title: How life uses sound to reorganise matter: The role of anharmonic phonon exchange in enzyme catalysis

authors: Batterton, Christopher

subjects: enzyme catalysis

abstract: Biological enzyme catalysis is the name for life's ability to rapidly invoke coordinated rearrangements of molecular structures using highly specialised, relatively-large functional proteins called enzymes. It is well established that enzymes reduce the activation energy barrier, which vastly accelerates the rate of reaction, however the specific dynamics and quantum mechanics are largely uncharted. Recent experimentation and modelling hints that there is a phase transition dynamic that is fundamental to enzymatic catalysis. The hypothesis that I explore in this thesis is that a mathematical model of a substrate molecule based upon anharmonic quantum vibrational modes (molecular phonons) will predict phase transition dynamics due to the presence of the appropriate enzyme. A molecular phonon is one particular individualised wave pattern in the locations of atomic nuclei from the total molecular dance that spans the low-frequency bulk swaying motions, mid-frequency bond stretches, to the high-frequency oscillations of the hydrogen bond network. 


In this thesis, I derive a generalised set of equations of motion for the anharmonic response behaviour of molecular phonons to enzyme stimulus via a dissipative quantum master equation, and I explore the phase transition dynamics by determining the stability bifurcation of the steady states. I then determine the critical minimum stimulus required for a molecular vibrational mode to exhibit a phase transition. The primary catalytic reaction of focus for this thesis is the cleavage of the glycosidic carbon-oxygen bond of the complex sugar isomaltose into two individual glucose molecules via the action of the enzyme MalL. Prior to this thesis, the atomic structure of MalL was obtained experimentally via X-ray diffraction crystallography of prepared MalL crystals, then digitised into the Gromacs software package and energy minimised in a simulated water bath to approximate the vibrational modes of the in vivo configuration. I obtain the substrate molecule's harmonic frequencies and anharmonic shifts via molecular dynamics performed using the Gaussian 09 normal mode analysis and simulated anharmonic infrared spectroscopy packages, respectively. I construct a generalised coding package in Matlab to extract the molecule and enzyme data, perform a quantum anharmonic analysis of the molecule--enzyme complex and their interactions, and then simulate the response of the molecule to stimulus from the enzyme. 

 
I determine that the vibrational modes of isomaltose that significantly contribute to stretching the glycosidic carbon-oxygen bond occur within the 21 to 35 THz (700 to 1,170 cm^{-1}) frequency bandwidth, and the dominant stretching modes are contained within 28 to 33 THz (930 to 1,100cm^{-1}), which is in agreement with the experimental literature of polysaccharides. In the final chapter, I perform numerical simulations of the equations of motion to compute the energy response spectrogram for a proxy substrate (benzene) under conditions that are informed by literature and the theoretical findings of this thesis. In lieu of anharmonic isomaltose data, I selected benzene as it is a small molecule with a high degree of symmetry which has several bond stretching modes within the aforementioned bandwidth. The results show that while the stimulus from water is insufficient, there are vibrational modes pertaining to glycosidic bond stretching that can be selectively excited to phase transition behaviour due to a reasonable stimulus from the supply of phonons from the MalL enzyme.

text: How life uses sound to reorganise matter: The role of anharmonic phonon exchange in enzyme catalysis Biological enzyme catalysis is the name for life's ability to rapidly invoke coordinated rearrangements of molecular structures using highly specialised, relatively-large functional proteins called enzymes. It is well established that enzymes reduce the activation energy barrier, which vastly accelerates the rate of reaction, however the specific dynamics and quantum mechanics are largely uncharted. Recent experimentation and modelling hints that there is a phase transition dynamic that is fundamental to enzymatic catalysis. The hypothesis that I explore in this thesis is that a mathematical model of a substrate molecule based upon anharmonic quantum vibrational modes (molecular phonons) will predict phase transition dynamics due to the presence of the appropriate enzyme. A molecular phonon is one particular individualised wave pattern in the locations of atomic nuclei from the total molecular dance that spans the low-frequency bulk swaying motions, mid-frequency bond stretches, to the high-frequency oscillations of the hydrogen bond network. 


