Mathematical models, explanation, laws, and evolutionary biology

It is commonly agreed in the literature on laws of nature that there are at least two necessary conditions for lawhood--that a law must have empirical content and that it must be universal. The main reason offered for the requirement that laws be empirical is as follows: a priori statements are consistent with any imaginable set of observations, so they cannot be informative about the world and therefore they cannot provide explanations. However, we care about laws because we think that laws provide explanations and allow us to make predictions. Thus, if one of the functions of laws is to provide explanations and a priori propositions cannot fulfill this function, they cannot properly be viewed as laws. In this paper, I will aim to show that this argument for the claim that laws must be empirical does not work.     

PNA-DNA triplexes: stability and specificity

The review considers the properties and some applications of complexes formed by peptide nucleic acid (PNA) molecules with complementary DNA sites, with emphasis on the structure and properties of PNA2/DNA triplexes.     

Waddington redux: models and explanation in stem cell and systems biology

Stem cell biology and systems biology are two prominent new approaches to studying cell development. In stem cell biology, the predominant method is experimental manipulation of concrete cells and tissues. Systems biology, in contrast, emphasizes mathematical modeling of cellular systems. For scientists and philosophers interested in development, an important question arises: how should the two approaches relate? This essay proposes an answer, using the model of Waddington’s landscape to triangulate between stem cell and systems approaches. This simple abstract model represents development as an undulating surface of hills and valleys. Originally constructed by C. H. Waddington to visually explicate an integrated theory of genetics, development and evolution, the landscape model can play an updated unificatory role. I examine this model’s structure, representational assumptions, and uses in all three contexts, and argue that explanations of cell development require both mathematical models and concrete experiments. On this view, the two approaches are interdependent, with mathematical models playing a crucial but circumscribed role in explanations of cell development.     

Causation at different levels: tracking the commitments of mechanistic explanations

This paper tracks the commitments of mechanistic explanations focusing on the relation between activities at different levels. It is pointed out that the mechanistic approach is inherently committed to identifying causal connections at higher levels with causal connections at lower levels. For the mechanistic approach to succeed a mechanism as a whole must do the very same thing what its parts organised in a particular way do. The mechanistic approach must also utilise bridge principles connecting different causal terms of different theoretical vocabularies in order to make the identities of causal connections transparent. These general commitments get confronted with two claims made by certain proponents of the mechanistic approach: William Bechtel often argues that within the mechanistic framework it is possible to balance between reducing higher levels and maintaining their autonomy at the same time, whereas, in a recent paper, Craver and Bechtel argue that the mechanistic approach is able to make downward causation intelligible. The paper concludes that the mechanistic approach imbued with identity statements is no better candidate for anchoring higher levels to lower ones while maintaining their autonomy at the same time than standard reductive accounts are, and that what mechanistic explanations are able to do at best is showing that downward causation does not exist.     

Induction of polarity in mouse 8-cell blastomeres: specificity, geometry, and stability

We studied the cellular mechanisms underlying the induction of polarity in individual blastomeres of the 8-cell mouse embryo. The ability to induce polarity is lacking in the membranes of unfertilized and newly fertilized mouse eggs, then develops during the 2-cell stage, and is present in membranes of cells from 4-, 8-, and 16-cell stages. The axis of polarity takes 3-5 h to become established and thereafter appears to be stable. Multiple cell contacts affect the orientation of the axis of polarity, and no polarity develops in cells which are totally surrounded. Polarized cells show evidence of an limited capacity for slight adjustments in their position relative to other cells. The implications of these results for the mechanisms by which a blastocyst is generated are discussed briefly.     

Of arrows and flows. Causality, determination, and specificity in the Central Dogma of molecular biology

From its first proposal, the Central Dogma had a graphical form, complete with arrows of different types, and this form quickly became its standard presentation. In different scientific contexts, arrows have different meanings and in this particular case the arrows indicated the flow of information among different macromolecules. A deeper analysis illustrates that the arrows also imply a causal statement, directly connected to the causal role of genetic information. The author suggests a distinction between two different kinds of causal links, defined as 'physical causality' and 'biological determination', both implied in the production of biological specificity.     

Integrative biology: linking levels of organization

Biological systems are composed of different levels of organization. Usually, one considers the atomic, molecular, cellular, individual, population, community and ecosystem levels. These levels of organization also correspond to different levels of observation of the system, from microscopic to macroscopic, i.e., to different time and space scales. The more microscopic the level is, the faster the time scale and the smaller the space scale are. The dynamics of the complete system is the result of the coupled dynamical processes that take place in each of its levels of organization at different time scales. Variables aggregation methods take advantage of these different time scales to reduce the dimension of mathematical models such as a system of ordinary differential equations. We are going to study the dynamics of a system which is hierarchically organized in the sense that it is composed of groups of elements that can be themselves divided into further smaller sub-groups and so on. The hierarchical structure of the system results from the fact that the intra-group interactions are assumed to be larger than inter-group ones. We present aggregation methods that allow one to build a reduced model that governs a few global variables at the slow time scale.     

