion of whether the biblical destruction of the Canaanites actually occurred or was ordered by God, there still remains the philosophical question of whether any good at all justifies an omnipotent, omniscient, perfectly good being in permitting or orchestrating the destruction of an entire society. If we grant that the existence of God is incompatible with gratuitous evil, then God must terminate a society when it reaches a point in its history where the net moral value of permitting it to continue becomes negative. This raises at least four concerns which are discussed here.

Measuring the functional sequence complexity of proteins

Theoretical Biology and Medical Modelling, 2007

Background: Abel and Trevors have delineated three aspects of sequence complexity, Random Sequenc... more Background: Abel and Trevors have delineated three aspects of sequence complexity, Random Sequence Complexity (RSC), Ordered Sequence Complexity (OSC) and Functional Sequence Complexity (FSC) observed in biosequences such as proteins. In this paper, we provide a method to measure functional sequence complexity. We have extended Shannon uncertainty by incorporating the data variable with a functionality variable. The resulting measured unit, which we call Functional bit (Fit), is calculated from the sequence data jointly with the defined functionality variable. To demonstrate the relevance to functional bioinformatics, a method to measure functional sequence complexity was developed and applied to 35 protein families. Considerations were made in determining how the measure can be used to correlate functionality when relating to the whole molecule and submolecule. In the experiment, we show that when the proposed measure is applied to the aligned protein sequences of ubiquitin, 6 of the 7 highest value sites correlate with the binding domain. For future extensions, measures of functional bioinformatics may provide a means to evaluate potential evolving pathways from effects such as mutations, as well as analyzing the internal structural and functional relationships within the 3-D structure of proteins.

The consequential complexity of history and gratuitous evil

Religious Studies, 2000

History is composed of a web of innumerable interacting causal chains, many of which are composed... more History is composed of a web of innumerable interacting causal chains, many of which are composed of millions of discrete events. The complexity of history puts us in a position of having knowledge of only a minuscule portion of the consequences of any event, actual or proposed. Our almost complete lack of knowledge of the data necessary to know if an event is gratuitous makes it very likely that we would be mistaken about a very large number of events. The complexity of history, therefore, poses a significant challenge to certain types of evidential arguments from evil that begin with our observations of evils that appear to be gratuitous.For want of a nail the shoe is lost,For want of a shoe the horse is lost,For want of a horse the rider is lost,And all for the want of a nail.Benjamin Franklin, 1757

The Failure of Type-4 Arguments from Evil, in the Face of the Consequential Complexity of History

Philo, 2005

Bruce Russell has classified evidential arguments from evil into four types, one of which is the ... more Bruce Russell has classified evidential arguments from evil into four types, one of which is the type-4 argument. Rather than begin with observations of evils that appear to be gratuitous, type-4 arguments simply begin with observations of evils. The next step, and the heart of a type-4 argument, is an abductive inference (inference to the best explanation) from those observations, to the conclusion that there is gratuitous evil. Reflection upon the consequential complexity of history, however, reveals that we have no objective grounds for making the key, abductive inference, thus, all type-4 arguments from evil fail. Tires were exploding all over the place. That poor girl was screaming, God, it must have been for ten minutes. We just couldn't help her. eyewitness, multi-vehicle inferno, Hwy 401 In the instance of suffering described in the above prelude, the girl's heartrending screams for help as she was slowly incinerated would have, and did, move anyone with even a shred of compassion to do everything in their power to save her. If there is an omnipotent, omniscient and morally perfect being, surely such a being should have been moved to intervene when all human efforts failed. Such an intervention never occurred. The best explanation for the lack of a theistic rescue, some would argue, is that such a being does not exist. Bruce Russell has classified evidential arguments from evil into four major types. 1 I have dealt elsewhere with the effect of the consequential complexity of history upon type-1 and type-2 arguments. 2 Russell indicates that there is no known example of a type-3 argument. Thus, this paper shall focus only on type-4 arguments. By Russell's taxonomy, the sort of argument from evil given in the previous paragraph would classify as a type-4 evidential argument from evil. In this paper I shall argue that the complexity of history, with it's innumerable, interacting causal chains, puts us in a position of such ignorance, that type-4 arguments are neutralized. I will begin with a review of Russell's explanation of the type-4 argument. Following this, I will examine the consequential complexity of history and its effect on type-4 arguments. Finally, I will look at some possible objections to the counter-argument I lay out in this paper.