In this thesis, I derive a generalised set of equations of motion for the anharmonic response behaviour of molecular phonons to enzyme stimulus via a dissipative quantum master equation, and I explore the phase transition dynamics by determining the stability bifurcation of the steady states. I then determine the critical minimum stimulus required for a molecular vibrational mode to exhibit a phase transition. The primary catalytic reaction of focus for this thesis is the cleavage of the glycosidic carbon-oxygen bond of the complex sugar isomaltose into two individual glucose molecules via the action of the enzyme MalL. Prior to this thesis, the atomic structure of MalL was obtained experimentally via X-ray diffraction crystallography of prepared MalL crystals, then digitised into the Gromacs software package and energy minimised in a simulated water bath to approximate the vibrational modes of the in vivo configuration. I obtain the substrate molecule's harmonic frequencies and anharmonic shifts via molecular dynamics performed using the Gaussian 09 normal mode analysis and simulated anharmonic infrared spectroscopy packages, respectively. I construct a generalised coding package in Matlab to extract the molecule and enzyme data, perform a quantum anharmonic analysis of the molecule--enzyme complex and their interactions, and then simulate the response of the molecule to stimulus from the enzyme. 

 
I determine that the vibrational modes of isomaltose that significantly contribute to stretching the glycosidic carbon-oxygen bond occur within the 21 to 35 THz (700 to 1,170 cm^{-1}) frequency bandwidth, and the dominant stretching modes are contained within 28 to 33 THz (930 to 1,100cm^{-1}), which is in agreement with the experimental literature of polysaccharides. In the final chapter, I perform numerical simulations of the equations of motion to compute the energy response spectrogram for a proxy substrate (benzene) under conditions that are informed by literature and the theoretical findings of this thesis. In lieu of anharmonic isomaltose data, I selected benzene as it is a small molecule with a high degree of symmetry which has several bond stretching modes within the aforementioned bandwidth. The results show that while the stimulus from water is insufficient, there are vibrational modes pertaining to glycosidic bond stretching that can be selectively excited to phase transition behaviour due to a reasonable stimulus from the supply of phonons from the MalL enzyme.

year: 2024

title: Macrofossils and pollen representing forests of the pre-Taupo volcanic eruption (c. 1850 yr BP) era at Pureora and Benneydale, central North Island, New Zealand.

authors: Clarkson, Beverley R.

subjects: macrofossil

abstract: Micro- and macrofossil data from the remains of forests overwhelmed and buried at Pureora and Benneydale during the Taupo eruption (c. 1850 conventional radiocarbon yr BP) were compared. Classification of relative abundance data separated the techniques, rather than the locations, because the two primary clusters comprised pollen and litter/wood. This indicates that the pollen:litter/wood within-site comparisons (Pureora and Benneydale are 20 km apart) are not reliable. Plant macrofossils represented mainly local vegetation, while pollen assemblages represented a combination of local and regional vegetation. However, using ranked abundance and presence/absence data, both macrofossils and pollen at Pureora and Benneydale indicated conifer/broadleaved forest, of similar forest type and species composition at each site. This suggests that the forests destroyed by the eruption were typical of mid-altitude west Taupo forests, and that either data set (pollen or macrofossils) would have been adequate for regional forest interpretation.
The representation of c. 1850 yr BP pollen from the known buried forest taxa was generally consistent with trends determined by modern comparisons between pollen and their source vegetation, but with a few exceptions.
A pollen profile from between the Mamaku Tephra (c. 7250 yr BP) and the Taupo Ignimbrite indicated that the Benneydale forest had been markedly different in species dominance compared with the forest that was destroyed during the Taupo eruption. These differences probably reflect changes in drainage, and improvements in climate and/or soil fertility over the middle Holocene.