Phytotoxic activity of chernozem saprophytic micromycetes: specificity, sorption and stability of phytotoxins in soil

Micromycetes of the complex of typical chernozem saprotrophic fungi released phytotoxic metabolites into medium. The metabolites displayed their phytotoxic activities directly in soil. Evaluation of the toxicities, range of biological effects activities, and stabilities of phytotoxins in soil and the rates of their biodegradation allowed the species that can serve as indicators of chernozem microbial toxicosis to be selected, namely, Aspergillus clavatus, Fusarium solani, Talaromyces flavus, Penicillium rubrum, and P. funiculosum.     

Female choice in Drosophila: evidence from Hawaii and implications for evolutionary biology

Details of female choice of mate in Drosophila silvestris of Hawaii strikingly parallels epigamic behavioral systems in many other animals and may be common in other species of Drosophilidae. Females respond selectively to male circling, wing displays, songs and tactile stimulation with foreleg cilia, a quantitative character that is highly variable in some populations. I hypothesize that the female can exert choice based on these cues from individual males that differ genetically by quantitative trait loci. Laboratory tests show that one third of courting males are repeatedly rejected in favor of a minority of alpha males. This result imposes non-random mating at the local population level. Past multiple-choice lab tests, widely used to measure isolation between pairs of populations or species of Drosophila may be flawed, since random mating has been assumed in the interpretation of results. Pre-mating sexual selection is clearly a powerful intrapopulation force in population biology. This view creates difficulties for discerning any proposed simultaneous interpopulation selective events in the presence of strong female choice. The long-held theory assuming that there is significant selection for pre-mating isolation between groups is questionable.     

Site-directed mutagenesis of an alkaline phytase: influencing specificity, activity and stability in acidic milieu

Site-directed mutagenesis of a thermostable alkaline phytase from Bacillus sp. MD2 was performed with an aim to increase its specific activity and activity and stability in an acidic environment. The mutation sites are distributed on the catalytic surface of the enzyme (P257R, E180N, E229V and S283R) and in the active site (K77R, K179R and E227S). Selection of the residues was based on the idea that acid active phytases are more positively charged around their catalytic surfaces. Thus, a decrease in the content of negatively charged residues or an increase in the positive charges in the catalytic region of an alkaline phytase was assumed to influence the enzyme activity and stability at low pH. Moreover, widening of the substrate-binding pocket is expected to improve the hydrolysis of substrates that are not efficiently hydrolysed by wild type alkaline phytase. Analysis of the phytase variants revealed that E229V and S283R mutants increased the specific activity by about 19% and 13%, respectively. Mutation of the active site residues K77R and K179R led to severe reduction in the specific activity of the enzyme. Analysis of the phytase mutant-phytate complexes revealed increase in hydrogen bonding between the enzyme and the substrate, which might retard the release of the product, resulting in decreased activity. On the other hand, the double mutant (K77R-K179R) phytase showed higher stability at low pH (pH 2.6-3.0). The E227S variant was optimally active at pH 5.5 (in contrast to the wild type enzyme that had an optimum pH of 6) and it exhibited higher stability in acidic condition. This mutant phytase, displayed over 80% of its initial activity after 3 h incubation at pH 2.6 while the wild type phytase retained only about 40% of its original activity. Moreover, the relative activity of this mutant phytase on calcium phytate, sodium pyrophosphate and p-nitro phenyl phosphate was higher than that of the wild type phytase.     

Structure, dynamics, and stability variation in bacterial albumin binding modules: implications for species specificity

Protein G-related albumin-binding (GA) modules are frequently expressed on the surfaces of bacterial cells. The limited amino acid sequence variation among GA modules results in structural and functional differences with possible implications for bacterial pathogenesis and host specificity. In particular, the streptococcal G148-GA3 and F. magna ALB8-GA albumin-binding domains exhibit a degree of structural and dynamic diversity that may account for their varied affinities for different species of albumin. To explore the impact of GA module polymorphisms on albumin binding and specificity, we recently used offset recombinant PCR to shuffle seven artificially constructed representatives of the GA sequence space and scan the phage-displayed recombinant domains for mutations that supported binding to the phylogenetically distinct human and guinea pig serum albumins (HSA and GPSA) (Rozak et al. (2006) Biochemistry 45, 3263-3271). Surprisingly, phage selection revealed an overwhelming preference for a single recombinant domain (PSD-1, phage-selected domain-1) regardless of whether the phages were enriched for their abilities to bind one or both of these albumins. We describe here the NMR-derived structure, dynamics, and stability of unbound PSD-1. Our results demonstrate that increased flexibility is not a requirement for broadened specificity, as had been suggested earlier (Johansson et al. (2002) J. Mol. Biol. 316, 1083-1099), because PSD-1 binds the phylogenetically diverse HSA and GPSA even more tightly than G148-GA3 but is less flexible. The structural basis for albumin-binding specificity is analyzed in light of these new results.     