Statistical discovery of site inter-dependencies in sub-molecular hierarchical protein structuring

EURASIP Journal on Bioinformatics and Systems Biology, 2012

Background: Much progress has been made in understanding the 3D structure of proteins using metho... more Background: Much progress has been made in understanding the 3D structure of proteins using methods such as NMR and X-ray crystallography. The resulting 3D structures are extremely informative, but do not always reveal which sites and residues within the structure are of special importance. Recently, there are indications that multipleresidue, sub-domain structural relationships within the larger 3D consensus structure of a protein can be inferred from the analysis of the multiple sequence alignment data of a protein family. These intra-dependent clusters of associated sites are used to indicate hierarchical inter-residue relationships within the 3D structure. To reveal the patterns of associations among individual amino acids or sub-domain components within the structure, we apply a k-modes attribute (aligned site) clustering algorithm to the ubiquitin and transthyretin families in order to discover associations among groups of sites within the multiple sequence alignment. We then observe what these associations imply within the 3D structure of these two protein families. Results: The k-modes site clustering algorithm we developed maximizes the intra-group interdependencies based on a normalized mutual information measure. The clusters formed correspond to sub-structural components or binding and interface locations. Applying this data-directed method to the ubiquitin and transthyretin protein family multiple sequence alignments as a test bed, we located numerous interesting associations of interdependent sites. These clusters were then arranged into cluster tree diagrams which revealed four structural sub-domains within the single domain structure of ubiquitin and a single large sub-domain within transthyretin associated with the interface among transthyretin monomers. In addition, several clusters of mutually interdependent sites were discovered for each protein family, each of which appear to play an important role in the molecular structure and/or function. Conclusions: Our results demonstrate that the method we present here using a k-modes site clustering algorithm based on interdependency evaluation among sites obtained from a sequence alignment of homologous proteins can provide significant insights into the complex, hierarchical inter-residue structural relationships within the 3D structure of a protein family.

The complexity of history and evil: a reply to Trakakis

Religious Studies, 2006

I have presented an argument from the consequential complexity of history against certain types o... more I have presented an argument from the consequential complexity of history against certain types of evidential arguments from evil; ‘The consequential complexity of history and gratuitous evil’ Religious Studies, 36 (2000), 65–80. Nick Trakakis has responded with two objections; ‘Evil and the complexity of history: a response to Durston’ Religious Studies, 39 (2003), 451–458. He argues that the consideration of future consequences to the end of actual history may be irrelevant and, also, that one does not need detailed knowledge about possible worlds to conclude that there are better worlds. In this paper I show that, given the complexity of history, both of his objections fail to move us out of the state of agnosticism regarding what God should or should not permit. Thus, my original argument remains intact.

Durston, K.K.; Chiu, D.K.; Abel, D.L.; Trevors, J.T., 2007, Measuring the functional sequence complexity of proteins, Theor Biol Med Model, 4, 47