text: Macrofossils and pollen representing forests of the pre-Taupo volcanic eruption (c. 1850 yr BP) era at Pureora and Benneydale, central North Island, New Zealand. Micro- and macrofossil data from the remains of forests overwhelmed and buried at Pureora and Benneydale during the Taupo eruption (c. 1850 conventional radiocarbon yr BP) were compared. Classification of relative abundance data separated the techniques, rather than the locations, because the two primary clusters comprised pollen and litter/wood. This indicates that the pollen:litter/wood within-site comparisons (Pureora and Benneydale are 20 km apart) are not reliable. Plant macrofossils represented mainly local vegetation, while pollen assemblages represented a combination of local and regional vegetation. However, using ranked abundance and presence/absence data, both macrofossils and pollen at Pureora and Benneydale indicated conifer/broadleaved forest, of similar forest type and species composition at each site. This suggests that the forests destroyed by the eruption were typical of mid-altitude west Taupo forests, and that either data set (pollen or macrofossils) would have been adequate for regional forest interpretation.
The representation of c. 1850 yr BP pollen from the known buried forest taxa was generally consistent with trends determined by modern comparisons between pollen and their source vegetation, but with a few exceptions.
A pollen profile from between the Mamaku Tephra (c. 7250 yr BP) and the Taupo Ignimbrite indicated that the Benneydale forest had been markedly different in species dominance compared with the forest that was destroyed during the Taupo eruption. These differences probably reflect changes in drainage, and improvements in climate and/or soil fertility over the middle Holocene.

year: 1995-06-01

title: ‘He reka te wai o te hua pango: The darker the berry the sweeter the juice.' The experiences of Māori women in educational leadership in mainstream secondary schools.

authors: Taukamo, Trudy

subjects: New Zealand leadership

abstract: Although there has been a growing interest in Māori women in educational leadership, the research base in New Zealand is still limited. This study provides insights into the challenges and experiences of four Māori women who occupy a formal leadership position in a mainstream secondary school. It used a qualitative kaupapa Māori research framework. Data were collected using semi-structured one-on-one interview with open-ended questions. The four women were selected from Māori women who currently hold a formal leadership position at a senior management level in a mainstream secondary school and who identify as Māori. The reason for the purposive sample was the critical under-representation of Māori women in formal educational leadership roles. This study revealed three important aspects. Firstly, a person’s upbringing and background has a significant impact on the principles and values which underpin leadership. Secondly, it was evident that a support system whether personal or professional was crucial in a leadership position. Finally, the influences of opportunities and appointments to leadership were important in educational leadership. Clearly, the findings point to a need for a stronger mentoring programme and effective networking of Māori women. Tertiary studies and leadership programs can aid the career pathways for aspiring leaders. However, what is clear is the need for more research specific to the New Zealand context and Māori women.

text: ‘He reka te wai o te hua pango: The darker the berry the sweeter the juice.' The experiences of Māori women in educational leadership in mainstream secondary schools. Although there has been a growing interest in Māori women in educational leadership, the research base in New Zealand is still limited. This study provides insights into the challenges and experiences of four Māori women who occupy a formal leadership position in a mainstream secondary school. It used a qualitative kaupapa Māori research framework. Data were collected using semi-structured one-on-one interview with open-ended questions. The four women were selected from Māori women who currently hold a formal leadership position at a senior management level in a mainstream secondary school and who identify as Māori. The reason for the purposive sample was the critical under-representation of Māori women in formal educational leadership roles. This study revealed three important aspects. Firstly, a person’s upbringing and background has a significant impact on the principles and values which underpin leadership. Secondly, it was evident that a support system whether personal or professional was crucial in a leadership position. Finally, the influences of opportunities and appointments to leadership were important in educational leadership. Clearly, the findings point to a need for a stronger mentoring programme and effective networking of Māori women. Tertiary studies and leadership programs can aid the career pathways for aspiring leaders. However, what is clear is the need for more research specific to the New Zealand context and Māori women.

year: 2011