Proprotein convertase models based on the crystal structures of furin and kexin: explanation of their specificity

In eukaryotes, many secreted proteins and peptide hormones are excised from larger precursors by calcium-dependent serine proteinases, the proprotein/prohormone convertases (PCs). These PCs cleave their protein substrates very specifically following multiple basic residues. The seven mammalian PCs and their yeast orthologue kexin are multi-domain proteinases consisting of a subtilisin-related catalytic domain, a conserved P-domain and a variable, often cysteine-rich domain, which in some PCs is followed by an additional C-terminal trans-membrane domain and a short cytoplasmic domain. The recently published crystal structures of the soluble mouse furin and yeast kexin ectodomains have revealed the relative arrangement of catalytic and P domains, the exact domain fold and the detailed architecture of the substrate binding clefts. Based on these experimental structures, we now have modelled the structures of the other human/mouse PCs. According to topology and to structure-based sequence comparisons, these other PCs closely resemble furin, with PC4, PACE4 and PC5/6 being more similar, and PC1/3, PC2 and PC7 being less similar to furin. Except for PC1 and PC2, this order of similarity is valid for the catalytic as well as for the P domains, and is almost reversed using kexin as a reference molecule. A similar order results from the number and clustering of negative charges lining the non-prime subsites, explaining the gradually decreasing requirement for basic residues N-terminal to substrate cleavage sites. The preference of the different PCs for distinct substrates seems to be governed by overall charge compensation and matching of the detailed charge distribution pattern.     

Increased amylosucrase activity and specificity, and identification of regions important for activity, specificity and stability through molecular evolution

Amylosucrase is a transglycosidase which belongs to family 13 of the glycoside hydrolases and transglycosidases, and catalyses the formation of amylose from sucrose. Its potential use as an industrial tool for the synthesis or modification of polysaccharides is hampered by its low catalytic efficiency on sucrose alone, its low stability and the catalysis of side reactions resulting in sucrose isomer formation. Therefore, combinatorial engineering of the enzyme through random mutagenesis, gene shuffling and selective screening (directed evolution) was applied, in order to generate more efficient variants of the enzyme. This resulted in isolation of the most active amylosucrase (Asn387Asp) characterized to date, with a 60% increase in activity and a highly efficient polymerase (Glu227Gly) that produces a longer polymer than the wild-type enzyme. Furthermore, judged from the screening results, several variants are expected to be improved concerning activity and/or thermostability. Most of the amino acid substitutions observed in the totality of these improved variants are clustered around specific regions. The secondary sucrose-binding site and beta strand 7, connected to the important Asp393 residue, are found to be important for amylosucrase activity, whereas a specific loop in the B-domain is involved in amylosucrase specificity and stability.     

Omissions, Causation, and Responsibility

In this paper I discuss a recent exchange of articles between Hugh McLachlan and John Coggon on the relationship between omissions, causation, and moral responsibility. My aim is to contribute to their debate by isolating a presupposition I believe they both share and by questioning that presupposition. The presupposition is that, at any given moment, there are countless things that I am omitting to do. This leads both McLachlan and Coggon to give a distorted account of the relationship between causation and moral or (as the case may be) legal responsibility and, in the case of Coggon, to claim that the law??s conception of causation is a fiction based on policy. Once it is seen that this presupposition is faulty, we can attain a more accurate view of the logical relationship between causation and moral responsibility in the case of omissions. This is important because it will enable us, in turn, to understand why the law continues to regard omissions as different, both logically and morally, from acts, and why the law seeks to track that logical and moral difference in the legal distinction it draws between withholding life-sustaining measures and euthanasia.     

The relation between philosophy of science and biology exemplified by the problem of explanation

Summary This paper contains some considerations on the relation between philosophy of science and science, in particular biology. There is a contrast between formalistic and pragmatic approaches to the structure of scientific thought, which is illustrated by the different viewpoints on the nature of explanation. In an appendix some aspects of the logical structure of teleological explanation are discussed.