by David L Abel and Kirk Durston

BACKGROUND: Abel and Trevors have delineated three aspects of sequence complexity, Random Sequenc... more BACKGROUND: Abel and Trevors have delineated three aspects of sequence complexity, Random Sequence Complexity (RSC), Ordered Sequence Complexity (OSC) and Functional Sequence Complexity (FSC) observed in biosequences such as proteins. In this paper, we provide a method to measure functional sequence complexity. METHODS AND RESULTS: We have extended Shannon uncertainty by incorporating the data variable with a functionality variable. The resulting measured unit, which we call Functional bit (Fit), is calculated from the sequence data jointly with the defined functionality variable. To demonstrate the relevance to functional bioinformatics, a method to measure functional sequence complexity was developed and applied to 35 protein families. Considerations were made in determining how the measure can be used to correlate functionality when relating to the whole molecule and sub-molecule. In the experiment, we show that when the proposed measure is applied to the aligned protein sequences of ubiquitin, 6 of the 7 highest value sites correlate with the binding domain.

CONCLUSION: For future extensions, measures of functional bioinformatics may provide a means to evaluate potential evolving pathways from effects such as mutations, as well as analyzing the internal structural and functional relationships within the 3-D structure of proteins.

5. Functional Sequence Complexity in Biopolymers Introduction: sequence complexity in biopolymers

It is generally recognized that biopolymers such as DNA, RNA and proteins demonstrate a form of s... more It is generally recognized that biopolymers such as DNA, RNA and proteins demonstrate a form of sequence complexity. Recent work has provided a more detailed insight into biopolymeric complexity by introducing three types of sequence complexity, Random Sequence Complexity (RSC), Ordered Sequence Complexity (OSC) and Functional Sequence Complexity (FSC). The primary feature of FSC that distinguishes it from RSC and OSC, is the imposition of functional controls upon the sequence. In this paper, we propose that it can be measured using an extended form of Shannon uncertainty that includes a variable of functionality.

The Failure of Type-4 Arguments from Evil, in the Face of the Consequential Complexity of History

Bruce Russell has classified evidential arguments from evil into four types, one of which is the ... more Bruce Russell has classified evidential arguments from evil into four types, one of which is the type-4 argument. Rather than begin with observations of evils that appear to be gratuitous, type-4 arguments simply begin with observations of evils. The next step, and the heart of a type-4 argument, is an abductive inference (inference to the best explanation) from those observations, to the conclusion that there is gratuitous evil. Reflection upon the consequential complexity of history, however, reveals that we have no objective grounds for making the key, abductive inference, thus, all type-4 arguments from evil fail.

The consequential complexity of history and gratuitous evil

History is composed of a web of innumerable interacting causal chains, many of which are composed... more History is composed of a web of innumerable interacting causal chains, many of which are composed of millions of discrete events. The complexity of history puts us in a position of having knowledge of only a minuscule portion of the consequences of any event, actual or proposed. Our almost complete lack of knowledge of the data necessary to know if an event is gratuitous makes it very likely that we would be mistaken about a very large number of events. The complexity of history, therefore, poses a significant challenge to certain types of evidential arguments from evil that begin with our observations of evils that appear to be gratuitous.

Statistical discovery of site inter-dependencies in sub-molecular hierarchical protein structuring

by David Chiu and Kirk Durston

Background: Much progress has been made in understanding the 3D structure of proteins using metho... more Background: Much progress has been made in understanding the 3D structure of proteins using methods such as NMR and X-ray crystallography. The resulting 3D structures are extremely informative, but do not always reveal which sites and residues within the structure are of special importance. Recently, there are indications that multiple-residue, sub-domain structural relationships within the larger 3D consensus structure of a protein can be inferred from the analysis of the multiple sequence alignment data of a protein family. These intra-dependent clusters of associated sites are used to indicate hierarchical inter-residue relationships within the 3D structure. To reveal the patterns of associations among individual amino acids or sub-domain components within the structure, we apply a k-modes attribute (aligned site) clustering algorithm to the ubiquitin and transthyretin families in order to discover associations among groups of sites within the multiple sequence alignment. We then observe what these associations imply within the 3D structure of these two protein families. Results: The k-modes site clustering algorithm we developed maximizes the intra-group interdependencies based on a normalized mutual information measure. The clusters formed correspond to sub-structural components or binding and interface locations. Applying this data-directed method to the ubiquitin and transthyretin protein family multiple sequence alignments as a test bed, we located numerous interesting associations of interdependent sites. These clusters were then arranged into cluster tree diagrams which revealed four structural sub-domains within the single domain structure of ubiquitin and a single large sub-domain within transthyretin associated with the interface among transthyretin monomers. In addition, several clusters of mutually interdependent sites were discovered for each protein family, each of which appear to play an important role in the molecular structure and/or function. Conclusions: Our results demonstrate that the method we present here using a k-modes site clustering algorithm based on interdependency evaluation among sites obtained from a sequence alignment of homologous proteins can provide significant insights into the complex, hierarchical inter-residue structural relationships within the 3D structure of a protein family.

