Stochastic transport processes in discrete biological systems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
Springer
1982
|
| Series: | Lecture notes in biomathematics
47 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 169 S. |
| ISBN: | 3540119647 0387119647 |
Staff View
MARC
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| 245 | 1 | 0 | |a Stochastic transport processes in discrete biological systems |
| 264 | 1 | |a Berlin u.a. |b Springer |c 1982 | |
| 300 | |a VIII, 169 S. | ||
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| 490 | 1 | |a Lecture notes in biomathematics |v 47 | |
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| 650 | 4 | |a Transport biologique | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Biological Transport | |
| 650 | 4 | |a Biological transport |x Mathematics | |
| 650 | 4 | |a Probability | |
| 650 | 4 | |a Stochastic processes | |
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Record in the Search Index
| _version_ | 1804114623083839488 |
|---|---|
| adam_text | Contents
A. Stochastic Processes 1
1. Expectation Values, Moments, Variance, Correlations 2
2. Probabilities 4
2.1 Expectation Values and Probabilities 5
3. Binomial, Poisson, Normal Distributions 7
4. Stationarity and Ergodicity 10
B. Analysis of Stationary Stochastic Processes 13
1. Basic Concepts of Noise Analysis 13
1.1 Spectral Density 13
1.2 Autocorrelation Function and Wiener Khintchine Relations.15
2. Poisson Processes, Carson s Theorem 17
2.1 Variance, Autocorrelation Function, Spectral Density 18
2.2 Special Examples 19
2.3 Ions Crossing Membranes: Shot Noise 21
3. The Master Equation Approach to Fluctuations 24
3.1 Markov Processes 25
3.2 Master Equation and Phenomenological Equations 26
3.3 Linearized Phenonenological Equations and Fundamental
Sol utions 29
3.4 Variances, Correlations, Spectra 32
3.5 Correlation and Spectra of Measurable Quantities 35
3.6 Direct Calculation of Fluctuations from the Fundamental
Solutions of the Master Equation 36
3.7 Current Noise Generated by the Opening and Closing of
Channels 39
VI
C. Transport Fluctuations Around Steady States 42
1. Introductory Remarks on Transport Fluctuations 42
1.1 Characterization 42
1.2 A simple Example: Channels with one Binding Site....44
2. The Concept of Transport in Discrete Systems..... 49
2.1 The Fluxes 49
2.2 Current as a Transport Observable 52
2.3 Conservative Systems, Open Systems 53
2.4 Interactions Neglected 55
3. Transport Fluctuations at Equilibrium 58
3.1 The Nyquist or Fluctuation Dissipation Theorem 58
3.2 Voltage Dependence of the Rate Constants 59
3.3 Linear Response and Complex Admittance 61
4. Theory of transport Fluctuations Around Equilibrium
and Nonequi 1 i brium Steady States 64
4.1 The Flux Correlation Matrix 64
4.2 Autocorrelation Function and Spectral Density of
Current Fluctuations 66
4.3 More Rigorous Treatment of the Time Correlation
Matrix 68
5. Transport Fluctuations in Basic Membrane Transport
Systems 71
5.1 Current Noise in Open Channels 71
5.2 The Influence of Voltage and Barrier Structure
on the Fluctuations 76
5.3 Carrier Noise , 86
6. Transport Fluctuations in More Sophisticated Channel
Models 90
6.1 Single File Diffusion Through Narrow Channels 90
VII
6.2 Numerical Calculations of Single File Noise in Open
Channels 96
6.3 Single File Noise: Coupling Between Transport and
Open Closed Kinetics of the Channels 103
7. Invalidity of the Fluctuation Dissipation Theorem
for Transport Fluctuations Around Nonequi1ibrium
Steady States 118
7.1 Special Examples: Channel Noise, Carrier Noise,
Noise Generated by Permanently Open Channels 120
7.2 Different Behaviour of Scalarand Vectorial
Quantities at Nonequi 1 i brium 126
8. Current Noise: The Limit of High Applied Voltage 130
8.1 Interactions Neglected: Shot Noise 130
8.2 Reduction of Noise as Consequence of Ionic
Interactions in the Single File Model 133
D. Nonstationary Processes, Fluctuations at Transient States...139
1. A Simple Example: Identical, Independent Channels 139
2. Time Dependent States in Markov Processes 141
2.1 General Equations for the Moments 141
2.2 One Variable Birth Death Processes 143
3. Linear Birth Death Processes With One Variable 147
3.1 Expectation Value and Variance 147
3.2 Application: Linear Two State Channel Models 149
4. Nonlinear Processes 152
4.1 Approximation Procedures 152
4.2 Bilinear One Variable Birth Death Processes 154
Vill
4.3 Bimoiecular Reactions: The
Gramicidin Channel 155
5. Transport Noise at Transient States 159
References 161
Subject index 166
|
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| dewey-search | 574.87/5/015192 |
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| dewey-tens | 570 - Biology |
| discipline | Biologie Mathematik |
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| id | DE-604.BV000163704 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:09:39Z |
| institution | BVB |
| isbn | 3540119647 0387119647 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000092830 |
| oclc_num | 9151724 |
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| physical | VIII, 169 S. |
| psigel | TUB-nveb |
| publishDate | 1982 |
| publishDateSearch | 1982 |
| publishDateSort | 1982 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in biomathematics |
| series2 | Lecture notes in biomathematics |
| spelling | Frehland, Eckart Verfasser aut Stochastic transport processes in discrete biological systems Berlin u.a. Springer 1982 VIII, 169 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in biomathematics 47 Processus stochastiques Transport biologique Mathematik Biological Transport Biological transport Mathematics Probability Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Biologisches System (DE-588)4122930-7 gnd rswk-swf Stofftransport Biologie (DE-588)4443397-9 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s Stofftransport Biologie (DE-588)4443397-9 s Biologisches System (DE-588)4122930-7 s DE-604 Lecture notes in biomathematics 47 (DE-604)BV005875746 47 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000092830&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Frehland, Eckart Stochastic transport processes in discrete biological systems Lecture notes in biomathematics Processus stochastiques Transport biologique Mathematik Biological Transport Biological transport Mathematics Probability Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd Biologisches System (DE-588)4122930-7 gnd Stofftransport Biologie (DE-588)4443397-9 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4122930-7 (DE-588)4443397-9 |
| title | Stochastic transport processes in discrete biological systems |
| title_auth | Stochastic transport processes in discrete biological systems |
| title_exact_search | Stochastic transport processes in discrete biological systems |
| title_full | Stochastic transport processes in discrete biological systems |
| title_fullStr | Stochastic transport processes in discrete biological systems |
| title_full_unstemmed | Stochastic transport processes in discrete biological systems |
| title_short | Stochastic transport processes in discrete biological systems |
| title_sort | stochastic transport processes in discrete biological systems |
| topic | Processus stochastiques Transport biologique Mathematik Biological Transport Biological transport Mathematics Probability Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd Biologisches System (DE-588)4122930-7 gnd Stofftransport Biologie (DE-588)4443397-9 gnd |
| topic_facet | Processus stochastiques Transport biologique Mathematik Biological Transport Biological transport Mathematics Probability Stochastic processes Stochastischer Prozess Biologisches System Stofftransport Biologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000092830&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005875746 |
| work_keys_str_mv | AT frehlandeckart stochastictransportprocessesindiscretebiologicalsystems |