The Incompatibility of God and Gratuitous Evil: Implications for the Termination of Civilizations

Setting aside the question of whether the biblical destruction of the Canaanites actually occurre... more Setting aside the question of whether the biblical destruction of the Canaanites actually occurred or was ordered by God, there still remains the philosophical question of whether any good at all justifies an omnipotent, omniscient, perfectly good being in permitting or orchestrating the destruction of an entire society. If we grant that the existence of God is incompatible with gratuitous evil, then God must terminate a society when it reaches a point in its history where the net moral value of permitting it to continue becomes negative. This raises at least four concerns which are discussed here. You shall utterly destroy them, You shall make no covenant with them, And show no favour to them. Deuteronomy 7:2

The complexity of history and evil: a reply to Trakakis

I have presented an argument from the consequential complexity of history against certain types o... more I have presented an argument from the consequential complexity of history against certain types of evidential arguments from evil; ' The consequential complexity of history and gratuitous evil' Religious Studies, 36 (2000), 65–80. Nick Trakakis has responded with two objections; 'Evil and the complexity of history: a response to Durston' Religious Studies, 39 (2003), 451–458. He argues that the consideration of future consequences to the end of actual history may be irrelevant and, also, that one does not need detailed knowledge about possible worlds to conclude that there are better worlds. In this paper I show that, given the complexity of history, both of his objections fail to move us out of the state of agnosticism regarding what God should or should not permit. Thus, my original argument remains intact.

Measuring the functional sequence complexity of proteins

by Kirk Durston, David Chiu, and David Abel

Background: Abel and Trevors have delineated three aspects of sequence complexity, Random Sequenc... more Background: Abel and Trevors have delineated three aspects of sequence complexity, Random Sequence Complexity (RSC), Ordered Sequence Complexity (OSC) and Functional Sequence Complexity (FSC) observed in biosequences such as proteins. In this paper, we provide a method to measure functional sequence complexity.

PSICalc: a novel approach to identifying and ranking critical non-proximal interdependencies within the overall protein structure

Bioinformatics Advances

Motivation AlphaFold has been a major advance in predicting protein structure, but still leaves t... more Motivation AlphaFold has been a major advance in predicting protein structure, but still leaves the problem of determining which sub-molecular components of a protein are essential for it to carry out its function within the cell. Direct coupling analysis predicts two- and three-amino acid contacts, but there may be essential interdependencies that are not proximal within the 3D structure. The problem to be addressed is to design a computational method that locates and ranks essential non-proximal interdependencies within a protein involving five or more amino acids, using large, multiple sequence alignments (MSAs) for both globular and intrinsically unstructured proteins. Results We developed PSICalc (Protein Subdomain Interdependency Calculator), a laptop-friendly, pattern-discovery, bioinformatics software tool that analyzes large MSAs for both structured and unstructured proteins, locates both proximal and non-proximal inter-dependent sites, and clusters them into pairwise (seco...

Apparently unjustified evil and the existence of God

Trevors: Measuring the functional sequence complexity of proteins. Theor Biol Med Model

This is an Open Access article distributed under the terms of the Creative Commons Attribution Li... more

Functional Sequence Complexity in Biopolymers

It is generally recognized that biopolymers such as DNA, RNA and proteins demonstrate a form of s... more It is generally recognized that biopolymers such as DNA, RNA and proteins demonstrate a form of sequence complexity. Recent work has provided a more detailed insight into biopolymeric complexity by introducing three types of sequence complexity, Random Sequence Complexity (RSC), Ordered Sequence Complexity (OSC) and Functional Sequence Complexity (FSC). The primary feature of FSC that distinguishes it from RSC and OSC, is the imposition of functional controls upon the sequence. In this paper, we propose that it can be measured using an extended form of Shannon uncertainty that includes a variable of functionality. Clearly, FSC can be found in human languages and carefully designed computer code, but the measure we propose in this paper reveals that it is also found in biopolymers. In the case of proteins, the measure of FSC provides an estimate for the target size of a protein family in the amino acid sequence space, revealing that functional sequences occupy an extremely small frac...

The incompatibility of God and gratuitous evil: implications for the termination of civilizations

Religious Studies, 2015

Setting aside the discussion of whether the biblical destruction of the Canaanites actually occur... more Setting aside the discussion of whether the biblical destruction of the Canaanites actually occurred or was ordered by God, there still remains the philosophical question of whether any good at all justifies an omnipotent, omniscient, perfectly good being in permitting or orchestrating the destruction of an entire society. If we grant that the existence of God is incompatible with gratuitous evil, then God must terminate a society when it reaches a point in its history where the net moral value of permitting it to continue becomes negative. This raises at least four concerns which are discussed here.

Measuring the functional sequence complexity of proteins

Theoretical Biology and Medical Modelling, 2007

Background: Abel and Trevors have delineated three aspects of sequence complexity, Random Sequenc... more Background: Abel and Trevors have delineated three aspects of sequence complexity, Random Sequence Complexity (RSC), Ordered Sequence Complexity (OSC) and Functional Sequence Complexity (FSC) observed in biosequences such as proteins. In this paper, we provide a method to measure functional sequence complexity. We have extended Shannon uncertainty by incorporating the data variable with a functionality variable. The resulting measured unit, which we call Functional bit (Fit), is calculated from the sequence data jointly with the defined functionality variable. To demonstrate the relevance to functional bioinformatics, a method to measure functional sequence complexity was developed and applied to 35 protein families. Considerations were made in determining how the measure can be used to correlate functionality when relating to the whole molecule and submolecule. In the experiment, we show that when the proposed measure is applied to the aligned protein sequences of ubiquitin, 6 of the 7 highest value sites correlate with the binding domain. For future extensions, measures of functional bioinformatics may provide a means to evaluate potential evolving pathways from effects such as mutations, as well as analyzing the internal structural and functional relationships within the 3-D structure of proteins.

The consequential complexity of history and gratuitous evil

Religious Studies, 2000

History is composed of a web of innumerable interacting causal chains, many of which are composed... more History is composed of a web of innumerable interacting causal chains, many of which are composed of millions of discrete events. The complexity of history puts us in a position of having knowledge of only a minuscule portion of the consequences of any event, actual or proposed. Our almost complete lack of knowledge of the data necessary to know if an event is gratuitous makes it very likely that we would be mistaken about a very large number of events. The complexity of history, therefore, poses a significant challenge to certain types of evidential arguments from evil that begin with our observations of evils that appear to be gratuitous.For want of a nail the shoe is lost,For want of a shoe the horse is lost,For want of a horse the rider is lost,And all for the want of a nail.Benjamin Franklin, 1757

The Failure of Type-4 Arguments from Evil, in the Face of the Consequential Complexity of History

Philo, 2005

Bruce Russell has classified evidential arguments from evil into four types, one of which is the ... more Bruce Russell has classified evidential arguments from evil into four types, one of which is the type-4 argument. Rather than begin with observations of evils that appear to be gratuitous, type-4 arguments simply begin with observations of evils. The next step, and the heart of a type-4 argument, is an abductive inference (inference to the best explanation) from those observations, to the conclusion that there is gratuitous evil. Reflection upon the consequential complexity of history, however, reveals that we have no objective grounds for making the key, abductive inference, thus, all type-4 arguments from evil fail. Tires were exploding all over the place. That poor girl was screaming, God, it must have been for ten minutes. We just couldn't help her. eyewitness, multi-vehicle inferno, Hwy 401 In the instance of suffering described in the above prelude, the girl's heartrending screams for help as she was slowly incinerated would have, and did, move anyone with even a shred of compassion to do everything in their power to save her. If there is an omnipotent, omniscient and morally perfect being, surely such a being should have been moved to intervene when all human efforts failed. Such an intervention never occurred. The best explanation for the lack of a theistic rescue, some would argue, is that such a being does not exist. Bruce Russell has classified evidential arguments from evil into four major types. 1 I have dealt elsewhere with the effect of the consequential complexity of history upon type-1 and type-2 arguments. 2 Russell indicates that there is no known example of a type-3 argument. Thus, this paper shall focus only on type-4 arguments. By Russell's taxonomy, the sort of argument from evil given in the previous paragraph would classify as a type-4 evidential argument from evil. In this paper I shall argue that the complexity of history, with it's innumerable, interacting causal chains, puts us in a position of such ignorance, that type-4 arguments are neutralized. I will begin with a review of Russell's explanation of the type-4 argument. Following this, I will examine the consequential complexity of history and its effect on type-4 arguments. Finally, I will look at some possible objections to the counter-argument I lay out in this paper.

Statistical discovery of site inter-dependencies in sub-molecular hierarchical protein structuring

EURASIP Journal on Bioinformatics and Systems Biology, 2012

Background: Much progress has been made in understanding the 3D structure of proteins using metho... more Background: Much progress has been made in understanding the 3D structure of proteins using methods such as NMR and X-ray crystallography. The resulting 3D structures are extremely informative, but do not always reveal which sites and residues within the structure are of special importance. Recently, there are indications that multipleresidue, sub-domain structural relationships within the larger 3D consensus structure of a protein can be inferred from the analysis of the multiple sequence alignment data of a protein family. These intra-dependent clusters of associated sites are used to indicate hierarchical inter-residue relationships within the 3D structure. To reveal the patterns of associations among individual amino acids or sub-domain components within the structure, we apply a k-modes attribute (aligned site) clustering algorithm to the ubiquitin and transthyretin families in order to discover associations among groups of sites within the multiple sequence alignment. We then observe what these associations imply within the 3D structure of these two protein families. Results: The k-modes site clustering algorithm we developed maximizes the intra-group interdependencies based on a normalized mutual information measure. The clusters formed correspond to sub-structural components or binding and interface locations. Applying this data-directed method to the ubiquitin and transthyretin protein family multiple sequence alignments as a test bed, we located numerous interesting associations of interdependent sites. These clusters were then arranged into cluster tree diagrams which revealed four structural sub-domains within the single domain structure of ubiquitin and a single large sub-domain within transthyretin associated with the interface among transthyretin monomers. In addition, several clusters of mutually interdependent sites were discovered for each protein family, each of which appear to play an important role in the molecular structure and/or function. Conclusions: Our results demonstrate that the method we present here using a k-modes site clustering algorithm based on interdependency evaluation among sites obtained from a sequence alignment of homologous proteins can provide significant insights into the complex, hierarchical inter-residue structural relationships within the 3D structure of a protein family.

The complexity of history and evil: a reply to Trakakis

Religious Studies, 2006

I have presented an argument from the consequential complexity of history against certain types o... more I have presented an argument from the consequential complexity of history against certain types of evidential arguments from evil; ‘The consequential complexity of history and gratuitous evil’ Religious Studies, 36 (2000), 65–80. Nick Trakakis has responded with two objections; ‘Evil and the complexity of history: a response to Durston’ Religious Studies, 39 (2003), 451–458. He argues that the consideration of future consequences to the end of actual history may be irrelevant and, also, that one does not need detailed knowledge about possible worlds to conclude that there are better worlds. In this paper I show that, given the complexity of history, both of his objections fail to move us out of the state of agnosticism regarding what God should or should not permit. Thus, my original argument remains intact.

Durston, K.K.; Chiu, D.K.; Abel, D.L.; Trevors, J.T., 2007, Measuring the functional sequence complexity of proteins, Theor Biol Med Model, 4, 47

by David L Abel and Kirk Durston

BACKGROUND: Abel and Trevors have delineated three aspects of sequence complexity, Random Sequenc... more BACKGROUND: Abel and Trevors have delineated three aspects of sequence complexity, Random Sequence Complexity (RSC), Ordered Sequence Complexity (OSC) and Functional Sequence Complexity (FSC) observed in biosequences such as proteins. In this paper, we provide a method to measure functional sequence complexity. METHODS AND RESULTS: We have extended Shannon uncertainty by incorporating the data variable with a functionality variable. The resulting measured unit, which we call Functional bit (Fit), is calculated from the sequence data jointly with the defined functionality variable. To demonstrate the relevance to functional bioinformatics, a method to measure functional sequence complexity was developed and applied to 35 protein families. Considerations were made in determining how the measure can be used to correlate functionality when relating to the whole molecule and sub-molecule. In the experiment, we show that when the proposed measure is applied to the aligned protein sequences of ubiquitin, 6 of the 7 highest value sites correlate with the binding domain.

CONCLUSION: For future extensions, measures of functional bioinformatics may provide a means to evaluate potential evolving pathways from effects such as mutations, as well as analyzing the internal structural and functional relationships within the 3-D structure of proteins.

5. Functional Sequence Complexity in Biopolymers Introduction: sequence complexity in biopolymers

It is generally recognized that biopolymers such as DNA, RNA and proteins demonstrate a form of s... more It is generally recognized that biopolymers such as DNA, RNA and proteins demonstrate a form of sequence complexity. Recent work has provided a more detailed insight into biopolymeric complexity by introducing three types of sequence complexity, Random Sequence Complexity (RSC), Ordered Sequence Complexity (OSC) and Functional Sequence Complexity (FSC). The primary feature of FSC that distinguishes it from RSC and OSC, is the imposition of functional controls upon the sequence. In this paper, we propose that it can be measured using an extended form of Shannon uncertainty that includes a variable of functionality.

The Failure of Type-4 Arguments from Evil, in the Face of the Consequential Complexity of History

Bruce Russell has classified evidential arguments from evil into four types, one of which is the ... more Bruce Russell has classified evidential arguments from evil into four types, one of which is the type-4 argument. Rather than begin with observations of evils that appear to be gratuitous, type-4 arguments simply begin with observations of evils. The next step, and the heart of a type-4 argument, is an abductive inference (inference to the best explanation) from those observations, to the conclusion that there is gratuitous evil. Reflection upon the consequential complexity of history, however, reveals that we have no objective grounds for making the key, abductive inference, thus, all type-4 arguments from evil fail.

The consequential complexity of history and gratuitous evil

History is composed of a web of innumerable interacting causal chains, many of which are composed... more History is composed of a web of innumerable interacting causal chains, many of which are composed of millions of discrete events. The complexity of history puts us in a position of having knowledge of only a minuscule portion of the consequences of any event, actual or proposed. Our almost complete lack of knowledge of the data necessary to know if an event is gratuitous makes it very likely that we would be mistaken about a very large number of events. The complexity of history, therefore, poses a significant challenge to certain types of evidential arguments from evil that begin with our observations of evils that appear to be gratuitous.

Statistical discovery of site inter-dependencies in sub-molecular hierarchical protein structuring

by David Chiu and Kirk Durston

Background: Much progress has been made in understanding the 3D structure of proteins using metho... more Background: Much progress has been made in understanding the 3D structure of proteins using methods such as NMR and X-ray crystallography. The resulting 3D structures are extremely informative, but do not always reveal which sites and residues within the structure are of special importance. Recently, there are indications that multiple-residue, sub-domain structural relationships within the larger 3D consensus structure of a protein can be inferred from the analysis of the multiple sequence alignment data of a protein family. These intra-dependent clusters of associated sites are used to indicate hierarchical inter-residue relationships within the 3D structure. To reveal the patterns of associations among individual amino acids or sub-domain components within the structure, we apply a k-modes attribute (aligned site) clustering algorithm to the ubiquitin and transthyretin families in order to discover associations among groups of sites within the multiple sequence alignment. We then observe what these associations imply within the 3D structure of these two protein families. Results: The k-modes site clustering algorithm we developed maximizes the intra-group interdependencies based on a normalized mutual information measure. The clusters formed correspond to sub-structural components or binding and interface locations. Applying this data-directed method to the ubiquitin and transthyretin protein family multiple sequence alignments as a test bed, we located numerous interesting associations of interdependent sites. These clusters were then arranged into cluster tree diagrams which revealed four structural sub-domains within the single domain structure of ubiquitin and a single large sub-domain within transthyretin associated with the interface among transthyretin monomers. In addition, several clusters of mutually interdependent sites were discovered for each protein family, each of which appear to play an important role in the molecular structure and/or function. Conclusions: Our results demonstrate that the method we present here using a k-modes site clustering algorithm based on interdependency evaluation among sites obtained from a sequence alignment of homologous proteins can provide significant insights into the complex, hierarchical inter-residue structural relationships within the 3D structure of a protein family.

The Incompatibility of God and Gratuitous Evil: Implications for the Termination of Civilizations

Setting aside the question of whether the biblical destruction of the Canaanites actually occurre... more Setting aside the question of whether the biblical destruction of the Canaanites actually occurred or was ordered by God, there still remains the philosophical question of whether any good at all justifies an omnipotent, omniscient, perfectly good being in permitting or orchestrating the destruction of an entire society. If we grant that the existence of God is incompatible with gratuitous evil, then God must terminate a society when it reaches a point in its history where the net moral value of permitting it to continue becomes negative. This raises at least four concerns which are discussed here. You shall utterly destroy them, You shall make no covenant with them, And show no favour to them. Deuteronomy 7:2

The complexity of history and evil: a reply to Trakakis

I have presented an argument from the consequential complexity of history against certain types o... more I have presented an argument from the consequential complexity of history against certain types of evidential arguments from evil; ' The consequential complexity of history and gratuitous evil' Religious Studies, 36 (2000), 65–80. Nick Trakakis has responded with two objections; 'Evil and the complexity of history: a response to Durston' Religious Studies, 39 (2003), 451–458. He argues that the consideration of future consequences to the end of actual history may be irrelevant and, also, that one does not need detailed knowledge about possible worlds to conclude that there are better worlds. In this paper I show that, given the complexity of history, both of his objections fail to move us out of the state of agnosticism regarding what God should or should not permit. Thus, my original argument remains intact.

Measuring the functional sequence complexity of proteins

by Kirk Durston, David Chiu, and David Abel

Background: Abel and Trevors have delineated three aspects of sequence complexity, Random Sequenc... more Background: Abel and Trevors have delineated three aspects of sequence complexity, Random Sequence Complexity (RSC), Ordered Sequence Complexity (OSC) and Functional Sequence Complexity (FSC) observed in biosequences such as proteins. In this paper, we provide a method to measure functional sequence complexity.